Dynamic evaluation of 4D robust optimisation
for motion management in scanned proton therapy
of hepatocellular carcinoma
DISSERTATION
Zur Erlangung des akademischen Grades
eines Doktors der Naturwissenschaften (Dr. rer. nat.)
Fakultät Physik
Technische Universität Dortmund
M.Sc. Tina Pfeiler
geboren am 27.10.1989 in Oberhausen
Essen im Dezember 2018
vorgelegt von
.
.Dissertation to obtain the degree Doctor Rerum Naturalium (Dr. rer. nat.) at
the Faculty of Physics, Technical University of Dortmund.
1st Referee: Prof. Dr. Bernhard Spaan
Technical University of DortmundI
2nd Referee: Prof. Dr. Kevin Kröninger
Technical University of DortmundI
This thesis has been conducted at the West German Proton Therapy Centre
Essen (WPE) under supervision of Dr. Christian Bäumer.
.
Abstract
Pencil beam scanning (PBS) proton therapy is due to its steep dose gradients a promising
treatment option for many cancer patients, particularly if the tumour is surrounded by critical
organs. Currently, organ motion often poses an obstacle for the irradiation of tumours in the
thorax or abdomen since the interference of pencil beam and tumour motion can lead to dis-
tortions of the intended dose distribution and requires dedicated motion mitigation techniques.
A technique which has been recommended by recently published guidelines to reduce motion
effects in PBS therapy of thoracic malignancies is 4D robust optimisation. 4D robust optimisa-
tion uses time-resolved CT images from different respiratory phases to incorporate uncertainties
due to physiologic motion in treatment plan optimisation. Its effect has not yet been sufficiently
examined and further research is needed to establish it in clinical routine.
Within this thesis, the utility of 4D robust optimisation to mitigate motion effects was in-
vestigated for hepatocellular carcinoma, representative for mobile abdominal targets. For this
purpose, a 4D dynamic dose calculation routine including an empirical beam delivery time
model was developed based on a non-clinical, preliminary script from a global software pro-
vider for radiation therapy. The customised 4D tool enables prospective estimations before
treatment, 4D dose reconstruction after treatment and comprehensive in silico examinations
for research purposes. The validity of the routine and the time model was confirmed for typical
beam settings in clinical end-to-end tests. In the treatment planning study on 4D robust op-
timisation, the routine revealed no significant improvement of the target coverage under motion
for the investigated patients. A great advantage over conventional PBS plans was, however,
that the same level of robustness against motion was reached for lower organ at risk doses.
Since dose inhomogeneities averaged out for the applied fractionation scheme of 15 fractions,
4D robust optimisation was found to generate clinically acceptable sum plans. Due to the un-
known biological effect of strong over- and underdosage in a single fraction, the method should
be supplemented by further motion mitigation techniques in case of large tumour motion.
The use of computer generated CTs for more comprehensive 4D evaluations was successfully
tested in a proof of concept study and will allow to model a broad range of clinical cases in
upcoming research projects. Thus, the benefit of 4D robust optimisation can be systematically
investigated on a large scale for different subgroups. Although the elaboration of operating
procedures for the irradiation of moving targets at the West German Proton Therapy Centre
Essen (WPE) is still in process, the 4D dynamic dose calculation routine is already in clinical
use to assess potential motion effects for current patients with minor tumour motion.
.
Zusammenfassung
Die Protonentherapie mit magnetisch gelenkten Nadelstrahlen, englisch pencil beam scanning
(PBS), stellt aufgrund ihrer steilen Dosisgradienten eine erfolgversprechende Behandlungsopti-
on für viele Tumorpatienten dar. Dies gilt insbesondere, wenn der Tumor von lebenswichtigen
Organen umgeben ist. Aktuell sind atmungsbedingte Organbewegungen oft ein Hindernis für die
Bestrahlung von Tumoren im Thorax oder Abdomen, weil das Zusammenspiel von Tumor- und
Strahlbewegung zu Verzerrungen der geplanten Dosisverteilung führen kann. Die Anwendung
spezieller Techniken zur Reduzierung von Bewegungseffekten ist daher erforderlich. Kürzlich
veröffentlichte Richtlinien für die Bestrahlung von thorakalen Tumoren mit PBS empfehlen
die Anwendung von 4D-robuster Optimierung. Diese berücksichtigt physiologische Organbewe-
gungen bei der Optimierung von Bestrahlungsplanungsparametern anhand von zeitaufgelösten
CT-Aufnahmen zu verschiedenen Atemphasen. Ihre Wirkung ist noch nicht ausreichend unter-
sucht und es bedarf weiterer Forschungsarbeit, um die Technik in der Klinik zu etablieren.
Diese Arbeit hatte zum Ziel, den Nutzen von 4D-robuster Optimierung zur Abschwächung von
Bewegungseffekten für hepatozelluläre Karzinome zu untersuchen, repräsentativ für bewegte
Ziele im Abdomen. Zu diesem Zweck wurde eine Routine entwickelt, die retrospektive, dyna-
mische 4D-Dosisberechnungen ermöglicht. Sie basiert auf einer nicht klinischen Vorläuferversi-
on eines führenden Anbieters für Bestrahlungsplanungs-Software. Ein empirisches Zeitmodell
der Feldapplikation vervollständigt die Routine und erlaubt umfangreiche in silico Studien zu
Forschungszwecken sowie prospektive Untersuchungen zur Abschätzung von Risiken vor der
Behandlung. Die Gültigkeit der Routine und des integrierten Zeitmodells wurde in klinischen
End-to-End-Tests für typische Strahlparameter nachgewiesen. In der Bestrahlungsplanungs-
studie zu 4D-robuster Optimierung zeigte die Routine keine signifikante Verbesserung in der
Zielvolumenabdeckung bei Atembewegungen für die untersuchten Patienten. Ein großer Vor-
teil war jedoch, dass, im Vergleich zu konventionellen PBS-Plänen, der gleiche Robustheits-
grad gegenüber Bewegungen bei geringerer Belastung des gesunden umliegenden Gewebes er-
zielt werden konnte. Da sich Dosisinhomogenitäten für das angewandte Fraktionierungsschema
von 15 Fraktionen herausmittelten, generierte 4D-robuste Optimierung klinisch akzeptable 4D-
Summenpläne. Aufgrund der nicht ausreichend bekannten biologischen Wirkung von starken
Unter- und Überdosierungen in einzelnen Fraktionen, ist es jedoch erforderlich, im Fall von
großen Bewegungsamplituden, begleitend zusätzliche Maßnahmen zur Einschränkung von Be-
wegungseffekten zu ergreifen.
Die Anwendung von computergenerierten CTs für umfangreichere 4D-Evaluierungen wurde
erfolgreich in einer Machbarkeitsstudie getestet. Sie macht es möglich, zukünftig eine große
Bandbreite an klinischen Fällen in Forschungsprojekten zu modellieren. Somit kann der Nutzen
von 4D-robuster Optimierung systematisch im großen Rahmen für verschiedene Untergrup-
pen untersucht werden. Obwohl die Ausarbeitung von Arbeitskonzepten für die Behandlung
von bewegten Tumoren am Westdeutschen Protonentherapiezentrum Essen (WPE) noch nicht
abgeschlossen ist, wird die 4D-Dosisberechnungsroutine bereits für derzeitige Patienten mit ge-
ringer Tumorbewegung klinisch genutzt, um potenzielle Bewegungseffekte zu erfassen und zu
bewerten.
.
Publications related to this work
• Pfeiler T, Bäumer C, Engwall E, Geismar D, Spaan B, Timmermann B. Experimental
validation of a 4D dose calculation routine for pencil beam scanning proton therapy. Z
Med Phys 2018;28:121–33.
• Pfeiler T, Ahmad Khalil D, Bäumer C, Blanck O, Chan M, Engwall E, Geismar D,
Peters S, Plaude S, Spaan B, Wulff J and Timmermann B. 4D robust optimization in
pencil beam scanning proton therapy for hepatocellular carcinoma. J Phys Conf Ser.
Submitted 2018.
• Pfeiler T, Ahmad Khalil D, Ayadi M, Bäumer C, Blanck O, Chan M, Engwall E, Geis-
mar D, Peters S, Plaude S, Spaan B, Timmermann B, Wulff J. Motion effects in proton
treatments of hepatocellular carcinoma - 4D robustly optimised pencil beam scanning
plans vs double scattering plans. Phys Med Biol 2018;63 235006.
Conference contributions
• Pfeiler T, Bäumer C, Engwall E, Spaan B, Timmermann B. A routine for the evaluation
of interplay effects in Intensity-Modulated Proton Therapy (IMPT). 47th Annual Meeting
of the DGMP, Würzburg, Germany, 2016. Oral presentation.
• Pfeiler T, Bäumer C, Engwall E, Spaan B, Timmermann B. A routine for the evaluation
of interplay effects in pencil-beam scanning proton therapy. 4D Treatment Planning
Workshop, Groningen, Netherlands, 2016. Poster.
• Pfeiler T, Bäumer C, Engwall E, Spaan B, Timmermann B. 4D dose computation in
pencil beam scanning proton therapy has been clinically implemented and experimentally
verified. PTCOG 56, Yokohama, Japan, 2017. Oral presentation.
• Pfeiler T, Ahmad Khalil D, Bäumer C, Blanck O, Chan M, Engwall E, Geismar D,
Peters S, Plaude S, Spaan B, Wulff J, Timmermann B. 4D robust optimization in pen-
cil beam scanning proton therapy for hepatocellular carcinoma. MMND, Mooloolaba,
Australia, 2018. Oral presentation.
• Pfeiler T, Ahmad Khalil D, Bäumer C, Blanck O, Chan M, Engwall E, Geismar D,
Peters S, Plaude S, Spaan B, Wulff J, Timmermann B. 4D evaluation of proton pencil
beam scanning and double scattering for hepatocellular carcinoma. ESTRO 37, Barcelona,
Spain, 2018. E-Poster.
• Moustakis C, Blanck O, Andratschke N, Boda-Heggemann J, Wilke L, Tanadini-Lang S,
Gauer T, Alraun M, Bäumer C, Beckers E, Blaschek M, Brunner T, Chan MK, Dierl M,
Droege S, Duma MN, Ebrahimi F, Eich HT, Fleckenstein J, Ganswindt U, Garbe S,
Gkika E, Heinz C, Henkenberens C, Hennig A, Henning S, Köhn J, Kornhuber C, Kretsch-
mer M, Krieger T, Loufti-Kraus B, Mayr M, Mensing T, Pfeiler T, Pollul G, Ramm U,
Rieder F, Rieken S, Schmidthalter D, Schmitt D, Schöffler J, Ulm C, Walke M, Wei-
gel R, Wiehle R, Wiezorek T, Wolf U, Zimmer J, Baus W, Guckenberger M. Referenz
Planvergleichsstudie für Leber-SBRT – Ergebnisse DEGRO AG/DGMP AK Stereotaxie.
Strahlenther Onkol 2018;194:1.
.
Nomenclature
3D PBS plan non-robustly optimised PBS plan
4D CT respiratory correlated computed tomography
4D PBS plan 4D robustly optimised PBS plan
4D XCAT phantom 4D extended cardiac-torso phantom
4DD 4D accumulated dose
4DDD 4D dynamically accumulated dose
AP anterior-posterior
CT computed tomography
CTV clinical target volume
DIR deformable image registration
DS double scattering
DSC Dice similarity coefficient
gEUD generalised EUD
GTV gross tumour volume
HCC hepatocellular carcinoma
HI homogeneity index
HU Hounsfield unit
IMPT intensity-modulated proton therapy
ITV internal target volume
LET linear energy transfer
LKB model Lyman-Kutcher-Burman model
LQ model linear-quadratic model
LR left-right
MC Monte Carlo
MCS multiple coulomb scattering
MU monitor unit
NLP non-linear optimisation problem
NTCP normal tissue complication probability
OAR organ at risk
PBS pencil beam scanning
PLD file PBS layer definition file
PMMA polymethyl methacrylate
POI point of interest
PTV planning target volume
QP quadratic programming
RBE relative biological effectiveness
RF radio frequency
RFA radiofrequency ablation
RILD radiation-induced liver disease
ROI region of interest
SBRT stereotactic body radiotherapy
SD standard deviation
SEM standard error of the mean
SI superior-inferior
SOBP spread-out Bragg peak
SQP sequential quadratic programming
TACE transarterial chemoembolisation
TPS treatment planning system
WPE West German Proton Therapy Centre Essen
.
Contents
1 Introduction 1
2 Research principles and background of proton beam therapy 3
2.1 Physical fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Proton interactions in matter . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Dosimetric quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.3 Depth dose profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Cell survival and biological effectiveness . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Cell survival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Relative biological effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Biological dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Equivalent uniform dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Proton beam therapy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Beam delivery: Pencil beam scanning (PBS) and double scattering (DS) . . 10
2.4 Treatment planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Treatment planning system (TPS) . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.2 Computed tomography (CT) . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.3 Contouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.4 Deformable image registration . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.5 Proton dose calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.6 Treatment planning in pencil beam scanning and 4D robust optimisation . 21
2.4.7 Treatment planning in double scattering . . . . . . . . . . . . . . . . . . . . 23
2.5 Treatment of mobile targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.1 Intra- and inter-fraction motion . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.2 Impact of organ motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.3 Interplay effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.4 Respiratory correlated computed tomography . . . . . . . . . . . . . . . . 25
2.5.5 Motion mitigation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning 27
3.1 Modelling of interplay effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Experimental validation of the 4D dose computation . . . . . . . . . . . . . . . . . 28
3.2.1 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Development and validation of a beam delivery time model . . . . . . . . . . . . . 42
3.3.1 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Clinical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients 49
4.1 Hepatocellular carcinoma (HCC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.1 Clinical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1.2 Treatment options and the role of proton therapy . . . . . . . . . . . . . . . 50
4.2 Design of the treatment planning study . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 Patient collective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.2 CT scanner calibration, contouring and deformable image registration . . . 53
4.2.3 Treatment plan optimisation in PBS and DS . . . . . . . . . . . . . . . . . 53
4.2.4 CTV coverage and robustness evaluation . . . . . . . . . . . . . . . . . . . . 54
4.2.5 4D dose accumulation in pencil beam scanning and double scattering . . . . 55
4.2.6 Evaluation methods and criteria . . . . . . . . . . . . . . . . . . . . . . . . 55
i
4.2.7 Supplementary analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.1 Evaluation of the deformable image registration . . . . . . . . . . . . . . . . 58
4.3.2 Perturbation analysis of the nominal treatment plans . . . . . . . . . . . . . 58
4.3.3 Analysis of the 4D dynamically accumulated dose distribution . . . . . . . 58
4.3.4 Supplementary analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4.1 Evaluation of the deformable image registration . . . . . . . . . . . . . . . . 71
4.4.2 Perturbation analysis of the nominal treatment plans . . . . . . . . . . . . . 71
4.4.3 Analysis of the 4D dynamically accumulated dose distribution . . . . . . . 72
4.4.4 Supplementary analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.5 Robust optimisation for motion management of hepatocellular carcinomas . 78
5 Usage of computer generated 4DCTs in interplay studies - a proof of concept 81
5.1 4D XCAT phantom and CT simulation . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Study design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.2.1 Simulated 4DCT data and deformable image registration . . . . . . . . . . 82
5.2.2 Treatment planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.3 Evaluation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.1 Evaluation of the deformable image registration . . . . . . . . . . . . . . . . 84
5.3.2 CTV coverage and perturbation analysis of the nominal treatment plans . . 84
5.3.3 Analysis of the 4D dynamically accumulated dose distribution . . . . . . . 84
5.3.4 Feasibility of interplay studies using simulated 4DCT data . . . . . . . . . 85
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4.1 Evaluation of the deformable image registration . . . . . . . . . . . . . . . . 85
5.4.2 Analysis of the 4D dynamically accumulated dose distribution . . . . . . . 86
5.4.3 Feasibility of interplay studies using simulated 4DCT data . . . . . . . . . 86
6 Summary and outlook on future research 87
6.1 Summary - Implementation of 4D dynamic dose accumulation . . . . . . . . . . . . 87
6.2 Summary - Evaluation of 4D robust optimisation for HCC patients . . . . . . . . . 88
6.3 Summary - Usage of computer generated 4DCTs in interplay studies . . . . . . . . 89
6.4 Outlook on future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7 Conclusion 91
A Appendix 93
A.1 Scripting in RayStation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
A.1.1 Python file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
A.1.2 XAML file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
References 101
ii
1 Introduction
Cancer represents a major and growing public health problem. According to the World Health
Organisation (WHO), in 2016, malignant neoplasms caused worldwide about 9.0 million deaths
and were thus the second leading cause of mortality after cardiovascular diseases [1]. This fact
underlines the need for more effective cancer treatment. Proton therapy enables high-precision
irradiation of malignant tumours owing to the characteristic absorption profile of swift protons
in matter. Unlike conventional photon beams, which lead to an exponential dose decay after a
short buildup region, therapeutic proton beams exhibit a distinct dose maximum (Bragg peak)
followed by a steep dose fall-off at the end of the particle range. This characteristic allows
for normal-tissue sparing while escalating the dose to the tumour to improve local control and
overall survival (see for example Ref. [2, 3, 4, 5]). An advanced form of proton beam delivery is
pencil beam scanning (PBS) which uses two perpendicular magnetic fields to deflect the proton
beam laterally to predefined spot positions for a series of iso-energy layers. PBS offers a high
degree of dose conformity even in anatomically challenging cases. However, the susceptibility
of proton therapy to range uncertainties, setup errors and organ motion may affect the dose
distribution. Due to the finite range of protons, not only the lateral but also the longitudinal
conformity is compromised in the presence of organ motion. Active delivery methods such as
PBS are additionally affected by the interference of organ motion and beam scanning which can
lead to over- and underdosage of the target and exposure of organs at risk (OARs), an effect
known as interplay effect [6, 7, 8, 9]. Nonetheless, many proton therapy centres plan to apply
PBS for moving targets and first centres have even started treating tumours in liver and lung
with scanned pencil beams [10, 11]. The reasons behind this are (1) the greater tumour con-
formity enabled by PBS technique and (2) the fact that the majority of recently built particle
therapy centres is equipped with active scanning systems only [10].
The trend towards PBS for the treatment of moving targets requires, even more than passive
delivery methods, adequate motion mitigation techniques. Various approaches have been made
to mitigate motion induced effects, such as abdominal compression, rescanning (the beam vis-
its a spot position several times per treatment until the prescribed dose is delivered), gating
(the beam is turned off for certain phases of the respiratory cycle) or four-dimensional treat-
ment planning (the fourth dimension refers to the time) [12, 13, 14]. However, for some of
the above supplementary techniques, interplay effects – although reduced – persist on a low
level. Four-dimensional dynamically accumulated dose (4DDD) calculations therefore represent
a key ingredient of motion management in PBS to evaluate the available treatment options and
determine residual deviations from the intended dose distribution.
Current challenges to implementing PBS for moving targets arise from the facts that, firstly, not
all proton therapy centres have the expertise and tools (hardware and/or software) to appro-
priately reduce motion effects and, secondly, commercial treatment planning systems (TPSs)
do not provide a clinical 4DDD computation tool [15].
A motion mitigation technique which does not require any additional hardware and is already
implemented in some commercial TPSs is 4D robust optimisation [16, 17, 18]. Clinical 4D
robust optimisation tools do not explicitly account for interplay effects but consider anatomical
changes in different respiratory phases. Recently published guidelines of the Particle Therapy
Co-Operative Group (PTCOG) recommend the application of 4D robust optimisation for the
treatment of thoracic malignancies in PBS [15]. The methodology of 4D robust optimisation has
not yet been established. The recommendation on the use is based on two exploratory studies
only, which used an in-house developed TPS and investigated two different tumour sites, lung
and oesophagus [17, 18]. Dosimetric investigations of 4D robust optimisation for a wide range
of tumour sites and optimisation algorithms are lacking not least because an appropriate, site-
specific 4DDD computation tool is required. Such a tool depends on the knowledge of the time
structure of the beam delivery. As there is no standard time structure and vendors of TPSs
and delivery machines do not yet provide the option to access relevant scanning control system
information from the TPS, prospective interplay effect evaluations currently require in-house
development.
1
1 Introduction
This dissertation focuses on the question whether treatment planning based on 4D robust optim-
isation can help to reduce motion effects and the dose to normal tissue in PBS proton therapy
for hepatocellular carcinomas (HCCs). HCC, which is the most common type of primary liver
cancer and the third leading cause of cancer related mortality worldwide [19, 20], was selected
as a model system for moving targets because it is less affected by tissue heterogeneities and
related range uncertainties than thoracic targets [21, 22, 23, 24, 25]. The work was divided into
two main parts:
1. A customised 4DDD routine simulating interplay effects in PBS had to be implemented
in treatment planning. The routine was experimentally validated in an end-to-end test
using a dynamic phantom. A time model of the beam dynamics was established based
on empirical measurements to allow for prospective evaluations and the simulation of
possible variations in the beam delivery time structure. Although interplay effects have
been subject of numerous investigations both experimental and in silico (see for example
Ref. [26, 27, 28, 29, 30]), there are only a few approaches for the experimental validation
of the 4DDD calculation itself [31, 32, 33]. This part of the dissertation extends previous
works with its beam time model and a more realistic scenario by utilising different tissue
equivalent phantom materials, creating treatment plans with multiple energy layers and
including measurement points close to the target boundary.
2. The developed 4DDD routine was applied to evaluate 4D robust optimisation regarding
target coverage and OAR sparing in comparison to conventional PBS planning, in which
uncertainties are considered by uniform safety margins, and to the former standard for
moving targets, double scattering (DS). DS, a passive beam delivery technique, is less
susceptible to motion than PBS since the entire tumour is continuously repainted by the
usage of scatterers and a fast spinning range modulator wheel [34]. In contrast to PBS, DS
requires patient-specific beam shaping devices, deposits unnecessary dose proximal to the
target and does not allow for intensity modulation. The novelty of the in silico study on
4D robust optimisation is that a different methodology to achieve plan robustness against
motion was investigated than in previous publications. Furthermore, the performance was
evaluated for another target site and compared to DS. Since the evaluated optimisation
tool is part of a commercial TPS, the outcome is of relevance for many institutes.
Within the scope of the treatment planning study, the idea for a follow-up project arose, for
which a first proof of concept will be provided in this work. Due to the poor availability of
suitable patient data, 4D treatment planning studies often have two major deficits: (1) The
patient cohort cannot be divided into subgroups of sufficient size to systematically investig-
ate different influencing factors and (2) the study results are not representative for the entire
spectrum of patients. Thus, the validity is restricted to the underlying conditions and it is not
possible to draw universal conclusions. In a feasibility study, the use of simulated computed
tomography (CT) images was tested to overcome these issues. To this end, the computer gen-
erated image data were imported in the TPS and had to go through the whole workflow of
4D treatment planning and evaluation. The study examined exemplarily the dependence of
interplay effects on the target size.
The structure of this dissertation is as follows. Chapter 2 provides an overview on the physical
and radiobiological fundamentals of proton beam therapy and introduces treatment planning
concepts and the topic of moving targets. Chapter 3 deals with the implementation and exper-
imental validation of a four-dimensional dynamic dose calculation routine to assess the impact
of organ motion on the dose delivery for scanned pencil beams. In Chapter 4, the capability of
4D robust optimisation to maintain target dose coverage and spare normal tissue in the pres-
ence of organ motion is studied for hepatocellular carcinomas based on the developed routine.
Chapter 5 presents a proof of concept study which examines the application of computer gener-
ated CTs to systematically analyse motion interplay effects in scanned proton beam treatments.
A summary of the results and future directions are given in Chapter 6. Chapter 7 concludes
the dissertation.
2
2 Research principles and background of proton beam
therapy
2.1 Physical fundamentals
2.1.1 Proton interactions in matter
There are three predominant types of interactions of swift protons with matter: (1) inelastic
Coulomb interactions with atomic electrons, (2) elastic Coulomb interactions with atomic nuclei
and (3) nuclear reactions [35].
Inelastic Coulomb interactions with atomic electrons dominate the slowing down process of a
proton in an absorber. The energy loss per interaction is small and multiple ionisation events
lead to a quasi-continuous energy loss. The range of the liberated electrons can reach a few
millimetres but is usually less than 1mm in tissue so that the energy is deposited locally.
Even for a high proton energy of 200MeV, the maximum energy of secondary electrons is only
around 400 keV [36]. Due to the mass ratio between protons and atomic electrons, most of the
protons do not experience considerable changes in their direction of motion and travel almost
along a straight line. Only protons passing close to a nucleus will be elastically scattered or
deflected by the repulsive Coulomb force. The energy loss of a proton is negligible for this kind
of interaction but even small deviations of the initial trajectory due to scattering will have an
impact on the spatial distribution of the energy deposition. Nuclear reactions in which the
proton retains approximately its initial energy and angle are of minor importance compared
to occasional (non-elastic) nuclear reactions in which the absorption of a swift proton by a
nucleus lead to the liberation of neutrons, secondary protons, deuterons, tritons or heavier
ions [35]. These reactions are less frequent than Coulomb interactions. Nonetheless, they have
a noticeable effect on the dose profile since they remove primary protons from the incident
beam (see Sec. 2.1.3).
2.1.2 Dosimetric quantities
The mass stopping power 1
ρ
S describes the average energy loss dE per path length dl of
an ion traversing an absorber with density ρ. It is given by the sum of
• the mass electronic (or collision) stopping power 1ρ
(
dE
dl
)
el
caused by inelastic collisions
with the atomic shell as well as binary inelastic collisions with single shell electrons,
• the mass radiative stopping power 1ρ
(
dE
dl
)
rad
arising from the emission of bremsstrahlung
and
• the mass nuclear stopping power 1ρ
(
dE
dl
)
nuc
due to elastic Coulomb interactions (the
energy loss due to non-elastic nuclear reactions is usually not described by the nuclear
stopping power) [37]:
S
ρ
= −1
ρ
(
dE
dl
)
el
− 1
ρ
(
dE
dl
)
rad
− 1
ρ
(
dE
dl
)
nucl
,
[
S
ρ
]
= J m
2
kg
. (2.1)
At therapeutic proton beam energies from about 70MeV to 250MeV, the slowing-down process
of protons is, as already mentioned above, dominated by the electronic stopping power and
can be expressed analytically by the Bethe-Bloch formula [38, 39]. Here, the relativistic version
derived by Fano [40] is stated including a shell correction term CZt and a density effect correction
term δ2 :
S
ρ
≈ −1
ρ
(
dE
dl
)
el
= NZt
4piZ2pe4
mev2
[
ln 2mev
2
I
− ln (1− β2)− β2 − C
Zt
− δ2
]
, (2.2)
where N denotes the number of target atoms (or molecules) per unit volume, Zt the atomic
number of the target atom, Zp the nuclear charge of the projectile, e the charge and me
3
2 Research principles and background of proton beam therapy
the mass of an electron, v the velocity of the projectile, I the mean ionisation energy of the
absorbing material and β = v/c the ratio of the projectile velocity and the speed of light. The
shell correction term is significant at proton energies below approximately 10MeV only [41].
It corrects for the fact that the approximation of stationary electrons is no longer valid at
small particle velocities. The density correction term takes into account that incident protons
polarise the target medium leading to an effective shielding of the electric field far from the
particle track. This effect reduces the stopping power but is only relevant for proton energies
above several hundred MeV [41].
The mass stopping power is proportional to the inverse square of the velocity of the projectile,
the square of the particle charge and the electron density of the absorber (NZt).
The linear energy transfer (LET) L4 is the differential quotient of deposited energy
per unit length of a charged particle within a tube-shaped volume around the particle track.
The volume is determined by the range of secondary electrons whose kinetic energy equals the
cut-off value 4. The LET can thus be written as the difference of the electronic stopping power
and the kinetic energy of electrons leaving the regarded volume
(
Eδ4
)
on the line segment dl:
L4 =
(
dE
dl
)
el
− dE
δ
4
dl
, [L4] =
keV
µm
, (2.3)
where electrons with kinetic energies smaller than 4 are considered to be part of the track core
and L∞ equals the electronic stopping power [37]. Heavy charged particles, such as carbon ions,
are rated as high-LET radiation, i.e. densely ionising, whereas photons or electrons are rated
as low-LET radiation, i.e. sparsely ionising. Therapeutic proton beams are usually considered
as low-LET radiation.
The absorbed dose D is given by the mean local energy d delivered by ionising radiation
to a mass element dm with density ρ and volume dV :
D = d
dm
= 1
ρ
· d
dV
, [D] = Gy, (2.4)
where one gray (Gy) equals one Joule per kilogram [37]. It can be calculated based on the
stopping power and particle fluence Φ (number of particles per unit area) using the following
formula [42]:
D = S
ρ
· Φ. (2.5)
2.1.3 Depth dose profile
The depth dose profile of monoenergetic protons is depicted in Figure 2.1a. With increasing
depth different effects contribute to the Bragg peak curve:
• Electronic buildup region: Incident high-energy protons liberate secondary electrons which
have sufficient energy to produce further ionisation in the tissue several millimetres away
from the primary proton beam (delta rays). The electronic buildup region extends
from the surface to a depth which corresponds to the highest range of a recoil elec-
tron (Emaxelectron ≈ Eproton/500 [36]) . Within that region, the dose increases approaching
asymptotically the dose level of the sub-peak region. The electronic buildup might not
be observable if material upstream of the surface, e.g. beam shaping devices or patient
immobilisation devices, create a charged particle equilibrium or if it is superimposed by
the protonic buildup.
• Protonic buildup region: Secondary protons arising from non-elastic, proton-induced nuc-
lear interactions cause an increase of the absorbed dose with depth near the surface of
the absorber.
4
2.1 Physical fundamentals
• Sub-peak region: The sub-peak region extends from the surface to the beginning of the
peak. It results from the 1/v2 dependence of the energy-loss rate and nuclear interactions
which remove protons from the incident beam and liberate secondary particles. Secondary
particles exhibit shorter ranges and larger angles with respect to the incident beam.
Therefore, they deposit their energy further upstream than primary protons. For small
fields, the proton fluence on the central axis is reduced due to the lack of lateral multiple
Coulomb scattering equilibrium.
• Bragg peak: As protons slow down, the energy-loss rate increases (Eq. 2.2) leading to a
Bragg peak near the end of range, where protons are absorbed by the medium. Statistical
fluctuations of the energy loss broaden the Bragg peak and lower the maximum deposited
energy (energy-/ range-straggling) [35]. This effect is more pronounced for high energy
particles which travel longer distances. The range of a monoenergetic proton beam is
consequently an average quantity and defined as the depth in which 50% of the incident
protons have stopped. This depth coincides with the position in the Bragg peak curve
where the absorbed dose falls down to 80% of the maximum dose [43]. A good approxim-
ation of range for clinical applications, assuming a continuous energy loss and neglecting
lateral scattering, is the projected range. It is given by the integral of the inverse stopping
power over the kinetic energy in the interval [Emax, Emin]:
R (E) =
Eminˆ
Emax
1
S(E′)dE
′. (2.6)
The introduction of a lower energy limit Emin serves to exclude the case S(0) = 0. It
does not affect the result since very low particle energies only have minor contribution to
the total path length. The correlation between range and energy determines the clinical
energy spectrum for a therapeutic application [44].
• Distal fall-off region: The region downstream of the Bragg peak is called distal fall-off
region. It is caused by range straggling. In addition a momentum spread, attributable to
the energy selection system (Sec. 2.3.1), contributes to this region [45].
The dosimetric manifestation of the predominant interaction types can be summarised as fol-
lows: inelastic Coulomb interactions with atomic electrons determine the proton range in an
absorber, elastic Coulomb interactions with atomic nuclei the lateral penumbra and nuclear
reactions the peak-to-plateau ratio.
In proton therapy, the initial beam energy is varied to reach different depths. A homogeneous
dose in the target volume can be created by combining multiple Bragg peaks with appropriate
weighting factors to a so-called spread-out Bragg peak (SOBP) (see Fig. 2.1b).
Comparison with photon beams
Conventional radiotherapy usually utilises megavoltage x-rays with energies ranging from about
1MeV to 20MeV [46]. At this energy range, the Compton effect is the dominant interaction
type in tissue. The photoelectric effect dominates in water only for energies below 30 keV and
can be neglected above 100 keV. Photons with energies higher than 1.022MeV can produce
electron-positron pairs in interactions with the nuclear Coulomb field. But pair production
only becomes relevant for energies above approximately 10MeV in tissue.
When passing through matter, the fluence of a monoenergetic photon beam decreases expo-
nentially. However, the depth dose curve does not reach its maximum at the surface as can
be seen in Figure 2.1b. This is due to the buildup effect arising from Compton interactions.
Secondary electrons produced close to the surface spread their kinetic energy over their range.
Thus, they contribute to the dose deposition in deeper layers. The full buildup is reached at
a depth which corresponds to the average range of secondary electrons. The range depends on
the initial beam energy and is typically in-between 5mm and 5 cm [44]. This allows better skin
sparing compared to proton therapy. On the downside, photon beams deposit a high amount
5
2 Research principles and background of proton beam therapy
120
100
80
60
40
20
0
0 5 10 15 20
depth (cm)
ab
so
rb
ed
 d
os
e 
(%
)
electronic buildup
protonic buildup
sub-peak
Bragg peak
distal
fall-off
(a) Bragg peak
120
100
80
60
40
20
0
0 5 10 15 20
bi
ol
og
ic
al
 d
os
e 
(%
)
SOBPphoton beam
proton beams
tumournormal tissue normal tissue
depth (cm)
(b) spread-out Bragg peak
Figure 2.1: (a) Depth dose profile of a broad, monoenergetic proton beam (reproduction according
to Ref. [35]): Due to the low entrance dose in the sub-peak region and the steep dose fall-off behind
the Bragg peak, proton beams are particularly suitable for clinical use. The different regions of the
Bragg peak curve and the underlying interactions are described in Section 2.1.3. (b) Depth dose profile
of a spread-out proton Bragg peak (SOBP): Multiple pristine Bragg peak curves (blue lines) can be
superimposed to an SOBP (red line) when using appropriate beam energies and weighting factors.
Thus, it is possible to deliver a homogeneous dose to the tumour. In contrast to conventional photon
beams (black line), proton therapy enables normal tissue sparing proximal and distal to the tumour.
The biological dose states the photon dose which would yield the same biological effect as the absorbed
proton dose (see Sec. 2.2.3).
of dose in the normal tissue proximal and distal to the tumour, while protons exhibit no exit
dose and a lower entrance dose.
