Intensity modulated radiotherapy (IMRT) in head and neck cancer

UMEÅ UNIVERSITY
June 11, 2008
DEPARTMENT OF RADIATION SCIENCES,
RADIATION PHYSICS
SE-901 87 UMEÅ
SWEDEN
Intensity modulated radiotherapy (IMRT)
in head and neck cancer
A comparative treatment planning study using
physically and biologically based optimization
Elin Styf
Examiner
Heikki Tölli
Supervisors
Per Nilsson, Michael Blomquist and Mikael Karlsson
Thesis for Master of Science in Medical Radiation Physics
Abstract
The ordinary way of optimizing intensity modulated radiotherapy (IMRT) treatment
plans is by defining physical dose-volume objectives and/or constraints to target volumes
and organs at risk (OAR). This project aims to evaluate another approach of IMRT
optimization. Instead of using physically based treatment goals, biological optimization
parameters, derived from radiobiological models, were used in the optimization process.
Both normal tissue complication probability (NTCP) and equivalent uniform dose (EUD)
based optimization were investigated.
The main purpose of the project was to investigate advantages and/or disadvantages
with this method compared to conventional IMRT optimization and, hopefully, a
continuation of this study will result in improvements of the treatment planning in head and
neck cancer in the future.
Five patients with head and neck cancer, already treated with IMRT, were chosen for
the study. Physical dose constraints were defined for the target volumes in all plans, i.e. the
optimizations using the biological models were limited to the organs at risk (OARs). The
OARs included in the optimization process were spinal cord, brainstem and parotid glands.
The treatment planning system (TPS) used in this project was the research prototype
ORBIT Workstation (RaySearch Laboratories AB, Stockholm, Sweden).
A decrease in mean dose to the parotid glands were obtained when using biologically
compared to physically based optimization and still keeping the same target dose coverage.
The maximum dose to the serially organized OARs, spinal cord and brainstem, obtained
with biological optimization, were not significantly different from the maximum dose
constraints set in the physical optimization process.
The physically and biologically optimized plans were further compared in terms of
NTCP for the parotids. NTCP was significantly reduced with the biologically optimized
plans. Spinal cord and brainstem NTCP were zero with both techniques and could therefore
not be analyzed in this way.
It could be argued that both optimization techniques can in principle produce the same
result. Several hours were, however, spent on the physically optimized plans to make them
“optimal” and to meet the dose-volume criteria set for target volumes and OARs in the
optimization process. In the biological optimization the adjustable parameter is only one
(EUDmax or NTCPmax) for each OAR, which makes this method much simpler and easy to
apply. An improved result was always obtained regarding the mean dose to the parotids
when using biologically based optimization.
Sammanfattning
Det vanliga sättet att optimera dosplaner med s.k. intensitetsmodulerad radioterapi
(IMRT) är genom att definiera fysikaliska dos-volymmål och/eller dos-volymbivillkor för
tumörvolymer och riskorgan (eng. Organs At Risk, OAR). Det här projektet syftar till att
studera en annan metod för IMRT optimering. Istället för att använda fysikaliska
optimeringsmål, används biologiska kriterier i optimeringsprocessen, baserade på
radiobilologiska modeller. Både optimering baserad på risk för biverkningar hos den
normala vävnaden (eng. Normal Tissue Complication Probability, NTCP) och ekvivalent
homogen dos (eng. Equivalent Uniform Dose, EUD) undersöktes.
Huvudsyftet med projektet var att undersöka för- och nackdelar med denna metod och
jämföra den mot konventionell IMRT optimering. Förhoppningsvis kan detta så
småningom leda till förbättringar av metoden för dosplaneringen vid behandling av huvud
och hals cancer.
Dosplaneringsunderlag (CT-bilder med utridade tumörvolymer och riskorgan) för fem
patienter med huvud-halscancer, redan behandlade med IMRT, valdes ut för studien.
Fysikaliska doskriterier definierades för behandlingsvolymerna i alla planerna, d.v.s.
optimering med biologiska modeller begränsades till riskorganen. De riskorgan som
inkluderades i studien var ryggmärgen, hjärnstammen och öronspottkörtlarna.
Dosplaneringssystemet som användes var forskningsprototypen ORBIT Workstation
från RaySearch Laboratories AB i Stockholm.
I samtliga planer optimerade med parametrar baserade på biologiska modeller
uppnåddes en lägre medeldos till öronspottkörtlarna, med bibehållen dostäckning i
behandlingsvolymerna, jämfört med fysikaliskt baserad optimering.
Den maximala dosen till de seriellt organiserade OARs, d.v.s. ryggmärgen och
hjärnstammen, förändrades inte nämnvärt från de maximala doskriterierna satta i den
fysikaliskt baserade optimeringen.
De fysikaliskt och biologiskt baserade planerna jämfördes även med NTCP för
öronspottkörteln. NTCP minskade väsentligt med biologiskt baserad optimering, medan
NTCP för ryggmärgen och hjärnstammen var noll med båda metoderna och kunde därför
inte evalueras på detta sätt.
Det kan diskuteras huruvida båda metoderna i princip kan uppnå samma resultat. Flera
timmar spenderades däremot på att försöka uppnå ”optimala” planer med fysikaliskt
baserad optimering. Dosplaneringsprocessen baserad på biologiska parametrar tog betydligt
kortare tid i anspråk för att uppfylla ställda krav på planen.
I de biologiskt baserade optimeringarna var det endast en justerbar parameter (EUDmax
eller NTCPmax) för varje OAR, vilket medför att denna metod är mycket enklare att tillämpa.
Ett förbättrat resultat uppnåddes alltså för samtliga planer vad gäller medeldos och
NTCP till öronspottkörtlarna genom att använda biologiskt styrd optimering.
Contents
Introduction............................................................................................................... 1
1.1
Intensity modulated radiotherapy (IMRT)................................................... 2
1.2
Treatment planning techniques – Optimization ........................................... 3
1.3
Aim of the report ........................................................................................ 4
Background............................................................................................................... 5
2.1
Optimization process .................................................................................. 5
2.1.1 Optimization criteria....................................................................................................5
2.2
Biological models ....................................................................................... 5
2.2.1 Normal Tissue Complication Probability, NTCP ........................................................7
2.2.2 Tumour Control Probability, TCP ...............................................................................7
2.2.3 Equivalent Uniform Dose, EUD..................................................................................8
2.3
RaySearch – ORBIT Workstation ............................................................... 8
2.4
Optimization process (continuation).......................................................... 11
2.4.1 Objective functions....................................................................................................11
2.4.1 Optimization algorithms ............................................................................................11
2.5
Terminology in Radiotherapy ................................................................... 15
2.5.1 General volume definitions in photon beam therapy.................................................15
2.5.2 TNM classification ....................................................................................................16
2.6
Head and neck cancer ............................................................................... 17
2.6.1 OAR – serial and parallel organs...............................................................................17
2.6.2 Dose volume restrictions and dose objectives ...........................................................18
Materials and methods ............................................................................................ 20
3.1
Patient material......................................................................................... 20
3.2
OARs included in the optimization ........................................................... 25
3.3
Treatment planning................................................................................... 25
3.3.1 Physically optimized treatment plans ........................................................................25
3.3.2 Biologically optimized treatment plans .....................................................................26
3.4
Evaluation of the treatment plans .............................................................. 27
3.5
Additional investigations .......................................................................... 28
3.5.1 Effect of changing number of segments ....................................................................28
Results .................................................................................................................... 29
4.1
Evaluation of the treatment plans .............................................................. 29
4.1.1 Target volumes ..........................................................................................................29
4.1.2 Parotid glands ............................................................................................................31
4.1.3 Spinal cord and brainstem .........................................................................................33
4.1.4 “Surrounding tissue” .................................................................................................34
4.2
Additional investigations .......................................................................... 35
4.2.1 Effect of changing number of segments ....................................................................35
Discussion............................................................................................................... 37
Conclusions ............................................................................................................ 40
Acknowledgements ................................................................................................. 41
References .............................................................................................................. 42
Appendix A............................................................................................................. 44
A.1
Optimization objectives and/or constraints................................................ 44
Appendix B............................................................................................................. 52
B.1
DVHs - only physical optimization parameters ......................................... 52
B.2
DVHs - EUD opt. parameters on OAR versus physical ............................. 57
B.3
DVHs - NTCP opt. parameters on OAR versus physical ........................... 62
Appendix C............................................................................................................. 67
C.1
Mean doses, D99 and D1 to OAR ............................................................... 67
List of Abbreviations and a small Medical
English-Swedish Dictionary
List of Abbreviations
3DCRT
CT
CTV
dx
DVH
EUD
GTV
IMRT
NTCP
OAR
P+
PRV
PTV
sin
TCP
TPS
Three-Dimensional Conformal Radiotherapy
Computerised Tomography
Clinical Target Volume
dexter (right)
Dose Volume Histogram
Equivalent Uniform Dose
Gross Tumour Volume
Intensity Modulated Radiotherapy
Normal Tissue Complication Probability
Organ at Risk
Probability of complication free tumour control
Planning Organ at Risk Volume
Planning Target Volume
sinister (left)
Tumour Control Probability
Treatment Planning System
Small Medical English-Swedish Dictionary
English
Swedish
Bladder
Bowel
Brainstem
Esophagus
Larynx
Lymph node
Mandible
Oral cavity
Parotid gland
Pharynx
Rectum
Salivary glands
Spinal cord
Tonsils
Urinblåsa
Tarm
Hjärnstam
Matstrupe
Struphuvud
Lymfkörtel
Underkäke
Munhåla
Öronspottkörtel
Svalg
Ändtarm
Spottkörtel
Ryggmärg
Halsmandlar
Malignant
Xerostomia (dry mouth)
malign, elakartad, svårartad
Torr mun pga. minskad salivproduktion.
Chapter 1
Introduction
The number of patients in Sweden with a cancer diagnosis has approximately doubled
since 1970. According to the Swedish Cancer Society 1 (2008) there were 50776 new
diagnosed patients in 2006. One explanation for the increase is that people live longer than
before and the risk for cancer is considerably increased by age. The relative number of cured
patients is increasing as well. This is due to earlier and better diagnostics as well as due to
improved treatment methods.
About one third of the cancer patients receive radiation treatment (The Swedish Cancer
Society, 2007). Surgery (the most common method) and chemotherapy are examples of two
other cancer treatments. The choice of therapy depends upon tumour site and grade, regional
and metastatic spread, etc. The general state of the patient does also affect the choice of
treatment method (The Swedish Cancer Society 2006).
In treatment with radiation, so called radiotherapy, radiation is used to damage the
DNA of the malignant cells. When the DNA is damaged, the cell can no longer proliferate
and eventually the cell dies. It is the fact that tumour cells are not able to recover from DNA
damages in the same way as normal tissue that makes radiotherapy possible.
Different types of radiation may be used in radiotherapy, for example photons, electrons,
protons and light ions. Photons are the commonly used radiation type in Sweden today. In a
few years a national proton therapy centre located in Uppsala will be started, which enables
the clinical use of protons in treatment of cancer. The radiation may be given with either
external beam or internal techniques. In external beam radiotherapy the radiation is
delivered from a source (usually an accelerator) outside the body with beams directed
towards the tumour. In internal radiotherapy on the other hand the source, e.g. a radioactive
material, is placed in or in the vicinity of the tumour. Radiotherapy can be given in order to
cure the patient, curative treatment, or as a palliative treatment, where cure is not possible
and the aim of the treatment is local tumour shrinkage or alleviation of the pain.
External beam radiotherapy is most often delivered in a fractionated fashion, i.e. the
radiation is given in several fractions instead of giving the whole radiation dose at only one
occasion. Between the fractionations (usually 24 hours) the normal tissues recover more
efficiently than the tumour cells. For head and neck cancer patients a treatment course with
curative intention is conventionally given in 32-35 2.0 Gy fractions with 1 fraction per day.
If five fractions are given each week, and the total dose given is in the range of 64-70 Gy it
means that the treatment will go on for 6-7 weeks. Other treatment regimens are also
1
The Swedish Cancer Society is an independent non-profit organisation. Their main task is to raise
and distribute money for cancer research.
1
sometimes used for head and neck cancer, e.g. hyper-fractionated schedules with two
fractions per day, then with daily doses less than 2 Gy.