2.2 Cell survival and biological effectiveness
The availability of data on treatment outcome is limited for proton therapy which is why
treatment concepts are usually based on experiences in the field of photon therapy. Although
protons are in general considered as low-LET irradiation, their microscopic energy deposition
pattern differs from that of photons resulting in a different biological effect [47]. This must
be taken into account in treatment planning. The most studied endpoint to determine the
relative biological effectiveness of protons is clonogenic cell survival which will be explained in
the following. Molecular mechanisms of DNA and chromosome damage are not discussed in
the scope of this thesis. A detailed description can be found in Ref. [48].
2.2.1 Cell survival
There are different definitions for the term cell survival and its antonym cell death. In radiobi-
ology, cell death means the loss of ability to proliferate indefinitely. This is due to the fact that
the prevention of tumour growth and dissemination of malignant tumour cells in the body is of
major relevance. A cell survived by definition if it is able to produce a colony of at least fifty
daughter cells within a certain period of time [49].
The biological effect of a test irradiation on a tissue can be studied based on cell survival
curves. To this end, a known number of cells is irradiated in a Petri dish and after one to two
weeks of incubation cell colonies are counted. The fraction of surviving cells is plotted semi-
logarithmically against the dose. Characteristic curves for low- and high-LET radiation are
depicted in Figure 2.2a. Low-LET radiation exhibits a finite initial slope at low doses, followed
by a bending region (shoulder) and a linear decrease at higher doses (note the semi-logarithmic
scale). In contrast, the curve for high-LET radiation does not feature a shoulder and runs
almost straight over the whole dose range, i.e. the surviving fraction decreases exponentially
with dose. As a consequence, a lower amount of dose is needed to reach the same level of
6
2.2 Cell survival and biological effectiveness
0.001
0.01
0.1
1
ce
ll 
su
rv
iv
al
absorbed dose (Gy)
0 4 8 12 16
high LET
low LET
(a) single fraction
0.001
0.01
0.1
1
single dose tumour cell
normal cell
fractionated course
ce
ll 
su
rv
iv
al
absorbed dose (Gy)
irreparable
0 2 4 6 8
damage
(b) multiple fractions
Figure 2.2: Schematic illustration of cell survival (reproduction according to Ref. [50]): (a) comparison
of a densely ionising radiation (high LET) and a sparsely ionising radiation (low LET) for a single
fraction, (b) comparison of a single fraction and a fractionated radiation course for normal tissue and
tumour cells.
survival as with low-LET radiation. The shoulder in the low-LET curve indicates the ability of
the cell to repair sub-lethal damage. A simple interpretation is given by the biologic concept
of dual-radiation action below. The time needed for repair depends on the tissue type and
takes several hours. Conventional radiotherapy exploits the fact that tumour cells have a lower
ability to repair from sub-lethal damage than normal cells. The prescribed dose is given in a
fractionated course with small daily doses. Thus, the normal tissue can recover in-between the
treatment sessions (see Fig. 2.2b).
Linear-quadratic model
Mathematically, cellular survival can be described using the linear-quadratic (LQ) model. The
model is based on the assumption that two components, a linear (proportional to dose) and
a quadratic (proportional to the square of dose), contribute to the cell damage by ionising
radiation. The fraction of cells surviving a dose D is given by
S = exp(−αD − βD2) (2.7)
and is usually fitted by a second-order polynomial in a semi-logarithmic plot: − ln(S) =
αD + βD2 (see Fig. 2.2). The constants α
(
Gy−1
)
and β
(
Gy−2
)
are chosen to obtain the
best agreement with the experimental data and depend therefore on the irradiation and tis-
sue type. The mathematic formulation as a two-component model might be justifiable by the
biologic concept of dual-radiation action. According to the concept, the probability that two
chromosome breaks are caused by a single particle track and form a lethal exchange-type ab-
erration1 increases linearly with dose. If the two breaks result from two independent tracks,
however, the probability is proportional to the square of the dose. For D = α/β, both compon-
ents contribute equally. The ratio of α to β determines the shape of the curve and therefore the
radiation sensitivity of a tissue. Late-responding tissues exhibit small α to β ratios, whereas
early-responding tissues are characterised by a large α to β ratio [48].
2.2.2 Relative biological effectiveness
Cell experiments have demonstrated the higher biological effectiveness of protons compared to
photons. The relative biological effectiveness (RBE) is defined by the ratio of the reference
1Chromosomal aberrations: changes in the normal structure or number of chromosomes.
7
2 Research principles and background of proton beam therapy
dose Dref , e.g. the dose of 6MV photons, and the proton dose Dtest which lead to the same
biological endpoint (e.g. cell survival):
RBE =
[
Dref
Dtest
]
isoeffect
. (2.8)
The RBE depends on various parameters, such as dose, biological endpoint, irradiated tissue,
number of dose fractions, dose rate and LET. In proton therapy, a generic RBE value of 1.1 is
used. This value is a conservative estimate to ensure that the tumour receives the prescribed
dose despite considerable uncertainties in the experimental RBE determination [47].
2.2.3 Biological dose
The biological dose DRBE is defined as the product of the absorbed dose and the RBE:
DRBE = D ·RBE. (2.9)
It equals the photon dose which would achieve the same biological effect as the radiation under
consideration. DRBE is an important quantity in particle therapy because it incorporates the
higher biological efficacy of charged particles in the optimisation process.
2.2.4 Equivalent uniform dose
The equivalent uniform dose is the absorbed dose which yields the same radiobiological ef-
fect (cell survival), when given homogeneously to the whole tumour, as a studied non-uniform
dose distribution. A general formula, valid for tumours and normal tissue, has been intro-
duced by Niemierko in 1997 [51] and is hereinafter referred to as generalised equivalent uniform
dose (gEUD):
gEUD =
(∑
i
viD
1/n
i
)n
, (2.10)
where vi denotes a fractional organ volume and Di the corresponding absorbed dose. The
tissue-specific parameter n indicates the dependence on the irradiated partial volume and is
the only parameter which has to be fitted for a given radiation and tissue type. The formula is
based on the power law behaviour of cell survival with dose.
2.3 Proton beam therapy system
The West German Proton Therapy Centre Essen (WPE) is equipped with a cyclotron-based
IBA ProteusrPlus proton therapy system (IBA, Louvain-La-Neuve, Belgium). It has four
different treatment rooms: three 360° beam rotation isocentric gantry rooms and one 90° fixed
beam line room including an eyeline, which is not yet clinically used. A floor plan of the proton
therapy facility can be seen in Figure 2.3. The following sections describe the generation of a
therapeutic proton beam at WPE.
2.3.1 Components
Proton source
Protons are produced by a hot filament Penning Ion Gauge (PIG) source in the centre of the
cyclotron. Free electrons originating from the hot filament are accelerated in a strong electric
field and ionise inflowing molecular hydrogen (H2) gas in a hollow cylinder (chimney). The ions
and electrons form a plasma which shields external electric fields. Only ions diffusing through a
slit in the wall of the gas chimney experience the electric field of the closest cyclotron electrode.
The beam intensity is regulated by the filament heating through a feedback loop [53, 54, 55].
8
2.3 Proton beam therapy system
cyclotron
ESS
BTS
MCR
TCR
gantry gantry gantryfixed beam
eye line
TCR TCR TCR
Figure 2.3: Layout of the IBA proton therapy system at WPE showing the main control room (MCR),
treatment control rooms (TCRs), the cyclotron, the energy selection system (ESS), the beam transport
and switching system (BTS), the fixed beam treatment room including an eye line and three gantry
treatment rooms [52].
Isochronous cyclotron
An isochronous cyclotron accelerates the protons to a fixed energy of about 227 MeV. In contrast
to a classical cyclotron, the magnetic field increases with radius to compensate for the relativistic
mass increase at high particle energies [53]:
B (r) = m (r) B0
m0
= γB0, (2.11)
where γ = 1/
√
1−( vc )2 denotes the Lorentz factor. Thus, the azimuthal frequency of the protons
becomes independent of the radius and remains synchronised with the radio frequency (RF)
voltage between the cyclotron electrodes:
ω = v
r
= qB (r)
m (r) = constant. (2.12)
The main advantage of an isochronous cyclotron is the quasi-continuous character of the beam.
Prior to the invention of isochronous cyclotrons, the RF frequency had to be adjusted synchron-
ously to the proton mass (synchrocyclotron) so that only particle bunches with phase parameters
matching the RF frequency could be accelerated [54]. In IBA cyclotrons, the increase of the
magnetic field with radius is realised by a decreasing gap between the magnetic poles. The
increasing magnet field, however, compromises the vertical beam stability. Without corrections
vertical deflected protons would be pushed towards the poles and be lost in collisions [53]. To
reduce the particle loss, hills with stronger magnetic fields (small gaps) and valleys with weaker
magnetic fields (large gaps) are added to the magnetic pole. The azimuthally varying magnetic
field provides a focusing force keeping the protons within a horizontal plane.
Energy selection system and beam transport and switching system
At the exit of the cyclotron, the beam energy is reduced to an appropriate therapeutic value by
the energy selection system. The energy selection system consists of a wheel-mounted energy
degrader wedge of variable thickness and material, a magnetic analyser and slits defining the
energy width. Beam energies from 100MeV to 227MeV are clinically available. From the
energy selection system, the proton beam is transported within a vacuum tube to the treatment
rooms, whereby dipole and quadrupole magnets serve to bend and focus the beam. For the
9
2 Research principles and background of proton beam therapy
field shaping, it is important that the beam transport and switching system provides a centred
beam with appropriate optical characteristics such as spot size, beam intensity, average energy,
energy spread and angular spread (emittance).
Nozzle
The delivery technique and thus the beam characteristics are determined by the beam delivery
system (’nozzle’) at the exit of the beam line. The nozzle contains all technical devices which
are required to shape the irradiation field and to monitor the beam properties. It is either
mounted horizontally (fixed beam treatment room) or on a 360° beam rotation isocentric gantry.
At WPE, dedicated pencil beam scanning nozzles and universal nozzles supporting different
delivery techniques are available for treatment (see below).
2.3.2 Beam delivery: Pencil beam scanning (PBS) and double scattering (DS)
In order to distribute a prescribed dose over the whole target volume the irradiation field has
to be shaped in lateral and longitudinal direction. The longitudinal modulation of the beam
is done by adjusting the beam energy according to the depth and thickness of the tumour in
beam direction. As already mentioned, a homogeneous depth dose distribution (SOBP) can be
created by combining different beam energies with appropriate weighting.
The lateral shaping of the field can be active or passive. In an active system, a narrow beam is
scanned across the target energy layer by energy layer. Whereas in a passive system, the beam
is scattered to increase the beam cross section and to spread the dose over the target. In the
following, the two delivery techniques which are referred to in this thesis will be described.
Pencil beam scanning is an active delivery technique in which the narrow beam scans the
target three-dimensionally. A dedicated pencil beam scanning nozzle is depicted in Figure 2.4a.
It includes
• an ionisation chamber (IC1) to monitor the centring of the beam at the nozzle entrance,
• two quadrupoles to focus the beam,
• a pair of dipole magnets to scan the beam laterally,
• an x-ray tube which can be inserted and retracted to enable beam’s eye view imaging,
• two ionisation chambers (IC2 and IC3) to measure the dose and to verify the position,
size, and shape of the pencil beam
• and a removable range shifter which enables range degradation up to the patient’s skin
to treat superficial tumours.
At WPE, scanning is performed in discrete steps with a fast and a slow magnet [56] using
a ’step-and-shoot’ method (spot scanning). In contrast to passive systems, this technique al-
lows to modulate the intensity and enables thus multi-field optimisation. In spot scanning,
the intensity is modulated by varying the dwell time of the pencil beam at each spot position.
Therefore, no modulation in scanning speed or beam intensity is required. The irradiation is
delivered energy layer by energy layer and starts with the most distal range (highest energy)
(see Fig. 2.5). Spots optimised by the treatment planning system are reordered by the IBA
scanning control system aiming for a short delivery time. The spots are placed consecutively
on a line along the fast scanning direction. After changing the position in the slow direction
the order within the next line of spots is optimised with regard to the shortest scanning path
in-between the lines. The difference in the scanning speeds results from the fact that the dedic-
ated PBS nozzle is equipped with the same scanning magnets which were originally developed
for optimum beam delivery in uniform scanning mode (diamond pattern). Besides, the magnets
have a different distance to the isocentre (see Fig. 2.4a). The fast scanning magnet is ten times
faster than the slow scanning magnet.
10
2.3 Proton beam therapy system
In the following, typical clinical values for spot size, spot distance, spot weight and energy layer
spacing are presented. The spot size at the isocentre ranges from about 6.6mm for 227MeV
to 13.4mm for 100MeV in air (full-width at half-maximum) [57]. The spot spacing can be
scaled automatically depending on the radial spread in the Bragg peak for an energy layer or
is chosen to be constant. Usually, a spot spacing of 6mm to 8mm is applied. Spot weights
used in clinical practice range from 0.04 monitor units (MUs) to a few MUs, where 1000MUs
correspond to about 108 cGy within the entrance plateau of the Bragg peak curve for a 10 cm
x 10 cm field, 160MeV and a spot spacing of 2.5mm [57]. The energy layer spacing is scaled
depending on the width of the Bragg peak. The distance increases with larger scaling factor. In
clinical scenarios, the energy of two adjacent layers differs by approximately 2MeV to 4MeV.
The beam delivery is documented in irradiation log files which record parameters such as the
spot position and the amount of charge collected by the ionisation chambers on a 0.25ms time
grid. Variables which determine the time structure are the spot delivery time, the scanning
speed and the energy layer switching time. The spot delivery time varies with the beam cur-
rent. Depending on the material and the thickness of the energy degrader for a certain range,
a higher beam current is requested by the IBA system to compensate for scattered protons and
a reduced transmission efficiency of the energy selection system. The lowest energy selection
system efficiency determines the maximum beam current requested from the cyclotron at the
beginning of each irradiation. During the irradiation, the ’beam current regulation unit’ adjusts
the current for each energy layer by tuning the arc voltage of the ion source. A feed-back is
received by an ionisation chamber at the exit of the cyclotron.
The scanning magnets are driven by a digitally controlled scanning magnet power supply, which
consists of two pulse width modulation amplifiers. Due to the ’slew rate’ of the magnet power
supply, the time to move from one spot position to the next will never be zero [53]. The settling
time for the magnetic field takes several hundred microseconds. Since the magnets are prone
to hysteresis effects, longer settling times are required for larger distances.
A change of the beam energy involves adaptations of all magnets in the beam line. The total
energy layer switching time takes less than 2 s according to the ProteusrPlus product descrip-
tion [55].
Double scattering is a passive beam delivery technique in which the narrow beam is spread
laterally by a pair of scattering devices on the central beam axis (see Fig. 2.6). The first spread-
ing device, a lead foil, increases the width of the beam based on multiple Coulomb scattering
in the high-Z material. After passing the first scatterer, the lateral beam profile has an approx-
imate Gaussian shape. A flat and symmetric beam profile is however required to generate a
uniform dose distribution. Without a second scatterer, only the beam fraction around the centre
exhibiting a rather flat intensity profile is clinically usable (single scattering technique). Since
most of the beam has to be blocked by a collimator in single scattering, the system efficiency
is very low and only small target volumes can be treated. DS introduces a second scatterer
composed of high- and low-Z material to flatten the beam on a large field area (maximum field
radius: 12 cm). The thickness of the high-Z material (lead) decreases with increasing radius.
Thus, protons passing the thicker, central part are scattered more than those hitting the outer
regions of the foil. The dome shape of the lead component is designed such that the amount
of in and out scattered protons yields a flat lateral intensity distribution at the height of the
isocentre. To compensate for resulting differences in energy loss, a low-Z component (lexan) is
added to the foil. The thickness of the lexan component is larger the thinner the lead foil is
so that the range is the same for all beam rays. Due to the contoured scatter foil, an accurate
centring of the beam is particularly important in DS [55].
The modulation of the beam energy in DS is done by a range modulator wheel which is located
in-between the first and the second scatterer. The range modulator is divided into steps of
different material thicknesses and spins at 600 rounds per minute [55]. It is composed of low-Z
material (carbon/lexan) and high Z-material (lead), whereby the low-Z material serves to lower
the beam energy. The high Z-material is used to adjust the amount of scattering such that each
step has the same scattering effect on the beam independent of the range. The Bragg peaks
11
2 Research principles and background of proton beam therapy
x-ray tube
scanning
magnets
range shifter
IC2 and IC3 quads
IC1
(a) IBA’s pencil beam scanning nozzle
first 
scatterer 
scanning magnets
(Uniform Scanning 
and Pencil Beam 
Scanning)  
variable 
collimator 
snout 
holder 
IC2 and IC3 second 
scatterer 
range 
modulator 
or quads 
compensator IC1
aperture
x-ray tube
(b) IBA’s universal nozzle
Figure 2.4: Technical drawing of a dedicated pencil beam scanning nozzle from IBA (a) and a
universal nozzle supporting four different delivery types (b) [55]. A description of the elements is given
in Section 2.3.2.
12
2.3 Proton beam therapy system
last layerfirst magnet
horizontal
scanning
second magnet
scanning
vertical
pole-faces
minimum energy
first layer
maximum energy
tumorof dipole magnets
pole-faces
of dipole magnets tu our
first magn t second mag
horizontal
scanningscanning
vertical
maximum energy
minimum energy
first layer
last layer
Figure 2.5: Schematic drawing of the pencil beam scanning (PBS) delivery technique described in
Section 2.3.2 (reproduction according to Ref. [58]).
are weighted by the angular length of the corresponding wheel step in order to create a flat
SOBP. The optimum Bragg peak weights depend on the beam energy at the nozzle entrance
which is set by the energy selection system dependent on the most distal point of the target.
To use the same wheel for different energy spans, the weight of each step has to be fine-tuned
by modulating the beam current with angular rotation. The respective values are stored in
a beam current modulation file. IBA developed three wheels each containing three concentric
tracks dedicated for different clinical demands. Eight out of the nine tracks are available in
DS to create SOBPs of variable modulation and range according to the maximum depth and
thickness of the tumour.
Patient-specific beam shaping devices are required to adjust the field laterally and longitud-
inally to the shape of the target. In lateral direction, field shaping is done by the use of an
aperture made of brass (see Fig. 2.7a). It limits the field to the size of the target from beam’s
eye view so that different apertures have to be fabricated for each beam angle. To minimise the
penumbra the aperture is mounted close to the patient on the so-called ’snout’. The snout holds
all patient-specific devices. Unfortunately, the majority of unwanted neutron dose received by
the patient is produced by the aperture. A variable collimator behind the second scatterer
serves to minimise the neutron amount by reducing the field size to the smallest rectangle that
still encloses the patient aperture.
For longitudinal beam shaping, an individually produced range compensator is attached to the
snout right behind the aperture. The range compensator represents the last element in front
compensator
aperture
range modulator wheel 
first scatterer
second scatterer
high Z
low Z
high dose region
tumour
Figure 2.6: Schematic drawing of the double scattering (DS) delivery technique described in Sec-
tion 2.3.2.
13
2 Research principles and background of proton beam therapy
of the patient. It is made of polymethyl methacrylate (PMMA) and conforms the distal range
of the SOBP to the distal shape of the target including a safety margin. The thickness of a
compensator pixel is given by the treatment planning system. Due to multiple Coulomb scatter-
ing, setup uncertainties and anatomical changes, range gradients between neighbouring pixels
cannot be infinitely large. In a smearing process, the thickness of each pixel is reduced to the
smallest thickness of all neighbouring pixels whose centre is located within a specified smearing
radius from the centre of the current pixel to add robustness against position uncertainties and
to prevent from undershooting [59]. The arrangement of all technical devices in the universal
nozzle can be seen in Figure 2.4b.
An advantage of DS is the continuous repainting of the whole tumour. There is negligible energy
layer switching time. Thus, the treatment is faster and less sensitive to organ motion. Disad-
vantages of DS in comparison to PBS include a lower dose conformality proximal to the target, a
higher neutron production, a higher sensitivity to beam misalignment compromising the lateral
uniformity and additional costs for the production of individual beam shaping devices.
2.4 Treatment planning
Treatment planning aims at finding the optimal dose distribution for each individual patient
to increase the probability of a curative treatment without side effects. A decisive factor for
the treatment quality is the choice of the treatment plan parameters such as spot positions
and weights in PBS or the shape of blocks and compensators in DS. Due to the large number
of variables, forward planning, a manual trail-and-error process, is not a convenient strategy
to find the best suited set of parameters. For that reason, most of the beam parameters
are determined by automated computation methods based on specified plan criteria (inverse
planning). Only the number of fields and the couch and gantry angles are chosen manually by
the treatment planner. Finding the optimal dose distribution still remains an iterative process.
After each dose calculation the optimised plan has to be analysed and specified criteria for
targets and OARs may have to be adjusted in order to improve the plan quality. In general, a
good treatment plan is characterised by a high target coverage and low doses to surrounding
healthy tissues. However, in some cases OARs overlap with the target volume or are very close
to it so that trade-offs must be made.
2.4.1 Treatment planning system (TPS)
The treatment planning system RayStation from RaySearch (RaySearch Laboratories AB,
Stockholm, Sweden) is clinically used for treatment planning and evaluation at WPE since
2015. In Europe, WPE was the first proton therapy centre treating a patient with RayStation.
The planning software provides dose engines for photon, electron, proton and carbon ion ther-
apy and features advanced treatment planning techniques such as Multi-Criteria Optimisation
or 4D treatment planning.
A scripting interface, in form of an embedded IronPython console, offers maximum flexibility.
IronPython is an open-source implementation of the scripting language Python with access to
the .NET Framework [60]. It allows for automation of treatment planning processes, execution
of actions which are not available in the standard interface and systematic, retrospective data
analysis of patient cohorts. Thus, scripting in RayStation does not only save valuable time in
clinical routine, but also represents an important research tool. An example of a script, which
was developed within the scope of the dissertation, is provided in section A.1 in the appendix.
In this thesis, the research versions of RayStation 5, 6 and 7 operated within the clinical in-
stallation were used to compute dynamic dose distributions in the presence of motion and to
evaluate and compare different treatment planning techniques for moving targets.
2.4.2 Computed tomography (CT)
Computed tomography is a diagnostic imaging technique in which a series of x-ray images
is taken from different angles and is processed into cross-sectional images of inner physical
structures to get a three-dimensional image of the patient. The attenuation of x-rays in the
14
2.4 Treatment planning
(a) aperture (b) compensator
Figure 2.7: Patient and field specific beam shaping devices in passively scattered proton therapy.
patient’s body yields information on tissue characteristics. In proton therapy planning, CT
data sets are needed to determine the water equivalent path length of protons in tissue.
The current generation of CT scanners produces narrow, cone-shaped x-ray beams. During
a CT scan, the x-ray tube and an opposing detector array rotate around the patient while
the patient table is moving through the scanner (see Fig. 2.8). Thus, it is possible to acquire
intensity profiles from different angles. The attenuation of the photon intensity after passing
objects can be described by
I =
Emaxˆ
0
I0(E) · e
−
L´
0
µ(E)ds
dE, (2.13)
where Emax is the maximum photon energy, I0 the incident photon spectrum, L the total
path length and µ the photon attenuation coefficient. The attenuation coefficient µ states the
probability of photon interactions for a tissue/material and is given by the product of the atomic
cross section σa and the number of atoms in the absorber volume n:
µ = n · σa = NA · ρ · Z
A
· σe (2.14)
with the density ρ, the atomic number Z, the mass number A, Avogadro’s number NA and
the electron cross section σe [61]. µ depends on the electron density, the atomic number and
the photon energy. The latter is expressed by the electron cross section in Equation 2.14.
For diagnostic x-ray energies between 30 peak kilo voltage (kVp) and 140 kVp, photoelectric
absorption processes as well as incoherent and coherent scattering contribute to the atomic
cross section:
σa = σphotoa + σcoha + σincoha . (2.15)
Profile data from many directions are taken to calculate µ for individual volume elements
(voxel) and reconstruct the image. Comparability between different CT scanners is established
by defining a CT number which states the photon attenuation with reference to water [62]:
CT number = µtissue − µwater
µwater
· 1000, [CT number] = HU. (2.16)
The CT number is measured in Hounsfield units (HU). By definition, the CT number of wa-
ter is 0HU and the CT number of air -1000HU. Bones can exhibit CT numbers of up to
3000HU, whereas the CT numbers of soft tissues and fluids typically range from about -100HU
to +100HU.
15
2 Research principles and background of proton beam therapy
In proton therapy, a CT calibration relating CT numbers to stopping powers is required for dose
computation. RayStation’s dose engine calculates the stopping power based on the Bethe-Bloch
formula (Sec. 2.1.2). As a consequence, mass density, mean ionisation energy and material com-
position of a voxel must be deduced from the CT.
The elemental composition and mean ionisation energy are defined based on a list of reference
materials stored in RayStation. For each reference material, the mass fraction of atomic ele-
ments ω (Z) has been interpolated from ten well-established core materials which are found in
patients, such as lung, muscle or aluminium [59]. The reference material with the most similar
mass density is assigned to a voxel. The mass density itself is not taken from the reference
material. Instead, CT numbers are converted to mass densities by linear interpolation from
CT-to-density calibration curves. Since the CT number for a given mass density can vary with
the CT scanner, the scan protocol or the patient geometry, it might be necessary to create
different calibration curves [59]. At WPE, for example, calibration curves exist for CT scans of
the patient’s head at 120 kV, the patient’s trunk at 120 kV and the patient’s trunk at 140 kV,
the latter being used for corpulent patients.
Common calibration approaches are the tissue substitute and the stoichiometric method. The
tissue substitute calibration is straightforward. A CT scan of a phantom with different tissue
surrogates of known densities is acquired. Subsequently, the mass densities are assigned to the
measured CT numbers. The stoichiometric calibration requires more effort but yields higher
accuracy for biological tissues [63]. It considers also the chemical composition of the materials
which differs for tissue substitutes and real tissues and affects the attenuation of x-rays. For
photon energies of up to 1MeV, the attenuation of x-rays can be described by the photoelectric
effect, incoherent scattering and coherent scattering. In the stoichiometric approach, the contri-
bution of each of those effects to the linear attenuation coefficient is calculated as a function of
the atomic number based on CT scans of tissue surrogates of known chemical composition. The
contributions are specified by the so-called K-coefficients and depend on the CT scanner and
the used scan protocol. Therefore, they have to be determined for each calibration individually.
Once the K-coefficients are known, theoretical CT numbers can be calculated for a wide variety
of biological tissues, whose chemical composition is taken from literature.
The tissue substitute method was applied within the scope of this thesis to create an individual
calibration curve for the used, artificial phantom materials (Sec. 3.2.1), whereas a stoichiometric
calibration curve was applied to convert CT numbers to stopping powers for CT data of real
patients (Sec. 4.2.2).
If a material does not fit to a CT-to-density calibration curve or CT artefacts distort the meas-
urement, it is possible to override the affected volume by a specified mass density and elemental
composition.
2.4.3 Contouring
Contoured structures in form of regions of interest (ROIs) are required to guide the treatment
plan optimisation. They are used for the specification of site-specific dose limits in PBS and for
the definition of margins in the treat and protect settings in DS. Target volumes and nearby
OARs are delineated manually on 2D slices of tomographic image data sets or with the aid of
segmentation tools.
Target volume definitions in radiotherapy are described in ICRU Report 78 [65] and are illus-
trated in Figure 2.9. The gross tumour volume (GTV) refers to the macroscopic malignancy,
which is clinically demonstrable. In clinic, an extra margin is added to the GTV to account for
a sub-clinical, microscopic spread of tumour cells. The expanded volume is called clinical target
volume (CTV). Expected changes in shape, size and position of the CTV due to physiological
processes are considered by an internal margin. The corresponding volume is termed internal
target volume (ITV). It can be generated for example by encompassing the CTV in all res-
piratory phases of a respiratory correlated CT (Sec. 2.5.4). Motion mitigation techniques as
respiratory gating or abdominal compression reduce the size of the ITV (Sec. 2.5.5). The plan-
ning target volume (PTV) takes additionally uncertainties in patient positioning and proton
range calculation into account.
16
2.4 Treatment planning
CT machine
motorised table
motorised table
rotating direction
x-ray source
fan-shaped
x-ray beam
rotating
rotating
x-ray detectors
Figure 2.8: Schematic illustration of a CT scan [64]: The x-ray source and an opposing detector
array rotate synchronously around the patient. At the same time, the motorised patient table moves
continuously through the scanner resulting in a helical scan.
In RayStation, a ROI covering the patient’s body as well as all support and fixation devices
is required for each plan. The so-called External defines the volume for the dose computation
problem. Every structures which lies outside of the External or the dose grid is considered as
vacuum [59]. In addition, a ROI which presents the patient’s body in the CT image is created
in treatment planning. The body ROI facilitates contouring of OARs close to the surface with
segmentation tools, can be applied as controlling structure or focusing region in deformable
image registrations (see Sec. 2.4.4) and is used to determine the dose maximum within the
patient.
2.4.4 Deformable image registration
Deformable image registrations (DIRs) were performed using the ANAtomically CONstrained
Deformation Algorithm (ANACONDA) [66]. ANACONDA pursues a hybrid approach which
combines intensity and geometric based algorithms. The registration involves the computation
of a deformation vector field whose parameters are determined by solving a non-linear optim-
isation problem. The objective function, which is minimised during the optimisation process,
is formed by the weighted sum of four non-linear terms:
1. an image similarity term to optimise the similarity between the deformed image and the
target image by means of the Pearson correlation coefficient,
2. a grid regularisation term to ensure local smoothness and invertibility of the deformation
vector field,
3. a shape based grid regularisation term to inhibit large shape deviations of selected con-
toured structures (controlling structures) and
4. a penalty term to guide the algorithm such that controlling structures in the reference
image are deformed to the corresponding structures in the target image.
17
2 Research principles and background of proton beam therapy
GTV
PTV
ITV
CTV
OAR
Figure 2.9: Schematic illustration of target volume definitions in radiotherapy: gross tumour
volume (GTV), clinical target volume (CTV), internal target volume (ITV) and planning target
volume (PTV). An organ at risk (OAR) is depicted next to the tumour.
A detailed mathematical description can be found in reference [66]. The image similarity term
is invariant to linear intensity transformations. Thus, ANACONDA can be used when images
describe the same data but were acquired with different imaging modalities, e.g. CT and cone
beam CT. By including ROIs or points of interest (POIs) as controlling structures or focusing
regions a higher accuracy of the DIR can be reached. A focusing ROI is applied to reduce the
size of the region considered by the algorithm for large scans or to exclude regions containing
image artefacts. ANACONDA has been validated in terms of landmark tracking accuracy,
contour propagation accuracy and image similarity [66, 67, 68, 69].
2.4.5 Proton dose calculation
RayStation provides two different dose engines for PBS, one that is based on a Pencil Beam
algorithm and one that is based on Monte Carlo (MC) simulations. The Pencil Beam al-
gorithm is usually faster but less accurate than MC. Therefore, it is recommended to use the
MC engine in cases which exhibit large inhomogeneities (e.g. lung tissue) or include a range
shifter [59, 21, 23, 25, 24].
At the time when the PhD project started, the MC engine was not yet implemented in RaySta-
tion (version 5) and the latest TPS version (RayStation version 7) supports MC dose calculations
only for PBS and not for DS. For that reason, the main focus of this section is on the Pencil
Beam algorithm. Nonetheless, a short description of the MC dose engine is provided since the
project was complemented by a review of the calculated PBS dose distributions with MC on a
sample basis.
Pencil Beam dose engine
The Pencil Beam algorithm assumes that any incident proton beam can be regarded as an
accumulation of smaller, narrow beams of pencil like shape, giving rise to the name of the
algorithm. These pencil beams should not be confused with the physical pencil beams which
are delivered in the PBS technique (’spots’). The algorithm uses a infinite slab approximation,
i.e. the patient is treated as a stack of semi-infinite layers and lateral inhomogeneities are
disregarded. The decomposition of spots into pencil beams is made to better account for
inhomogeneities in the patient within the volume of a spot and thus reduces errors due to the
infinite slab approximation. Given the differences in mean direction of protons at a certain
point in the fluence plane for different spots, every spot has to be handled separately and it is
not appropriate to use a common fluence grid in PBS. Instead, RayStation arranges 18 pencil
beams per spot in two concentric circles around a high weighted centre pencil beam. The
18
2.4 Treatment planning
number of 19 sub-spots is a compromise between computation time and sufficient accuracy in
the sampling of the patient geometry and the reproduction of the initial spot fluence. The
distance between sub-spots depends on the spot size.
In contrast to PBS, DS exhibits a uniform intensity distribution within an energy layer and the
fluence plane can be discretised into an orthogonal grid, each pixel corresponding to one pencil
beam.
For both, PBS and DS, the dose contribution of a pencil beam along its central axis z is
determined by the product of the lateral proton fluence Φ and the integrated depth dose IDD:
dose(z, r) = Φ(z, r) IDD(z), (2.17)
where r is the radial coordinate in the lateral plane [59]. The lateral proton fluence can be
deduced from the phase space parameters which are computed along the central axis of each
pencil beam with a sub-spot multi tracing algorithm considering stopping power, multiple Cou-
lomb scattering (MCS) and non-elastic nuclear interactions. The effect of energy loss straggling
is not explicitly accounted for during ray tracing but it is included in the IDD curves.
In PBS, the initial phase space parameters of a spot are the mean direction of the protons, the
energy spectrum dN/dE, spatial-angular distribution moments (angular variance Θ2, spatial-
angular covariance rθ and spatial variance r2 of the Gaussian spot fluence) and the absolute
spot weight ωa, whereas in DS the parameters for an energy layer e include the mean direction
of the protons, the mean beam energy at the patient surface Em,e, the integrated depth dose
curve in water IDDwe (without compensator), the local angular variance at the compensator
entrance plane Θ2C,e and the relative weight of the energy layer ωe. The ray tracing grid equals
the dose grid and the tracing process stops either when the ray leaves the grid or when the
energy falls below 1MeV. The average HU value of a voxel is calculated based on the planning
CT, which often has a higher resolution.
The integrated depth dose for energy layer e and pencil beam j at depth zej is given by the
reference integrated depth dose curve in water IDDwe at the water equivalent depth zwej :
IDDej = IDDwe
(
zwej
)
. (2.18)
zwej equals the integral of the medium to water stopping power ratio over the path length zej :
zwej (zej) =
zejˆ
0
S (z′)
Sw (z′)
dz′. (2.19)
The water reference IDD with the unit cGy cm2/proton is the weighted superposition of Monte
Carlo pre-calculated, mono-energetic IDDs and provided by the beam model.
The stopping power model used in RayStation is based on the Bethe-Bloch formula omitting
the clinically non-relevant shell and density correction terms (Sec. 2.1.2). It serves to compute
water equivalent depths (Eq. 2.19) and absolute energy loss.