Different delivery techniques may be used in external beam radiotherapy. The most
common techniques are so called three-dimensional conformal radiotherapy (3DCRT),
often referred to as “conventional technique”, and Intensity Modulated Radiotherapy
(IMRT), discussed in more detail in section 1.1. Figure 1 summarizes and gives an overview
of the concepts of radiotherapy.
Examples of treatment methods
Radiation types
•
•
•
•
Photons
Electrons
Protons
Light ions
•
•
3D conformal radiotherapy
Intensity Modulated Radiotherapy (IMRT)
Radiotherapy
Intention
•
•
•
•
External radiotherapy
Internal radiotherapy
Curative treatment
Palliative treatment
Figure 1. The figure gives an overview of radiotherapy, showing different radiation types,
examples of treatment methods, the intention with the treatment and that the treatment may be
either external or internal.
Especially in external beam radiotherapy there is always risk for complications, since
when irradiating the tumour the normal tissues gets irradiated as well and damaged to some
extent. Even though normal tissue has larger ability to recover from its DNA damage,
complications will arise if the surrounding healthy tissue gets too much radiation. The ideal
treatment would be to give a high dose to the tumour and no dose to the surrounding healthy
tissue, but unfortunately this is impossible. There will always be a dose to the healthy tissue,
as the radiation enters the body from outside and attenuates on its way to the treatment
volume. However the dose to the surrounding tissue can be kept fairly low by optimising the
treatment plan, as described in section 1.2.
1.1
Intensity modulated radiotherapy (IMRT)
Conformal radiotherapy uses computer-controlled linear accelerators (linac) to
distribute the radiation dose to the tumour. It conforms or shapes the beam to the
geometrical projection of the target to be treated. Modern linacs use multileaf collimators
(MLC), see Figure 2, to shape irregular fields to fit the geometrical extension of the target.
The MLC consists of 20 to 80 pairs of thin, closely adjacent tungsten leaves. Each leaf is
individually motorized and computer controlled, allowing positioning with an accuracy of
1mm (Podgorsak 2005).
2
Figure 2. MLC for shaping the radiation field to fit the
geometrical extension of the target volume. (Varian Medical Systems)
IMRT is an advanced form of 3DCRT. In IMRT not only the geometrical projection of
the target is shaped, the intensity of the beam is also controlled or modulated. Combining
this with radiation beams from many angular directions, the dose distribution can be tailored
to the three-dimensional shape of the tumour.
The intensity modulation or, more physically correct, the fluence modulation can be
obtained with the MLC operating in one of two basic modes, the step and shoot technique or
the technique called sliding window. The first, also called static IMRT, implies that the
fields are delivered in a sequence of small segments, each segment with a uniform intensity.
The beam is only turned on when the MLC leaves are stationary in each of the prescribed
segment positions. The other method is a dynamic technique, also called dynamic IMRT.
The intensity modulation is performed by irradiating the patient while the MLC leaves are
moving. By this technique one gains time compared to step and shoot. There is also a third,
new delivery mode that should be mentioned in this context, the intensity modulated arc
therapy (IMAT). In this mode the sliding window approach is used and at the same time,
while irradiating, the gantry rotates around the patient. This mode has the potential to create
even better dose distributions than the two first mentioned.
3DCRT is still used extensively in clinical routine, but the use of IMRT is growing for
several tumour sites such as CNS (central nerve system), head and neck, prostate, breast and
lung.
The pattern of radiation delivery in IMRT is determined by computerized optimization,
i.e. treatment planning, described in more detail in the next section.
1.2
Treatment planning techniques – Optimization
The treatment planning process starts with a 3D computerised tomography (CT) study
of the patient. Tumour volumes and adjacent normal tissues are delineated in these CT
images. Often magnetic resonance imaging (MRI) and positron emission tomography (PET)
images are registered and fused with the CT study for the target delineation. Different
treatment planning techniques are used depending on the delivery technique for the external
beam radiotherapy. They are known as forward planning for 3DCRT and inverse planning
for IMRT.
In forward planning, the beam geometry (beam orientation, shape, wedges2, etc.) is first
defined, followed by calculation of the 3D dose distribution. After review of the dose
distribution, plan improvement is performed by modifying the initial geometry (e.g.
2
Wedges are used to modify the attenuation and “tilt” the dose distribution in the direction
perpendicular to the central axis of the beam.
3
changing the beam weights and/or modifiers, adding another beam, etc.), to improve the
target dose coverage and/or decrease the dose to the OARs. This forward planning
procedure is manually repeated until a satisfactory plan is obtained.
To create an IMRT plan one uses so called inverse planning. Instead of the planner
trying a variety of configurations of beams, treatment angles and wedges until a satisfactory
solution is found, as in forward planning, the focus is on the desired dose distribution
outcome. The user stages different kinds of objectives and/or constraints to define the
treatment goals. Then an optimization algorithm in the treatment planning system (TPS)
adjusts the beam parameters (mainly the beam intensity) in an attempt to achieve the desired
outcome. After review of the computer-optimized dose distribution, some modifications
might be needed. Thus, both forward and inverse planning involve iteration to find the best
possible treatment plan (Intensity Modulated Radiation Therapy Collaborative Working
Group 2001). To better understand the inverse planning method (computer optimization), it
is helpful to separate the process into two components: (1) the definition of the optimization
criteria by which a plan is to be judged; and (2) the optimization algorithm used. The latter
problem is described later in this report.
At present, most IMRT optimization systems use dose-based and/or dose-volume-based
criteria, called physically based optimization in this report. Next step may be to supplement
dose and dose-volume criteria with biological (or dose-response-based) criteria, called
biologically based optimization in this report. This technique is not used in clinical practice
today, but is a topic of on-going investigations.
1.3
Aim of the report
The aim of this project is to compare biological and physical optimization of external
photon beams in treatment of head and neck cancer. The CT images from five patients,
already treated with IMRT, were chosen for the study. Treatment plans optimized on
physical and biological parameters were carried out for the patients and then compared. The
optimizations were performed in the research software ORBIT Workstation (RaySearch
Laboratories AB, Stockholm, Sweden). The biological optimization implemented in the
program is based on models for NTCP, TCP, P+, and EUD, described in more detail in
section 2.2.
4
Chapter 2
Background
2.1
Optimization process
The concept of physical optimization was the first strategy implemented in commercial
inverse treatment planning systems and has become an accepted standard. Even the
modification of the original concept, referred to as biological optimization, basically keeps
the same logical structure of the optimization, where only the mathematical formulation of
the objectives of the optimization is modified.
2.1.1 Optimization criteria
Physically-based clinical objectives
The usual way to optimize is to use physical dose-volume criteria. In this optimization a
specification of dose and/or dose-volume objectives is made to the delineated volumes
into the inverse-planning computer system (Thieke et al. 2003). For example, a maximum
and minimum dose to the Planning Target Volume (PTV) can be specified. For Organs at
Risk (OAR) the specification may be of the kind that “no more than x % of the OAR may
receive a dose more than y Gy” or as maximum dose, see illustration in Figure 16. The
optimization process starts and the computer calculates an inhomogeneous dose per beam
angle to fulfil the objectives in the best possible way. The treatment planning system used in
the radiotherapy department at the University hospital in Umeå (NUS) is Oncentra
MasterPlan (Nucletron B.V., The Netherlands).
Radiobiologically-based clinical objectives
Instead of using dose criteria, radiobiological treatment goals are suggested as
objectives and/or constraints. They are based on models for tumour and normal tissue
response to radiation, i.e. Normal Tissue Complication Probability (NTCP) models and
Tumour Control Probability (TCP) models, respectively. More details about these models
are given later in the report. Another biological parameter to mention is Equivalent Uniform
Dose (EUD), see definition in section 2.2.3. Maximum allowed NTCPs or EUDs can thus be
specified as optimization criteria for the OARs and minimum allowed TCP can be specified
for the tumour volume.
2.2
Biological models
The goal in radiotherapy is to maximize the dose to the tumour, and at the same time
spare the surrounding normal tissues. The physicians often have to estimate the likelihood
for complications due to the radiation and decide which levels of damage are acceptable in
each patient case. A helpful tool for this is biological models, which describe the doseresponse relation for tumours and normal tissues. For example, biological models may be
used to estimate the probability for normal tissue complications, i.e. normal tissue
complication probability (NTCP), or for tumours estimate the tumour control probability
(TCP).
5
A keystone in the biological models is the underlying cell survival curve for tumours
and normal tissues, which is often described by the linear-quadratic (LQ) model.
Mathematically the surviving fraction (SF), can be expressed as (if the dose is delivered in a
single fraction):
2
SF = e−α D − β D ,
(1)
where D is the dose in Gy, and α and β are parameters representing the amount of
lethal and sub-lethal cell damage, respectively. If the total dose D is given in n fractions
each with a dose d, and full repair of sub-lethal damage is assumed between the fractions,
SF becomes
(
SF = e −α d − β d
2
)
n
=e
− nd (α + β d )
,
(2)
The ratio α/β describes the fractionation sensitivity of the tissue. For acute reacting tissues
and for most tumours α/β is considered to be approximately 10 Gy and for late reacting
normal tissue it is about 3 Gy.
Given the LQ-model, the dose-response relation for tumours and normal tissue can be
described by the linear-quadratic-Poisson model, having the form (Lind et al. 1999,
Mavroidis et al. 2001, Tsougos et al. 2005):
(
Pj ( D) = exp − N 0, j e
−α j nd − β j nd 2
) = exp ( −e
eγ j −α j nd − β j nd 2
) = exp ( −e
eγ j − ( D / D50, j )( eγ j − ln ln 2)
) , (3)
where P(D) is the probability of controlling the tumour or inducing a specific injury to an
organ that is irradiated uniformly with a dose D=nd. D50 is the total dose where the
probability of response is 50% and γ is the maximum normalized value of the dose-response
gradient. N0,j is the initial number of clonogenic3 cells for tumours or the initial number of
functional subunits for healthy tissue. The index j indicates that the probability and the
parameters are valid only for tissue type j. Parameters D50 and γ (or α and β) are specific for
every organ and specific for the kind of injury (endpoint) considered and can only be
derived from clinical data (Mavroidis et al. 2001).
If d is assumed constant, the values of αj and βj can be derived from the corresponding
values of D50 and γj (Lind et al. 1999) according to
αj =
eγ j − ln ( ln 2 )

d
D50  1 +
 (α / β )
j





and
βj =
3
αj
.
(α / β ) j
(4)
Clonogenic means giving rise to a clone of cells.
6
2.2.1 Normal Tissue Complication Probability, NTCP
Several NTCP models have been described in the literature, for example in Tsougos et
al. 2005, where some of the existing models are described. In this report the model called
the seriality model is used (Lind et al. 1999, Källman et al. 1992, etc).
The seriality model
The normal tissue response of the entire organ when the dose distribution is nonuniform can be described by the seriality model (Källman et al. 1992, Lind et al.1999,
Tsougos et al. 2005)
1/ s j
s ∆v 
 M
NTCPj = 1 − Π[1 − Pj ,i ( Di ) j ] j ,i 
 i =1

,
(5)
where Pj,i(Di) is the probability of response in voxel i of organ, j, irradiated to the uniform
dose Di according to Eq. (3). ∆vj,i is the relative volume of organ j that is occupied by voxel i.
M is the total number of voxels in the organ j, and sj is the relative seriality parameter that
characterizes the internal organization of the organ. If the organ is of parallel structure, it
can still function although a part of it is damaged. These organs have a relative seriality
close to zero (s ≈ 0), e.g. the lung and the parotid, whereas s ≈ 1 corresponds to a completely
serial structure which becomes non-functional when at least one functional subunit is
damaged (Tsougos et al. 2005). If several organs are involved the combined NTCP for all
organs at risk can be calculated according to
N organs
NTCP = 1 − Π [1 − NTCPj l ] ,
l =1
(6)
where NTCPjl is the probability of injuring organ l, calculated according to Eq. (5), and
Norgans is the total number of vital organs at risk, OAR (Lind et al. 1999).