The lateral spread of the proton beam is caused by MCS and nuclear interactions. It can be
divided in a central Gaussian shaped distribution, the core, and a low dose region surrounding
the core, the nuclear halo. The halo is largely attributable to charged secondary particles from
nuclear interactions and has a radius of approximately one third of the beam range [70]. MCS
is mainly associated with the Gaussian core but also contributes to the non-Gaussian tail of
the distribution. Even though the nuclear halo exhibits a low dose which is spread over a large
volume, it must be modelled with sufficient accuracy since it removes a significant fraction of
the integrated dose of the core.
MCS is handled by the Fermi–Eyges theory [71]. The theory describes the phase space distri-
bution of a Gaussian beam when it propagates through a stack of slabs of different materials.
The Gaussian distribution remains Gaussian at any slab of the stack. Drawbacks of the theory
19
2 Research principles and background of proton beam therapy
are that it neglects the non-Gaussian tail created by MCS and that it does not consider lateral
inhomogeneities.
Nuclear interactions are modelled in RayStation using look-up formulas from Soukup et al. [59,
72]. A correction term is included to account for differences in the output for certain field sizes
and energies which were detected in a field size study. Details on the calculation methods can
be found in the RayStation reference manual [59].
In PBS, the total dose in point (x, y, z) is given by the sum of all spot contributions:
dose(x, y, z) =
∑
e
∑
j
Seω
MU
ej dej (x, y, z) , (2.20)
where dej is the dose contribution from spot j in energy layer e, Se (protons/MU) the energy
dependent dose monitor sensitivity and ωMUej the meterset weight of the spot. dej is determ-
ined by the MCS dose contribution of each sub-spot k and the nuclear interaction (NI) dose
contribution of spot j:
dej(x, y, z) =
19∑
k=1
(
ωkΦMCSejk IDDejk
)
+ ΦNIej IDDej . (2.21)
with ωk being the relative weight of sub-spot k. The nuclear interaction dose can be approx-
imated by a single pencil beam trace since its contribution is small compared to MCS.
In DS, the total dose in point (x, y, z) is calculated based on the dose contribution of each
fluence pixel j, the meterset weight of the beam MU , the collimator transparency aj and the
number of protons per MU Ie:
dose(x, y, z) = MU
∑
j
aj
∑
e
Ie
(
ΦMCSej + ΦNIej
)
IDDej . (2.22)
Ie is the product of the relative weight of the energy layer ωe, the dose monitor sensitivity SN(
protons/
(
MU cm2
))
and the pixel area A: Ie = ωeSNA.
Monte Carlo dose engine
This section gives an overview of the RayStation MC dose engine without going into mathemat-
ical details. Formulas can be found in the RayStation reference manual [59] and the references
therein.
The current MC dose engine supports only PBS beams and was developed with the goal to
achieve a good trade-off between computation time and sufficient accuracy of the applied phys-
ical models. Some of the concepts are identical to those used in the Pencil Beam dose engine.
For example, both dose engines share the same initial phase space parameters for a spot. The
protons are transported through the patient geometry through a sequence of so-called random
hinges. Each step of the sequence is represented by two straight legs and a connecting hinge
point. The angle between the legs simulates the deflection of the proton due to MCS and is
randomly selected from a probability distribution defined by the Goudsmit-Saunderson the-
ory [59, 73, 74]. One hinge can extend over several voxels of the transport grid. MCS and
energy loss straggling are calculated once per random hinge to speed up the computation time.
They are taken into account until the energy falls below an energy cut-off value of 30.7MeV.
Above this value, energy loss straggling is handled by the Bohr approximation which assumes
that the spread can be described by a Gaussian distribution [59]. In contrast to MCS and en-
ergy straggling, energy loss and nuclear absorption have to be considered for each voxel which
is traversed due to their impact on the kinetic energy of the proton and the elemental compos-
ition. As in the Pencil Beam dose engine, energy loss is calculated based on the Bethe-Bloch
formula neglecting the shell and density correction terms.
Nuclear interactions which are considered by the MC engine are non-elastic nuclear reactions,
20
2.4 Treatment planning
elastic proton-proton scattering and elastic proton-nucleus scattering. Non-elastic nuclear reac-
tions are difficult to model which is why RayStation uses a cross section data library based on
the ICRU report 63 [75]. A continuous slowing down approximation is applied for heavy second-
ary particles such as deuterons and alphas, i.e. MCS, nuclear absorption and energy straggling
are disregarded. Elastic proton-proton scattering is modelled by replacing the primary proton
by two secondary protons in the transport process. The differential cross sections are calculated
from parametrised models described in Ref. [59, 76]. Elastic proton-nucleus scattering events
at large angles are rare and the angular distribution is approximated by ICRU63 data on the
elastic scattering of protons on hydrogen [75, 76]. Neutrons and gammas are not included in
the transport process but their energy is considered in the energy balance. Secondary electrons
are also disregarded by the transport mechanics since they deposit their energy very close to
the track within a volume which is usually smaller than the voxel size.
2.4.6 Treatment planning in pencil beam scanning and 4D robust optimisation
In PBS, objective functions and constraints are used to penalise deviations from specified dose
limits to reach the clinical goals. The chosen dose limits often coincide with the values stated
in the clinical goals. But in some cases it might be necessary to choose higher or lower limits
to avoid conflicts with competing optimisation functions with regard to the overall treatment
quality. There are different optimisation functions which might lead to a certain goal. For
instance, a homogeneous dose distribution in the target volume can be realised by penalising
deviations from a desired dose level (Uniform Dose function) or by penalising doses under
and above specified threshold values (a combination of Min and Max Dose functions). If a
Uniform Dose function is applied, the optimizer will try to ensure that exactly the stated dose
is delivered to each voxel of the ROI. Using Min and Max Dose functions provides more scope
for the optimizer, especially in view of the fact that it is more important to eliminate cold spots
than hot spots within the target. One example for a mathematical formulation of an objective
function i is:
fi(d) =
ˆ
V
ρ
(
d(p)− dˆ
)2
dp. (2.23)
d(p) denotes the dose at point p within the volume V of the considered ROI, dˆ indicates
the reference dose level which shall not be exceeded or fallen below and ρ is a ramp function.
Depending on whether a Min or Max function has to be applied, ρ is defined as ρ (y) =min {y, 0}
or ρ (y) =max {y, 0}. Further functions in RayStation relate to the dose volume histogram,
the equivalent uniform dose or the dose fall-off (see Ref. [77, 78] for details). The composite
function f of all objectives f1 , ..., fn and, where appropriate, constraint functions form together
the optimisation problem. Since the functions f1, ..., fn penalise deviations from desired dose
criteria, a minimum of f has to be found. However, it is most likely that a common minimiser
for all functions does not exist due to conflicting criteria involving high target doses and low
doses to normal tissues. A trade-off between the desired qualities is made based on the relative
weighting of the functions:
f =
n∑
i=1
ωi fi , (2.24)
where ω1 , ..., ωn are non-negative weights.
The constraints are divided into physical constraints x and planning constraints c1 , ..., cm. The
latter are optimisation functions chosen by the planner which represent important planning
criteria that have to be fulfilled without making compromises. Physical constraints x arise
from hardware limitations or laws of nature and are part of a given set of feasible parameters χ.
Altogether, the non-linear optimisation problem (NLP) can be written as follows:
minimise
over x
f (d(x))
subject to cj(d(x)) ≤ 0 , j = 1 , ...,m
x ∈ χ,
(2.25)
21
2 Research principles and background of proton beam therapy
where x stands for the optimisation variables and d(x) for the corresponding dose distribu-
tions [79, 80]. In PBS, the optimisation variables are the spot weights.
A sequential quadratic programming (SQP) algorithm is used to solve the inverse planning
problem in RayStation. SQP is an iterative procedure in which an approximate solution of a
NLP is found by solving a sequence of quadratic programming (QP) subproblems. The object-
ive function of each QP subproblem is given by the local quadratic Taylor serious approximation
of the Lagrangian function L(x, λ) = f (x)+
m∑
j=1
λTj cj(x), where λ is the Lagrangian multiplier
vector associated with the constraints c1 , ..., cm:
L(x, λ) ≈ L(xk, λk) +∇L(xk, λk)T (x − xk) + 12 (x − xk)
T∇2xxL(xk, λk) (x − xk). (2.26)
With the linearisation of the constraints in the original problem, the QP subproblem in itera-
tion k takes the form:
minimise
over x
f (xk) +∇f (xk)T (x − xk) + 12 (x − xk)T ∇2xxL(xk , λk) (x − xk)
subject to cj (xk) +∇cj (xk)T (x − xk) ≤ 0 , j = 1 , ...,m
x ∈ χ,
(2.27)
where xk is the initial estimate and the function and gradient values of the Lagrangian equal
those of the objective function at x = xk : L(xk, λk) =f (xk), ∇L(xk, λk) = ∇f (xk) [81]. The
search direction (x− xk) for the next iteration is determined by the solution of the QP sub-
problem. Based on this, new variables (xk+1, λk+1) are constructed such that the sequence
converges to a local minimum of the NLP for k →∞. The optimisation of a subproblem is
itself an iterative procedure including numerical approximations. A review on different SQP
methods with detailed mathematical descriptions can be found in Ref. [82].
Robust optimisation
PBS enables a conformal dose delivery to the target in three dimensions, but at the same
time it is susceptible to setup uncertainties, range uncertainties and especially organ motion
due to its steep dose gradients [83, 84]. Setup uncertainties include positioning errors of the
patient and mechanical inaccuracies of the equipment [65]. Range uncertainties are attributable
to errors in the CT calibration and the conversion of Hounsfield units to stopping power [85,
86]. In conventional treatment planning, these uncertainties are taken into account by adding
margins to the target volume as for example in the PTV concept introduced in Section 2.4.3.
This concept is not necessarily suited for proton therapy, where the assumption of a rigid
displacement of the dose cloud is not valid in the case of beam misalignment or interplay
effects [87]. A possibility to increase the robustness of a treatment plan is to incorporate the
uncertainties already in the optimisation process. This is done in RayStation by the minimax
optimisation. The robust optimisation minimises the objective functions considering the worst
case scenario for user defined uncertainties which are discretised into a set of scenarios S [88, 59]:
minimise
over x
max
s∈S
{f (d (x, s))}
subject to x ∈ χ.
(2.28)
Each scenario s represents a certain motion phase, setup error and density error. Setup errors,
in form of a misalignment of the patient relative to the gantry, are simulated by shifts of the
isocentre. The resulting displacement of spot positions depends on the traversed material. Con-
sequently, the dose deformation is non-rigid and gets large for steep density gradients. Density
errors are modelled by a uniform scaling of the mass density which leads to a material dependent
stretching or contraction of the depth dose curve. By computing the dose for every setup and
density scenario on selected patient image data sets, e.g. on different motion phases of a 4DCT,
uncertainties due to organ motion are taken into account. The number of scenarios which is
22
2.5 Treatment of mobile targets
considered by the robust optimisation is given by the product of the selected patient image
scenarios, setup error scenarios and density error scenarios. The nominal scenario assuming
no errors is included in each category [59]. By determining the worst case based on scenarios
and not independently for each voxel, only physically realisable scenarios are considered. If
more than one function is selected to be robust, the worst case scenario is the scenario in
which the weighted sum of these functions becomes maximal. It is possible to combine nominal
and robust objectives and constraints in the formulation of the robust optimisation problem in
Equation 2.28.
2.4.7 Treatment planning in double scattering
The ’Treat and Protect’ concept forms the basis for treatment planning in DS. The planner
has to specify for each beam which target ROIs shall be treated (hereinafter referred to as
’treat ROIs’) and which OAR ROIs have to be protected by the shape of the aperture or com-
pensator (hereinafter referred to as ’aperture protect ROIs’ and ’compensator protect ROIs’).
To this end, lateral, distal and proximal margins, the density uncertainty and the air gap must
be defined. Optional settings include the smearing radius (see Sec. 2.3.2) and the maximum
allowed gradient for the compensator. Based on these specifications, the TPS computes auto-
matically the shape of the aperture, the compensator matrix, the range and modulation of the
SOBP and the snout position.
The contour of the aperture is given by the projected area of all treat ROIs from beam’s eye
view plus the specified lateral margins. If the beam’s eye view projection of any aperture pro-
tect ROI plus margins intersects this area, it is subtracted from the first contour to protect the
OAR. In a last step, the contour might have to be expanded to make the aperture millable.
The compensator matrix is characterised by the milling tool diameter and the thickness of each
pixel. It is calculated for an area which covers the aperture contour plus a margin of about
1 cm. The physical thickness of a pixel is either determined based on the maximum radiological
depth of the treat ROIs at that point considering the distal margin and the density uncertainty
or by the minimum radiological depth of the compensator protect ROIs at that point minus the
proximal margin and the density uncertainty factor, dependent on which radiological depth is
shorter. Furthermore, the thickness depends on the maximum allowed gradient and the smear-
ing radius between neighbouring pixels (see Sec. 2.3.2). For both aperture and compensator
design, the protection of OARs has a higher priority than the treatment of targets.
The range of the SOBP is defined by the maximum radiological depth of the target considering
the distal margin and the density uncertainty. The modulation of the SOBP equals the SOBP
range minus the minimum radiological depth of the target decreased by the proximal margin
and the density uncertainty factor. Range and modulation are determined by the TPS such
that the the whole target including margins and density uncertainty is covered by at least 95%
of the prescribed dose, provided that there is no contradiction with the protection of OARs.
The snout is set to a position where the distance between the most downstream beam shaping
device and the patient or patient fixation matches the specified air gap [59].
2.5 Treatment of mobile targets
Proton therapy aims at creating steep dose gradients and minimising the irradiated volume
to escalate the dose to the tumour without harming nearby OARs. Target motion, however,
requires an increase of the planning target volume/ larger uncertainties in the robustness set-
tings to cover the tumour with sufficient dose at any point of the motion trajectory. As a
consequence, the favourable conformity of proton plans is limited and the dose to the tumour
might be restricted by dose constraints for nearby OARs. In some cases, this may result in a
deterioration of the local control rate.
This section will explain the difference between intra- and inter-fraction motion, the impact
of organ motion on the delivered dose distribution, interplay effects in PBS and techniques to
mitigate tumour motion.
23
2 Research principles and background of proton beam therapy
2.5.1 Intra- and inter-fraction motion
Motion can occur on different time scales. A distinction is made between intra- and inter-
fraction motion. Intra-fraction motion takes place during the irradiation on a time scale of
seconds. It is usually related to respiration motion or the heart beat. In the abdomen,
respiratory-induced organ motion is mainly in superior-inferior (SI) direction. The displace-
ments in anterior-posterior (AP) and left-right (LR) direction usually do not exceed a few
millimetres [89]. The human respiratory cycle length is typically three to five seconds and thus
much shorter than the treatment time which takes several minutes depending on the tumour
volume, the prescribed dose and the number of irradiation fields.
The term inter-fraction motion is used for changes which occur between different treatment
fractions. The time scale range from minutes to days. Sources of inter-fraction motion are
for instance tumour shrinkage, loss in weight, changes in the baseline of the motion pattern, a
different filling of the bladder or patient positioning errors [89, 90, 91, 92]. A treatment course
extends over several weeks depending on the number of fractions.
Patient motion can cause both intra- and inter-fractional changes. In radiotherapy, it is com-
mon to suppress it by patient immobilisation masks.
This work focuses on intra-fraction motion of liver tumours. The displacement of a liver tu-
mour due to regular breathing can be larger than 2 cm [93]. Hu et al. reported mean motion
amplitudes of 3mm (LR), 10mm (SI) and 3mm (AP) for 4DCT data sets of 46 liver cancer
patients treated without abdominal compression and mean amplitudes of 3mm (LR), 5mm (SI)
and 2mm (AP) for 53 liver cancer patients treated with abdominal compression [94]. Mean
motion amplitudes of 2mm (LR), 8mm (SI) and 4mm (AP) were observed by Case et al. for
29 liver cancer patients which were partly treated with abdominal compression [95]. Kitamura
et al. measured mean motion amplitudes of 4mm (LR), 9mm (SI) and 5mm (AP) for 20 liver
cancer patients during free-breathing (without abdominal compression) [96].
2.5.2 Impact of organ motion
Mobile targets such as lung or liver tumours, which continuously change their position during
the respiratory cycle, pose a challenge for proton therapy. Since tissue is moving in and out
of the irradiation field, steep dose gradients at the edge of the target volume are blurred. In
addition, motion-induced range changes might lead to a deformation of the dose distribution.
This is for example the case if ribs are located within the beam path and change their position
with respect to the planning CT. Even small changes in the density of the traversed tissue have
a great impact on the dose deposition due to the shift of the Bragg peak. By comparison,
photon plans exhibit similar dose blurring as proton plans but are only marginally affected
by density changes (except for the short buildup region) due to the exponential decay of the
depth dose curve (see Fig. 2.1). Both, proton and photon beams, are sensitive to inter-fraction
motion such as patient positioning errors or baseline drifts which affect the relative position of
the tumour to the beam.
Active proton beam delivery techniques such as PBS are additionally affected by interplay
effects between organ motion and beam scanning. The effect is explained in detail in the next
section (2.5.3). In comparison to PBS, DS plans are more robust against motion (Sec. 2.3.2).
The beam energy changes quasi-continuously because of the fast rotation speed of the range
modulator wheel (600 revolutions per minute) in relation to the respiratory cycle length (about
3 s to 5 s).
2.5.3 Interplay effects
In radiotherapy, the term ’interplay effect’ refers to the deformation of a planned dose distri-
bution due to the temporal interference between organ motion and dynamic beam delivery.
Interplay effects impact for example the dose deposition in lung and liver tumours in PBS
therapy, where intra-fractional tumour motion occurs on a similar time scale as beam scanning.
The simultaneous motion of the tumour and the proton beam results in a displacement of the
24
2.5 Treatment of mobile targets
individual proton spots with respect to the planned positions, which may cause under- and over-
dosage of the target and unintended exposure of OARs [6, 7, 8, 9]. The formation of interplay
effects in PBS is schematically illustrated in Figure 2.10. The extent of the dose degradation
depends on several factors such as the tumour motion amplitude, the beam delivery sequence,
the relative direction of tumour and beam motion, the length of the respiratory cycle and the
initial respiratory phase at the beginning of the irradiation. Modelling of interplay effects is a
key ingredient of motion management in PBS and is discussed in Chapter 3.
2.5.4 Respiratory correlated computed tomography
Respiratory correlated computed tomography (4DCT) is utilised to assess tumour and organ
motion for treatment planning. It requires respiratory monitoring devices to assign CT projec-
tion data to the respective motion phases. A common acquisition method, which is also used at
WPE, is a helical CT scan with a very low couch speed. The couch speed must be low enough
to ensure that each slice is illuminated by the x-rays at least for the duration of a respiratory
cycle. It cannot be set arbitrarily low due to a maximum ’x-ray on time’ of the CT scanner.
Retrospectively, the acquired data is binned into a series of three-dimensional CT data sets,
usually eight or ten, representing different motion phases. The binning is either based on the
phase or the amplitude of a surrogate motion signal. Commercial available motion monitoring
devices are for example air bellows that measures the air pressure in the bellow when the ab-
domen contracts or stretches or plastic blocks with infrared reflectors which are positioned on
the abdomen of the patient and are recorded by a digital camera [97].
2.5.5 Motion mitigation techniques
In the following, existing techniques to mitigate motion effects in proton therapy are briefly
summarised. The tumour motion amplitude can be reduced by abdominal compression using
pressure plates or belts. Another strategy is to freeze the motion, e.g. by breath hold techniques
or anaesthesia. In treatments under free breathing, it is possible to decrease the ITV by
beam gating. Gating controls the field application depending on the respiratory cycle and
requires motion monitoring systems. The beam is only turned on for a certain fraction of
the respiratory cycle (gating window). As a consequence, the treatment time is prolonged (on
average by a factor of two to five compared to a treatment without gating) [14]. The gating
window determines the amount of residual motion. Usually, the residual motion is comparable
to tumour motion under abdominal compression and can still cause under- and overdosage due
to interplay effects for dynamic beam delivery techniques [12].
In PBS, a frequently studied motion mitigation technique is rescanning, also referred to as
repainting. Rescanning smoothes the interplay pattern by irradiating the target volume multiple
times per fraction with a reduced dose until the prescribed fraction dose is reached (averaging
effect) [6, 12]. Different rescanning strategies exist like for example layered rescanning, in which
all rescans of a layer are completed before the energy is changed, or volumetric rescanning, in
which all energy layers are irradiated in each rescan. In contrast to gating, rescanning reduces
the amount of over- and underdosage by dose smearing but requires a larger treatment volume
to account for the internal motion. Thus, more normal tissue is exposed to high doses and
rescanning used on its own is rather suited for moderate than large motion amplitudes. Effects
similar to rescanning are achieved when increasing the number of irradiation fields [12]. A high
number of treatment fractions and a large spot size in PBS are also associated with a reduction
of motion effects [98]. A particularly robust approach to mitigate motion effects in PBS is to
combine gating and rescanning and was investigated by Zhang et al. for different scanning
dynamics [99]. However, prolonged treatment times of up to 20 minutes limit the applicability.
There are also approaches in treatment planning to increase the robustness against tumour
motion, such as 4D robust optimisation (Sec. 2.4.6). In this thesis, 4D robust optimisation was
evaluated for liver cancer patients. The results are presented in Chapter 4.
25
2 Research principles and background of proton beam therapy
reference phase
actually delivered:
PTV
time
reference phase
PTV PTV
PTV
PTV
m
ot
io
n 
am
pl
itu
de
m
ot
io
n 
am
pl
itu
de
m
ot
io
n 
am
pl
itu
de
m
ot
io
n 
am
pl
itu
de
timetimetimetime
spot application
liver
reference phase
PTV
liver
planned spot pattern:
phase 2 phase 3 phase 4phase 1 =
Figure 2.10: Schematic representation of motion interplay effects in pencil beam scanning proton
therapy: The planned spot positions for the irradiation of the planning target volume (PTV) are marked
by white spots. During spot application, the pencil beam is deflected according to the predefined
scanning path (white line). At the same time, the liver is moving due to respiratory motion. The
reference position of the liver is indicated by a grey contour for each time interval. The spot delivery over
time and the respective motion phases are displayed in red (phase 1), blue (phase 2), green (phase 3) and
purple (phase 4) (simplified time model for illustration purposes). Since the liver continuously changes
its position, some spots are delivered at different positions than planned. The image on the bottom
right illustrates the resulting spot pattern on the reference phase. Local underdosage of the PTV
occurs in regions where spots are missing, whereas overdosage of the PTV and exposure of the normal
liver tissue occur for regions with too high spot densities. The delivered spot pattern in the presence
of organ motion depends among others on the respiratory phase at the beginning of the irradiation,
the respiratory cycle length, the tumour motion amplitude and the beam delivery sequence. In this
example, the irradiation started within the reference phase.
26
3 Implementation of 4D dynamic dose accumulation in
PBS treatment planning
A dedicated 4D dynamic dose computation routine, which enables the simulation of interplay
effects, was created in the scope of this thesis and is described in Section 3.1. Interplay effect
scripts, which easily encompass several hundred lines of code, require thorough validation due
to their complexity. The experimental validation of the developed routine is presented in
Section 3.2. End-to-end tests were performed using a dynamic phantom and included 4D
imaging, treatment planning, irradiation and quality assurance according to clinical standards.
An empirical beam time model was built to enable in silico studies. It was applied for the
treatment planning study on hepatocellular carcinomas addressed in the next chapter. The
creation of the beam time model is subject of Section 3.3. Partial results of the presented work
in this chapter have been published in Ref. [100].
3.1 Modelling of interplay effects
A standard procedure for the evaluation of motion effects in radiotherapy is the averaging of the
dose over all respiratory phases of a 4DCT set. However, this method neglects any dynamics
of the beam delivery. In order to visualise interplay effects, information on the time structure
of the field as well as on the temporally resolved organ motion is needed. A routine tailored to
4DDD computations of irradiations with an IBA Proteus®Plus proton therapy system has been
developed based on a rudimental script provided by RaySearch (E. Engwall, June 2015) using
a similar approach as Zeng et al. [29]. The individual steps of the procedure are illustrated in
Figure 3.1. Patient motion is assessed based on a 4DCT with respiratory phases CT1, CT2, ...,
CTr. The phases, together with the respiratory cycle length and the initial phase at the begin-
ning of the irradiation, determine the organ motion sequence. The respiratory cycle length is
assumed to be constant and defined as the average breathing rate measured during the 4DCT
scan. A treatment plan is created on the reference CT. Based on the optimised spot positions,
weights and energies, the beam delivery sequence is generated either from irradiation log files
(retrospective analysis) or from a dedicated beam time model. The advantage of a model-based
computation is that possible fluctuations of the beam delivery parameters can be simulated and
considered for planning studies or patient-specific quality assurance. Furthermore, it simplifies
the clinical workflow. A description of the IBA implementation of PBS including the scanning
control system is given in Section 2.3.2. The information on organ motion and beam delivery
is used to determine in which respiratory phase each spot is delivered. The resulting fraction
dose dfx,CTi for respiratory phase i is calculated and subsequently mapped to the reference
phase using deformable image registrations (see Sec. 2.4.4 for details). This procedure is re-
peated for all respiratory phases. In the end, the deformed doses dReffx,CTi and the dose delivered
within the reference phase are added up to the fractional ’interplay dose distribution’:
dfx = dReffx,CT1 + d
Ref
fx,CT2 + ...+ d
Ref
fx,CTr, (3.1)
where fx denotes the fraction number and r the number of respiratory phases. The 4DDD
delivered over the whole treatment course is given by: D =
N∑
fx=1
dfx.
Implementation in RayStation
Interplay effect evaluations were conducted using the scripting interface of RayStation (see
Sec. 2.4.1) [60]. A graphical user interface has been created to facilitate the input of patient-
and machine-specific parameters as well as different evaluation options (Fig. 3.2). Evaluation
options include for example the evaluation type (single or multiple fractions) and the number
of evaluation scenarios in prospective analyses (with varying energy layer switching times and
starting phases).
27
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
Treatment plan on reference CT
Spot positions and weights
Time structure of the pencil beam
(on the basis of irradiation protocols or model based)
4D CT data set
(single respiratory phases)
Length of breathing cycle, variable start phase
Temporally resolved organ motion
Assign each spot position to one respiratory phase
Dose delivered on 
phase 1: 𝐝𝐟𝐱,𝐂𝐓𝟏
Dose delivered on 
phase 2: 𝐝𝐟𝐱,𝐂𝐓𝟐
Dose delivered on 
phase r: 𝐝𝐟𝐱,𝐂𝐓𝒓
Compute fraction dose for each phase 
Dose mapped from 
phase 1 to reference 
CT: 𝐝𝐟𝐱,𝐂𝐓𝟏
𝐑𝐞𝐟
4D dynamically accumulated dose on reference CT:
𝒅𝒇𝒙 =෍
𝒊
dfx,CTi
Ref
⋯
⋯
Dose mapped from 
phase 2 to reference 
CT: 𝐝𝐟𝐱,𝐂𝐓𝟐
𝐑𝐞𝐟
Dose mapped from 
phase r to reference 
CT: 𝐝𝐟𝐱,𝐂𝐓𝒓
𝐑𝐞𝐟
Deform all dose maps to the reference CT using deformable image registration
Accumulate the deformed doses on the reference CT
Figure 3.1: Flow chart illustrating the workflow of interplay effect simulations automated by a Python
script in RayStation: The 4D dynamically accumulated fraction dose dfx is calculated based on a
time-resolved CT (4DCT), a treatment plan and the corresponding beam delivery sequence to assess
interplay effects in pencil beam scanning proton therapy. White boxes indicate active processes and
light blue boxes outputs/ inputs. In prospective analyses, the computation is repeated for different
pencil beam time structures to consider possible fluctuations of the beam delivery parameters. Adopted
from Ref. [100].
3.2 Experimental validation of the 4D dose computation
The accuracy of the interplay effect routine was examined by comparing calculated 4DDD dis-
tributions with two-dimensional, dynamic dose measurements. In a first experiment, the dose
was measured by a static detector downstream of a dynamic buildup (setup A). Setup A served
as a simplified technical model for dose validations in quasi-static anatomical regions behind
moving structures, such as ribs. A second series of experiments was performed with a dynamic
detector (setup B) simulating the dose validation within a moving tumour. Details on the ex-
perimental setups as well as on 4DCT acquisition, treatment planning and evaluation methods
are given in the following section. Subsequently, the results are presented and discussed.
3.2.1 Materials and methods
MatriXX PT detector
The MatriXX PT detector (IBA Dosimetry, Schwarzenbruck, Germany), a two-dimensional ion-
isation chamber array, has been designed for machine quality assurance and pretreatment plan
verifications in proton therapy. It consists of 1020 vented, plane parallel cylindrical chambers,
each with a diameter of 4.2mm and a centre-to-centre spacing of 7.6mm [101]. The chambers are
arranged in a 32 x 32 grid yielding an active measurement area of 24.4 cm x 24.4 cm (Fig. 3.3a).
A 6mm thick acrylonitrile butadiene styrene buildup covers the array [102]. Measurements are
28
3.2 Experimental validation of the 4D dose computation
Interplay effect evalua�on
Beam delivery se�ngs
Se�ling �me of the fast scanning magnet (ms):
Se�ling �me of the slow scanning magnet (ms):
Energy layer switching �me
Average value (s):
Standard devia�on (s):
Respiratory mo�on
Respiratory cycle length (s):
Evalua�on se�ngs
Evalua�on type:
Single frac�on Mul�ple frac�ons
Number of frac�ons:
Number of scenarios per frac�on:
None Ga�ng
No Yes
Plot DVH:
Select respiratory start phase(s):
Supplementary mo�on mi�ga�on technique:
CT1 0%
CT3 20%
CT5 40%
CT7 60%
CT9 80%
CT2 10%
CT4 30%
CT6 50%
CT8 70%
CT10 90%
2.5
2.25
1.23
0.26
4.0
15
5
Deselect allSelect all
Start evalua�on
Figure 3.2: Graphical user interface of the interplay effect routine for prospective evaluations: The
interface allows for quick adoptions of the beam delivery parameters, e.g. in the case of a software
update of the scanning control system or to model different proton therapy facilities. To determine the
time structure of the organ motion, the average respiratory cycle length of the patient must be entered.
The evaluation settings include among others the evaluation type, the number of evaluation scenarios
and the start phase(s) at which the irradiation commences. One of the selected respiratory start phases
is randomly chosen by the routine for each scenario. For retrospective evaluations, another version of
the interplay effect routine enables the input of the beam delivery sequence gained from log files. Only
the respiratory start phase which was recorded at the time of the treatment is selected.
29
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
rate, is measured and digitalized by a non-multiplexed 1020 channel
sensitive analog to digital converter.
The measured data are transmitted to a PC via a standard Ethernet 
available on most PCs.
Depending on the applications, the measurements are controlled by 
designated software produced by IBA Dosimetry:
MatriXX PT
detector array electronics
(a) MatriXX PT detector
1
2
3
4 5
6
(b) CIRS dynamic platform
Figure 3.3: (a) Top view of the MatriXX PT detector, a two-dimensional ionisation chamber ar-
ray [101], (b) components of the CIRS dynamic platform [103]: 1. base platform, 2. surrogate platform,
3. phantom motion actuator box, 4. surrogate motion actuator box, 5. motion control unit, 6. CIRS
motion control software.
controlled by the designated software OmniPro-I’mRT (IBA Dosimetry, Schwarzenbruck, Ger-
many). Within the scope of this thesis, two measurement modes were used: single shot mode
and movie mode. In single shot mode, one measurement is accumulated over a pre-selected
integration time. In movie mode, a continuous set of single measurements is acquired during a
pre-defined time. The acquisition time for a single measurement is specified by the user. The
sum over all measurements of the set is created and saved automatically by the software.
CIRS dynamic platform
The CIRS dynamic platform (CIRS, Norfolk, USA) is designed for the study of tumour motion
in radiotherapy and can be used in end-to-end tests including four-dimensional imaging, treat-
ment planning and dose delivery. It is composed of a base platform, which supports almost
any phantom up to 32 kg, a small surrogate platform, which imitates the motion of the chest
wall, motion actuators and a multi-axis motion controller (Fig. 3.3b). Respiratory monitor-
ing devices can be attached to the surrogate platform in order to perform 4DCT imaging or
respiratory gated irradiations. The CIRS dynamic platform provides precise and repeatable
inferior-superior motion of the base platform and posterior-anterior motion of the surrogate
platform through bipolar stepper motors. Optical sensors control the accurate mechanical po-
sitioning. For both platforms, the motion is limited by a total range of 50mm. The spatial
accuracy is 0.05mm and the accuracy of the motion period approximately 5ms [103]. The CIRS
dynamic platform is operated through the CIRS motion control software. Motion patterns can
be selected from a menu or imported from tab delimited or comma separated files. The menu
offers five different wave functions with variable amplitude, motion period and phase shift.
Setup
The two setups used for the validation of the interplay effect routine are depicted in Figure 3.4a
and 3.4c. For setup A, the MatriXX PT detector was placed on the patient couch. The dose
was measured in a horizontal plane perpendicular to the beam (gantry angle: 0°). 2.1 cm of
RW3 plates (SP34 solid plate phantom, IBA Dosimetry, Schwarzenbruck, Germany) served as
buildup material in front of the detector. The phantom consisted of a PMMA cylinder with a
30
3.2 Experimental validation of the 4D dose computation
Table 3.1: 4DCT scanning parameters used for the experimental validation of the 4D dynamic dose
computation (Sec. 3.2)
slice thickness (mm) 2
increment (mm) 1
field of view (mm) 600
voltage (kV) 120
mAs/slice 360
reconstruction filter standard B
rotation time (s) 0.5
pitch 0.042
diameter of 16 cm, a height of 8.5 cm and five holes for tissue equivalent Gammex rods (GAM-
MEX INC., Middleton, USA). Surrogates for liver, cortical bone, adipose tissue, inner bone and
lung were chosen as inserts. The first three of them were located within the irradiation field to
simulate liver tumour irradiations (see Fig. 3.4b). The dimensions of the technical phantom,
e.g. the thickness of the cortical bone surrogate, do not correspond to human anatomy and rep-
resent an extreme case. Phantom motion was realised by placing the cylinder onto the dynamic
CIRS platform. The platform with the phantom had to be set up on a PMMA table in order
to position it upstream of the detector in the beam path. During the 4DCT acquisition and
irradiation, the phantom moved back- and forwards along the y axis (fixed reference system
according to IEC 61217 [104]), which equals the main direction of breathing induced motion for
a patient at a couch angle of 0°. The motion curve was set to a sinus function with an amplitude
of 5mm. A comparatively long motion period of 10 s was chosen for the first test series due
to the complexity of the dynamic dose assessment. After successful trials, the time period was
reduced to 5 s in a second test series, which is a realistic value for the human respiratory cycle
length.