2.2.2 Tumour Control Probability, TCP
To eradicate the tumour all of its clonogenic cells have to be destroyed and therefore
tumours can be considered as parallel organized structures (Lind et al. 1999). The response
of a tumour with a homogenous clonogenic cell sensitivity to a uniform dose distribution
can be calculated from the linear-quadratic-Poisson model, Eq. (3). The control response for
a non-uniform dose distribution may then be described by the LQ-Poisson model for every
individual tumour voxel i, according to the following expression (Lind et al. 1999)
M
TCPj = Π ( Pj ,i ( Di ))
i =1
∆v j ,i
,
(7)
where Pj,i(Dj) is the probability of injuring voxel i of tumour, j, irradiated to the uniform
dose Dj according to Eq. (3). If two or more targets are present, which is the situation in
most clinical cases, where you often have the gross tumour volume, GTV, and the lymph
nodes, the TCP will be calculated by
Ntumours
TCP = Π TCPj l ,
(8)
l =1
7
where TCPjl is the probability for controlling tumour j, calculated according to Eq. (7), and
Ntumours is the total number of tumours.
2.2.3 Equivalent Uniform Dose, EUD
The idea behind the concept of EUD was introduced by Niemierko (Niemierko 1997).
This mechanistic EUD model is based on the linear quadratic cell survival formalism and
was originally intended for tumours, defining the biologically equivalent dose that, if given
uniformly, would lead to the same biological effect as the actual non-uniform dose
distribution. Later Niemierko extended the EUD concept in a phenomenological singleparameter model to be valid for normal tissues as well (Niemierko 1999), resulting in the
generalized Equivalent Uniform Dose, gEUD.
1
 N
a
gEUD =  ∑ν i di a  ,
 i =1

(9)
where di is the dose in voxel i, N is the number of voxels, vi denotes the fraction that is
occupied by voxel i, and a is a tissue-specific parameter.
2.3
RaySearch – ORBIT Workstation
The TPS used in this project was the research prototype ORBIT Workstation
(RaySearch Laboratories AB, Stockholm, Sweden). Both the physical and the biological
optimization were performed in this TPS.
In the ORBIT WS plans can be optimized with either ordinary physical optimization
parameters or with biological constraints/objectives based on different radiobiological
models. It is also possible to use a combination of physical constraints and radiobiological
treatment goals. In addition, the software contains a number of different evaluation tools for
presenting and comparing treatment plans. Figure 3 illustrates the so called “IMRT view” of
the ORBIT Workstation.
8
[E]
[F]
[A]
[B]
[C]
[D]
[G]
Figure 3. The so called “IMRT view” of the ORBIT Workstation.
In the upper left corner in Figure 3 the dose volume histograms (DVHs) of the defined
regions of interest (ROI) are displayed. The names of the ROIs and their corresponding
colours are shown to the right [A].
CT images of the patient are shown in the transversal and sagittal (or coronal) planes [B
and C] together with the delineated structures. The dose distribution from the optimization is
superimposed on the images.
In the “fluence view” [D] it is possible to view the fluence modulation of each beam.
Lighter means higher intensity and darker means lower intensity. The fluence modulation is
also shown in a 3D view for all beams in the upper right corner [E].
The “progress of optimization graph” [F] shows the rate at which the optimization is
converging. The x axis shows the iteration number and the y axis the composite objective
value.
The optimizer will strive to reduce the physical objective function values [G] to zero
and if biological, the function values show the actual value of biological parameters, e.g.
NTCP or TCP.
The evaluation of a treatment plan is performed in the so called “Biology Evaluation
Tool”, see Figure 4.
9
[H]
Figure 4. A screen dump of the “Biological Evaluation Tool”
in the ORBIT Workstation.
The DVHs of the ROIs are shown in the upper left corner of Figure 4 in the same way
as [A] in Figure 3.
The response plots in the upper right corner indicate how the response would change if
the dose per fraction were scaled for the current number of fractions or how the response
would change if the number of fractions would change for the current dose per fraction.
The two columns to the right in the response function table [H] show the calculated TCP
and NTCP values for the current plan and the alternative plan, if one has been selected.
10
2.4
Optimization process (continuation)
The following sections describe some optimization algorithms in general.
2.4.1 Objective functions
In inversely planned IMRT, the clinical objectives, i.e. the treatment goal of the
optimization in terms of dose, dose-volume or dose-response, are specified mathematically
in the form of an objective function. Optimization algorithms are then employed for
calculating the beam parameters (often only the energy fluence patterns) in order to fulfil the
objectives. The term score is often used to denote the value of the objective function, and it
is an index of the quality of the result. Thus, the aim of the optimization is to minimize (or,
maximize depending on the choice of objective function) the score.
One method commonly used to create dose-based and dose-volume based objective
functions is based on minimizing the variance of the dose relative to the prescribed dose for
the target volumes or dose limits for the OARs. Variance is defined as the sum of the
squares of the differences between the calculated dose and the prescribed dose or dose limit.
(Intensity Modulated Radiation Therapy Collaborative Working Group. 2001) One
constituent objective function is specified for each individual constraint and tissue. For
example, the objective function OFT(-) for avoidance of an under-dosage of the target takes
the form
( −)
T
OF
1
( x) =
NT
NT
∑ [C (D
2
T
min
+
T
i
−D
( x) )] .
(10)
i =1
The voxels of the tumour volume are labelled with index i ranging from 1…NT, and the
respective doses Di should all satisfy the constraint: Di > Dmin. (Bortfeld et al. 2006) The
analogue term for the avoidance of global over-dosage effects for either target or OARs
reads
OFk( + ) ( x) =
1
Nk
Nk
∑ [C (D
+
k
i
2
k
( x) − Dmax
)] .
(11)
i =1
The operator C+ defined by C+ = x for x ≥ 0 and C+ =0 for x < 0, to ensure that only
constraint violations contribute to the objective function. For the final mathematical
formulation of the optimization problem, the individual objective functions have to be
combined to yield a single valued quality measure of the complete treatment plan. Since the
objective functions for the target (OFT) and OARs (OFk) refer to conflicting goals of the
optimization, one has to introduce weighting factors w such that the planner can steer the
result towards the optimal treatment plan. The weighted sum of individual objective
functions are formed as follows
OF ( x) = wT( + )OFT( + ) ( x) + wT( − ) OFT( − ) ( x) + ∑ wk OFk( + ) ( x) .
(12)
k
This approach is sometimes referred to as the standard quadratic objective function.
2.4.1 Optimization algorithms
The process of optimizing the intensity distribution for a given set of constraints and a
selected objective function may be carried out using one of several mathematical algorithms
11
(referred to as optimization or search method). Not all optimization algorithms can be used
for all objective functions due to the mathematical properties of the objective function. In
general, these algorithms can be divided into two categories: deterministic algorithms and
stochastic methods. The main difference between the two methods is that the deterministic
algorithm, e.g. the gradient method, is only applied to optimization problems where the
objective functions are convex and therefore only a global minimum and no local minima
exist. See Figure 5 for illustration of global and local minima, respectively. For these
convex objective functions like the standard quadratic objective function the deterministic
algorithm can calculate the optimal solution very fast and are therefore currently used in
most commercially available IMRT treatment planning systems. (Bortfeld et al. 2006)
OF(x)
Local min.
x3 x2
x1 x0
x
Global min.
Figure 5. The figure illustrates local and global minima.
If local minima exist, for example when dose-response based objective functions are
used, some form of stochastic method need to be considered. (Intensity Modulated
Radiation Therapy Collaborative Working Group. 2001) In the next section the most
frequently used algorithms will briefly be discussed. First, as examples of deterministic
algorithms, simple gradient methods are described. Secondly, the basic idea of one of the
most commonly used stochastic algorithms, simulated annealing, is discussed.
Deterministic approaches
Steepest descent
This method is mostly used for finding the global minimum of a convex objective
function OF(x), where x represents the set of variable treatment parameters which have to be
adjusted to their optimal value. In Figure 5 a one-dimensional example of a non-convex
objective function is shown. The idea of this method is very simple. The key role in the
method has the first derivative or the gradient of the objective function. The gradient
∇OF (x) determines the steepest direction along the objective function. The minimum of
the objective function is found via an iterative method requiring that the values of the
intensities x are updated at each step of the iteration i. The update of x while advancing from
iteration i to i+1 is given by the rule
x(i + 1) = x(i ) − α ⋅ ∇OF ( x(i )) .
(13)
The constant factor α (often referred to as the damping factor) determines the step size of
the iterative process. (Bortfeld et al. 2006) This procedure is visualized in Figure 5. The
reason why this method is not suitable for objective functions is realized if the algorithm in
12
the example in Figure 5 starts on the left side instead. It will be trapped in the local
minimum and not find the global one.
Newton’s method
The Newton method is very similar to the steepest descent method. The difference is
that this method takes into account the second order derivatives of the objective function for
the determination of the damping factor α, which controls the speed and success of the
optimization. The damping factor can be expressed in terms of the inverse Hessian H-1 of
the second order derivatives of OF(x) (Bortfeld et al. 2006), i.e.
x(i + 1) = x(i ) − H −1 ( x(i))∇OF ( x(i))
= x(i) − α Newton ∇OF ( x (i )) .
(14)
The problem with the Newton approach is that for each step the complete inverse
Hessian has to be calculated, which is a time-consuming process. One possible solution to
this problem is to use an approximation for the Hessian instead. (Bortfeld et al. 2006) This
optimization algorithm is called “Quasi Newton” approach. The steepest descent method
can be viewed as a special case of this approach.
Stochastic method
The advantage with stochastic optimization algorithms is that they allow the
optimization process to escape from the local minima traps and thus find the global
minimum. The prize to pay for this nice feature is a significantly increased optimization
time in comparison to the described deterministic algorithms above. In this section one basic
idea of a stochastic method will be discussed, simulated annealing. More recently, even
more complex optimization engines based on genetic algorithms are employed for treatment
plan optimization. This method will not be described in this report, but more details can be
found in e.g. Goldberg (1989) and Falkenauer (1998).
Simulated annealing
There are basically two strategies of how the method of simulated annealing escapes
from the trap of local minima – climbing uphill and tunnelling. The two methods are
illustrated in the following example by Webb (1997).
Imagine a walker, instructed to find well in a hilly landscape. The well is assumed to be
at the lowest point of the landscape, illustrating the global minimum. Since the walker has
no previous knowledge of the landscape he does not know in which way he should go. He
starts by walking downhill, because he is aware that the mountains are higher than the well.
In this example the potential energy (V) is the objective function and it is clear that Vwell <
VHill. His task is therefore to minimize |V-Vwell|. Consequently, he walks in the direction of
the steepest descent until he founds a valley. Unfortunately, the walker cannot se more than
a few meters in front of him due to some fog and therefore he doesn’t know if he has found
a local valley or the global one. The only way to find out is to walk uphill for some time to
further explore the whole landscape.
Alternatively, the walker can enlarge his step size so enormously that he leaves the
valley in one step. This process is referred to as tunnelling through the walls of the valley,
see illustration in Figure 6, where the black arrow shows tunnelling and grey arrow shows
climbing uphill.
13
OF(x)
Local min.
x
Global min.
Figure 6. The figure illustrates simulated annealing with two different methods to escape from the
local minimum, ‘climbing uphill’ and ‘tunnelling’.
In summary, the advantage of deterministic approaches like the steepest descent or
Quasi Newton in contrast to the stochastic methods is the optimization speed. On the other
hand, if complex non-convex objective functions with local minima are used, there is no
alternative than to use stochastic algorithms like simulated annealing or genetic algorithms.
14
2.5
Terminology in Radiotherapy
2.5.1 General volume definitions in photon beam therapy
When planning a radiotherapy treatment it is necessary to define in a clear way volumes
to be treated and adjacent normal tissues to be spared. It is important to ensure a common
language between different clinics to avoid confusion. The terminology to use is specified
by the International Commission on Radiation Units and measurements (ICRU) in reports
50, 62 and 71. Figure 7 illustrates the different volumes, according to ICRU report 62.
Target
Organ at Risk,
OAR
Gross Tumour Volume
GTV
Subclinical disease
Clinical Target Volume
CTV
Internal Margin
IM
Internal Target Volume
ITV (=CTV+IM)
Setup Margin
SM
Planning Target Volume
PTV (=CTV+combined IM and SM)
Organ at Risk
OAR
Planning Organ at Risk Volume
PRV
Figure 7. The figure illustrates the different volumes and margins used in
photon therapy treatment, according to ICRU Report 62.
For the tumour or the target several three-dimensional volumes are defined, see Figure 7.