According to the manufacturer, the CIRS dynamic platform moves any phantom with sub-
millimetre accuracy (±0.1mm) and reproducibility [103]. Measurements with a laser tracker
(model Absolute Tracker 901B, LeicaGeosystems AG, Unterentfelden, Switzerland) could con-
firm the high accuracy in positioning with an average value of 0.02mm and a standard devi-
ation (SD) of 0.02mm for the positional deviation.
A second series of experiments was performed with a dynamic detector (setup B). In this setup,
the MatriXX PT was positioned on the moving CIRS platform (see Fig. 3.4c). There was no
need for supplementary RW3 plates or a table since the cylinder could be placed directly onto
the MatriXX PT. The same settings were used as for setup A.
4DCT acquisition
4DCTs were acquired with a Philips Brilliance CT BigBore (Philips GmbH, Hamburg, Ger-
many). The settings for the CT scan are listed in Table 3.1. Retrospective spiral correlated
imaging was chosen as scanning mode. The simulated breathing pattern was monitored by a
pneumatic belt (‘Philips bellows’) so that the 4D projection data could be retrospectively sor-
ted. Ten 3DCT sets were reconstructed from one respiratory cycle equally spaced at 10% time
intervals (phase binning), where 0% corresponds to end-inspiration and 50% to end-expiration.
Treatment planning
Two separate treatment plans corresponding to setup A and setup B were created in a research
version of RayStation 5 using the Pencil Beam dose algorithm and a 2mm dose grid. For both
plans, the PTV was defined by a rectangular shaped ROI with the following dimensions: 4 cm
(LR), 9 cm (SI) and 1 cm (AP), where the SI direction corresponds to the direction of motion.
31
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
DYNAMIC
PHANTOM
beam
Philips bellows
PMMA cylinder
Gammex rod
RW3 plates
direction of
motion (y)
z
MatriXX PT
dynamic phantom
(a) setup A
16 cm
PTV
3 cm
cortical bone
liver
inner bone
adipose tissue
lung
(b) PMMA cylinder
DYNAMIC
PHANTOMdirection of
motion (y)
z
beam
(c) setup B
Figure 3.4: (a) Sketch of setup A: The dose is measured by a static, two-dimensional ionisation
chamber array downstream of the dynamic phantom. The pneumatic belt (‘Philips bellows’) used for
the 4DCT acquisition was removed prior to the irradiation, (b) sketch of the PMMA cylinder: The top
view shows the arrangement of the tissue equivalent Gammex rods. The relative position of the planning
target volume (PTV) to the cylinder geometry is indicated by a dashed red line for setup A (considering
all motion phases) and by a solid black line for setup B (constant relative position), (c) sketch of setup B:
The two-dimensional ionisation chamber array moves perpendicular to the incoming beam.
The small modulation width (AP direction) was chosen to be sensitive to changes in the proton
range. In view of the HCC treatment planning study (Chap. 4), the field size of the PTV
was adjusted to the geometrical arrangement of the Gammex rods, so that the surrogates for
liver, cortical bone and adipose tissue were located within the irradiation field (see Fig. 3.5).
The effective plane of measurement of the MatriXX PT, as defined in Ref. [102], was at the
same height as the centre of the PTV. A total dose of 63 GyRBE was prescribed to the PTV in
15 fractions referring to the fractionation scheme proposed by Bush et al. for HCC patients [2].
Neither robust planning nor repainting was applied in order to render interplay effects visible
to the full extent. Each treatment plan consisted of a single field at 0°. The isocentre corres-
ponded to the centre of the effective plane of measurement. None of the plans required the
use of a range shifter. The air gap between the snout and the phantom was 20 cm for setup A
and 33.8 cm for setup B2. In addition, there was another air gap of 8.8 cm in-between the CIRS
motion platform and the buildup material in front of the detector in setupA. The resolution
of the dose grid was set to 2mm per voxel in all directions and spots were placed on a regular
grid with a spacing of 6mm. The objective functions in the optimisation included maximum
and minimum dose settings for the PTV, a dose fall-off objective for the External ROI (which
2At the time of the experiment, a movable snout minimising the air gap between a range shifter and the patient
was not yet installed at WPE. Since no range shifter had to be applied, this did not represent a disadvantage
for the study.
32
3.2 Experimental validation of the 4D dose computation
comprised the whole phantom and the patient couch) and maximum dose settings for technical
planning structures proximal and distal to the PTV in order to improve the dose conformity.
CT data of synthetic tissue surrogates can deviate from clinical CT number to density cal-
ibration curves tailored to human tissue data. Therefore, a dedicated CT number to density
calibration curve was created based on the known mass densities of the Gammex rods to ensure
an accurate estimation of proton stopping power (see Fig. 3.6). Because PMMA has a distinct
relation between mass density and CT number, a material override was used for PMMA in plan-
ning (density: 1.18 g/cm3). An example of how the usage of the clinical calibration curve (Body,
120 kV, PBS) can impact the dose comparison is provided in Section 3.2.2 for setup A.
Image registration
Using the dynamic CIRS platform, the phantom was translated but not deformed. Con-
sequently, a rigid registration algorithm would have been the method of choice for 4D image
registration. However, for a 4DCT group, RayStation enables only deformable image regis-
trations since the functionality has been developed for planning and evaluation in real patient
geometries. Image registrations therefore had to be performed with ANACONDA (Sec. 2.4.4).
Another issue was the symmetry of the ionisation chamber array, which made it impossible
to rely solely on a CT intensity based registration approach. Multiple positions within the
ionisation chamber array yielded the same image similarity measure leading to an irregular
deformation vector field. To overcome these problems, a grid of 225 POIs was created and
shifted for each phase according to the displacement of the phantom via scripting. The grid
covered an area of 15 cm×15 cm at the height of the isocentre and was used to guide the DIR.
Furthermore, the accuracy of the deformable registrations was investigated for the presented
rigid geometry based on five controlling POIs in the measuring plane. The POIs were manually
marked in each motion phase and mapped to the reference CT. The error introduced by the
DIR in the direction of motion was on average 0.1mm with a standard deviation of 0.4mm.
Irradiation
A fraction dose of 4.2Gy was delivered to the PTV in each experimental run. The delivery was
neither synchronised with the phantom motion nor triggered manually based on the displayed
motion pattern. In order to determine the start phase at the beginning of the irradiation for the
interplay effect evaluation, a camera recorded the screen of the laptop showing the motion curve
and a time display (synchronised with a time server). The time structure of the field delivery was
gained from the corresponding irradiation log files which also contain time information referred
to a time server. Each experiment was performed five times (two times with a motion period of
10 s and 3 times with 5 s). Two stationary irradiations served as reference. Measurements were
performed in single shot mode and movie mode. The latter served for time resolved evaluations
(described below).
Evaluation methods
The interplay effect routine was validated based on a relative comparison of the measured and
the calculated dose distribution since an absolute dose comparison requires thorough calibration
processes which are, contrary to measurements in a water phantom, not straightforward for the
given setup. Discrepancies in the absolute dose were compensated by a normalisation of the
dose distributions.
4DDD distributions were reconstructed in RayStation based on the acquired 4DCT data set
(setup A or B), the corresponding irradiation log file and the determined start phase using
the interplay effect routine. The dose plane at the depth of the isocentre was exported and
compared to the measured dose distribution with the software OmniPro-I’mRT. First, the grid
resolution of the measured and the calculated dose plane was interpolated to 1mm by means
of cubic spline. Next, the distributions were normalised to a common point in the dose plane.
33
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
% of
RBE
 MatriXX PT
PTV
livercortical adipose
tissuebone
63 Gy
110
107
95
90
80
60
40
0
Figure 3.5: Sagittal view of the static dose distribution (overlayed as colour wash) for setup B in
RayStation: The centre of the rectangular shaped PTV (red contour) is at the same height as the
effective plane of measurement of the MatriXX PT. The PTV is located downstream of the surrogates
for cortical bone, liver and adipose tissue. Depending on the motion phase, the pencil beam might pass
a different material than in the nominal treatment plan. The direction of motion corresponds to the
left-right direction in the image.
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
−1000 −500 0 500 1000
m
as
s 
de
ns
ity
 (g
/c
m
3 )
CT number (HU)
CT number to density calibration curve
PMMA
clinical calibration curve 
dedicated calibration curve 
Figure 3.6: CT number to density calibration curve for the experimental validation of the 4D dose
computation: To improve the accuracy of proton stopping power calculations in synthetic tissue sur-
rogates a dedicated calibration curve (blue line) was created based on the mass densities taken from
data sheets. Since the PMMA data (red point) did not fit to the composite curve, a material override
was used for PMMA in planning. The clinical calibration curve (Body, 120 kV, PBS) is plotted for
comparison purposes (black dashed line).
34
3.2 Experimental validation of the 4D dose computation
Analyses were performed using the gamma evaluation method by Low et al. [105, 106]. The
gamma value for a measurement point rm is given by
γ (rm) = min {Γ (rm, rc)} ∀ {rc} (3.2)
with
Γ (rm, rc) =
√
r2 (rm, rc)
4d2m
+ δ
2 (rm, rc)
4D2m
, (3.3)
where 4dm denotes the distance-to-agreement criterion and 4Dm the dose-difference criterion.
r (rm, rc) and δ (rm, rc) are the differences in distance and dose between measurement and
calculation:
r (rm, rc) =| rc − rm |, (3.4)
δ (rm, rc) = Dc (rc)−Dm (rm) , (3.5)
where Dc is the calculated dose in point rc and Dm the measured dose in point rm. The passing
criteria 4dm and 4Dm were set to 3mm and 3%, respectively, as used for the patient-specific
quality assurance at WPE [107, 108]. A point rm passes the gamma criterion if γ (rm) ≤ 1.
The threshold dose value for relevant signals was set to 20%.
Even though the measurements could not be calibrated using a water phantom and in-house
reference irradiation fields, the measured absolute dose was exemplarily compared with the 4D
dose calculation for setup A.
The sensitivity of the routine to its input parameters was tested by comparing the original dose
distribution to manipulated computations. To this end, the 4DDD distribution was calculated
for different start phases and motion periods. Motion periods from 4.4 s to 5.6 s were investig-
ated in increments of 0.2 s.
In addition to the evaluation of the whole fraction dose, time-resolved computations were com-
pared with measurements in movie mode. For this purpose, the interplay effect routine had to
be adapted so that partial dose distributions could be computed for any time interval during
the irradiation. The functionality of the time-resolved interplay effect routine was tested by
comparing exported dose planes from the original routine and the time-resolved version. First,
it was demonstrated that both routines yielded the same dose distribution when choosing the
total irradiation time as time interval. Next, the dose delivery was split into five time intervals.
The sum of the resulting partial dose distributions equalled the dose distribution obtained by
the original routine.
In time-resolved 4DDD experiments, the sampling time of the MatriXX PT was set to 2 s res-
ulting in 14 partial dose distributions. The sampling time for the experimental test was more
or less arbitrarily chosen. It should be low enough to visualise the dose delivery with time over
different respiratory phases on the one hand and, on the other, it should be large enough to
ensure a certain amount of dose per measurement to reduce the impact of inaccuracies induced
by the design of the experiment. An offset had to be considered in the computation to account
for the time difference between the start of the measurement and the beginning of the irradi-
ation. The offset could not be recorded. It was determined using a try and error approach
with the aim to maximise the gamma pass rate of a measurement sample which started and
ended within an energy layer and was not separated by irradiation pauses from the previous or
subsequent sample of the measurement set. Two time-resolved measurements were performed
for setup A.
3.2.2 Results
Comparison with two-dimensional dose measurements
Figure 3.7 shows by the way of example the relative dose comparison of one experimental meas-
urement and the corresponding 4D simulation for setup A. Both the measured dose and the 4D
35
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
reconstructed dose reveal a distortion of the planned dose distribution due to motion, e.g. a
slight underdosage in the lower half of the PTV (colour wash: light red). The gamma analysis
demonstrates a good agreement between the simulated and experimental data with a gamma
pass rate of 99.7% (see Fig. 3.7f). The corresponding dose profiles differ only slightly with a
maximum deviation of about 3% (see Fig. 3.7d and e).
For both test series (5 s and 10 s motion period), the gamma pass rate remained in-between
97.8% and 99.7% (average 98.7%) meeting the acceptance requirement of 95% used for the
patient-specific quality assurance at WPE. The reference gamma pass rates of the two station-
ary irradiations were 98.6% and 98.3%.
Using the clinical CT number to density calibration curve tailored to human tissue data instead
of the specially created calibration, the gamma pass rate decreased from 99.7% to 92.9% for
the investigated test case.
For setup B, the dynamic detector, the distortion of the planned dose distribution was partic-
ularly pronounced as can be seen in Figure 3.8b. Interplay effects could be reproduced by the
routine (Fig. 3.8c). A few locally restricted deviations of up to about 4% were detected (see
Fig. 3.8e). Nevertheless, the gamma pass rate was 98.0%. Unlike setup A, setup B exhibited
differences in the gamma pass rate depending on the motion period. For 10 s, the pass rate was
better than 96.1%, whereas for 5 s it ranged from 88.8% to 90.2%.
The comparison of the absolute dose values revealed an overestimation of the dose of 7.6% by
the routine for setup A. The two stationary reference irradiations deviated by 7.8% and 7.5%,
respectively, from the planned dose distribution. These discrepancies were equalised by norm-
alisations in the relative comparisons.
Sensitivity towards start phase and motion period
In the following, the results of the sensitivity analysis are presented for manipulated motion
periods and start phases. A change of the motion period in the computation by ±0.2 s resulted
in a decrease of the gamma pass rate by about 1–2.5% compared to the original measurement.
For a shift of 0.4 s and more, the percentage decrease of the gamma pass rate was already within
the double-digit range.
Regarding the start phase, the deterioration of the gamma pass rate was less for a shift towards
earlier phases. For instance, a change to the previous motion phase led in average to a decrease
of 1.7% and a shift to the subsequent phase to 4.1%. A phase shift of pi, representative for the
highest deviation, resulted almost in a reduction of the gamma pass rate of 20%.
Time-resolved evaluation
The dose delivery over the course of time is depicted in Figure 3.9 and 3.10 for one meas-
urement and the corresponding time-resolved 4DDD reconstruction. The 4DDD computation
reproduces the measured dose distributions well on a qualitative level, in particular the shape
of the irradiation field over time. Local differences in the intensity become visible in the second
half of the irradiation for image number 8, 9, 10 and 13 (see Fig. 3.10). The gamma pass rate
is on average 98.3% for the first and 73.1% for the second half of the irradiation.
The time-resolved dose distribution looked different for the repeated measurement since the
irradiation started at another respiratory phase, the energy layer switching times changed and
the offset between measurement and irradiation was not the same. The time-resolved interplay
routine was able to reproduce these changes. Again, higher gamma pass rates were obtained
for the first than for the second half of the irradiation (average 98.7% and 79.3%, respectively).
36
3.2 Experimental validation of the 4D dose computation
y (mm)
x (mm)
-20 0 40 6020-40
0
20
40
60
80
-20
-40
-60
(a) treatment plan
y (mm)
x (mm)
-20 0 40 6020-40
0
20
40
60
80
-20
-40
-60
(b) 4D measurement
y (mm)
x (mm)
-20 0 40 6020-40
0
20
40
60
80
-20
-40
-60
(c) 4D simulation
100
80
60
40
20
0
spectral
level (%)
signal (%)
x (mm)measurement
simulation
-16 0 32 4816-32-48
48
80
64
96
32
16
0
(d) x profile
signal (%)
y (mm)measurement
simulation
-20 0 40 6020-40-60
48
80
64
96
32
16
0
(e) y profile
y (mm)
x (mm)
0
20
40
60
-20
-40
-60
-20 0 4020-40
(f) gamma analysis
gamma
 level
0.00
0.25
0.50
0.75
1.00
1.25
Figure 3.7: Relative dose analysis for the static dose measurement downstream of the dynamic
phantom (setup A): (a) static treatment plan, (b) measured 4D dose distribution, (c) 4D reconstructed
dose distribution, (d) comparison of the 4D dose profiles in x direction (left-right), (e) comparison of
the 4D dose profiles in y direction (superior-inferior), (f) gamma analysis of the 4D dose distribution
with a 3mm/3% passing criterion, gamma pass rate = 99.7%.
3.2.3 Discussion
The relative motion of the different phantom materials to the beam induced changes of the
proton range for both, setup A (static detector) and setup B (dynamic detector). The dynamic
dose measurement was additionally affected by shifts of the spot positions in relation to the
spatial frame of reference of the detector. As a result, larger distortions of the planned dose
distribution were expected for setup B. The measurements could confirm this. For setup A
and the first test series of setup B, the gamma pass rates gave evidence of the good agreement
between measurement and simulation. The fact that the pass rates were above the 95% level
and not worse than for the static reference irradiations proved the adequate performance of
the 4DDD routine. In some cases, the gamma pass rates were even slightly higher for the 4D
experiments than for the two stationary control measurements. A possible reason might be
that large density gradients are smoothed in the dynamic case. In addition, inaccuracies due to
the dose calculation with the Pencil Beam algorithm and a coarse sampling of dose propagate
to the total dose differently than for the stationary case [109].
Reducing the motion period to 5 s (second test series), the gamma pass rate deteriorated from
above 95% to about 90% for setup B. This is because the phantom travelled larger distances
in a shorter amount of time, which causes motion artefacts in the 4DCT and increases the
37
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
y (mm)
x (mm)
0
20
40
60
-20
-40
-60
-20 0 4020
(a) treatment plan
y (mm)
x (mm)
0
20
40
60
-20
-40
-60
-20 0 4020
(b) 4D measurement
y (mm)
x (mm)
0
20
40
60
-20
-40
-60
-20 0 4020
(c) 4D simulation
100
80
60
40
20
0
spectral
level (%)
signal (%)
x (mm)measurement
simulation
48
80
64
96
32
16
0
112
-16 0 32 4816-32-48
(d) x profile
signal (%)
y (mm)measurement
simulation
-20 0 40 6020-40-60
48
80
64
96
32
16
0
112
(e) y profile
y (mm)
x (mm)
-20.0 0.0
-20 0 4020
0
20
40
60
-20
-40
-60
(f) gamma analysis
gamma
 level
0.00
0.25
0.50
0.75
1.00
1.25
Figure 3.8: Relative dose analysis for the dynamic dose measurement (setup B): (a) static treatment
plan, (b) measured 4D dose distribution, (c) 4D reconstructed dose distribution, (d) comparison of
the 4D dose profiles in x direction (left-right), (e) comparison of the 4D dose profiles in y direction
(superior-inferior), (f) gamma analysis of the 4D dose distribution with a 3mm/3% passing criterion,
gamma pass rate = 98.0% .
impact of small timing errors. Further, the 4D dynamic dose accumulation is more prone to
errors for a moving detector (setup B). Even small uncertainties and approximations can have a
visible impact on the dose distribution since the measurement points on the matrix are shifted.
Contrary, for setup A, the positions of measurement points on the matrix remain unaffected
and the same uncertainties and approximations can only cause range changes.
Even though there were some local quantitative deviations, changes in the relative dose dis-
tribution due to interplay effects were simulated correctly. Differences between the dynamic
simulation and the measurement probably arise from the division of the continuous motion into
10 phases, CT artefacts, residual uncertainties of the DIR and the CT number to density cal-
ibration curve, the conversion of the dose grid and slight shifts in the setup for the irradiation
compared to the CT acquisition.
The lower gamma pass rate for the second test series of setup B does not primarily indicate
shortcomings of the routine but rather points out potential for improvement of the experimental
conduct. For example, errors in the time structure could be reduced by determining the time
offset of the start phase, an aspect which is addressed in more detail in the context of the
sensitivity analysis below.
The differences in the absolute dose of about 8% are the same as for the static control meas-
urement and therefore not attributable to errors in the 4DDD computation. They result more
38
3.2 Experimental validation of the 4D dose computation
10
0%
 =
 49
.9 
cG
y
10
0%
 = 
47
.3 
cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0%
 = 
75
.9 
cG
y
10
0%
 = 
75
.8 
cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0 90 80 70 60 50 40 30 20 10 0
sp
ec
tra
l
 le
ve
l (
%
)
10
0%
 = 
20
4.1
 cG
y
10
0%
 = 
22
0.2
 cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0%
 = 
12
1.5
 cG
y
10
0%
 = 
11
7.0
 cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0%
 = 
15
2.4
 cG
y
10
0%
 = 
15
1.0
 cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0%
 =1
57
.3 
cG
y
10
0%
 = 
15
7.2
 cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
10
0%
 =
 14
0.6
 cG
y
10
0%
 = 
13
0.0
 cG
y
x 
(m
m
)
y 
(m
m
)
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
0
20
40
60
-2
0
-4
0
-6
0
80 60 40 20 0 -2
0
-4
0
-6
0
-8
0
y 
(m
m
)
x 
(m
m
)
0
20
40
-2
0
-4
0
m
ea
su
re
m
en
t
si
m
ul
at
io
n
99
.8
%
99
.8
%
10
0%
99
.7
%
10
0%
99
.7
%
92
.2
%
γ  p
as
s 
ra
te
s a
m
pl
e 
#
1
2
3
4
5
6
7
10
0 90 80 70 60 50 40 30 20 10 0
sp
ec
tra
l
 le
ve
l (
%
)
F
ig
ur
e
3.
9:
C
om
pa
ris
on
of
a
tim
e-
re
so
lv
ed
do
se
m
ea
su
re
m
en
t
in
m
ov
ie
m
od
e
w
ith
4D
dy
na
m
ic
do
se
co
m
pu
ta
tio
ns
fo
r
se
tu
p
A
:T
he
sa
m
pl
in
g
tim
e
w
as
2s
pe
r
im
ag
e.
Im
ag
es
1
to
7
co
rr
es
po
nd
to
th
e
tim
e
in
te
rv
al
fr
om
0s
to
14
s.
39
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
100%
 = 100.3 cGy
100%
 = 130.1 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
100%
 = 96.6 cGy
100%
 = 125.3 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
1009080706050403020100
spectral
 level (%
)
100%
 = 90.3 cGy
100%
 = 93.0 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
100%
 = 71.2 cGy
100%
 = 73.0 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
100%
 = 104.7 cGy
100%
 = 111.7 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
100%
 = 42.7 cGy
100%
 = 65.5 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
100%
 = 9.6 cGy
100%
 = 10.2 cGy
x (m
m
)
y (m
m
)
806040200
-20
-40
-60
-80
0
20
40
60
-20
-40
-60
806040200
-20
-40
-60
-80
y (m
m
)
x (m
m
)
0
20
40
-20
-40
m
easurem
ent
sim
ulation
78.5%
78.1%
55.2%
93.2%
99.5%
65.4%
85.2%
γ  pass rate
s am
ple #
8
9
10
11
12
13
14
1009080706050403020100
spectral
 level (%
)
F
igure
3.10:
C
om
parison
ofa
tim
e-resolved
dose
m
easurem
ent
in
m
ovie
m
ode
w
ith
4D
dynam
ic
dose
com
putations
for
setup
A
:T
he
sam
pling
tim
e
w
as
2s
per
im
age.
Im
ages
8
to
14
correspond
to
the
tim
e
intervalfrom
14s
to
28s.
40
3.2 Experimental validation of the 4D dose computation
likely from deficiencies of the Pencil Beam dose algorithm (Sec. 2.4.5) in combination with the
chosen phantom geometry which exhibit an air gap of 8.8 cm. Since the transport algorithm
does not account for inhomogeneities, it underestimates the lateral spread of the nuclear halo.
This is usually not critical for normal patient geometries but may become an issue if a thick
compensator or range shifter is used with a large air gap (a setup with large inhomogeneities).
The underestimation of the spread of large angle scattered protons lead to an overestimation
of the dose on the central axis, particularly for small- and medium-sized fields. The resulting
dose difference may amount to several percent [59]. This could be the case for setup A where
the phantom has a similar effect as a range shifter or compensator due to the air gap in front
of the detector.
Sensitivity towards start phase and motion period
The sensitivity of the routine towards its input parameters could be demonstrated. Differences
of the specified start time larger than the length of a motion phase or deviations of the motion
period by more than 0.2 s led to measurable differences in the dose distributions. Since the
motion period of the dynamic platform is highly reproducible and the uncertainty in the exper-
imental determination of the start phase by camera records is less than the length of a motion
phase, inaccuracies of the input are not expected to distort the calculation. Nonetheless, there
is still potential for improvement. For instance, it would be more accurate to pass the exact
delivery start point of the motion curve to the routine instead of the start phase which takes up
to 0.6 s for a patient (assuming 10 respiratory phases). First attempts showed that the gamma
pass rate would improve slightly for cases in which the delivery started in the middle or at the
end of a motion phase. However, a more practicable solution than camera records of the motion
pattern and the time display should be applied in future. AlignRT (Vision RT Ltd., London,
United Kingdom), a system which uses 3D stereo camera units to track a patient’s position,
could fulfil this function for technical validations and in clinical use.
Time-resolved evaluation
The time-resolved 4DDD computations showed qualitatively a good agreement with movie mode
measurements. It was possible to reproduce differences in the dose delivery over time arising
from variations in the beam delivery sequence for the same treatment plan. However, despite
a gamma pass rate of above 98% for the sum of all partial dose distributions, the pass rate
of a single measurement went down to 55% (first trial) and 48% (second trial) in the worst
case. This could be caused by limitations of the methodology applied. For instance, the offset
between the start of the measurement and the irradiation was determined with an accuracy of
up to two decimals but the delivery time of a single spot takes only a few ms (see Sec. 3.3.2).
Spots which were delivered at the beginning or end of a time interval might have been assigned
to the wrong time interval. The risk of misassignments does not exist if the beginning/end of a
time interval coincides with the change of an energy layer when the irradiation is paused. The
hypothesis, that some spots were assigned to wrong time intervals by the routine, is supported
by the visual examination of the measurements. For example, the upper right point in image
number 8 (see Fig. 3.10) exhibits a lower intensity in the simulation than in the measurement.
In the subsequent time interval (image number 9), looking at the same area, the simulated
intensity is increased compared to the measurement.
Another reason for low gamma pass rates is that the number of spots which contribute to a
partial dose distribution is much smaller than for the total dose distribution. Thus, the relative
impact of spots which were assigned mistakenly to a wrong respiratory phase increases. The
determination of an exact start point within the first respiratory phase as stated previously
would prevent incorrect assignments. Another aspect could be the volume averaging effect
of the ionisation chambers. Due to their relatively large diameter of 4.2mm, the dose might
be perturbed when averaging over the active volume, a well-known problem especially for
the dosimetry of small fields [110]. A better agreement between measured and calculated
dose distributions is expected when simulating the volume averaging effect by a low-pass filter
41
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
function. The function must correspond with the lateral dose response function of an ionisation
chamber and therefore has to consider the shape (circular) and size (diameter=4.2mm) of the
chamber profile. The dead time of the MatriXX PT could be excluded as a possible cause since
the detected dose differences between movie mode and single shot mode measurements were
smaller than 0.3%.
The following aspects were investigated in order to explain the differences in the gamma pass
rates between different images: the coincidence of the energy layer switching with the start/end
of the time interval, contributing respiratory phases, dose differences between measurement and
simulation, the number of spots and the amount of dose. The majority of distributions which
exhibited a low gamma pass rate started and ended within an energy layer so that spots could
have been assigned to the wrong time interval. But there were also some distributions with high
gamma pass rates for which that applied. In these cases, the dose rate might have been lower at
the interval boundary. It was expected that a wrong allocation of a proton spot to a respiratory
phase would have a greater impact on the dose distribution for phases near the mid-ventilation
position, where larger organ motions occur. Indeed, most of the distributions with a low gamma
pass rate were delivered close to the mid-ventilation phase - but again, a few distributions with
high gamma pass rates existed which also included phases near the mid ventilation position.
A large difference in the absolute dose between measurement and simulation was found to be
a good indication for low gamma pass rates. Conversely, small dose differences did not ensure
high gamma rates. A low dose or a small number of spots in combination with a mismatch of
proton spots to a wrong time interval or respiratory phase was expected to significantly affect
the pass rate. However, a clear correlation could not be observed, except that the average
amount of dose which was delivered in the first half of the irradiation was slightly higher.
Both test runs revealed on average a deterioration of the gamma pass rate for the second half
of the irradiation. Since the start time of each spot was gained from log files, the worse gamma
pass rates in the second half of the irradiation cannot be explained by the summation of time
errors. Contributing factors might be differences in the amount of dose and the dose rate or
a small deviation between the depth of the exported dose plane and the measurement depth.
Such a difference in depth would affect proximal energy layers (second half of the irradiation) to
a greater extent because they generate steeper dose gradients in the measurement plane which
was located in the middle of the SOBP. However, there are still images with high gamma pass
rates in the second half of the irradiation and errors might not be attributable to a single source
of error but maybe to a coincidence of several of the above listed factors.
3.3 Development and validation of a beam delivery time model
The implementation of 4DDD computation in RayStation, discussed in the previous section,
enables retrospective dose analyses based on irradiation log files, e.g. after a treatment fraction.
However, there are some instances in clinical praxis and research, where prospective analyses
are demanded. These include for example the evaluation of different treatment approaches for
patients or in silico studies on motion mitigation techniques for a huge patient cohort. In such
cases, it is unpractical or even not feasible to perform the required number of test irradiations
due to the limited manpower and beam time. In order to estimate a 4DDD distribution a priori,
access to the scanning control system calculations or an appropriate, facility-specific beam time
model are needed. Since the exact logic of the control system is confidential information of
IBA, an empirical beam delivery time model had to be developed within the scope of this thesis
and will be presented in the following.
3.3.1 Materials and methods
The construction of an empirical beam time model involved the thorough examination of beam
delivery parameters, i.e. the spot delivery time, the scanning speed and the energy layer
switching time, and their dependencies on the delivered dose per spot, spot distance and beam
energy for typical clinical values (see Sec. 2.3.2). Test irradiations were carried out based on
dedicated PBS layer definition files (PLD files) to enable systematic analyses. A PLD file is used
42
3.3 Development and validation of a beam delivery time model
to transfer predefined irradiation settings to the treatment machine and contains information
on the number of energy layers, the cumulative meter set weight of all spots, the total amount
of monitor units to be delivered, the beam energies, the number of rescans, the position in
the isocentre plane and the meter set weight of each spot. For the investigation of the spot
delivery time, seven PLD files were created with maximum energies ranging from 130MeV
to 192MeV and minimum energies ranging from 100MeV to 120MeV being representative
for clinical treatment scenarios. Each energy layer contained spots weights from 0.04MUs to
2.5MUs. After the irradiations, the corresponding log files were evaluated. The average delivery
time per MU was calculated based on 210 data points for each spot weight. The scanning speed
was studied separately for the x and y directions for 19 energies ranging from 102MeV to
160MeV. Spot distances of up to 9mm were included in the PLD files. The measurements were
repeated four times in a time interval of about three months and served also for the evaluation
of the energy layer switching time. Since the acquired data formed the basis for the beam
delivery time model, the standard deviation was an important statistical measure. It was used
to assess whether the data were spread out over a wide range or whether they could be well
described by average values.
Besides the above-mentioned beam parameters, the order of the spots must be known for the
interplay evaluation. A description of the spot sorting for the IBA scanning control system is
provided in Sec. 2.3.2. The implementation of the spot sorting in the interplay effect routine
was tested based on the reference positions documented in the log files.
The resulting beam delivery time model was validated by comparing 4DDD distributions based
on the actual delivery times extracted from log files with 4DDD distributions based on the
delivery times calculated by the beam time model. Time differences were assessed for each
energy layer and for the total delivery time of each field. This was done for the two treatment
plans presented in Section 3.2.1 using the log files which correspond to a motion period of 5 s
(three measurements per plan, six log files in total).
3.3.2 Results
Determination of the beam delivery parameters
The dependency of the spot delivery time on the spot weight is shown in Figure 3.11. For spot
weights higher than 0.4MU, the delivery time per MU was approximately constant. Below
0.4MU, the time needed per MU started to increase strongly with decreasing spot dose since
the relative contribution of the turn-off time of the system grows. Depending on the energy of
the layer under consideration and the maximum energy of the field, the delivery time varied
slightly which is represented by error bars indicating the standard deviation in Figure 3.11. For
spot weights above 0.1MU, the standard deviation remained below 0.3ms/MU. The maximum
standard deviation was about 2.7ms/MU at 0.04MU (lowest spot weight). In order to describe
the observed time behaviour with an accuracy better than ±2% (with the exception of one data
point in the gradient region of the curve) while keeping the number of fit parameters low, a
rational function was used for fitting the data with the Nelder–Mead algorithm [111] from GNU
Octave, version 4.0.0.
The scan time, here defined as the time needed to change between two spot positions, is depicted
in Figure 3.12 as a function of the spot distance. For both scanning directions, x and y, the scan
time grew with increasing spot distance. While it took only about 2.25ms to 2.5ms to scan
in x direction for spot distances in-between 1mm and 9mm, it took about 2.25ms to 4.75ms
for the same distances in y direction. Step functions were defined for the beam time model
resembling the trend of the data points as close as possible.
The energy layer switching time did not show a correlation with the energy or the energy
difference between layers. It exhibited strong variations even for repeated irradiations of the
same PLD file. Outliers due to longer irradiation pauses which can occur after monitoring
interlocks were excluded from the evaluation. The measured average value µ was 1.23 s and the
standard deviation σ was 0.26 s. For the beam time model, random values were generated from
a normal distribution (µ = 1.23 s, σ = 0.26 s). In addition, values below 0.9 s were set to 0.9 s
43
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
and values above 2.5 s were set to 2.5 s.
An algorithm which resorts the proton spots according to the scanning path of the treatment
machine was implemented in the interplay effect routine. The calculated spot order matched
the one recorded by log files.
Comparison with electronic irradiation protocols
The time structure calculated by the beam time model was compared to the actual beam
delivery sequence extracted from log files. In average, the time per energy layer differed by
0.03 s and the total time per field by 1.2% assuming identical energy layer switching times. The
impact of such small time differences on the simulation of interplay effects was examined by
comparing the resulting 4DDD distributions. Figure 3.13 shows exemplarily one of the 4DDD
analyses for setup A. The dose distributions were identical within the tolerances defined in
Section 3.2.1. Minor differences could be seen in the 2D profiles (less than 1.5% within the
plateau region). The gamma pass rate reached 100%.
3.3.3 Discussion
Since WPE has no access to the algorithms of IBA’s scanning control system, the beam time
model had to be created on the basis of empirical findings. The model is therefore only valid
for the tested clinically relevant spot distances, energies and spot doses.
Determination of beam delivery parameters
In the PBS implementation of the IBA Proteus®Plus system, the energy layer switching time
dominates the beam delivery process in terms of irradiation time. It is up to three orders of
magnitude larger than the spot delivery time or the scan time. Nevertheless, delivery and scan
times can add up to several seconds and the irradiation of an energy layer cannot be assumed
to be instantaneous. Since the typical respiratory cycle length of an adult is about 3 s to 5 s,
spots of one energy layer might be delivered over different respiratory phases. As a consequence,
appropriate timing is required. The fit for the spot delivery time describes the measured data
with high accuracy for spot weights above 0.1MU. But even for the highest standard deviation of
about 2.7ms/MU at the minimum spot weight, the absolute time error is negligible with 0.1ms.
The approximation of the scan time by step functions leads mainly to uncertainties for the y
direction, where one spot distance cannot always be assigned unambiguously to one scan time.
Since the quantisation error is smaller than 1ms and scanning is predominantly performed
in x direction (faster scanning component), these errors will not add up to an unacceptably
high value. To cope with the stochastic nature of the energy layer switching time, prospective
analyses should include multiple interplay effect evaluations per treatment plan, each with
random switching times. In this way, the most probable outcome of the treatment as well as
the worst case scenario can be investigated in advance.
Comparison with electronic irradiation protocols
The average time error per energy layer of 0.03 s, caused by the beam time model, is negligible
compared to the length of a 4DCT phase of typically 0.3 s to 0.6 s. The total time difference per
field, however, reached up to 0.44 s (1.7%). Comparisons of 4DDD distributions based on log
files and the beam time model could demonstrate that errors of this order of magnitude do not
have a noticeable effect on the dose distribution. Hence, the beam time model was considered
to be accurate enough for interplay effect evaluations.
In some in silico studies on interplay effects in proton therapy (for instance Ref. [30]), beam
delivery parameter were assumed to be constant. Therefore, the effects of an over-simplified
beam time model or an incorrect distribution of proton spots over the different respiratory
phases (e.g. only energy layer-wise) shall be demonstrated based on two examples: Assuming
44
3.3 Development and validation of a beam delivery time model
0
10
20
30
40
50
10−1 100
sp
ot
 d
el
iv
er
y 
ra
te
 (m
s/
M
U
)
spot weight (MU)
E = 100 MeV − 192 MeV
fit: y = 2588.986 / (x + 1.256)16.721 + 4.995
Figure 3.11: Beam delivery time per monitor unit as a function of spot weight: The average time
over all beam energies is marked by dots for the investigated spot weights. Error bars indicate the
corresponding standard deviation and a solid line represents the fitted curve. Note the logarithmic
scale of the x axis.
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.2 0.4 0.6 0.8 1.0
sc
an
 ti
m
e 
(m
s)
spot distance (cm)
x direction
y direction
step function x
step function y
Figure 3.12: Scan time in x and y direction as a function of the spot distance: Measurements were
performed for beam energies ranging from 102MeV to 160MeV. A solid and a dashed line represent
the step functions used to model the scanning speed in x and y direction in the facility-specific beam
time model.
45
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
y (mm)
x (mm)
-20 0 4020-40
0
20
40
60
-20
-40
-60
(a) beam time model
y (mm)
x (mm)
-20 0 4020-40
0
20
40
60
-20
-40
-60
(b) log file
y (mm)
x (mm)
-20 0 4020-40
0
20
40
60
-20
-40
-60
(c) gamma analysis
gamma
 level
0.00
0.25
0.50
0.75
1.00
1.25
100
80
60
40
20
0
spectral
 level (%)
signal (%)
x (mm)beam time model
log file
-20 0 4020-40
48
80
64
96
32
16
0
112
(d) x profile
signal (%)
y (mm)beam time model
log file
-40 0 8040-80
48
80
64
96
32
16
0
(e) y profile
Figure 3.13: Evaluation of the developed beam time model using the treatment plan which was
initially created for the irradiation of setup A (Sec. 3.2.1): (a) 4D reconstructed dose distribution
based on the beam time model (isocentre plane), (b) 4D reconstructed dose distribution based on
irradiation log files (isocentre plane), (c) gamma analysis with a 3mm/3% passing criterion, gamma
pass rate = 100%, (d) comparison of the dose profiles in x direction (left-right), (e) comparison of the
dose profiles in y direction (superior-inferior).
46
3.4 Clinical aspects
a constant scanning speed of 250 cm/s, a spot delivery time of 5ms/MU and an energy layer
switching time of 1.2 s, the gamma pass rate deteriorates from 99.7% to 91.6%. The approxim-
ation of an instant dose delivery for each energy layer even leads to a reduction of the gamma
pass rate by 10%.
3.4 Clinical aspects
Future challenges in interplay modelling emerge in the areas of 4D imaging, beam delivery and
treatment planning. The trend towards the treatment of moving targets with PBS results par-
ticularly in a demand for better motion monitoring also during irradiation. For this purpose,
imaging modalities such as 4DMRI, fluoroscopy or ultrasound could be suitable candidates.
The so gained information on organ motion and deformation has to be transferred to the plan-
ning CT in order to calculate the dose distribution for different motion phases. Thus, the
developed interplay effect routine can be easily combined with other imaging modalities than
CT.
Continuous developments in the beam delivery in the last few years led to shorter energy layer
switching times and changes in the scanning speed and delivery time. A development which
decreases the treatment time and improves the robustness against organ motion is for example
the continuous line scanning investigated by Fattori et al. and Klimpki et al. [112, 113]. But
also software and hardware upgrades of the beam delivery system can affect the time structure
and thus the interplay pattern. Therefore, it is crucial to keep the beam delivery model imple-
mented in the interplay effect script up to date. For retrospective analyses, the interplay effect
routine remains valid even after major changes of the beam dynamics since the timing is read
out from log files.
The interplay effect routine can be used not only to analyse the impact of actual changes in the
delivery process but also to actively search for the best delivery techniques and optimal beam
parameters with regard to the 4DDD distribution. The determination of the optimal pause
between two energy layers dependent on the respiratory cycle length or the optimal scanning
path could for instance improve the robustness against motion in future applications. The
time-resolved version of the interplay effect routine might be a helpful tool for such purposes.
However, a methodology to synchronise the OmniPro-I’mRT measurement with the irradiation
has to be developed before it can be used for dose reconstruction. Otherwise, the uncertainty
in the determination of the offset can affect the calculated dose distribution for certain time
intervals as discussed above. Another application of the time-resolved interplay routine could
be to determine individual gating windows for respiratory-gated irradiations. The comparison
of the static and the dynamic dose distribution over time reveals the magnitude of the dose
distortion for different time intervals of the respiratory cycle and enables to adjust the gating
window accordingly.
In treatment planning, it is expected that the potential benefits of intensity-modulated proton
therapy (IMPT) and 4D robust optimisation will be better exploited. Consequently, the stand-
ard robustness evaluation including range uncertainties and shifts of the isocentre (Ref. [114])
has to be extended by the interplay effect analysis to test additionally the robustness against
organ motion. The dose modulation in IMPT leads to different beam delivery time structures
compared to single field uniform dose plans which were used for the experimental validation of
the interplay effect routine. This does not pose a problem for prospective evaluations of IMPT
plans since the beam time model was created based on the analysis of a wide range of clinical
relevant beam delivery parameters including spot delivery times and spot distances used in
IMPT. Also the application of multiple fields can be easily simulated with the interplay effect
routine as shown in the scope of the hepatocellular carcinoma study in the next chapter. In
case of a prospective evaluation, the routine chooses random start phases for each field.
The use of motion mitigation techniques has to be considered in 4DDD evaluations. The
presented interplay effect routine already enables the simulation of beam gating and layered
rescanning (simplified model). The gating window can be selected through the graphical user
47
3 Implementation of 4D dynamic dose accumulation in PBS treatment planning
interface based on the choice of respiratory phases for which the beam should be turned on. The
number of rescans is automatically taken from the stored treatment plan parameters. Future
script versions should take into account the minimum spot weight for rescanning techniques.
The consideration of further motion mitigation techniques is possible by small modifications of
the script when needed.
The impact of variations in the breathing pattern on the interplay effect evaluation is a clinical
aspect which is beyond the scope of the current work and will be investigated in the future (see
Sec. 6.4 on future research).
48
4 Evaluation of 4D robust optimisation for hepatocellular
carcinoma patients
The treatment planning study presented in this chapter investigates the ability of 4D robust
optimisation to reduce motion induced dose distortions in PBS, while sparing surrounding
healthy tissue, for HCC patients. The liver is particularly suited to study motion interplay
effects since the treatment region exhibits smaller density gradients and more homogeneous
tissue than targets in the thorax, making it less prone to range errors. In case of thoracic
targets, for example, the microstructure of lung tissue cannot be resolved by CT images and
degrades the accuracy of the dose calculation [21, 22, 23, 24].
Due to the exceptional high mortality rate of HCC patients, an effective local therapy suitable
for a wide range of HCC patients is urgently needed as will be explained in Section 4.1. The
treatment of HCCs requires very high precision since a sufficient amount of healthy liver tissue
must be spared to maintain the liver function. Proton therapy could provide the demanded dose
conformality, particularly using PBS. However, contrary to DS, interplay effects in PBS might
compromise the target coverage in the presence of organ motion. The motion magnitude of liver
tumours depends on the location and ranges from a few millimetres to almost 2 cm [115, 116].
The largest motion magnitudes have been observed for the right upper lobe (adjacent to the
diaphragm) [115].
Within this study, it should be examined whether 4D robust optimisation in PBS
1. provides a better 4DDD target coverage than the conventional PTV concept and reduces
the disadvantage in dose homogeneity of PBS compared to DS,
2. ensures similar or better sparing of healthy liver tissue than the PTV concept and does
not lower the advantage in conformity over DS.
A conservative single field uniform dose approach was applied for PTV-based PBS plans since
geometric margins might be less resistant to disturbances which cause position-dependent
changes of the water equivalent thickness. In contrast, multi-field optimisation was used for
4D robustly optimised PBS plans to exploit the full potential of intensity-modulated proton
therapy.
Partial results of the presented work in this chapter have been submitted to/ published in
peer-reviewed journals [117, 118].
4.1 Hepatocellular carcinoma (HCC)
4.1.1 Clinical background
The liver fulfils important functions such as the production of bile, the metabolism of ingested
nutrients, the elimination of toxins, the production of hormones, the regulation of glycogen
storage and plasma protein synthesis. Since it is a parallel organ which is composed of numerous
functional subunits, it can tolerate local damage to a certain extent without losing functionality.
With a proportion of 85% to 90%, HCC represents the most common type of primary liver
cancer [19]. The incidence of HCC is highest in East and South-East Asia and Sub-Saharan
Africa, where hepatitis B is wide-spread. However, owing to the growing occurrence of hepatitis
C infections and, to a lesser degree, alcoholic liver damage, the prevalence of HCC is increasing
in Europe and in the United States [119]. HCC is often related to an underlying chronic liver
disease such as liver cirrhosis. Consequently, common causes of liver cirrhosis represent key risk
factors for HCC. The major risk factors are hepatitis B and C viruses, alcohol abuse and non-
alcoholic fatty liver disease. Other factors include aflatoxin intake, diabetes and immune-related
diseases of the liver such as autoimmune hepatitis and primary biliary cirrhosis [120, 121].
Symptoms of HCC are often manifestations of a decompensated cirrhosis and usually appear
at a late stage of the disease. Non-specific general signs include asthenia (weakness), anorexia
(loss of appetite), nausea, weight loss and fever. Furthermore, clinical signs such as jaundice,
49
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
gastrointestinal bleeding, peripheral oedemas, abdominal pain or portal vein thrombosis can
be an expression of onset of HCC. The disease is associated with a poor prognosis and an
exceptionally high mortality rate with a five-year survival of less than 5% [2]. That makes it
the third leading cause of cancer-related mortality worldwide even though it is only the fifth
most common malignancy in men and the seventh in women [20, 122]. Since symptoms of HCC
often do not show up in the early stages, 10% to 20% of the tumours already have a diameter
of more than 10 cm at the time of first diagnosis [123]. In order to preserve as much of the
surrounding healthy liver tissue as possible local treatment methods are demanded.
4.1.2 Treatment options and the role of proton therapy
The treatment of HCC is often a challenging task since more than 80% of the patients suf-
fer from an underlying liver cirrhosis [124]. A cirrhosis is associated with an impaired liver
function and thus represents an exclusion criterion for many treatment options. New therapy
recommendations are therefore usually based on the Barcelona Clinic Liver Cancer staging clas-
sification which not only considers the number and size of tumours but also the general state of
health and the liver function status according to the Child-Pugh score [120]. While a curative
approach is followed to treat HCCs in early stages, local control and prolongation of life are
clinical goals for advanced HCCs [121].
Commonly applied curative treatment methods are surgical resection, transplantation and ra-
diofrequency ablation. The best long-term survival was demonstrated for surgery (resection
or transplantation) with a five-year survival rate of about 70% [125]. However, most patients
cannot undergo a surgical resection due to comorbidities such as cirrhosis and the eligibility
criteria for liver transplantation are strict. The Milan criteria established itself as the worldwide
standard for transplant patient selection to ensure excellent post-transplant survival. They are
based on clinical experience and restrict transplantation to patients with a single tumour smal-
ler than 5 cm or two to three tumours smaller than 3 cm each, who do not have an extrahepatic
disease or macrovascular involvement [126, 127].
If neither resection nor transplantation can be performed, radiofrequency ablation (RFA) might
be a treatment option. RFA, a minimally invasive procedure, uses a needle electrode to create
an alternating electric field within the tumour and destroys tumour cells through frictional
heat. It can be applied for tumour sizes up to 5 cm but is not suited for locations close to major
vessels, the major bile duct, the diaphragm or other abdominal organs. Due to a high local
recurrence rate, the long-term survival is worse than for surgery [128].
Other, non-curative local treatment options exist for patients who do not meet the criteria of
those approaches or have to wait for the transplantation. In the latter case, the treatment
serves as bridging method to prevent tumour growth. If the tumour size exceeds the Milan
criteria, non-curative therapies can be applied in some cases to decrease the tumour so that the
patient becomes eligible for a transplantation (down-staging) [129].
The most frequently used non-curative therapy for intermediate stages is transarterial chemoem-
bolisation (TACE). The technique is based on the injection of small particles coated with chemo-
therapeutic drugs in the hepatic artery and kills tumour cells in two ways. Firstly, particles
block or slow down the blood supply to the tumour and secondly the chemotherapeutic agents
induce cytotoxicity. In contrast to the tumour, which is supplied through the hepatic artery,
normal liver tissue gets blood from the portal vein and is thus not affected from cutting off the
blood flow. After TACE, a small improvement in local control and overall survival was observed
but also significant complications [130, 131]. Contraindications for TACE include main portal
vein thromboses.
Further treatment options, which can be applied either individually or in combination with
other therapies, are external beam radiation therapy, systemic treatment with the multi-kinase
inhibitor sorafenib and internal radiation therapy with radioisotopes [127]. Apart from modern
irradiation techniques, each approach is only suited for a small subgroup of patients, not very
effective or associated with unacceptable toxicities. An effective local therapy which can be
applied for a wide range of patients independent of tumour size, location and underlying liver
disease is needed.
50
4.2 Design of the treatment planning study
In the past, radiotherapy only had a minor role in the treatment of HCC because of the low
tolerance dose of normal liver parenchyma3, which is even reduced in case of a chronic liver dis-
ease [132]. Since early radiation techniques were not able to spare an adequate amount of normal
liver parenchyma, they caused high incidence rates of radiation-induced liver disease (RILD).
RILD, occurring typically two weeks to four month after the treatment, is associated with an
increase in hepatic enzymes (particularly alkaline phosphatase), hepatomegaly (an enlargement
of the liver) and ascites (accumulation of fluids in the peritoneal cavity4). It is caused by a
venoocclusive disease, i.e. the obstruction of small veins in the liver [133]. In severe cases,
RILD can lead to irreversible hepatic failure and death [121]. An effective therapy is still lack-
ing. The incidence rate of RILD is about 5% to 10% for irradiations of the whole liver with
30GyRBE to 35GyRBE in conventional fractions [134]. In the early days of HCC irradiations,
the prescribed dose was therefore limited to 30GyRBE. Since higher dose levels are required to
achieve a therapeutic effect, HCC was considered to be radioresistant for a long time. Modern
irradiation and imaging techniques enable an escalation of the dose to the tumour without
unacceptable side effects since large parts of the functional liver tissue can be kept out of the
high-dose region [134]. Thus, radiotherapy is no longer only a palliative approach but also an
effective treatment for patients who do not qualify for other curative options.
A particular promising approach in radiotherapy of HCC is proton therapy. Compared to
photons, protons exhibit a more favourable depth dose profile that allows for very conformal
dose delivery and thus better sparing of normal liver tissue (see Sec. 2.1.3). The efficacy
and safety of proton therapy for HCC is subject of current research. Encouraging results on
local tumour control and survival for HCC patients were already reported by investigators
from Japan, where HCC is common and the number of proton therapy facilities comparat-
ively large [124, 135]. Also phase II trials conducted by the Loma Linda University Medical
Center (Loma Linda, California, USA) and the Massachusetts General Hospital (Boston, Mas-
sachusetts, USA) demonstrated high local control rates and minimal acute toxicities for HCC
patients [2, 136]. Korean researchers observed a complete response rate of 100% in a dose
escalation study for the highest delivered dose, 72GyRBE in 24 fractions corresponding to an
equivalent dose in 2Gy fractions of 78GyE10 (calculated using the linear quadratic model with
an alpha to beta ratio of 10) [137].
So far, the majority of proton therapy studies on HCC has been performed with passive scatter-
ing techniques. However, recently built proton therapy centres use active pencil beam scanning.
PBS is associated with a lower neutron dose, provides better conformity at the proximal edge of
the target and enables IMPT. Thus, it potentially reduces the occurrence of acute toxicities and
radiation-induced secondary cancer. On the downside, PBS exhibit a larger lateral penumbra
and is more sensitive to motion (Sec. 2.3.2).
Different planning strategies (e.g. beam-specific margins or robust optimisation) and motion
mitigation techniques can be applied for the treatment of moving targets in PBS. The effect of
these features still needs to be examined for HCC patients.
4.2 Design of the treatment planning study
4.2.1 Patient collective
The patient collective consisted of nine HCC patients with a total of eleven CTVs. Without
loss of generality, the CTV was defined as the GTV for the plan comparison. 4DCT data
sets of the patients were kindly provided by O. Blanck and M.K. Chan from the University
Clinic Schleswig-Holstein (Kiel, Germany) and M. Ayadi from the Centre Léon Bérard (Lyon,
France). Seven of the 4DCTs have been acquired within the scope of a previous study [138] and
exhibited good tumour contrast due to the selective uptake of lipiodol by the tumour cells after
TACE. Tumour motion was restricted by abdominal compression for these patients (ID 1-7),
3Liver parenchyma: functional part of the liver tissue.
4Peritoneal cavity: potential space between the parietal peritoneum which surrounds the abdominal wall and
the visceral peritoneum which surrounds the abdominal organs
51
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
0
100
200
300
400
500
600
700
1 2 3 4 5 6 7 8a 8b 9a 9b
C
TV
 v
ol
um
e 
 c
m
patient ID
3 )
(
I
II
III
I
II
II
II
III
III
III
III
(a) CTV volume
patient ID
d 
   
   
(c
m
)
iC
TV
1 2 3 4 5 6 7 8a 8b 9a 9b
0.0
0.5
1.0
1.5
2.0
(b) tumour motion amplitude
Figure 4.1: CTV volume (a) and tumour motion amplitude (b) as defined in Equation 4.1 for the
selected patient collective. CTVs were categorised in groups according to their homogeneity level, where
category I includes iCTVs encompassed entirely by liver tissue, category II iCTVs extending into other
parts of the abdomen and category III iCTVs adjacent to the ribs or lung. Patient IDs labelled with
the letters ’a’ or ’b’ refer to different CTVs of one patient.
whereas for patient 8 and 9 4D imaging was carried out during free breathing. Patient 8 had
two 4DCT scans, one with contrast agent injection to localise the tumour and one without
to calculate the treatment plan. Implanted fiducial markers served for the localisation of the
tumour for patient 9. All 4DCTs were acquired with a Philips Brilliance Big Bore CT scanner
(Philips Medical Systems, Cleveland, OH, USA) using retrospective spiral correlated imaging
(see Sec. 2.5.4). Three-dimensional CT data sets were reconstructed from 10% time intervals
equally spaced over the respiratory cycle (phase binning), yielding 10 motion phases. The 0%
phase corresponded to end-inspiration and the 50% phase to end-expiration. The CT slice
thickness was 3.0mm for patients 1 to 7, 1.0mm for patient 8 and 2.0mm for patient 9. The
lateral pixel spacing in x and y was 1.2mm for patients 1 to 7, 1.1mm for patient 8 and 1.0mm
for patient 9.
The CTV volume, shown in Figure 4.1a, ranged from 3 cm3 to 640 cm3. The tumour mo-
tion amplitude diCTV was defined as the average deformation vector length of the deformable
registration in-between end-expiration and end-inspiration [30]:
diCTV =
N∑
i=1
√
x2i + y2i + z2i
N
, (4.1)
where the internal CTV (iCTV) represents the union of all CTVs on the different 4DCT phases,
xi, yi and zi are the deformation vector components of voxel i within the iCTV and N is the
total number of iCTV voxels. diCTV varied between 0.4 cm and 1.5 cm and is displayed in
Figure 4.1b.
Depending on the homogeneity level of the iCTV and its surroundings, all CTVs were divided
into three categories. Category I comprised all iCTVs surrounded by liver tissue (ID 4 and
6). Category II included iCTVs extending partly into other parts of the abdomen such as the
stomach or the kidney (ID 2, 7, 8b and 9a). Category III contained iCTVs adjacent to the ribs
or the lung (ID 1, 3, 5, 8a and 9b). In the following, the CTV corresponding to patient ID n
is referred to as CTV n.
52
4.2 Design of the treatment planning study
4.2.2 CT scanner calibration, contouring and deformable image registration
CT numbers were converted into densities using a stoichiometric calibration curve which covers
a range from -1000HU to 2976HU and has been created within the scope of a Master’s thesis at
WPE [139]. Material overrides were used to correct for image artefacts and contrast enhanced
regions in the liver. To this end, the average liver density was determined by placing a spherical
ROI with a radius of 1 cm to 2 cm in a homogeneous region of the normal liver tissue (liver
volume minus CTV).
Contours for the CTV, the body and the External had to be delineated on every 4DCT phase
for each patient since they were required for deformable image registrations, 4D dose compu-
tation and the creation of the iCTV. OARs were only contoured on the planning CT for the
reasons explained below. In this study, the liver, the ribs, the heart, the lung, the stomach,
the kidneys and the myelon were included as OARs. They were used to define objectives in
treatment planning and to evaluate the 4D dynamic dose distribution in the end. A PTV was
constructed for non-robust optimised treatment plans by adding margins for setup and range
uncertainties to the iCTV (see Sec. 4.2.3). After contouring, all delineated ROIs were controlled
and approved by experienced radiotherapists.
The deformable image registration algorithm ANACONDA described in Section 2.4.4 served
for the registration of the 4DCT phases. Since contouring is very time-consuming for a 4DCT
data set, a compromise was made between DIR accuracy and expenditure of time. The choice
of controlling structures fell on the CTV and the body contour. In addition, the body was
selected as focusing region. The reason why no further structures were included as controlling
ROIs is that OARs in the abdomen typically exhibit similar contrasts as their surroundings and
would have to be manually delineated for each motion phase, whereas the outer body contour
can be easily created and transformed to other motion phases using automated planning tools.
The CTV had to be contoured for each phase anyway since it was needed to create the iCTV.
Further, it represents the most important controlling structure with regard to the dynamic dose
evaluation.
The planning CT was chosen as reference phase of all DIRs in order to enable dose mapping for
the 4D evaluation. Even though the algorithm has been validated before [66, 67, 68, 69], regis-
tration errors were assessed on a sample basis for the current patient cohort as recommended
by the Task Group No. 132 of the Radiation Therapy Committee of the American Association
of Physicists in Medicine (AAPM) [140]. For this purpose, the target registration error and the
Dice similarity coefficient (DSC) were determined for randomly selected patients. The target
registration error states the distance between an identified point a in phase A and the corres-
ponding point a′ mapped from phase B to phase A by means of image registration [140]. The
average target registration error was determined based on two to three landmarks per patient
considering six patients in total. Landmarks were identified in the 0% phase and 50% phase
representative for the maximum deformation. Another four phases were exemplarily examined
for two patients.
The DSC is a measure for the overlap between the reference segmentation volume S and the cor-
responding segmentation volume S′ mapped from the deformable registered image. It is defined
as double the volume of overlapping pixels divided by the sum of the two single volumes [141]:
DSC = 2 · S ∩ S
′
S + S′ . (4.2)
A DSC value of 1 indicates a perfect match and a value of zero no overlap at all. The DSC
value of the liver structure was exemplarily examined for 4 patients considering the 0% and the
50% phase and required additional manual contouring of the liver on the 0% phase.
4.2.3 Treatment plan optimisation in PBS and DS
Treatment plans were created in a research version of RayStation 6 using the Pencil Beam
dose algorithm and a dose grid of 2mm. A uniform dose of 63GyRBE (Dpresc) was prescribed
53
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
to the CTV in 15 fractions according to Bush et al. [2]. The 50% phase served as planning
CT since it is more reproducible and less affected by organ motion than the other respiratory
phases [89, 142].
4D robustly optimised and 3D non-robustly optimised PBS plans
Two types of PBS treatment plans were generated per patient, a 4D robustly optimised plan
and a non-robustly optimised, margin-based plan for comparison purposes. These plans are
referred to as 4D PBS and 3D PBS plans hereinafter. The same gantry and couch angles were
chosen for both techniques using two treatment fields per plan. The initial proton energy ranged
from 100MeV to 195MeV. Range shifters were applied to reach shallow-seated tumours, when
necessary. The air gap between a range shifter and the patient varied between 2 cm and 5.4 cm
and was kept as low as reasonably possible. Distances between adjacent energy layers were set
automatically with a scale factor of 1.1 with respect to the Bragg peak width (80% dose level).
The spot distance was determined by multiplying 1.06 times the radial spread in the Bragg
peak (average projected sigma) with a scale factor of 0.8 for each energy layer [77].
In 4D PBS plans, the robust optimisation settings were chosen to achieve plan robustness
against 2mm setup error, 5% range uncertainty and morphological changes in 10 respiratory
phases. For the optimisation process, the resolution of the dose grid had to be set to 3mm or
4mm in order to prevent the TPS from reaching its limit due to the high data volume. After
the optimisation, the final dose was calculated on a 2 mm dose grid based on the optimised
plan parameters.
The applied perturbation parameters originate from the setup uncertainties (2mm) and range
uncertainties (2mm plus 3.5%) clinically used at WPE. For the given energy range, a range
uncertainty of 2mm and 3.5% corresponds to a percentage uncertainty of about 5%. The robust
optimisation considered CTV objectives. Objectives referring to OARs were only evaluated
for the nominal scenario. The spots of all fields were simultaneously optimised using multi-
field optimisation to achieve the best possible conformality through intensity modulation while
ensuring robust CTV coverage.
In 3D PBS plans, uncertainties were taken into account by beam-specific PTVs and the whole
optimisation was based on the 50% phase. The robustness settings listed above were used as
margins in this case. The beam specific PTVs comprised the iCTV, a uniform setup margin
and a geometric margin accounting for range uncertainties in beam direction (proximal and
distal to the target). Contrary to the 4D PBS plans, a single field uniform dose approach was
applied since geometric margins might be less robust against changes in the water equivalent
path length.
Double scattering plans
A three-field concept was necessary to achieve adequate dose conformality for DS plans. The
same setup and range uncertainties as for PBS were considered. The target was defined as the
iCTV plus setup margin (2mm). The range uncertainty (2mm and 3.5%) was incorporated
into the dose computation. In addition, the smearing radius of the compensator was set to
3mm. Like for 3D PBS plans, only the 50% phase was considered in the dose computation.
The SOBP range varied between 8.0 cm and 19.2 cm and the modulation width of the SOBP
ranged from 3.5 cm to 13.6 cm.
4.2.4 CTV coverage and robustness evaluation
All plans had to fulfil the clinical goal V95(CTV ) = 100%, where V95 is the percentage volume
receiving at least 95% of the prescribed dose. In addition, a robustness evaluation was performed
for each plan including a density perturbation, a shift of the isocentre and dose computation
on different respiratory phases. Since it was not feasible to check all possible perturbation
scenarios for every respiratory phase, a set of representative scenarios was chosen and evaluated
54
4.2 Design of the treatment planning study
using the scripting interface of RayStation. The script is shown in section A.1 in the appendix.
The permutation of the following cases
isocentre shift : dx = dy = dz = ±2 mm
density perturbation : ±5%
respiratory phases : 0%, 50%
resulted in eight perturbation evaluations. For large tumours, V95(CTV )>99% was demanded
in each perturbation scenario, whereas for very small tumours with a size smaller than 20 cm3
V95(CTV )>98% was required. Exceptions to this rule were made when it compromised the
sparing of close-by OARs. Once a plan passed these criteria and was approved from medical
physics experts and physicians, it underwent a detailed interplay effect analysis (PBS plans) or
a less complex 4D dose analysis (DS plans), respectively (Sec. 4.2.5).
4.2.5 4D dose accumulation in pencil beam scanning and double scattering
The performance of 4D PBS, 3D PBS and DS plans was evaluated for the selected HCC pa-
tients based on 4D dose computations. In the following, a distinction is made between the
4DDD, which considers organ motion and sequential beam delivery, and the 4D accumulated
dose (4DD), which assumes a uniform dose delivery over the respiratory cycle.
Pencil beam scanning
In PBS, 4DDD distributions were calculated using the developed interplay effect routine
(Sec. 3.1). The beam delivery was simulated with the empirical beam time model presen-
ted in Section 3.3. The advantage of the model-based computation over the use of irradiation
log files was that possible fluctuations of the beam delivery parameters could be simulated
and considered for the planning study and that no beam-time was required. Respiratory start
phases were randomly selected for each field by the routine and energy layer switching times
were sampled from a normal distribution (see Sec. 3.3.2). For all evaluations, a constant respir-
atory period of 4 s was assumed and the default beam delivery settings defined in Section 3.3.2
were applied (settling time of the fast/slow scanning magnet= 2.25ms/ 2.5ms, average/ stand-
ard deviation of the energy layer switching time= 1.23 s/ 0.26 s).
In order to distinguish between motion effects in general and interplay effects in particular,
4DD distributions were computed in addition to the 4DDD distributions for PBS plans. To
this end, the original treatment plan was recomputed on all respiratory phases with a weighting
factor of one over the number of phases. Subsequently, the calculated dose distributions were
mapped to the planning CT using DIRs and summed up.
Double scattering
In DS, the 4DDD was approximated by the 4DD. Since the frequency of IBA’s range modulator
wheel is much higher than the typical human respiratory rate (600 revolutions per minute versus
10-20 breaths per minute), the exact time structure of the beam delivery could be neglected
assuming a uniform distribution of the dose over all motion phases. The computation procedure
was the same as for PBS 4DD computations described above.
4.2.6 Evaluation methods and criteria
The outcome of a single treatment fraction was evaluated for 60 simulations per PBS plan with
varying start phases and energy layer switching times. The number of scenarios could not be
further increased in RayStation 6 because of the long computation times and the high memory
consumption which caused data storage problems. The outcome of a whole treatment course
consisting of 15 fractions was modelled five times, yielding 75 simulations per plan. Due to the
high memory load, the evaluation doses had to be deleted after each run, i.e. after 15 fractions,
in order to release memory. The computation time depended on the load of the server and
55
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
the number of energy layers of a patient. It took about six to ten hours to complete 60 single
fraction evaluations on a server equipped with two Intel Xeon E5 2680 v2 CPUs with a total
of 20 cores and 128 GB RAM (Intel Corporation, Santa Clara, USA) when the dose volume
histogram plot option was selected in addition to the default analysis of specific dose volume
histogram metrics.
The standard deviation (SD) was used as a measure for the variability of interplay effects for a
treatment plan due to different start phases and energy layer switching times which can occur
during irradiation. The precision of the mean value was exemplarily analysed for one 4D PBS
and one 3D PBS plan of patient 2 based on the standard error of the mean (SEM) [143]:
SEM = SD√
n
, (4.3)
where n denotes the number of samples. For this purpose, the single fraction interplay evalu-
ation including 60 scenarios was repeated five times per plan.
4DD distributions only had to be calculated once per plan since they do not depend on the
start phase or energy layer switching times.
Based on the results of the 4DDD PBS single fraction evaluations and the 4DD DS evaluations
the average value and SD of each technique was determined for the plan comparison. Since
there was only one patient cohort, it was not possible to check the reproducibility by means of
the SEM.
Evaluation criteria for the CTV coverage
Because of their sensitivity to interplay effects the homogeneity index HI
HI = D5 −D95
Dpresc
(4.4)
and the percentage over- and underdosage V107/95
V107/95 = V107 + (100− V95) (4.5)
were chosen as evaluation criteria for the plan comparison, where Dv is the dose delivered to
v% of the volume. The statistical significance of differences in HI and V107/95 between 4D PBS
and 3D PBS plans and between 4D PBS and DS, respectively, was tested using a paired t-test
(two-tailed) [144]. The significance level was set to 0.05.
Evaluation criteria for OAR sparing
Representative for close-by OARs, dose volume histogram metrics of the normal liver tissue
and ribs were analysed. The risk of RILD was calculated based on the empiric Lyman-Kutcher-
Burman (LKB) normal tissue complication probability (NTCP) model [145, 146] using the
scripting interface of RayStation. Following the example of Luxton et al. [147], the NTCP was
expressed as a function of the gEUD:
NTCP = 1√
2pi
uˆ
−∞
e−x
2/2dx (4.6)
u = gEUD − TD50
m · TD50 , (4.7)
where TD50 denotes the tolerance dose leading to a complication probability of 50% for a
uniform irradiation of the entire organ and m describes the steepness of the NTCP curve.