The Gross tumour volume (GTV) consists of primary tumour and possibly metastatic
lymphadenopathy or other metastases. It is the parts of the malignant growth where the
tumour density is largest. An adequate dose must be delivered to the whole GTV to obtain
local tumour control.
15
Next volume to define is the Clinical target volume (CTV). It contains GTV and/or
subclinical4 malignant diseases that must be eliminated. It can be described as including
structures with clinically suspected but unproved involvement, hence “subclinical diseases”.
One often finds subclinical diseases around the GTV, but it can also involve areas of
subclinical extensions at a distance from a GTV, e.g. regional lymph nodes. This implies
that there may be more than one CTV to be treated. If there are several CTV volumes the
one containing a known macroscopic tumour may, according to ICRU report 71 (2004), be
denoted CTV-tumour, CTV-T, and if the subclinical extensions are at a distance from the
GTV, the CTV may be denoted CTV-N. In DAHANCA (2004) (see below) the lastmentioned volume is denoted CTV-elective (CTV-E). Both GTV and CTV are purely
clinical-anatomical concepts.
Since there are variations and uncertainties in the positions, sizes and shapes, and
orientations of the tissues, patient, and the beams one need to add margins to the CTV. The
CTV with the added margins leads to the concept of Planning target volume (PTV). The
volume referred to as PTV contains CTV and two added margins. First, Internal margin (IM)
is intended to compensate for all movements and variations in size, shape and position of the
organs and tissues contained in or adjacent to the CTV. The alteration may result e.g. from
respiration, filling of the bladder, filling of the rectum, swallowing, heart beat, movements
of the bowel etc. The CTV together with IM is denoted internal target volume (ITV). The
second margin to add is the set-up margin (SM). This margin is to compensate for
uncertainties in patient positioning and alignment of the therapeutic beams during treatment
planning and throughout all treatment sessions. The uncertainties to be compensated for
may vary with different anatomical directions, thus a SM for each beam is needed. The PTV
is defined as the CTV and the two added margins, i.e. ITV plus SM.
The organs at risk (OAR) have similar volume definitions. Around the OAR a margin
need to be added for the same reasons as the target. The OAR with added margins is
denoted planning organ at risk volume (PRV), see Figure 7.
2.5.2 TNM classification
The Tumour, Node, Metastasis (TNM) system is a commonly used system to describe
the extent of an individual’s cancer, i.e. to stage the disease. It is based on the size of the
tumour (T), whether there are lymph nodes involved (N) and if the cancer has spread to
different parts of the body (M). (National Cancer Institute 2004), classified as:
Primary tumour (T)
Tx
Primary tumour cannot be assessed
T0
No evidence of primary tumour
T1,T2,T3,T4 Size of the primary tumour, with T1 being a small tumour and T4 a large one
Regional lymph nodes (N)
Nx
N0
N1,N2,N3
Regional lymph nodes have not been assessed
No regional lymph node involvement (no cancer found in the lymph nodes)
Involvement of regional lymph nodes, where N3 means many nodes involved
Distant metastasis (M)
Mx
M0
M1
4
Distant metastases has not been assessed
No distant metastases
Distant metastases (cancer has spread to distant parts of the body)
Subclinical relates to the stage in the development of a disease before the symptoms are observed.
16
2.6
Head and neck cancer
The term head and neck cancer refers to cancer arising in the head or neck region (e.g.
in the oral cavity, salivary glands, paranasal sinuses5, nasal cavity, pharynx, larynx, lymph
nodes in the upper part of the neck), see Figure 8. Most head and neck cancers begin in the
cells that line the mucosal surfaces6 in the head and neck area, e.g. mouth, nose, and throat
(RadiologyInfo 2005). This type of cancer is referred to as squamous cell carcinomas,
because normal mucosal cells look like scales (squamous) under the microscope (National
cancer institute 2005).
Figure 8. The region referred to as the head and neck region (CET Cancer Center).
Cancers of the brain, eye, and thyroid as well as those of the scalp, skin, muscles, and bones
of the head and neck are not usually grouped with cancers of the head and neck.
The five chosen patients of this study have three different locations of the primary
tumour, i.e. base of tongue, tonsil, and hypopharynx. The tonsils are lymphoid tissue that
can be seen on either side in the back of the throat. Hypopharynx is the lower part of the
pharynx, see Figure 8, i.e. the part of the throat that connects to the oesophagus.
2.6.1 OAR – serial and parallel organs
The most critical OARs in the head and neck region are the spinal cord and the
brainstem. These organs are so called serial organs. They have a serial architecture (the
functional sub-units are arranged in series). A too high dose may result in functional damage
to the whole organ even if it is only present in a small sub-volume (functional sub-unit) of
the organ (Metcalfe 2007). That is why it is extremely important not to exceed the specified
maximum dose objective in these type of organs.
Other organs like liver, lung, and parotid are parallel organs (Thieke et al. 2003), i.e.
they have their functional sub-units arranged in a parallel fashion. Their tolerance dose
depends strongly on the fraction of the volume irradiated and hence they exhibit a strong
dose-volume relationship. If only a small fraction of the organ is irradiated the tolerance
dose is much higher than if a larger fraction is irradiated. This is important to know when
5
Paranasal sinus is pared cavities in the bones of the face.
Mucosal surfaces are moist tissues lining hollow organs and cavities of the body open to the
environment.
6
17
planning a radiation treatment. For these parallel structures, it is often better to use the organ
mean dose than the max dose to measure the probability for complications.
In general the head and neck region is a complex area to treat with radiotherapy. Other
than the spinal cord and the brainstem the parotid glands are also important OARs. The
parotid gland is the largest of the three salivary glands. When irradiating the parotid glands,
depending on the volume irradiated, the treatment may cause xerostomia7. This is of course
unpleasant and may result in difficulties to swallow and/or take in enough food and liquids
by mouth.
2.6.2 Dose volume restrictions and dose objectives
In the physical optimization, described earlier in the report (section 2.1.1), a number of
constraints and/or objectives are specified in the optimization process. In all kinds of
radiation treatment it is useful to have guidelines for these dose-volume objectives in each
specific type of treatment. In our case the treatment area is head and neck. We have used the
guidelines of the Danish head and neck cancer group, DAHANCA (2004).