The used LKB model parameters for RILD, TD50=39.8GyRBE, m=0.12 and n = 0.97, were
taken from Dawson et al. [134]. The endpoint was defined as Radiation Therapy Oncology
Group Grade 3 or higher RILD in the study. Differences in the fractionation scheme compared
56
4.2 Design of the treatment planning study
to Dawson et al. (fraction dose 1.5Gy) were considered by a correction of the dose volume
histogram according to the LQ model (Sec. 2.2.1) when calculating the gEUD (see Eq. 2.10):
gEUD =
(∑
i
viLQED
1/n
i
)n
, (4.8)
where LQED is the LQ-based equivalent dose in dfx-Gy fractions for sub-volume (dose volume
histogram bin) i [148]:
LQEDi = Di
1 + Di/Nα/β
1 + dfxα/β
. (4.9)
The absorbed dose Di, corresponding to the ith dose volume histogram bin, was replaced by
the biological dose (DRBE)i. The total number of fractions N was set to 15. An α to β ratio
of 2.5 was assumed for the liver [149]. The reference fraction size dfx was 1.5Gy.
In addition to the risk of RILD, the mean dose, V42GyRBE , V33GyRBE and the volume receiving
less than 15GyRBE were calculated for the normal liver tissue.
The risk for radiation-induced rib fracture after hypofractionated proton beam therapy was
determined based on the dose volume histogram metric V60GyRBE (rib) [150]. Only the three
most exposed ribs per patient with V60GyRBE (rib) > 0 were included in the evaluation. Doses
to ribs ranked fourth or higher regarding V60GyRBE (rib) were not considered to be clinically
relevant.
The alimentary tract, the heart and the kidney, which were located adjacent to or even within
the iCTV for some of the patients, were excluded from the evaluation since sufficient CTV cov-
erage in the static plan was of primary importance to examine motion-induced dose distortions.
Compromises in the CTV coverage to spare these OARs would have significantly impacted the
magnitude of motion effects and thus the outcome of the study.
The following limits were used as evaluation criteria for the OARs: V42GyRBE(normal liver)=
33%, V33GyRBE(normal liver)= 67%, average normal liver dose= 24GyRBE and V60GyRBE(rib)=
4.5 cm3 [149, 150, 151].
4.2.7 Supplementary analyses
Two points which might have affected the outcome of the 4D dose comparison are the accuracy
of the applied dose engine and the selected number of irradiation fields. These aspects were
addressed in supplementary analyses. Details on the investigations are provided in the following.
Monte Carlo calculations
Although the Monte Carlo dose engine is known to be more accurate, the Pencil Beam dose
algorithm was explicitly chosen for the treatment planning study since RayStation does cur-
rently not support Monte Carlo dose calculations for DS. The Pencil Beam dose algorithm is
particularly prone to errors if a treatment plan includes range shifters or a beam traverses lung
tissue (Sec. 2.4.5). Therefore, static PBS treatment plans and 4DDD evaluations were reviewed
with MC on a sample basis. For this purpose, two targets, which required the use of range
shifters and were located adjacent to the bowel (patient ID 2) and the lung (patient ID 3),
respectively, were selected. The original 4D PBS plans were recomputed with MC, i.e. the spot
positions and weights remained unchanged. No automatic rescaling was applied, if the resulting
median dose of the CTV (D50) deviated from the prescription.
For the review of the 4DDD evaluation, new plans were created using the same objectives
but MC-based optimisation. It was decided not to use the MC-recomputed plans from the
static dose comparison in this case since they could already exhibit cold or hot spots in the
nominal scenario which would affect the interplay effect analysis. Thus, the same starting con-
ditions, namely homogeneous target coverage and optimal OAR sparing, were ensured. The
MC-optimised 4D PBS plans were evaluated based on 60 4DDD simulations as the original
57
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
plans before. Hereinafter, the original plans which were optimised with the Pencil Beam al-
gorithm are referred to as PB plans.
The final dose for both, MC-recomputed and MC-optimised plans, was calculated to 0.5%
statistical uncertainty.
Three-field PBS plans
A different number of fields was chosen for PBS and DS due to the differences in dose conform-
ality. In PBS, an adequate level of conformality could be achieved using two fields. Since a
third field prolongs the treatment time and increases the amount of normal tissue exposed to
irradiation, it would usually not be a clinical option. However, a third field increases the robust-
ness against motion as well as setup and range uncertainties and might have been an advantage
of the DS plans over the PBS plans regarding the 4D dose comparison. Therefore, the impact
of a third irradiation field was investigated for the test patients used in the MC review (see
above). Copies of the original 4D PBS plans were created. The settings remained unchanged,
except for the number of fields and the gantry and couch angles, which were taken from the
corresponding DS plans. Only if the plans did not fulfil the clinical goal V95(CTV ) = 100%, the
weights of the optimisation objectives were slightly adjusted. Like the original 4D PBS plans,
the three-field 4D PBS plans had to pass the robustness evaluation (Sec. 4.2.4). In the end,
they were evaluated based on 60 4DDD simulations and compared to the original PBS and DS
plans.
4.3 Results
4.3.1 Evaluation of the deformable image registration
The examined landmarks in the liver revealed an average three-dimensional target registration
error of 0.20 cm ± 0.12 cm (SD) for the maximum deformation (50% phase to 0% phase). The
superior-inferior direction, the main direction of motion, contributed most to the error. Smaller
registration errors were observed when other phases were included in the evaluation. A test
based on two patients with 10 landmarks mapped from the 50% phase to the 20%, 30%, 80%
and 90% phase yielded for example an average target registration error of 0.16 cm ± 0.12 cm.
The average Dice similarity coefficient of the liver was 0.96 ± 0.03 considering deformations
between the 50% and 0% phase.
4.3.2 Perturbation analysis of the nominal treatment plans
With one exception, the treatment plans passed the robustness analysis with V95(CTV ) values
of at least 99% and 98%, respectively for very small tumours, in all perturbation scenarios.
Only the 3D PBS plan for CTV 9b, which is located adjacent to the lung, did not achieve
sufficient plan robustness. For four out of eight perturbation scenarios, V95(CTV ) was below
98% with a minimum of 83.2%. One of the examined perturbation scenarios is shown by way
of example in Figure 4.2 for DS, 4D PBS and 3D PBS.
4.3.3 Analysis of the 4D dynamically accumulated dose distribution
For purpose of illustration, three examples of 4D dose distributions are depicted in Figure 4.3,
each representative of one treatment technique. The CT slice in subplot (a) shows no over-
or underdosage of the CTV for the selected DS plan. This fact holds true for all other slices
and CTVs as will be shown below. In contrast, the corresponding 4D and 3D PBS plans suffer
from cold and hot spots, displayed in yellow (90% - 95% of Dpresc), dark red (107% - 110% of
Dpresc) and pink (>110% of Dpresc). Another detail which can be seen on the images is that
4D PBS is superior to DS and 3D PBS in sparing OARs as ribs or the normal liver tissue.
Figure 4.4 demonstrates differences in the manifestation of interplay effects based on two dose
volume histograms using 4D PBS plans as example. The first dose volume histogram belongs
to a large CTV with a small motion amplitude (ID 7) and the second dose volume histogram
58
4.3 Results
liver
CTV
lung
(a) DS plan (b) 4D PBS plan
(c) 3D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
Figure 4.2: Exemplary illustration of a perturbation scenario (sagittal view) for DS, 4D PBS and
3D PBS: The perturbed dose (overlayed as colour wash) is shown for CTV 9b on CT50% for a density
perturbation of 5% and an isocentre shift of dx = dy = dz = -2mm. In this scenario, V95(CTV ) was
100.0% for DS, 99.3% for 4D PBS and 86.6% for 3D PBS.
to a small CTV with a large motion amplitude (ID 9a). Both dose volume histograms include
the static case, the 4DDD evaluations of the whole treatment course (15 fractions) and 60
4DDD single fraction evaluations forming a dose volume histogram band. The small tumour
with the large motion amplitude exhibits a much broader CTV dose volume histogram band,
an indication for a low robustness level. In addition, the difference in the normal liver dose
between the static and the dynamic evaluation is slightly larger for this tumour.
Quantitative measures of CTV coverage and OAR sparing are given in the following sections.
CTV coverage
The HI of the CTV was lowest for DS plans looking at the 4D outcome of a single treatment
fraction (see Fig. 4.5a). While an average value of 2.0% ± 0.9% (SD) was observed for DS,
4D PBS plans exhibited an average HI of 8.1% ± 1.3%. 3D PBS plans were slightly behind
with 8.4% ± 1.3%. The detected differences in HI between 4D PBS and DS were found to
be significant (P<0.001). 4D PBS and 3D PBS, by contrast, did not differ significantly in HI
(P=0.65).
For PBS plans, the HI reached up to 7.9% to 18.4% in the worst case scenario of 60 interplay
evaluations depending on the patient/ the CTV. On average, 4D robust optimisation led to
slightly lower HI values than 3D non-robust optimisation for homogeneity category II and III
(see Fig. 4.5a). For category I (patient ID 4 and 6), 3D PBS plans yielded smaller average
values.
The HI decreased to below 5% for 4D and 3D PBS simulating a whole treatment course
consisting of 15 fractions (Fig. 4.5b). Thus, the differences between DS and PBS plans became
much smaller and in three cases the lowest HI was even achieved by a PBS plan. The HI
values for 15 fractions almost approached the static plan results computed on the reference CT,
which ranged from 0.6% to 3.1% considering all treatment techniques.
V107/95 was zero for all 4DDD single fraction evaluations in DS, i.e. no over- or underdosage
could be detected. Unlike DS plans, 4D PBS plans exhibited on average a percentage over- and
59
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
CTV
ribs
liver
(a) DS plan (b) 4D PBS plan
(c) 3D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
Figure 4.3: Comparison of the 4D dynamically accumulated dose for DS, 4D PBS and 3D PBS
considering a single fraction (coronal view): The example shows CTV 3. An enlarged image section
illustrating the exposure of close-by ribs is depicted on the bottom right of each screenshot.
underdosage of 5.9% ± 3.4% in a single fraction, closely followed by 3D PBS plans with 6.9%
± 5.7%. The difference between 4D and 3D PBS plans was not significant (P=0.60).
Again, 4D robust optimised plans yielded on average smaller values for homogeneity category
II and III than 3D non-robustly optimised plans but performed worse for category I as can be
seen in Figure 4.6. In the worst case scenario, V107/95 ranged from 5.2% to 26.8% for patient
1 to 8 in 4D and 3D PBS plans. The maximum was even in-between 51.0% and 84.3% in 4D
and 3D PBS plans for patient 9 (CTV a and b). When averaging over 15 fractions, however,
V107/95 approached zero for both, 3D and 4D PBS plans. None of the static plans showed any
over- or underdosage.
The minimum and the maximum dose per fraction, D99.99(CTV ) and D0.01(CTV ), remained
in-between 95% and 107% of Dpresc for all DS plans (as is evident from the V107/95 analysis).
For PBS plans, the average maximum dose was below 114% of Dpresc considering 60 scenarios
per patient. The worst case scenario exhibited dose maxima from 111.6% to 121.8%. The
minimum dose per fraction was on average above 90% of Dpresc for a single fraction in 4D and
3D PBS. But, depending on the patient, D99.99(CTV ) could be as low as 77.4% to 91.3% in
the worst case.
The impact of tumour motion, CTV volume and tissue homogeneity on interplay effects in
PBS is illustrated in Figure 4.7 based on V107/95. In both, 4D PBS (subplot (a)) and 3D PBS
(subplot (b)), CTV 9a and 9b reached by far the highest V107/95 values. The CTVs exhibited
comparatively large motion amplitudes, had volumes of less than 15 cm3 and belonged to the
homogeneity categories II and III. Very large CTVs with small motion amplitudes, as ID 3 and
7, led to relatively small V107/95 values independent of the tissue homogeneity for 3D and 4D
PBS plans. 3D PBS plans performed better than 4D PBS plans, for tumours in homogeneous
regions (patient 4 and 6).
The 4DD evaluation of PBS plans revealed that there is no over- or underdosage of the CTV
60
4.3 Results
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80
vo
lu
m
e 
(%
)
dose (GyRBE)
CTV static
CTV 15fx
CTV 1fx
normal liver static
normal liver 15fx
normal liver 1fx
(a) DVH for patient ID 7
0 10 20 30 40 50 60 70 80
dose (GyRBE)
0
20
40
60
80
100
vo
lu
m
e 
(%
)
CTV static
CTV 15fx
CTV 1fx
normal liver static
normal liver 15fx
normal liver 1fx
(b) DVH for patient ID 9a
Figure 4.4: Static and 4D dynamically accumulated dose volume histograms (DVHs) of the CTV
and the normal liver tissue (liver minus CTV) representative for a large CTV with a small motion
amplitude (a) and a small CTV with a large motion amplitude (b) for 4D PBS plans: DVH (a)
corresponds to patient ID 7 with a CTV volume of about 640 cm3 and a motion amplitude of 0.37 cm.
DVH (b) corresponds to patient ID 9a with a CTV volume of 6 cm3 and a motion amplitude of 1.45 cm.
The 4DDD outcome of a single fraction (1 fx) was simulated 60 times with varying start phases and
energy layer switching times. In addition to the single fraction 4DDD evaluations, the static case and
a 4DDD evaluation of the whole treatment course (15 fx) are included in the plot.
61
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
if the beam dynamics are neglected, i.e. V107/95 is zero. Similar HI values as for the static
case were observed ranging from 0.8% to 3.9%. The 4DD distributions showed no significant
difference between 4D and 3D PBS plans regarding the HI. In six out of eleven cases, the HI
was lower for 3D than for 4D PBS plans.
OAR sparing
The average dose to the normal liver tissue was smallest for 4D PBS plans with 11.1GyRBE
± 6.8GyRBE (see Fig. 4.8a). 3D PBS plans deposited on average 5.7%± 6.0% more dose than
4D PBS plans and DS even 15.9%± 10.3%. In all cases, 4D PBS plans performed either better
or at least equivalent to 3D PBS and DS plans in sparing normal liver tissue. The limit of
24GyRBE for the average normal liver dose was satisfied by all plans except for one DS plan
which exceeded the limit by 2.5GyRBE (patient ID 7).
The percentage normal liver volume which received 42GyRBE or more is depicted for DS,
4D PBS and 3D PBS in Figure 4.8b. The plot shows that 4D PBS plans were slightly superior
to 3D PBS and DS plans with an average V42GyRBE value of 12.7% ± 8.4% compared to 15.5%
± 10.2% (DS) and 13.8% ± 8.9% (3D PBS). All plans remained below the 33% limit, but two
of the DS plans (patient ID 3 and 7) almost reached it.
The maximum observed V33GyRBE value for DS, 4D PBS and 3D PBS was 37.0%, which is far
below the 67% limit.
The normal liver volume receiving less than 15GyRBE is shown in Figure 4.9. In five out of
eleven cases (patient ID 5, 6, 8b, 9a and 9b), there was almost no difference in-between DS,
4D PBS and 3D PBS. For the rest, the volume receiving less than 15GyRBE was smallest for
DS (minimum: 450 cm3). 4D and 3D PBS performed equally well.
The calculated risk of RILD was zero for most of the patients. There were only two exceptions.
Patient 3 exhibited NTCP values of 19.2% (DS), 1.2% (4D PBS) and 3.4% (3D PBS) and
patient 7 of 30.8% (DS), 6.7% (4D PBS) and 7.0% (3D PBS).
For the examined ribs, the volume receiving 60GyRBE or more was on average 2.3 cm3 ± 2.2 cm3
for DS, 0.3 cm3 ± 0.5 cm3 for 4D PBS and 1.2 cm3 ± 1.4 cm3 for 3D PBS. In two cases, DS led
to irradiated volumes larger than the volume constraint of 4.5 cm3. The affected ribs belonged
to patient 3 and had a V60GyRBE value of 7.3 cm3 and 4.8 cm3, respectively (see Tab. 4.1). For
4D PBS plans, the maximum average value of V60GyRBE was 1.4 cm3 and for 3D PBS plans
4.0 cm3. The differences in the exposure of close-by ribs between DS, 4D PBS and 3D PBS
plans are exemplarily illustrated in enlarged image sections in Figure 4.3.
Reproducibility of the results
It was tested, exemplarily for one patient, whether the interplay effect analysis yielded reprodu-
cible mean values for the chosen number of interplay scenarios (60 single fraction evaluations).
Five repetitions with each 60 scenarios revealed an SEM of the HI of 0.1% for both, the 4D
and the 3D PBS plan (average values: 10.4% (4D PBS) and 9.6% (3D PBS)). For V107/95, the
SEM was 0.3% for 4D and 3D PBS (average values: 7.6% (4D PBS) and 5.6% (3D PBS)). A
two-tailed, paired t-test demonstrated that the differences in HI and V107/95 between the 4D
and the 3D PBS plan were significant (HI: P<0.001, V107/95: P<0.001).
The average dose of the normal liver tissue exhibited an SEM of only 0.4 cGyRBE for both
plans (average values: 1377.7 cGyRBE (4D PBS) and 1565.5 cGyRBE (3D PBS), P<0.001). For
V42GyRBE , the SEM was even zero. In the case of V<15GyRBE , the 4D and the 3D PBS plan had
an SEM of 0.1 cm3 (average values: 795.9 cm3 (4D PBS) and 766.1 cm3(3D PBS), P<0.001).
4.3.4 Supplementary analyses
Monte Carlo
For patient 2, the static dose distribution looks very similar for computations with the Pencil
Beam algorithm and the MC dose engine as can be seen in Figure 4.10. The dose difference
62
4.3 Results
0.0
5.0
10.0
15.0
20.0
1 2 3 4 5 6 7 8a 8b 9a 9b
H
I (
%
)
patient ID
DS
4D PBS
3D PBS
I I
(a) 1 fraction
0.0
1.0
2.0
3.0
4.0
5.0
6.0
H
I (
%
)
patient ID
DS
1 2 3 4 5 6 7 8a 8b 9a 9b
4D PBS
3D PBS
I I
(b) 15 fractions
Figure 4.5: Homogeneity index (HI) of the CTV for 4D dynamically accumulated dose distributions
of a single treatment fraction (a) and a whole treatment course including 15 fractions (b): Each bar
displays the average HI for a certain patient and treatment plan. A comparison is drawn between
DS, 4D PBS and 3D PBS. In case of PBS, error bars indicate the standard deviation among 60 single
fraction interplay simulations (subplot (a)) and 5 treatment course interplay simulations (subplot (b)),
respectively. In DS, only one 4DDD scenario exist per treatment plan since the dose is evenly distributed
over all respiratory phases. The patient ID is marked by an ’I’ if the iCTV belongs to the homogeneity
category I, i.e. it is completely encompassed by liver tissue.
63
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
0.0
10.0
20.0
30.0
40.0
5.0
15.0
25.0
35.0
1 2 3 4 5 6 7 8a 8b 9a 9b
V 
   
   
  (
%
)
10
7/
95
patient ID
4D PBS
3D PBS
I I
Figure 4.6: Percentage over- and underdosage (V107/95) of the CTV for 4D dynamically accumulated
dose distributions of a single fraction: The average V107/95 is plotted for 4D PBS and 3D PBS plans.
Error bars represent the standard deviation among 60 interplay simulations. The patient ID is marked
by an ’I’ if the iCTV belongs to the homogeneity category I, i.e. it is completely encompassed by liver
tissue. Since the 4D dynamically accumulated dose distributions for DS and 15 PBS fractions did not
exhibit any over- or underdosage, they are not included in the plot.
Table 4.1: Comparison of the rib volume receiving 60GyRBE or more (V60GyRBE) for 4D dynamically
accumulated dose (4DDD) evaluations of DS, 4D PBS and 3D PBS plans: The three most exposed ribs
per patient with V60GyRBE >0 cm3 were considered for the evaluation. For PBS, the standard deviation
among 60 interplay simulations with varying starting phases and energy layer switching times is stated.
In DS, only one 4DDD scenario exist per treatment plan since the dose is evenly distributed over all
respiratory phases.
V60GyRBE(rib) in cm3
ID 1 ID 3
rib a rib b rib c rib a rib b rib c
DS 3.8 1.7 0.2 7.3 4.8 1.2
4D PBS 1.3 ± 0.3 0.2 ± 0.1 0.0 ± 0.0 1.4 ± 0.2 0.4 ± 0.1 0.0 ± 0.0
3D PBS 4.0 ± 0.3 1.5 ± 0.3 0.4 ± 0.1 3.7 ± 0.4 2.2 ± 0.4 0.0 ± 0.0
V60GyRBE(rib) in cm3
ID 5 ID 7 ID 8a
rib a rib a rib b rib c rib a
DS 0.8 2.3 1.7 0.1 3.4
4D PBS 0.1 ± 0.1 0.2 ± 0.0 0.0 ± 0.0 0.0 ± 0.0 0.4 ± 0.1
3D PBS 0.7 ± 0.2 0.4 ± 0.1 0.4 ± 0.0 0.1 ± 0.3 1.1 ± 0.4
64
4.3 Results
0.2 0.4
0.6 0.8
1.0 1.2
1.4 1.6
I
II
III
ho
m
og
en
ei
ty
0
100
200
300
400
500
600
700
volume (cm  ) d        (c
m)
4
8
12
16
20
V107/ 95 (%)
iCTV
3
9a
9b
7
3
8b
4 6
5
2
1
8a
(a) 4D PBS plan
0.2 0.4
0.6 0.8
1.0 1.2
1.4 1.6
I
II
III
ho
m
og
en
ei
ty
0
100
200
300
400
500
600
700
volume (cm  ) d        (c
m)
4
8
12
16
20
V107/ 95 (%)
iCTV
3
9a
9b
7
3
8b
4 6
5
2
1
8a
(b) 3D PBS plan
Figure 4.7: Percentage over- and underdosage (V107/95) as a function of the tumour motion amplitude
diCTV (see Eq. 4.1), the CTV volume and the tissue homogeneity for 4D PBS (a) and 3D PBS plans
(b): Homogeneity category I encompasses targets which are surrounded by homogeneous liver tissue,
category II includes targets which are adjacent to other abdominal organs and category III comprises
targets next to the lung or ribs. The size and the colour code of the dots represent the magnitude of
V107/95. The corresponding patient ID is given by a number above each spot.
65
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1 2 3 4 5 6 7 8a 8b 9a 9b
av
er
ag
e 
do
se
  G
y
patient ID
normal liver tissue
DS
4D PBS
3D PBS
R
B
E)
(
(a) average dose
10.0
20.0
30.0
40.0
50.0
1 2 3 4 5 6 7 8a 8b 9a 9b
V 4
2G
y
(%
)
patient ID
normal liver tissue
DS
RB
E
4D PBS
3D PBS
(b) V42GyRBE
Figure 4.8: Average normal liver dose (a) and percentage normal liver volume receiving 42GyRBE
or more (V42GyRBE ) (b) for 4D dynamically accumulated dose evaluations: Each bar represents the
average value for a certain patient ID and treatment plan (DS, 4D PBS or 3D PBS). A dashed line
indicates the dose/ dose volume histogram constraint in subplot (a) and (b). The standard deviation
between different interplay scenarios in PBS was not plotted since it was less than 0.2GyRBE (average
dose) and 0.4% (V42GyRBE ), respectively, for all IDs. In DS, only one 4DDD scenario exist per treatment
plan since the dose is evenly distributed over all respiratory phases.
66
4.3 Results
0
1000
2000
200
400
600
800
1200
1400
1600
1800
1 2 3 4 5 6 7 8a 8b 9a 9b
V 
   
   
   
   
  c
m
  
patient ID
normal liver tissue
DS
<1
5G
y R
BE
3 )
(
4D PBS
3D PBS
Figure 4.9: Normal liver volume receiving less than 15GyRBE for 4D dynamically accumulated dose
evaluations of DS, 4D PBS and 3D PBS plans: The standard deviation between the different interplay
scenarios was below 2 cm3 for all PBS plans. In DS, only one 4DDD scenario exist per treatment plan
since the dose is evenly distributed over all respiratory phases.
map in subplot (c) shows that the plans deviate by less than 2% for the majority of the CTV
volume. There are some regions around the CTV which exhibit 2% to 4% more dose in the
original PB plan than in the MC-recomputed plan. The effect on the dose statistics was small
with regard to the clinical goals. V95 (CTV ) was for example for both plans 100%, the average
normal liver dose decreased from 15.0GyRBE to 14.8GyRBE and V42 (normal liver) from 18.9%
to 18.7%.
The differences in the static dose distribution between the PB and the MC-recomputed plan
were significantly larger for patient 3, who had a tumour adjacent to the lung (see Fig. 4.11).
The MC computation revealed a slight underdosage of the CTV (90% - 95% of Dpresc) for small
regions located close to the lung or behind the peritoneal cavity. In addition, the dose to the
heart was locally increased by up to 13% for the MC-recomputed plan. Differences could also
be seen in the dose statistics. The target coverage (V95 (CTV )) decreased from 100% to 98.1%,
the average normal liver dose from 20.1GyRBE to 19.6GyRBE , V42 (normal liver) from 25.4%
to 24.7% and V60GyRBE of the most exposed rib from 1.2 cm3 to 0.3 cm3.
The results of the 4DDD evaluation of MC- and PB-optimised 4D PBS plans are summarised
in Table 4.2. For both patients, the magnitude of interplay effects measured by HI(CTV ) and
V107/95(CTV ) was higher for MC computations. The average HI deviated by about 5% (ID 2)
and 13% (ID 3). The difference between the average values of V107/95 was 15% (ID 2) and
46% (ID 3), respectively. Besides the average value, also the standard deviation was slightly
increased.
PB plans exhibited a lower normal liver dose in 4DDD computations than MC plans. For
patient 2, the average dose, V42GyRBE and V33GyRBE were approximately 10% below the MC
values. The normal liver volume receiving less than 15GyRBE was about 3.5% higher for the
PB plan. For patient 3, the average dose, V42GyRBE and V33GyRBE were 1.2% to 3.7% smaller
and V<15GyRBE was 2.9% higher for PB than for MC.
67
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
CTV liver
(a) original 4D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
(b) MC-recomputed 4D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
(c) dose difference map
% of 63 GyRBE
8
6
4
2
0
-2
-4
10
-6
-8
-10
Figure 4.10: Comparison of the static dose distribution of the original 4D PBS treatment plan
calculated with the Pencil Beam algorithm (a) and a copy of the treatment plan which was recomputed
with the Monte Carlo (MC) dose engine (b) for patient 2: The differences in the dose distributions are
displayed as colour wash (c). The colour scale of the dose difference map is the same as for patient 3
(Figure 4.11c).
68
4.3 Results
CTV
liver
heart
(a) original 4D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
(b) MC-recomputed 4D PBS plan
% of 63 GyRBE
110
107
95
90
80
60
40
0
(c) dose difference map
% of 63 GyRBE
8
6
4
2
0
-2
-4
10
-6
-8
-10
Figure 4.11: Comparison of the static dose distribution of the original 4D PBS treatment plan
calculated with the Pencil Beam algorithm (a) and a copy of the treatment plan which was recomputed
with the Monte Carlo (MC) dose engine (b) for patient 3: The differences in the dose distributions are
displayed as colour wash (c).
69
4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
Table 4.2: 4D dynamically accumulated dose statistics for 4D PBS plans optimised with the Pen-
cil Beam algorithm (PB) and Monte Carlo (MC): The average values and standard deviations were
calculated based on 60 interplay scenarios per plan for two patients (ID 2 and 3).
ID 2 ID 3
PB MC PB MC
CTV HI (%) 10.6±1.6 11.1±2.2 8.1±0.6 9.1±0.7
V107/95 (%) 7.9±3.8 9.0±4.7 3.4±1.2 4.9±1.5
normal liver average dose (GyRBE) 13.8±0.0 15.0±0.0 19.9±0.0 20.6±0.0
V42GyRBE (%) 17.2±0.2 19.0±0.1 25.4±0.1 25.7±0.1
V33GyRBE (%) 20.7±0.1 22.7±0.2 29.7±0.1 30.2±0.1
V<15GyRBE (cm3) 796.2±2.2 769.4±2.5 562.4±0.8 546.2±0.8
Three-field PBS plans
The static dose distributions of the three-field 4D PBS plans were similar to the ones of the two-
field 4D PBS plans with regard to the CTV coverage. The percentage over- and underdosage
was zero for all plans. However, the third field increased the dose to the normal liver tissue.
The average dose was 22.6% (ID 2) and 2.5% (ID 3) higher than for two fields. The normal
liver volume which was exposed to less than 15GyRBE decreased by 9.7% for patient 2 and by
2.7% for patient 3 compared to the original plan with two fields.
4DDD evaluations demonstrated that the CTV coverage improved in the presence of organ
motion when using three fields instead of two. The average HI decreased by about 24.2%
(ID 2) and 4.6% (ID 3) as can be seen in Table 4.3. The percentage over- and underdosage
could be reduced by 65.6% (ID 2) and 41.2% (ID 3). On the downside, the normal liver was
exposed to a higher dose. The differences in the normal liver dose were similar to the differences
observed for the static dose distributions.
Table 4.3 shows that a third irradiation field in PBS still does not achieve comparable results
to three-field DS plans. With one exception, HI and V107/95 of the three-field PBS plans are
closer to the results of the two-field PBS plans than to the three-field DS plans. However, the
PBS plans are still better in sparing normal liver tissue than DS plans when using three fields.
Table 4.3: 4D dynamically accumulated dose statistics for two-field and three-field 4D PBS plans as
well as three-field DS plans: The average values are listed for patient 2 and 3. In addition, standard
deviations, considering 60 interplay evaluations per plan, are stated for PBS.
ID 2
two-field PBS three-field PBS three-field DS
CTV HI (%) 10.6±1.6 8.0±0.8 2.1
V107/95 (%) 7.9±3.8 2.7±1.7 0.0
normal liver average dose (GyRBE) 13.8±0.0 16.6±0.0 17.6
V42GyRBE (%) 17.2±0.2 19.8±0.1 22.0
V33GyRBE (%) 20.7±0.1 23.6±0.1 25.2
V<15GyRBE (cm3) 796.2±2.2 716.2±2.4 692.5
ID 3
two-field PBS three-field PBS three-field DS
CTV HI (%) 8.1±0.6 7.8±0.6 4.0
V107/95 (%) 3.4±1.2 2.0±1.0 0.0
normal liver average dose (GyRBE) 19.9±0.0 20.5±0.0 23.6
V42GyRBE (%) 25.4±0.1 26.0±0.1 31.8
V33GyRBE (%) 29.7±0.1 30.7±0.1 35.9
V<15GyRBE (cm3) 562.4±0.8 545.9±0.8 501.3
70
4.4 Discussion
4.4 Discussion
4.4.1 Evaluation of the deformable image registration
The DIR evaluation focused on the deformation between the end-exhale and end-inhale phase,
representative for the largest errors. The average target registration error is, consequently, even
smaller than the stated value of 0.20 cm for the investigated maximum deformations. That could
be demonstrated based on 10 additional samples including deformations to other phases. For
these samples, the average target registration error was reduced by about 20%. An improve-
ment is also expected for the Dice similarity coefficient when considering all motion phases.
Compared to the average tumour motion amplitude, which ranged from about 0.4 cm to 1.5 cm,
the target registration error was small but not insignificant. The largest contribution to the
registration error came from the SI direction. One reason is that it corresponds to the main
direction of motion. Another reason is that the spatial resolution was higher in the AP and LR
direction than in the SI direction for almost all patients (see Sec. 4.2.1).
The target registration error exhibited a much larger standard deviation (SD=60%) than the
Dice similarity coefficient (SD=3%). This can be explained by the fact that the target regis-
tration error of a single landmark strongly depends on the local CT contrast and the distance
to the nearest controlling contour, whereas the Dice similarity coefficient compares the volume
overlap of the liver contours which is not affected by errors of the deformation vector field in
the middle of the liver.
The comparison with former DIR validation studies [66, 68, 69] showed that Anaconda per-
formed well for the selected HCC patients. The target registration errors and Dice similarity
coefficients were very similar to and in some cases even better than previously reported values.
Only when comparing to lung studies, the quality was slightly worse. This was expected due
to the higher CT contrast in the case of lung which enables a better DIR quality.
The geometric errors induced by DIR can significantly impact 4DDD evaluations and depend
on the DIR method as recently shown for three liver cancer patients by Ribeiro et al. [152]. An
underestimation of dose inhomogeneities was reported for all six investigated DIR algorithms
by the study. The dosimetric error was smallest for a DIR method which included the liver con-
tour as controlling ROI (mean error of V95(CTV ): 0.1% to 2.0%). The magnitude of the error
decreased with the number of irradiation fields (one or three) and increased with the motion
amplitude (8mm to 21mm). For a single field and a DIR method which did not include any
controlling or focussing ROI, a mean error of up to 10.6% and an SD of 14.1% were observed.
The results cannot be transferred to the current work in the form of error bars due to differences
in the DIR method, the 4DDD computation and the number of fields. But they can help to
interpret the 4DDD outcome. In this study, treatment plans consisted of multiple fields redu-
cing the dosimetric uncertainties. Since the CTV served as controlling ROI, the registration
error is expected to be much smaller within the CTV area than in the rest of the liver. As a
consequence, the impact of deformation errors on the used interplay effect evaluation criteria,
namely the HI and V107/95 of the CTV, is rated comparatively low. Despite all measures,
the 4DDD evaluations must be treated with great caution since the exact extent of residual
uncertainties is not known for the given conditions.
4.4.2 Perturbation analysis of the nominal treatment plans
DS plans performed superior to 4D and 3D PBS plans in perturbation analyses. There are
several reasons why they provided the better CTV coverage in the different scenarios. One
decisive reason is that three fields were used instead of two. Further, the amount of dose
deposited proximal to the target is higher than for PBS. Last but not least, compensator
smearing was applied which leads to additional range margins. These characteristics make DS
plans more robust at the expense of OAR sparing.
4D PBS plans achieved comparatively good CTV coverage for inhomogeneous target regions
due to multi-field optimisation. For example, spots which were located directly behind a rib
from beam’s eye view received lower spot weights. In return, the amount of dose deposited by
the second field was increased for this region.
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4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
In 3D PBS plans, neither a third field nor multi-field optimisation were applied. Density
uncertainties were taken into account by adding uniform margins proximal and distal to the
target, which cannot adequately compensate for both, range changes in liver and lung tissue,
at the same time. As a consequence, it was not possible to create a robust 3D PBS plan for
CTV 9b which is directly adjacent to the lung. For all other cases, robustness against the
specified density perturbations, shifts of the isocentre and recomputations on the end-inhale
phase could be achieved for all three planning techniques. The dynamics of the beam delivery
were not considered in the robustness evaluation. Their impact on the dose distribution is
discussed in the next section.
4.4.3 Analysis of the 4D dynamically accumulated dose distribution
CTV coverage
On average, 4D robust optimised PBS plans exhibited slightly less dose distortions than non-
robustly optimised 3D PBS plans. However, interplay effects were still present and the observed
differences of HI and V107/95 between 4D and 3D PBS were not found to be significant. Due
to the small size of the patient collective, it was not possible to demonstrate whether the slight
improvement arose from statistical fluctuations of interplay effects or from an actual decrease of
motion effects due to the robust optimisation. One argument against a merely coincidental res-
ult is that an improvement was observed for almost all CTVs in inhomogeneous iCTV regions,
whereas 3D PBS plans performed better than 4D PBS plans for the two homogeneous target
regions (ID 4 and 6). The latter might be explained by the fact that the beam-specific PTV
margins in 3D PBS plans were chosen rather conservatively resulting in a larger volume covered
by the 95% isodose line than in robustly optimised 4D PBS plans for homogeneous regions (cat-
egory I). The larger safety margins are expected to reduce the magnitude of motion effects at
the edge of the CTV. Besides, a single field uniform dose approach increases the robustness
if no major density gradients are involved. In contrast, 4D PBS plans had an advantage over
3D PBS plans for homogeneity category II and III since the shift of high density gradients due
to motion, e.g. in the vicinity of ribs, was taken into account by the robust optimisation. The
hypothesis that the benefit of 4D robust optimisation depends on the homogeneity category
could not be tested for significance because of the small size of the subgroups and the unequal
distribution over them (see Fig. 4.1a).
The additional 4DD evaluations, which neglected the time structure of the beam delivery,
showed no over- or underdosage of the CTV for any PBS plan. The calculated HI values
were very similar to the static case for both, 4D and 3D PBS plans. Therefore, the over- and
underdosage and the dose inhomogeneities detected by 4DDD computations must have been
caused by interplay effects and not by other motion effects. As a consequence, also the dif-
ferences in the dose deterioration between 4D and 3D PBS plans are attributable to interplay
effects. The small, positive effect of 4D robust optimisation on interplay observed for homogen-
eity categories II and III could be due to the fact that 4D robust optimisation takes different
types of uncertainties into account. Even though 4D robust optimisation does not consider
the time structure of the beam delivery, the robustness against organ motion, setup shifts, and
range uncertainties might reduce the magnitude of interplay as a side effect. For example,
the consideration of motion-induced range changes may guide the optimiser toward a solution
with shallower 4D accumulated dose gradients which improves the 4DDD distribution. Besides,
multi-field optimisation was exploited by 4D PBS plans, whereas a uniform dose per field was
applied in non-robustly optimised 3D PBS plans following a conservative approach for CTV
coverage.
A proof of concept study recently published by Engwall et al. [153] investigated the inclusion
of uncertainties of the time structure in 4D robust optimisation. For simplicity reasons, only
variations in the respiratory pattern were considered in the 4D robust optimisation settings
but, in principle, uncertainties in the delivery time could be incorporated as well. For three
non-small cell lung cancer patients, Engwall et al. demonstrated an improvement in V95, V107
72
4.4 Discussion
and HI for the new optimisation approach compared to the standard 4D robust optimisation.
Even better results were achieved when 4D robust optimisation including respiratory motion
was combined with rescanning. The largest effect was observed for the patient with the highest
motion amplitude. The study was limited to evaluations of interplay effects and did not take
into account range and setup uncertainties. As a consequence, the number of optimisation
scenarios would be much higher for clinical treatment plans. The effect is comparable to an
increase of the safety margins in conventional treatment planning. In order to protect normal
tissue and realise acceptable computation times, the number of scenarios must be kept as low
as reasonable possible. For this purpose, motion mitigation techniques such as gating or ab-
dominal compression which decrease the motion amplitude could be combined with the new 4D
robust optimisation approach.
Looking at previous treatment planning studies on 4D robust optimisation, it can be seen that
the reported benefit strongly depends on the patient cohort (target location) and the treatment
technique used for the plan comparison, i.e. if a multi-field optimisation or single field uniform
dose approach is applied and if conventional margins or 3D robust optimisation are utilised for
the 3D PBS plan. In a study on non-small lung cancer (Dpresc=66GyRBE, 33 fractions), Liu et
al. showed a significant improvement of the target dose homogeneity (4D robust optimisation:
D5= 10.3GyRBE, 3D robust optimisation: D5= 17.7GyRBE; P=0.002) and target coverage (4D
robust optimisation: D95= 60.6GyRBE, 3D robust optimisation: D95= 55.2GyRBE; P=0.001)
using 4D robust optimisation [17]. The greater benefit is probably attributable to the larger
density variations in the thorax. The results are not directly comparable since Liu et al. used
3D robustly optimised PBS plans as a reference. Yu et al. compared 4D robustly optimised
IMPT plans with conventional IMPT plans for distal oesophageal cancer (Dpresc=50.4GyRBE,
28 fractions) [18]. They also observed a notable reduction of dose deviations arising from organ
motion (4D robust optimisation: D95 (iCTV )nominal −D95 (iCTV )4DDD=0.7GyRBE, conven-
tional margins: D95 (iCTV )nominal − D95 (iCTV )4DDD=1.4GyRBE; P=0.008) and proposed
to implement robust optimisation for IMPT in treatment planning.
In this study, PBS 4DDD distributions were additionally compared to DS, the previous stand-
ard for moving targets. DS plans are, contrary to PBS plans, not affected by motion interplay
effects due to the almost continuous, fast energy changes. In addition, their robustness against
organ motion is increased due to the use of three fields and compensator smearing as already
mentioned within the context of the perturbation analysis (Sec. 4.4.2). Looking at a single frac-
tion, DS plans clearly outperform 4D and 3D PBS plans with HI values similar to the static
case and no over- and underdosage at all. The HI is for DS even slightly better for 4DDD
analyses than for the static plan. This is due to the fact that small inhomogeneities in the
static plan are compensated by contributions of other 4DCT phases in the 4DDD evaluation.
4D and 3D PBS plans exhibit in contrast an average HI above 8% (4D and 3D PBS) and an
average V107/95 of about 6% (4D PBS) and 7% (3D PBS), respectively. However, it could be
demonstrated that these inhomogeneities were averaged out over the whole treatment course.
Local overdoses in single fractions were assumed to be non-critical as long as they were located
within the CTV. Worst case scenarios in which the minimum dose of a single fraction was as
low as 77% of Dpresc were not found to be correlated to poor V107/95 values. The underdosage
occurred rather locally (small cold spots) and thus did not necessarily compromise the coverage
of the entire target. Scenarios like that had a low likelihood, i.e. were single outliers among 60
simulations. On average, the minimum dose was above 90% for a single fraction. In stereotactic
body radiotherapy (SBRT), it is common to allow underdosage of the GTV and PTV up to a
certain degree even within the static plan. Examples for clinical goals from a liver SBRT plan
comparison are V90(GTV )> 98% and V70(PTV )> 98% [154]. In contrast to SBRT, the over-
and underdosage detected in this study is randomly introduced by motion interplay which is
why it averages out after some fractions. Therefore, both, PBS and DS, produce acceptable
4DDD distributions for the majority of investigated patients.
It has been shown by several studies that conventional fractionation schemes can mitigate inter-
play effects to a large extent [30, 98, 155]. However, the current trend in radiotherapy towards
hypofractionation reduces the averaging effect [156]. In addition, one may note that the bio-
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4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
logical effect of over- and underdosages in single fractions is not yet sufficiently well known.
Underdosage in some fractions possibly cannot be compensated by overdosage in other frac-
tions even if the fraction doses sum up exactly to the prescribed dose. This becomes an issue
for small CTVs with large motion amplitudes located in inhomogeneous tissue, such as CTV 9a
and 9b, for which interplay effects are particularly pronounced.
Since 4D robust optimisation alone cannot eliminate interplay effects in a single fraction, it
should be combined with other motion mitigation techniques, such as respiratory gating or
rescanning, for these indications. The difficulty is to decide a priori whether a patient can
be safely treated using solely 4D robust optimisation. Since the severity of interplay effects
depends on various parameters, such as CTV volume, motion amplitude, tissue heterogeneity,
the number of fields or field weighting, a very large patient cohort must be studied in order to
establish a correlation between the individual parameters and their impact on interplay effects.
So far, it is not possible to specify certain limits for each parameter beyond which supplement-
ary motion mitigation techniques become necessary and individual 4D analyses are required
for each patient. Prospective evaluations should be complemented by retrospective analyses as
the treatment conditions, e.g. the respiratory pattern or beam interruptions due to interlocks,
cannot be determined before irradiation.
The 3D scatter plot (Fig. 4.7) revealed low V107/95 values for large CTVs with small motion
amplitudes independent of the homogeneity category. It is not possible to conclude from the
available data whether the small magnitude of interplay effects is solely attributable to the low
motion amplitude or whether a large CTV volume is also associated with reduced interplay
effects. For instance, motion effects are expected to be more severe at the edge of the target
where steep dose gradients and tissue inhomogeneities appear. The impact of over- and under-
dosage due to effects at the CTV surface might therefore decrease with increasing volume.
ID 4 and 6 exhibited slightly less over- and underdosage for 3D than for 4D PBS plans. Both
cases belong to the homogeneity category I and their PTV margins were large compared to
their CTV volume. Therefore, the coverage of the 3D PBS plans was more conservative than
the coverage of the 4D PBS plans at the expense of OAR sparing.
A systematic investigation of the different variables on the basis of the available data was not
possible. This aspect has to be addressed in future studies as described in Section 6.4.
OAR sparing
The question which treatment technique, i.e. DS, 4D PBS or 3D PBS, performs best in sparing
OARs cannot be answered in general since it depends on the individual positions of OARs
relative to the target and gantry angles. But looking at the normal liver tissue and ribs, PBS
plans yielded lower OAR doses than DS, with 4D PBS being better than 3D PBS.
OARs proximal to the target from beam’s eye view, such as ribs, could be spared well with
4D PBS, whereas large parts of the OAR volume received more than 95% of the prescribed
target dose using DS or 3D PBS (see Tab. 4.1 and Fig. 4.3). A reason is that DS deposit
unwanted dose proximal to the target and that the third irradiation field causes a wider overlap
of the fields in the entrance region. 3D PBS plans led to higher OAR doses than 4D PBS plans
due to the single field uniform dose approach and uniform PTV margins which do not allow
for any flexibility of the optimiser to spare those structures. Therefore, 4D robust optimisation
could prevent side effects such as rib fractures or RILD for HCC patients.
OARs next to the tumour, such as the kidney or the heart, are expected to benefit from the
sharp lateral dose fall-off in DS. However, this advantage is often cancelled out by the third
irradiation field. On the one hand, the third field lowers the entrance dose of each field but
on the other hand more healthy tissue is exposed to irradiation, especially when the third field
angle lead to long path lengths through the body. The influence of the number of fields on the
plan comparison is discussed in more detail in Section 4.4.4.
It is possible to further improve the lateral dose fall-off of scanned beams, and thus the normal
tissue sparing capabilities of PBS, by mounting supplementary apertures on the nozzle like in
DS. This was shown for example by Yasui et al. [157], Moteabbed et al. [158] and Bäumer et
al. [159].
74
4.4 Discussion
The differences in the investigated dose volume histogram metrics were much larger when
compared between different patients than when compared between different techniques for one
patient due to the wide range of tumour volumes. While the average normal liver dose ranged
for example from about 2GyRBE (ID 5) to 26GyRBE (ID 7) and exhibited a standard deviation
of around 60% (DS: 8.20GyRBE, 4D PBS: 6.8GyRBE, 3D PBS: 7.0GyRBE), the maximum
detected difference between 4D PBS, 3D PBS and DS in the average dose for one patient was
less than 4GyRBE. Because of the large standard deviations for the patient collective, it was
not possible to demonstrate the significance of OAR exposure differences between 4D PBS and
3D PBS/ 4D PBS and DS using the t-test even though each patient showed better or at least
equal results for 4D PBS.
For small tumour volumes, the normal liver volume receiving less than 15GyRBE was similar
for all treatment techniques. But for large tumour volumes, such as patient ID 7, the additional
irradiation field in DS led to comparatively poorer results since the percentage irradiated liver
volume increased significantly. A notable difference in the irradiated normal liver volume was
observed for DS depending on whether the third field passed mainly through the liver (e.g.
patient ID 8a) or went partly through adjacent anatomical structures (e.g. patient ID 8b).
For two patients with large CTV volumes of almost 500 cm3 and 650 cm3, DS exceeded the
OAR dose constraints and reached unacceptable high probabilities to develop RILD. The risk
of RILD for the other tumours having less than 270 cm3 was zero. Hence, the size of the tumour
is an important criterion for the choice of the treatment technique and large CTV volumes might
not be safely treated with DS. The correlation between the size of a hepatocellular carcinoma
and the risk of RILD has been investigated for non-robustly optimised PBS proton plans and
intensity-modulated photon therapy plans by Toramatsu et al. [149]. The study reported much
lower risks of RILD for protons than for photons, particularly when the diameter of the tumour
was larger than 6.3 cm (average RILD risk: 94.5% for intensity-modulated photon therapy and
6.2% for PBS proton therapy). It is expected that the risk would even be lower applying
4D PBS proton therapy.
In this study, dose limits for close-by OARs, such as the stomach or bowel, were ignored in the
optimisation if the OAR was located adjacent to or within the iCTV in order to maintain the
target coverage. Otherwise, the interplay effect evaluation would be impacted. In clinic, the
PTV (3D PBS and DS) and the robustness settings (4D PBS), respectively, would have to be
compromised after some fractions to maintain vital OAR functions. Another solution could be
to place a surgical spacer in-between the liver and for example the gastrointestinal tract [160].
Reproducibility of the results
Average dose volume histogram values were better reproducible for the liver than for the CTV.
The percentage SEM was 0.0% for all liver dose volume histogram metrics for both plans,
whereas it was about 1.0% for HI (4D and 3D PBS) and 3.9%/ 5.3% for V107/95 (4D PBS/
3D PBS). This is due to the fact that the average normal liver dose, the normal liver volume
receiving at least 42GyRBE and the normal liver volume receiving less than 15GyRBE, are
less sensitive to changes of the dose distribution. For instance, the amount of normal liver
tissue exposed to 42GyRBE and more remains similar, even though the 42GyRBE isodose line
might slightly shift for different scenarios. Only a small portion of the normal liver volume
is exposed to high doses so that the average normal liver dose and V<15GyRBE do not show a
strong dependence on motion effects. In contrast, not only a certain fraction but the entire
CTV volume is affected by interplay effects. Nonetheless, it could be demonstrated that the
calculated mean values were representative for the respective treatment plan. The differences
between 4D and 3D PBS plans were significant even for V107/95 which exhibited the highest
SEM values. Thus, a number of 60 interplay scenarios per evaluation was found to be sufficient
for plan comparison purposes. With regard to the highly reproducible mean values for the
normal liver tissue, even less scenarios could be used.
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4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
Limitations of the treatment planning study
One of the limitations of the study is the small size of the patient cohort, which restricts the
validity of the outcome. At the time of the study, WPE did not treat any movable targets so
that 4DCT data sets had to be acquired from other clinics. It was not possible to gain more
suitable patient data since the 4DCTs must meet a number of requirements. For instance, the
tumour volume has to be visible on all respiratory phases (e.g. by use of contrast agents), the
length of the CT scan should be long enough to evaluate relevant OAR dose volume histogram
metrics and motion artefacts have to be low/ moderate. Furthermore, the patients must have
signed a declaration of consent.
A higher number of patients would also be beneficial with regard to statistical analyses. The
significance of differences was tested using a paired t-test which is subject to certain conditions.
For instance, the test assumes normality of the variable under investigation in the two sub-
groups. Due to the small sample size, it was not possible to demonstrate that the data follow
a normal distribution. Fortunately, the t-test is very robust toward data which are non-normal
distributed and an approximately symmetric distribution of the variable in the population is
sufficient to generate a more or less normal sample distribution. In case of a violation of the
assumption, the t-test is still valid if the sample sizes are equal and not too small (ideally
n1 = n2 > 30) [161]. Another assumption is that the two subgroups have the same variance.
However, if the sample sizes of the subgroups are equal, as it is the case here, the t-test is also
highly robust to unequal variances [162].
The availability of different HCC patient collectives would enable to assess the general validity
of the study by computing SEMs for 4D PBS, 3D PBS and DS.
As already discussed in Chapter 3, the Pencil Beam dose algorithm has some weak points in
comparison to the MC dose engine which might have affect the results. This issue was examined
for some test cases and is addressed in detail in Section 4.4.4.
Following the example of a previously published study on scanned proton treatments of
HCCs [149], the risk of RILD was calculated based on the LKB-NTCP model parameters
determined by Dawson et al. for patients treated with 3D conformal photon beams [134].
However, the use of biological models is prone to uncertainties. Even though the higher biolo-
gical effectiveness of protons compared to photons was considered in the calculations and dose
volume histograms were normalised to correct for differences in the fractionation scheme using
the LQ model, the results only represent estimates. Adequate follow-up data for the institution
specific patients would be required to assess the validity of a model for deviating conditions
(patient cohort, technique and fractionation scheme). Ideally, a NTCP model dedicated to the
respective patient population and treatment protocol should be created, but that was beyond
the scope of this work. Despite all uncertainties, the calculated NTCP values are well-suited
for a relative comparison of 4D PBS, 3D PBS and DS plans.
Due to the high number of interplay relevant parameters, not all influencing factors could be
studied within this work. For instance, a fixed respiratory cycle length was assumed. The
magnitude of interplay effects, however, may differ for other respiratory periods because of the
relative timing of dose application and organ motion. Further, another spot size might be more
beneficial regarding interplay effects and OAR sparing [98, 163].
The presented results are only valid for the machine characteristics described in Section 3.3.2.
Other institutes must determine their facility-specific beam delivery parameters or have to de-
velop their own beam time model when not using irradiation log files/ having access to the
scanning control system. Even then, treatment interruptions due to interlocks could prevent
’accurate’ predictions.
Furthermore, all 4DDD computations rely on the organ motion recorded by the 4DCT scan.
Any changes in the breathing pattern during treatment can potentially invalidate them. Sieben-
thal et al. reported for example liver drifts and deformations of more than 5mm on a time-scale
of tens of minutes after patient positioning [164].
Also the treatment conditions, e.g. the application of contrast agents, could influence the res-
ults.
76
4.4 Discussion
For the clinical implementation, this means that the knowledge gained from 4DDD planning
studies must be interpreted with great caution and one must bear in mind that individual 4DDD
evaluations for patients might suggest a false sense of security. Nevertheless, such studies are
crucial to test the suitability of motion mitigation techniques and to identify which types of
tumours and target regions benefit most.
4.4.4 Supplementary analyses
Monte Carlo
The assessment of the accuracy of the Pencil Beam dose algorithm for HCC patients was based
on the static plan comparisons with MC-recomputed plans. For patient 2, representative for
liver tumours in more or less homogeneous regions, only small dose differences were observed
even though range shifters had been applied. Therefore, and since the dose to the surrounding
healthy tissue was rather over- than underestimated by the PB plan, the Pencil Beam algorithm
was considered not to represent a safety risk for this patient and similar cases.
Patient 3, on the other hand, revealed comparatively large differences between PB and MC-
recomputed plans, mainly in regions behind lung tissue or the peritoneal cavity. The causes
were already explained previously (Sec. 2.4.5 and 3.2.3). Possible consequences of local over-
estimations of the target dose and local underestimations of OAR doses by the Pencil Beam
algorithm are reduced tumour control and increased normal tissue complications. Thus, in
clinic, the MC dose engine should be used for HCC patients with tumours in close proximity
to the lung.
The accuracy of interplay effect simulations was evaluated based on MC-optimised plans. The
PB plans underestimated the magnitude and standard deviation of interplay effects for both
investigated patients. Nonetheless, they enabled a good, qualitative assessment, especially in
view of the large variations among different scenarios (visualised by error bars in Fig. 4.5 and
4.6). The differences in the mean values of PB and MC-optimised plans were smaller than
(ID 2) or almost equal to (ID 3) the respective standard deviations and did not influence the
ranking of the plans.
One should bear in mind that the outcome of a single fraction can differ widely in terms of
target coverage and that the average value alone is not a good measure for it. Consequently,
a very precise determination of the average value is not required. What is needed instead is
a realistic estimate of magnitude and range to allow for 4DDD comparisons of different tech-
niques. The PB plans met this requirement.
If PB plans are used in clinic or treatment planning studies for superficial targets, the applied
range shifters should be as thin as possible (dependent on the minimum energy of the machine
and the available range shifters). Furthermore, the air gap should be reduced as much as the
setup allows. Thus, the errors in the dose distribution of PB plans due to the poor modelling
of secondary scattering can be decreased to a minimum.
Three-field PBS plans
The exposure of surrounding healthy tissue due to a third irradiation field in pencil beam scan-
ning depends on the tumour location and beam direction. Accordingly, the increase of the
dose to the normal liver tissue was different for patient 2 and 3. For some patients, a third
irradiation field might be beneficial since it reduces the entrance dose per beam. This is for
example the case for superficial targets where skin protection plays an important role. However,
if the third field passes close-by OARs, which could be spared using two fields (e.g. the bowel
or kidney), additional normal tissue complications can occur. Often, the path length of beams
in the patient increases with the number of fields since also suboptimal beam angles must be
chosen. Therefore, a larger volume of healthy tissue is exposed to ’low’ doses. Another issue
is that it might be necessary to irradiate through the patient couch when using three fields.
If that is the case, higher range uncertainties have to be considered in treatment planning by
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4 Evaluation of 4D robust optimisation for hepatocellular carcinoma patients
increasing the safety margins or the uncertainty in the robust optimisation settings.
With regard to organ motion, additional irradiation fields enhance the dose averaging effect
similar to rescanning. A considerable improvement in HI and V107/95 was observed for both
patients. But the averaging effect was too small to compete with DS plans. The normal
liver dose in different 4DDD scenarios was worse for three-field PBS plans than for two-field
PBS plans but still significantly better than for DS. Thus, the supplementary analysis demon-
strated that neither the higher homogeneity of the CTV nor the worse sparing of OARs of DS
plans compared to two-field PBS plans can be solely attributed to the difference in the number
of irradiation fields. For HCC patients with rather small to medium-sized tumours, which are
not located in close proximity to OARs, a third irradiation field might be a good option to
decrease interplay effects slightly. However, the third field should only be complementary to,
and should not replace, other motion mitigation techniques.
In general, gantry angles have to be chosen carefully to avoid an overlap of the entrance chan-
nels and the passage of OARs proximal to the target. Furthermore, the beams should not stop
directly in front of a critical structure due to the increased LET at the end of the particle
range. Depending on the tumour location, it is not always possible to find three different beam
directions that satisfy all these criteria. For such cases, PBS therapy which can also be realised
using two fields has a clear advantage over DS which usually needs a third irradiation field due
to the lower dose conformity.
4.4.5 Robust optimisation for motion management of hepatocellular carcinomas
4D robust optimisation incorporates motion, range uncertainties and setup uncertainties in the
optimisation process to determine optimal spot position and weights. Thus, it creates individual
’margins’ which are adapted to the tissue surrounding the HCC and minimises the irradiated
volume. Since HCCs are often diagnosed at a late stage (see Sec. 4.1), their size is usually
rather large and the probability that they are not only surrounded by liver tissue but border
on different anatomical structures, such as ribs, lung tissue, the right kidney or bowel, is high.
Consequently, HCC patients benefit particularly from customised ’margins’ which consider the
local density differences and achieve better sparing of normal tissue than the conventional PTV
concept. The superiority of 4D robust optimisation with regard to the dose to normal tissue was
shown for the investigated HCC patients in the second part of Section 4.3.3 on OAR sparing.
The actual goal of 4D robust optimisation, however, is to render PBS plans less sensitive to
uncertainties and motion. An increase of the robustness towards range and setup uncertainties
using 4D robust optimisation for HCC patients could be demonstrated based on a case where
the tumour was located next to the lung (Sec. 4.3.2). On average, a small improvement of
the target coverage in the presence of motion was detected for 4D robustly optimised plans.
But, unlike for studies on 4D robust optimisation for lung or oesophageal cancer, the difference
was not significant and it seemed that some HCC subgroups (homogeneity category II and III)
benefited more than others (Sec. 4.3.3).
Contrary to classic motion mitigation approaches such as gating or rescanning, 4D robust op-
timisation neither requires additional hardware nor software changes of the proton treatment
delivery system. As in many other facilities, rescanning and gating are not yet clinical avail-
able at WPE. Besides the technical requirements, the introduction of these techniques involves
thorough commissioning tests, i.e. additional manpower. Since 4D robust optimisation is an
integrated tool in the currently used TPS version, its implementation in treatment planning for
HCC patients is straightforward.
While gating, breath hold or rescanning reduce significantly the efficiency of proton therapy,
4D robust optimisation does not prolong the treatment or setup time. Thus, the workload for
the staff is less and more patients could be treated per day. Moreover, shorter treatment times
are beneficial for the patients who might suffer from pain and cannot remain in the treatment
position for a long time.
4D robust optimisation is neither related to any additional health risks, unlike anaesthesia, nor
78
4.4 Discussion
does it cause any inconvenience for the patients as it is the case for abdominal compression,
breath hold or spirometry, which is used at some facilities as gating signal.
On the downside, 4D robust optimisation is associated with an increased computation time.
Considering ten respiratory phases and the range and setup uncertainties specified above (res-
ulting in 210 optimisation scenarios), the optimisation usually takes about one hour for target
volumes smaller than 500 cm3 using the Pencil Beam dose algorithm. However, very large target
volumes, such as the CTV 7, represent an exception. Even though the resolution was tempor-
arily reduced to 4mm, the optimisation time was more than 30 hours for this CTV. This is not
suitable for clinical routine where usually several iterations are required to find the objectives
and constraints which lead to a reasonable treatment plan. Moreover, the application of the
MC engine would further prolong the computation time. In comparison, it took on average
only four minutes to optimise 3D PBS plans with the Pencil Beam dose algorithm.
RayStation does not yet offer a GPU-based dose engine or high-performance computing for
protons as it does for photons. The computing performance and memory consumption im-
proved in RayStation 7 compared to the TPS versions used in this study resulting in shorter
optimisation times and more interplay scenarios which can be computed in a single interplay
evaluation. A 4D robust optimisation including 210 optimisation scenarios can be performed
within 15 to 30 minutes (target volume<500 cm3). The optimisation time for the CTV 7 is
reduced to approximately 70 minutes.
In order to further decrease the optimisation time, it could be tested whether it is sufficient
to consider only the end-expiration and end-inspiration phase in the robust optimisation. This
would reduce the number of perturbation scenarios considered by the optimizer by a factor of
five. If gating is applied, the number of respiratory phases included in the 4D optimisation
settings is reduced depending on the size of the gating window.
The workflow of 4D treatment planning is most efficient when standard procedures have been
automated. For example, perturbation analyses and interplay effect evaluations of 4D robustly
optimised plans can be executed by scripts as done in the current work. But also preliminary
work steps such as contouring could be optimised, e.g. using atlas-based automatic segmenta-
tion. This was successfully tested within the scope of this thesis: The External and the body
contour delineated in only one respiratory phase of the HCC patients served to create a dedic-
ated atlas for the patient collective. Thus, the contours in all other phases could be generated
automatically.
In the HCC treatment planning study, it was assumed that the respiratory patterns during
the treatment course are identical to the one at the time of the 4DCT scan. However, for
real patients, changes in amplitude and breathing period might occur. Small variations of the
breathing period might be covered by the evaluation method since random start phases and en-
ergy layer switching times between 0.9 s and 2.5 s are sampled for each scenario (see Sec. 3.3.2).
But the analysis cannot cover uncertainties in the motion amplitude as it is based on a single
4DCT. Therefore, 4DCT scans should be performed on a weekly basis as recommended for
thoracic malignancies [15]. In order to assess whether the plan robustness is still sufficient or
replanning is needed, 4DDD computations based on the new 4DCT have to be conducted.
For large motion amplitudes, 4D robustly optimised PBS plans could not provide sufficient
target coverage. In such cases, 4D robust optimisation cannot replace conventional motion mit-
igation techniques and should be used as a supplementary method. Rescanning, breath hold,
gating or a combination of them would help to further reduce interplay effects for patients with
large motion. If the clinical goals cannot be met, e.g. because appropriate motion mitigation
techniques are not available at a centre, PBS therapy should not be offered and DS might be a
treatment option for the HCC patients concerned.
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5 Usage of computer generated 4DCTs in interplay stud-
ies - a proof of concept
This chapter presents a proof of concept study which investigates the application of computer
generated 4DCTs for systematic investigations of interplay effects in PBS. The project was
carried out in collaboration with the Institute of Medical Physics and Radiation Protection
of the TH Mittelhessen (Dr. Ulf Mäder/ Dr. Jörg Wulff). To minimise the effort involved,
interplay effects were studied for different tumour sizes while all other parameters such as
motion amplitude and tissue characteristics were kept constant. Thus, only a single virtual
patient had to be created. Spherical liver tumours with different diameter were delineated in one
respiratory phase of the 4DCT and mapped to the other phases using DIR. Even though it was
not necessary to generate modified 4DCT data sets for this specific test case, taken a simulated
4DCT instead of real patient image data was still an advantage. Since it was possible to assign
unique identification numbers to each structure, a large number of anatomical structures could
be easily contoured in different respiratory phases of the simulated 4DCT. These delineated
contours were required to improve the quality of the DIR on the basis of which the different
tumour contours were mapped to the other phases (see Sec. 5.2.1). For real patient data, it is
not possible to accurately map artificial contours if no controlling ROIs exist in close proximity
to them. Contrast agents and implanted markers are either missing or not at the right place to
indicate several different tumour positions required for such a study.
The magnitude of interplay effects for PBS plans was analysed dependent on the tumour size
using 4DDD computation.
In the event of a positive performance, different 4DCT series could be created in future studies
in which for example only the motion amplitude or the homogeneity of the liver tissue is altered.
5.1 4D XCAT phantom and CT simulation
There is an urgent need for realistic 4D phantoms in proton therapy to evaluate motion mitig-
ation techniques for PBS therapy of moving targets. An adequate physical, anthropomorphic
motion phantom which, firstly, provides similar physical properties as real tissues (regarding
proton stopping power, CT contrast and MRI contrast) and, secondly, mimics physiologic mo-
tion for different conditions seen in vivo is commercially not available. Due to the wide variety
of patient sizes and pathologies, the production of phantoms representing the entire spectrum
is anyhow not feasible. A good solution is therefore to use digital phantoms, i.e. realistic com-
puter simulations, for in silico studies.
Computerised phantoms represent a trade-off between realism and flexibility. A distinction is
made between voxelised and mathematical phantoms. Voxelised phantoms, which are usually
generated from MR or CT data sets, are more realistic but do not allow for exact ray tra-
cing due to their limited resolution. Mathematical phantoms, in contrast, are based on simple
equations and can be created with any resolution without interpolation errors. Variations in
anatomy or organ motion are easy to model but the reproduction of organ shapes is limited in
accuracy [165].
The 4D extended cardiac-torso (XCAT) phantom is a whole-body computer model of human
anatomy and physiology [166]. It represents a hybrid approach which combines the advantages
of mathematical and voxelised phantoms. Complex mathematical primitives were used to de-
scribe human anatomy based on 3D male and female image data sets provided by the National
Library of Medicine [167]. Thus, XCAT offers a high level of anatomical detail as well as flexible
organ shapes. The flexibility was mathematically realised by non-uniform rational b-spline sur-
faces [168]. An extension of the original XCAT phantom to four dimensions to simulate cardiac
and respiratory motion was achieved through the use of 4D cardiac- and respiratory-gated MR
and CT data. The 4D XCAT phantom is very well-suited for research purposes since it can be
used to create a realistic patient cohort consisting of males and females as well as children and
adults with varying anatomy and physiologic motion.
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5 Usage of computer generated 4DCTs in interplay studies - a proof of concept
Figure 5.1: Simulated CT data of a 4D extended cardiac-torso (XCAT) phantom at end-inhale (left)
and end-exhale phase (right).
CT images were created based on a discretisation of the mathematical phantom geometry as-
signing unique identifier to the voxels that compose an organ. Thus, they were neither impaired
by quantum noise nor any CT artefacts. This is a considerable advantage over real 4DCT pa-
tient data which often exhibit motion artefacts due to reconstruction errors in combination
with irregular breathing or artefacts due to implants. If the aim is to create more realistic CT
images, facility-specific image noise can be simulated by using the 4D XCAT phantom and an
x-ray CT projection algorithm which includes a model for quantum noise [165].
5.2 Study design
5.2.1 Simulated 4DCT data and deformable image registration
Figure 5.1 shows exemplarily two coronal views of the computer generated CT data for the end-
inhale and end-exhale simulation. In order to facilitate contouring of the different anatomical
structures in all respiratory phases two identical 4DCT data sets were created, one with realistic
CT numbers and one with artificial, unique identification numbers for each tissue so that the
intensity values of different structures did not overlap. Thus, it was possible to use a threshold-
based, automatic segmentation tool to contour easily a large number of structures in each
respiratory phase (see Fig. 5.2). In total, 48 OARs were created. The ROIs were copied to
the original 4DCT data set and served as controlling structures for the DIR. A high quality
of the DIR was essential since it had to be used to map artificial tumour volumes from the
planning CT to the other phases. Moreover, the quality of the DIR affects the accuracy of
4DDD computations.
The method was tested based on a ’leave one out’ analysis. To this end, a second series
of deformable registrations was created using the same controlling ROIs except for the gall
bladder. Subsequently, the contour of the gall bladder was mapped from the reference phase
to the other phases using the new registrations. The mapped and the original contour were
compared for each phase based on the Dice similarity coefficient (Eq. 4.2).
Five spherical liver tumours were created in the end-exhale phase with a radius of 1 cm, 2 cm,
3 cm, 4 cm and 5 cm, respectively, using the image segmentation tool of RayStation. All volumes
share a common central point, which was selected in such a way that it was surrounded by a
maximum amount of liver tissue in all directions. 5 cm was the largest possible radius for which
the tumour did not exceed the liver contour. The contours correspond to tumour volumes of
about 4 cm3 to 524 cm3. They were mapped to the other phases through DIR including all
OARs as controlling ROIs. The tumour motion amplitude defined as in Equation 4.1 was very
similar for all CTVs and ranged from 2.17 cm to 2.19 cm.
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5.2 Study design
Figure 5.2: Three-dimensional view of the different anatomical structures of the 4D extended cardiac-
torso (XCAT) phantom contoured in RayStation. The External, the body contour and muscle contours
were not displayed since they would obscure the view on the other ROIs. Small, detailed structures
are covered by the outer shapes of the organs and are therefore not visible.
5.2.2 Treatment planning
One PBS treatment plan was created for each CTV in the research version of RayStation 7.
Without loss of generality, 3D PBS plans were chosen for the feasibility study instead of 4D PBS
plans in order to keep the computation time low. As before, beam specific PTVs cover the
iCTV plus a 2mm setup margin and 2mm plus 3.5% range uncertainty in beam direction. The
isocentre of each beam was the centre of the iCTV. The prescription to the CTV was the same
as for the HCC treatment planning study (63GyRBE in 15 fractions). Two fields were applied
for each treatment plan using the same gantry and patient couch angles. For liver irradiations,
the patient positioning would be different than simulated. The patient has to raise his arms
above his head in order to provide greater freedom of choice between different beam angles.
In future studies, this aspect can be taken into account when creating the phantom. Here, a
material override with air was used for the right arm. The gantry angles were 20° (an angle
from above) and 110° (an angle from the right side), respectively, at a couch angle of 0° each
(patient position: head in, supine). Plans were optimised on a 2mm dose grid using the MC
dose engine and identical objectives/ constraints. For the large tumours extending almost to
the patient surface, range shifters had to be applied. The second smallest CTV (radius=2 cm)
required only a thin range shifter for one beam and the smallest CTV (radius= 1 cm) no range
shifter at all. The air gap was minimised by moving the snout (holding the range shifter) as
close to the patient’s surface as possible. Dependent on the tumour size and whether a range
shifter was present, the minimum energy ranged from 100MeV to 134MeV and the maximum
energy from 127MeV to 196MeV.
5.2.3 Evaluation methods
Each plan had to pass the CTV coverage test in the static case and the robustness evaluation
as explained in Section 4.2.4. The 4DDD evaluations were carried out in the same way as
described in the previous chapter (see Sec. 4.2.5). Since RayStation crashed during the 4DDD
computation for some of the MC-optimised plans, the final dose had to be recomputed with
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5 Usage of computer generated 4DCTs in interplay studies - a proof of concept
Table 5.1: Homogeneity index HI and percentage over- and underdosage V107/95 of the CTV in
dependence on the CTV size for 4D dynamically accumulated dose distributions of a single treatment
fraction: CTV 1 to CTV 5 correspond to radii from 1 cm to 5 cm.
CTV 1 CTV 2 CTV 3 CTV 4 CTV 5
HI (%) average 11.5 13.5 15.3 17.7 22.3
SD 3.0 2.9 2.2 1.9 2.4
V107/95 (%) average 24.5 22.4 22.3 26.8 39.9
SD 17.6 11.0 7.6 5.2 5.4
the Pencil Beam algorithm for all plans and the evaluations were repeated. Again, HI and
V107/95 served as evaluation criteria for interplay effects (Eq. 4.4 and 4.5). Each 4DDD plan
evaluation included 50 interplay scenarios. Besides the average value, the standard deviation
of HI and V107/95 was calculated for each plan to reveal interplay effect variations. In order to
test the reproducibility of the results the average value and the SEM (Eq. 4.3) of five repeated
evaluations were calculated for two CTVs (radius=1 cm and 5 cm).
5.3 Results
5.3.1 Evaluation of the deformable image registration
The Dice similarity coefficient was analysed for the gall bladder which has a very small volume
compared to the liver which was used for the test in the previous chapter. The average Dice
similarity coefficient of nine deformations for the gall bladder was 0.93 with a standard deviation
of 0.03. The highest coefficients were reached for the respiratory phases prior and subsequent
to the reference phase (0.98 and 0.97). The lowest value (0.89) was observed for the end-inhale
phase (0%) and the 10% phase.
5.3.2 CTV coverage and perturbation analysis of the nominal treatment plans
The static 3D PBS plans fulfilled the target coverage criterium (V95(CTV ) = 100%). They
showed no over- or underdosage and the HI values ranged from 1.4% (radius=1 cm) to 2.4%
(radius=5 cm).
Except for the smallest CTV, all treatment plans exhibited V95 (CTV ) values in-between 97.6%
and 100.0% for the tested perturbation scenarios. But even the CTV with a radius of 1 cm
reached in almost all perturbation scenarios values above 98.0%. There was only one case
in which V95 (CTV ) slightly remained under the percentage volume limit of 95% with 94.9%.
However, the minimum dose within the CTV was still 92.9% of the prescribed dose.
5.3.3 Analysis of the 4D dynamically accumulated dose distribution
Two 4DDD distributions are shown as examples for a small and a large CTV in Figure 5.3.
Table 5.1 summarises the results of the interplay effect evaluation for all investigated CTV radii
(1 cm to 5 cm). The HI rose with increasing CTV size from 11.5%±3.0% (average value ± SD)
to 22.3%±2.4%, whereas V107/95 did not follow a clear trend. The average value of V107/95 was
maximal for the largest CTV with 39.9%. The smallest value was observed for a radius of 3 cm
(V107/95=22.3%). V107/95 exhibited large SDs compared to the HI ranging from a percentage
volume of 5.2% to 17.6%.
Reproducibility of the results
Despite large fluctuations of HI and V107/95 among different interplay scenarios of a treatment
plan, the average value was reasonably well reproducible when considering 50 interplay scen-
arios. For the largest CTV (radius=5 cm), the SEM was 0.3% and 0.2% for HI and V107/95,
respectively (average HI= 22.5%, average V107/95=39.6%). The same reproducibility test for
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5.4 Discussion
liver
CTV
(a) CTV 1 (radius=1 cm)
liver
CTV
(b) CTV 5 (radius=5 cm)
RBE% of 63 Gy
110
107
95
90
80
60
40
20
0
Figure 5.3: 4D dynamically accumulated dose distribution (overlayed as colour wash) of a random
interplay scenario for the smallest and the largest CTV (transversal view): The beam-specific PTV
margins are coloured dark blue (gantry angle= 20°) and dark red (gantry angle= 110°).
the smallest CTV yielded an SEM of 0.3% for HI and an SEM of 1.6% for V107/95 (average
HI= 12.0%, average V107/95=25.6%).
5.3.4 Feasibility of interplay studies using simulated 4DCT data
The simulated CT data could be imported into RayStation without any difficulties after ad-
justing the header of the Digital Imaging and Communications in Medicine (DICOM) files to
that of a clinical 4DCT. RayStation tools such as automatic image segmentation could be ap-
plied and it was possible to perform deformable image registrations as well as treatment plan
optimisations with the Pencil Beam and the MC dose engine. The execution of scripts for the
robustness or interplay effect evaluation was successful. The event that the application crashes
when performing interplay evaluations of MC-optimised plans was also observed for real patient
images and is not attributable to the simulated CT data.
5.4 Discussion
5.4.1 Evaluation of the deformable image registration
The simulated 4DCT did not provide any contrast within the defined anatomical structures
since one identification number was assigned to all voxels of each object. It was not possible to
identify landmarks which could serve to calculate the target registration error.
The Dice similarity coefficient test was based on the gall bladder. Despite the small size of the
gall bladder compared to the liver which was used as test ROI in Chapter 4, the average Dice
similarity coefficient over all phases was 0.93 indicating a decent quality of the DIR. Nonetheless,
there is still potential for improvement. For example, it would be helpful to incorporate a grid
of small markers in the XCAT phantom which can be seen in the different respiratory phases of
the simulated 4DCT. Such markers could be used as controlling POIs to further improve the
quality of the deformation vector field, especially within large structures. Furthermore, a few
markers which do not serve as controlling POIs could be used to assess the target registration
error for different regions. One possible way to simulate CT markers are manual overrides of
individual voxels. Alternatively, a tumour could be modelled by the 4D XCAT software and
transformed in all respiratory phases.
In this approach, the same image values were assigned to the liver tissue and hepatic veins. If
more contrast is needed within the liver, different image values could be used even though such
a contrast might not be seen in real CT images.
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5 Usage of computer generated 4DCTs in interplay studies - a proof of concept
5.4.2 Analysis of the 4D dynamically accumulated dose distribution
Contrary to expectations based on the HCC treatment planning study (Chap. 4, Fig. 4.7), a
large target volume did not reduce the relative amount of interplay effects. The assumption
that severe interplay effects occur mainly at the edge of the target volume, where steep dose
gradients exist, and less commonly in the middle of a large irradiation volume could not be
confirmed. Quite the opposite, the highest HI and V107/95 values were observed for the largest
CTV and the corresponding 4DDD distributions revealed that interplay also causes significant
underdosage in central regions (Tab. 5.1 and Fig. 5.3).
The increase of the HI with the size of the CTV is probably related to the number of spots
and the treatment time which increase the likelihood that spots are superimposed or drift apart
due to interplay. For the five investigated CTVs, the treatment time increased approximately
linearly with the volume from about 38 s to 116 s. The exact treatment time depends on the
energy layer switching.
Another aspect which affects the amount of interplay are position-dependent motion amplitudes.
Indeed, the average motion amplitude was almost equal for all CTV sizes but the span width
between minimum and maximum amplitude differed. For the smallest CTV, for example, the
motion amplitude ranged from 2.1 cm to 2.2 cm, whereas for the largest CTV, it ranged from
1.7 cm to 2.4 cm. An inhomogeneous deformation vector field enhances interplay effects.
In case of V107/95, there is no clear correlation between the average value and the size of the
CTV. In contrast to HI, V107/95 does not consider small interplay effects leading to less than
7% ’overdosage’ and 5% ’underdosage’, respectively. Further analyses are required to find out
whether a correlation exists.
For the largest CTV, tissue inhomogeneities contributed to the increase of HI and V107/95 since
the beam specific PTVs encompassed ribs (see Fig. 5.3b).
The standard deviation of V107/95 was very high, especially for small CTV volumes. This result
shows that the severity of interplay effects can vary considerably for a given CTV and treat-
ment plan due to uncertainties of the time structure. As discussed in detail in Section 4.4.3,
supplementary motion mitigation techniques would be necessary to safely treat such patients
with PBS.
The proof of concept study indicates that individual variations in anatomy and physiologic
motion demand for patient-specific interplay effect evaluations and that a simple parametrisa-
tion could be critical. It would be interesting to analyse the impact of the tumour size in
more detail, for example for different CTV positions within the liver (only possible for small
to medium-sized CTVs) and for different anatomies. The complexity of the different influences
and their interference will probably prohibit a division into treatment subgroups solely based
on the CTV size, motion amplitude and tissue homogeneity. This has to be confirmed by fu-
ture 4D XCAT phantom studies focussing also on the dependence on motion amplitude and
tissue homogeneity. The studies should be based on a larger database and include 4D robust
optimisation.
5.4.3 Feasibility of interplay studies using simulated 4DCT data
All workflow steps from data import to interplay simulations were successfully completed for
the computer generated 4DCT. Thus, it is possible to conduct also more complex 4D XCAT
phantom studies requiring several 4DCTs with modified motion amplitudes or density distri-
butions. In future studies, it should be ensured that the phantom is positioned according to
the tumour site to avoid material overrides, e.g. the arms have to be raised above the head for
liver irradiations. Further, simulated CT markers would improve the quality of the DIR and
therefore the accuracy of the 4DDD computation.
Although this feasibility study was kept deliberately simple by using a single virtual patient
with different targets, the approach allows to simulate a wide range of patient anatomies and
physiologic motion.
Using the 4D XCAT phantom, 4D studies can be performed with perfect contouring, minimal
DIR uncertainties and realistic image quality without the influence of CT artefacts.
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6 Summary and outlook on future research
6.1 Summary - Implementation of 4D dynamic dose accumulation in
treatment planning
A 4D dose calculation routine dedicated to the assessment of interplay effects in scanned proton
beam therapy was developed for clinical use at WPE based on a rudimental script provided
by RaySearch (E. Engwall, June 2015). Interplay effect modelling relies on the knowledge of
the beam delivery sequence and the time structure of organ motion. They can be determined
on the basis of irradiation log files (retrospective evaluation), the algorithms of the scanning
control systems (subject to access rights) or an empirical beam delivery time model and 4DCT
data sets acquired prior to the treatment. The gained information is used to assign the delivery
of a proton spot to a respiratory phase/ CT image. Using deformable image registration, the
accumulated dose on each phase is mapped to the reference phase (planning CT). The sum of
all deformed doses yields the 4D dynamically accumulated dose distribution.
A two-dimensional ionisation chamber array and a 4D phantom made up of different tissue
surrogates and a dynamic platform served for the experimental validation of the routine. Res-
piratory motion was simulated by a sinusoidal motion with an amplitude of 5mm and a time
period of 10 s (first trial) and 5 s (second trial), respectively. The measured dose planes were
compared to the corresponding dose distributions simulated by the routine using irradiation log
files. Resulting gamma pass rates exceeded the 95% level demanded in patient quality assur-
ance tests and were comparable to static references, with the exception for some measurements
at a time period of 5 s. As discussed in Section 3.2.3, the worse gamma pass rates for these
measurements are most probably attributable to the design of the study and not to shortcom-
ings of the routine. For instance, the measurement was not synchronised with the irradiation
and the exact time offset of the start phase was not considered in the calculation. Nonetheless,
gamma pass rates higher than 88% could be reached for fast detector movements. A better
agreement is expected when using adequate equipment such as 3D stereo camera units to track
the phantom’s motion.
The sensitivity of the routine to its input parameters (start phase and motion period) was con-
firmed. A change of the motion period by more than 0.4 s caused a degradation of the gamma
pass rate in the double-digit range. Introducing a phase shift led to a reduction of the gamma
pass rate of up to 20%. The uncertainties in the determination of the input parameters were
much smaller.
Time resolved 4D dynamic dose calculations reproduced measurements in movie mode well on a
qualitative level for a sampling time of 2 s. It was possible to model changes in the dose delivery
with time (arising from differences in the irradiation start phase and the energy layer switching
times) for repeated irradiations. However, good gamma pass rates were not observed for all
time intervals. This might be explained by the fact that proton spots were assigned mistakenly
to the previous or subsequent time interval because of uncertainties in the timing of the pencil
beam and the phantom motion. Further reasons are stated in Section 3.2.3.
An empirical beam delivery time model was developed to allow for prospective treatment plan-
ning studies. To this end, the spot delivery time, the scanning speed and the energy layer
switching time of the machine were determined for typical clinical spot doses, spot distances
and beam energies. The spot delivery time as a function of the spot dose could be modelled
by a rational function. The scan time as a function of the spot distance was approximated
by step functions for the x and y direction. The energy layer switching time did not show a
correlation with the beam energy and varied strongly. Therefore, random values are generated
from a normal distribution based on the measured average value and standard deviation. In
addition, an upper and lower limit was introduced for the energy layer switching time. Due to
the fluctuations of the energy layer switching time, a certain number of simulations is required
to get a realistic estimate of the range of interplay effects for a patient.
The beam delivery time model was validated by comparing actual delivery times extracted
from log files with times calculated by the routine. The observed differences were on average
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6 Summary and outlook on future research
0.03 s per energy layer and 1.2% per field, assuming identical energy layer switching times. The
impact of these errors on the dose distribution was negligible and the gamma pass rate was
100%.
Tests using simplified versions of the beam time model showed that an accurate modelling of the
beam dynamics as in the current work is a prerequisite for prospective analyses of the impact
of interplay effects. The assumption of an instant dose delivery per energy layer, for example,
reduced the gamma pass rate by 10%.
6.2 Summary - Evaluation of 4D robust optimisation for HCC pa-
tients
The capability of 4D robust optimisation to improve the 4D dynamically accumulated dose
distribution was investigated for hepatocellular carcinoma patients which generally have a poor
prognosis and would benefit from an effective, local treatment. The study included eleven target
volumes with motion amplitudes ranging from 0.4 cm to 1.5 cm. A median dose of 63GyRBE
was prescribed to the clinical target volume in 15 fractions. Conventional PBS plans based on
beam-specific planning target volumes and DS plans served for comparison purposes regarding
target coverage and organ at risk sparing. The number of irradiation fields differed for PBS and
DS plans since DS plans required three instead of two fields to achieve sufficient dose conformity.
Since RayStation was not supporting Monte Carlo calculations for DS at the time of the PhD
project, optimisations were performed using the implemented Pencil Beam dose algorithm.
The evaluation of PBS plans was carried out with the developed 4D dynamic dose calculation
routine, whereas for DS a uniform dose distribution over all motion phases was assumed due
to the almost continuous energy changes. The possible outcome of a single treatment fraction
in PBS was analysed based on 60 simulations per treatment plan with varying energy layer
switching times and start phases. For the evaluation of the whole treatment course, the sum of
15 single fractions was modelled five times (75 simulations in total).
Looking at a single fraction, 4D robust optimisation did not improve the homogeneity index
and the percentage over- and underdosage significantly compared to conventional PBS plans
and the results remained far behind those of DS plans. However, for 15 PBS fractions, the
over- and underdosage averaged out and the homogeneity index almost approached the static
homogeneity index values. The number of patients was too small to draw general conclusions
on the potential benefit of 4D robust optimisation for different subgroups (e.g. for different
tumour sizes or tissue homogeneity degrees).
An advantage of 4D robust optimisation was demonstrated in terms of normal tissue sparing.
The average normal liver dose was 5.7% lower than for conventional PBS plans and 15.9% lower
than for DS plans. For large tumours, 4D robust optimisation could considerably reduce the
risk to develop radiation-induced liver disease. Moreover, the probability of rib fractures was
lowest for 4D robustly optimised plans.
The influence of the dose engine and the different number of irradiation fields for PBS and DS
plans was exemplarily examined for two plans. The Pencil Beam dose algorithm underestimated
the average magnitude and standard deviation of interplay effects compared to the Monte Carlo
dose engine and yielded lower dose values for the normal liver tissue. The differences of the
mean values, however, were smaller than or almost equal to the standard deviations for the
homogeneity index and the percentage over- and underdosage. Thus, the Pencil Beam dose
engine provided a good qualitative estimation and enables comparisons of different treatment
plans.
The application of a third irradiation field in PBS, using the same beam directions as in DS,
increased the robustness against motion as expected but the averaging effect was still too small
to achieve similar results as corresponding DS plans. The dose to the normal liver tissue
remained below that for DS plans although a deterioration was detected compared to the two-
field PBS plans. These cases show that the better target coverage and the worse organ at risk
sparing of DS plans revealed by the hepatocellular carcinoma study are mainly attributable to
the delivery technique and only to a small extent to the difference in the number of irradiation
fields. In some clinical cases, a third irradiation field might lead to an unacceptable high
exposure of organs at risk so that two-field PBS plans represent the only treatment option.
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6.3 Summary - Usage of computer generated 4DCTs in interplay studies
6.3 Summary - Usage of computer generated 4DCTs in interplay
studies
The applicability of computer generated 4DCTs for systematic interplay effect analyses in PBS
was tested for the 4D XCAT phantom, a whole-body computer model of human anatomy and
physiology. The feasibility study investigated the dependence of interplay effects on the target
size for one patient with different clinical target volumes. A generated 4D XCAT chest CT was
imported to RayStation 7. In addition to a set with typical clinical CT-numbers for treatment
planning, a copy with image-values representing organ IDs was imported. The segmentation
tools of RayStation thereby allowed to perfectly contour 48 anatomical structures in all phases
of the 4D CT copy and map them to the original 4D CT. The structures subsequently guided
the deformable image registration. Five spherical liver tumours with radii R of 1 cm to 5 cm
were manually delineated as clinical target volumes in the end-exhale phase and mapped to
all other phases by deformable image registration. The prescription was the same as for the
hepatocellular carcinoma treatment planning study. Conventional PBS plans were used for the
proof of concept study instead of 4D robustly optimised PBS plans to save computation time.
For comparison purposes, identical gantry and couch angles as well as optimisation objectives
and constraints were chosen for all targets. 50 interplay scenarios per treatment plan were
evaluated based on the Pencil Beam dose algorithm implemented in RaySearch.
All targets exhibited an average tumour motion amplitude of 2.2 cm. The homogeneity index
increased with increasing clinical target volume from 11.5%±3.0% (average value ± SD) for
R=1 cm to 22.3%±2.4% for R=5 cm. This trend might be a result of the growing probab-
ility for interplay effects with an increase in the number of spots and the irradiation time.
However, the percentage over- and underdosage did not follow the trend. The maximum
was detected for R=5 cm (V107/95=39.9%±5.4%), but the minimum was observed for R=3 cm
(V107/95=22.3%±7.6%). The results demonstrate the complexity of the manifestation of inter-
play effects and indicate that it might not be possible to determine the interplay effect level
based on parameters like the target size and the motion amplitude. Future investigations are
necessary to confirm this hypothesis and will show whether individual, time consuming inter-
play effect evaluations are still required for each patient. The application of computer generated
4D CTs can facilitate these studies and furthermore allows investigation of motion mitigation
strategies in a systematic approach.
The proof of concept study showed that simulated CT data of a 4D XCAT phantom provide
realistic image quality without CT artefacts, enable perfect contouring and can minimise de-
formable image registration uncertainties in 4D studies.
6.4 Outlook on future research
The study on 4D robust optimisation has shown that local cold and hot spots observed in single
treatment fractions due to interplay effects were averaged out during the treatment course. The
biological effect on tumour control and normal tissue complications, however, still needs to be
investigated. For this purpose, future studies should consider biological tumour control prob-
ability models for the target and normal tissue complication probability models for all relevant
organs at risk in the interplay effect evaluation. A tumour control probability model and two
normal tissue complication probability models are provided in RayStation 7 [169]. The tu-
mour control probability model and the first normal tissue complication probability model are
based on cell survival curves and Poisson statistics, whereas the Lyman-Kutcher-Burman model
presented in Section 4.2.6 forms the basis for the second normal tissue complication probability
model. For protons, the tumour control probability and the normal tissue complication probab-
ility are functions of the relative biological effectiveness (RBE)-weighted dose. The underlying
biological parameters were taken from published clinical and pre-clinical studies. They are only
valid for the endpoint and tissue for which they have been determined and it might become
necessary to use data from more recent studies. An aspect which should be addressed in future
research is whether a minimum dose exists for a single fraction to ensure eradication of tumour
cells. If this is the case, the prescribed fraction dose could be adjusted so that typical under-
dosage resulting from interplay effects does not lead to an violation of the determined limit.
89
6 Summary and outlook on future research
Another issue that needs to be explored is the effect of irregular respiration. The respiratory
pattern of a patient during treatment might be different from that at the time the 4DCT scan
was acquired. Changes can occur between treatment fractions or even within a fraction for
example due to normal fluctuations, acute breathing problems, coughing, anxiety or stress. A
variation in amplitude and/or the time period will affect the interplay pattern. The extent
could be studied based on the 4D XCAT phantom. To this end, virtual patients with different
anatomies should be evaluated. For each motion amplitude, another 4DCT must be created,
while the respiratory period can be modified in the user interface of the interplay effect routine.
For the study of irregular respiratory cycles within a fraction, minor modifications of the routine
are required. For example, a sequence of different cycle lengths could be passed instead of a
fixed value and each respiratory cycle could be referred to a specific 4DCT that determines the
organ motion and is used to calculate the respective evaluation dose.
In the near future, first hepatocellular carcinoma patients will be treated with DS at WPE.
Weekly 4DCTs of these patients could provide valuable information on realistic variations in
tumour motion. In addition, irradiation pauses due to interlocks of the machine can be included
in the study.
As discussed in the previous chapter, the usage of computer generated 4DCTs will enable sys-
tematic investigations of interplay effects. The influence of the motion amplitude, the location
of the tumour, the tumour size or the homogeneity of the surrounding tissue can be assessed
with the 4D XCAT phantom by altering only a single parameter and keeping the other in-
fluencing factors constant. The outcome of such studies will show whether the magnitude of
interplay effects can be estimated based on the knowledge of these parameters or whether the
optimal treatment option for a patient still has to be determined based on individual interplay
effect evaluations.
Future treatment planning system versions and improved hardware might allow to include more
scenarios in the 4D robust optimisation so that uncertainties of the time structure can be con-
sidered under realistic clinical settings.
Possibilities to decrease the computation time of the routine are not to select the dose volume
histogram plot option and to reduce the number of interplay scenarios at the expense of accur-
acy. If the focus of a study is for example on the exposure of organs at risk, a lower number
of interplay scenarios might be sufficient since standard deviations of dose volume histogram
parameters were much lower for organs at risk than for the target.
90
7 Conclusion
Within the scope of this dissertation, a customised routine simulating interplay effects in pen-
cil beam scanning proton therapy was successfully implemented in treatment planning. The
routine enables retrospective four-dimensional dose analyses using irradiation log files and, ow-
ing to a specially developed beam delivery time model, also prospective evaluations without the
need for beam-time. In daily clinical practice, the tool can extend the patient-specific quality
assurance into the temporal domain and may serve to assess the treatment plan robustness
against intra-fraction motion as well as to reconstruct the 4D dose distribution after a treat-
ment fraction. Thus, adaptations of a treatment plan can be made during the treatment course
if the actually delivered dose deviates substantially from the planned dose distribution.
The suitability of the routine for clinical use was thoroughly investigated in an end-to-end test.
Dynamic measurements with a two-dimensional ionisation chamber array and the correspond-
ing irradiation log files demonstrated the validity of the 4D calculations and the beam delivery
time model. It was shown that an inaccurate modelling of the beam sequence, e.g. assum-
ing constant values for the delivery time, scanning speed and energy layer switching time, can
cause considerable deviations between simulation and measurement. Therefore, 4D dynamic
dose calculation tools should not be applied for clinical use in a proton therapy facility without
making adequate adjustments to the respective beam delivery system and quality assurance
tests. Fluctuations of the beam delivery parameters, such as the energy layer switching time,
and different phase shifts between patient motion and start of the field application have to
be considered in simulations in order to obtain a realistic estimate of the extent of possible
interplay effects.
A commercial 4D robust optimisation algorithm was evaluated for the use in scanned pro-
ton therapy of hepatocellular carcinomas based on the developed 4D dynamic dose calculation
routine. For the investigated hepatocellular carcinoma patients, 4D robust optimisation did
not significantly improve the dose homogeneity of the clinical target volume in the presence of
organ motion compared to the conventional planning target volume concept, but the same level
of robustness was achieved for lower organ at risk doses. Both, conventional and 4D robustly
optimised PBS plans, exhibited motion-induced over- and underdosage for large tumour motion
amplitudes in a single fraction. Therefore, it is advisable to make use of supplementary motion
mitigation techniques for strongly moving tumours.
In contrast to PBS, DS did not cause any over- or underdosage and yielded homogeneous dose
distributions comparable to the static case within the clinical target volume. Although DS is
the method of choice in terms of target coverage, it is often not a clinical option, particularly
for large clinical target volumes, because of the less conformal dose distribution which causes
organ at risk dose limits to be exceeded. In addition, most of the recently built particle therapy
centres are not equipped with DS technique. Considering that 4D robustly optimised PBS plans
yielded (1) homogeneous 4D dynamically accumulated dose distributions looking at the sum
dose of all fractions, (2) on average a minimum dose above 90% within a single fraction and (3)
the lowest organ at risk doses compared to DS and conventional PBS plans, they represent a
good alternative to DS for many hepatocellular carcinoma patients.
Apart from the increased computation time, 4D robust optimisation offers nothing but advant-
ages compared to conventional PBS treatment planning so that it could become a standard in
future treatments of moving targets. Since it does not prolong the setup or treatment time, it
can be combined with commonly used motion mitigation techniques, such as gating or rescan-
ning, without exceeding a tolerable time limit for the patient or further decreasing the patient
throughput. Moreover, no additional hardware is required.
The size of the investigated patient cohort was too small to statistically analyse different pa-
tient subgroups and the benefit of 4D robust optimisation could be different for patients treated
under others conditions, e.g. without abdominal compression or lipiodol contrast. This needs
to be further investigated in a larger patient cohort. Improvements in computing power and
software could facilitate such large-scale studies in the next few years. Further, they might
allow to increase the number of optimisation scenarios which is important in view of recent 4D
robust optimisation approaches including uncertainties of time structures.
91
7 Conclusion
In a proof of concept study, the suitability of computer generated 4DCTs for interplay effect
evaluations based on 4D XCAT phantoms was confirmed. The generated CT images were
artefact-free and enabled perfect contouring due to unique organ IDs. By including a large
number of controlling structures, deformable image registration uncertainties could be reduced.
The usage of computer generated 4DCTs will allow to model a broad spectrum of clinical cases
and systematically investigate different influencing factors in upcoming research projects.
The feasibility study exemplarily examined the magnitude of interplay effects as a function
of the target size based on the homogeneity index and the percentage over- and underdosage.
While the homogeneity index increased with growing target volume, the percentage over- and
underdosage did not reproduce this trend. It could be a first indication that the categorisation
of patients according to tumour motion, size or tissue homogeneity into different treatment
groups might not be possible. Due to the high complexity, the developed 4D dose calculation
routine will most likely still be needed for individual patient evaluations in the future.
92
A Appendix
A.1 Scripting in RayStation
Within the scope of this thesis, several scripts have been written in Python programming
language to facilitate extensive calculations in RayStation, e.g. 4DD and 4DDD calculations.
In the following, the plan robustness evaluation script serves as an example for a developed
program code since it is shorter and less complex. In addition to the Python file (see A.1.1),
an Extensible Application Markup Language (XAML) file (see A.1.2) has been created to
provide a graphical user interface (GUI). XAML is a user interface markup language developed
by Microsoft to define visible user interface elements, bind data to them and create events.
Figure A.1 shows the GUI of the plan robustness evaluation script. The routine (see A.1.1)
calculates the perturbed dose distributions for all possible permutations of the specified/selected
range uncertainty, setup error and respiratory phases (the planning phase is by default included).
However, the same setup error is used for the x, y and z direction (e.g. dx=dy=dz=+2mm and
dx=dy=dz=-2mm) to keep the calculation time and the number of scenarios reasonably low.
The calculated evaluation doses are stored in RayStation. Additionally, the CTV coverage, in
form of V95, the average dose of the CTV, the minimum dose of the CTV, the dose maximum
of the CTV, the dose maximum of the patient’s body and the dose maximum of the selected
organs at risk are displayed by the console.
Robustness Evalua�on
Select beam set:
Range uncertainty (%):
Setup error (mm):
Select CTV:
Select Body:
Select OAR:
Select CT phases:
Specify robustness evalua�on parameters
CT1 0%
CT3 20%
CT5 40%
CT7 60%
CT9 80%
CT2 10%
CT4 30%
CT6 50%
CT8 70%
CT10 90%
Deselect allSelect all
Start evalua�on
5
2
CTV
BODY
Normal liver
4D robust
Figure A.1: Graphical user interface of the plan robustness evaluation script including TextBoxes,
ComboBoxes, CheckBoxes and event buttons which allow the user to specify parameters, choose items
from a predefined selection, select or deselect all items and start the evaluation.
93
A Appendix
A.1.1 Python file
Comment lines begin with a hashtag and are displayed in green. Numbers are coloured in red,
strings in grey, keywords in blue, triple-quotes in orange and the name of a function in pink.
The font style of class names is bold.
94
A.1 Scripting in RayStation
95
A Appendix
96
A.1 Scripting in RayStation
97
A Appendix
A.1.2 XAML file
In the depicted XAML file, tags are coloured in blue, attributes in red and strings in purple.
98
A.1 Scripting in RayStation
99

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Acknowledgment
At this point, I would like to express my deep gratitude to the people and institutions who have
supported and helped me throughout my PhD project. The last years at the West German
Proton Therapy Centre Essen (WPE) have been an intense period for me full of new experi-
ences and insights, not only on a scientific and professional level but also on a personal level.
This work would not have been possible without the support of various people from different
disciplines, such as medical physicists, clinicians, technicians and specialists from industry.
I would first like to thank Prof. Dr. Bernhard Spaan for being my first referee and providing
an external and independent view on the project. His questions, comments and advices have
always been constructive and encouraging. In addition, I would like to thank Prof. Dr. Kevin
Kröninger for agreeing to be my second referee on such a short notice. My special thanks go to
my supervisor at WPE, Dr. Christian Bäumer. He granted me maximum freedom in the design
of the project and the door to his office was always open whenever I had questions regarding
my research or academic writing. Furthermore, I am grateful for his critical reading of papers,
conference contributions and the first draft of my doctoral thesis. I would also like to thank
Xavier Vermeren, chief physicist at WPE, for the opportunity to pursue my research at WPE
and to present the results at various international conferences.
My grateful thanks are extended to the whole physics group for their support and the enjoyable
working atmosphere. I would particularly like to single out Dr. Jörg Wulff. His valuable and
constructive feedback after reviewing papers and the doctoral thesis, respectively, has been an
enormous help. Without him, the collaboration with the Institute of Medical Physics and Ra-
diation Protection of the TH Mittelhessen would not have been established. I am also grateful
to Dr. Jamil Lambert, a former colleague at WPE, for sharing his experiences in the field of
moving targets. Further, I wish to acknowledge the help provided by Sandija Plaude from the
physicist’s side and from Dr. Dirk Geismar and Dr. Dalia Ahmad Khalil from the physician’s
side in reviewing treatment plans and contours. There was also great support from Dr. Danny
Jazmati who reviewed the medical part of the dissertation on hepatocellular carcinomas. Special
thanks go to Ajvar Kern, Nico Verbeek, Isabel Vogt, Sabrina Smyczek, Samantha Kauer and
Carina Behrends for creating joyful moments at work, having good conversations and sharing
their knowledge. We not only spent a great number of early, late and Saturday shifts together
but also shared exciting and fun experiences outside of WPE. Cordial thanks go to the mech-
anists of our workshop, our IT team and to Dr. Anne-Katrin Nix and Dr. Andrija Matic´ from
the local IBA team for fruitful discussions about the physics of the proton therapy system.
Dr. Erik Engwall from RaySearch Laboratories AB (Stockholm, Sweden) greatly contributed to
this work by sharing his initial non-clinical draft for a 4D dose calculation routine and providing
advice and assistance during further development. I am thankful to Dr. Mark Chan, Dr. Oliver
Blanck and Prof. Dr. Jürgen Dunst from the Department of Radiation Oncology of the Uni-
versity Clinic Schleswig-Holstein (Kiel, Germany) for their support. They and Dr. Myriam
Ayadi from the Centre Léon Bérard (Lyon, France) provided the required 4DCT data sets of
hepatocellular carcinoma patients. The collaboration with Dr. Ulf Mäder from the Institute of
Medical Physics and Radiation Protection of the TH Mittelhessen opened up new opportunities
for 4D studies based on computer generated CT data.
Mein ganz besonderer Dank gilt meinen Eltern für ihre Unterstützung während meines Studiums
und der Promotion sowie in jeder anderen Lebenslage. Durch ihr Vertrauen, ihre Motivation,
Liebe und zuverlässige Hilfe haben sie mir stets den Rücken gestärkt. Abschließend möchte ich
mich bei meiner derzeitigen und meiner ehemaligen Mitbewohnerin und meinen langjährigen
Freunden bedanken, die mir selbst in arbeitsintensiven und stressigen Zeiten ein Lächeln ins
Gesicht zaubern konnten.
113