Dose volume restrictions and dose objectives according to DAHANCA
According to DAHANCA (2004) the dose to PTV volumes should be within 95-107%
of the prescribed dose. Up to 1% of the PTV is allowed to receive a lower dose, 90-95%.
The PTV volumes should be optimized with the prescribed doses according to Table 1,
where the dose to PTV-E is considered a minimum dose. In this work PTV-E and PTV-T
will be denoted PTVA and PTVB respectively. In Table 1 the prescribed doses to the
treatment volumes are shown.
Table 1. Prescribed doses to PTV volumes according to the DAHANCA guidelines.
PTV-T
PTV-E
Dose
66-68 Gy
min 50 Gy
Fractions
33-34
33-34
Following the prescriptions given in Table 1 it gives a minimum fraction dose of about 1.5
Gy in PTV-E.
Limiting doses to critical normal tissues
Around every organ at risk (OAR) there should be a margin to form the planning organ
at risk volume (PRV), see definitions earlier in this report (section 2.5.1). This is most often
performed in practice only for serial organs. In the treatment planning process one has to
specify dose objectives for the OAR. The limiting doses to OARs and PRVs used in this
project are taken from DAHANCA (2004) and specified in Table 2.
7
Xerostomia, the medical term for dry mouth due to lack of saliva.
18
Table 2. Limiting doses to OARs and PRVs according to
the DAHANCA guidelines.
Spinal cord
Brainstem
Parotid gland
OAR
max 45 Gy
max 54 Gy
mean 26 Gy
PRV
max 50 Gy
max 60 Gy
Priorities
According to DAHANCA (2004) the most important objectives to achieve are those for
the serial critical normal organs (spinal cord and brainstem) see Table 3. Then follows the
target volumes and last in the prioritization list are the less severe organs, e.g. parotid glands.
Table 3. Prioritization of dose objectives according to DAHANCA guidelines.
Prioritization of dose objectives
1. Critical normal tissues:
2. Targets:
3. Less severe normal tissues:
Spinal cord, brainstem
PTV-T, PTV-E
Parotid glands
19
Chapter 3
Materials and methods
Both the physically and the radiobiologically based optimization were performed using
the RaySearch prototype of ORBIT Workstation, RaySearch Laboratories AB, as described
in section 2.3.
3.1
Patient material
Five head and neck cancer patients were chosen. All of them have already been treated with
IMRT, one at the Umeå university hospital and four at Lund university hospital. The
patients had three different cancer diagnoses with various stages. In this section
representative CT images of the five patients are presented and also the beam angles and
collimator angle used in the treatment as well as in this study.
Patient 1
The first patient is a patient previously treated in Lund. Seven beams in a coplanar
arrangement, with beam angles 0º, 50º, 100º, 155º, 205º, 260º and 310º, were used and the
collimator was tilted 2º in order to minimize MLC leakage effects. The location of the
primary tumour was in the base of the tongue. The stage of the tumour was T4 N0 M0,
according to the TNM classification described earlier in the report. This implicates a large
tumour, with no regional lymph node involvement, and no metastases in other parts of the
body. The beam angles and the rotation of the collimators were kept constant during all
treatment plans for this patient.
GTV
PTVB
PTVA dx
PTVA sin
Spinal cord
Spinal cord PRV
Figure 9. A CT slice of Patient 1, displaying GTV, PTVs and spinal
cord (without and with margin).
20
In Figure 9, a CT slice of Patient 1 is shown. It displays the delineated volumes,
according to ICRU, described earlier in this report (section 2.5.1). In the figure the teeth and
the mandible are clearly shown. The only OAR delineated in the figure is the spinal cord
and PRV of the spinal cord, i.e. the spinal cord with added margin. Two types of PTV
volumes are delineated in the CT slice, denoted A and B depending on the prescribed
treatment dose, i.e. PTV-E and PTV-T using the DAHANCA notation.
In Figure 10 two other OARs are shown, the two parotid glands (right and left). Also the
PTVA volumes and spinal cord are present in this slice.
Parotid dx
Parotid sin
PTVA dx
PTVA sin
Spinal cord
Spinal cord PRV
Figure 10. A CT slice of Patient 1, displaying PTVs, parotid dx and sin, and
spinal cord (without and with margin).
In Figure 10 there is a small overlap between the left parotid and the left PTVA. This
overlap makes it hard to give low dose to the whole parotid and at the same time control the
tumour. Also the close contact between the right parotid and the PTVA volume to the right
makes it hard to fulfil both objectives. The teeth in the upper jaw, and some other bone
structures, are clearly shown in Figure 10 but not delineated as regions of interest (ROI).
Patient 2
The second patient is a patient treated in Umeå. Seven beams in a coplanar arrangement,
with angles 0º, 54º, 105º, 150º, 210º, 255º and 306º, were used with 0º collimator angle. The
cancer was located in the tonsil, stage T4 N0 M0. In Figure 11 the delineated volumes are
shown.
21
GTV
PTVB
PTVA
Parotid dx
Parotid sin
Spinal cord PRV
Figure 11. A CT slice of Patient 2, displaying GTV, PTVs, spinal
cord (with margin) and parotid dx and sin.
GTV in Figure 11 is the primary tumour. PTVB indicates the volume with a higher
treatment dose, 66-68Gy, according to the DAHANCA guidelines. For this patient it is the
volume of PTVA not containing PTVB that should be treated with the lower treatment dose,
50Gy, according to Table 1. In Figure 11 one can clearly se that the right parotid is
overlapping the target volume.
Patient 3
The third patient (treated in Lund), with beam angles 0º, 50º, 100º, 145º, 215º, 260º and
310º, with the collimator tilted 2º. The cancer was located in the tonsil, stage T2 N3 M0. In
Figure 12 the delineated volumes are shown.
Parotid dx
Parotid sin
GTV
PTVB
PTVA sin
Spinal cord
Spinal cord PRV
Figure 12. A CT slice of Patient 3, displaying GTV, PTVs, spinal cord
(with and without margin) and parotid dx and sin.
22
Also for this patient, a large part of right parotid is overlapping the target volume
similarly to patient 2.
Patient 4
The fourth patient (treated in Lund), with beam angles 0º, 50º, 100º, 145º, 215º, 260º
and 310º, and the collimator tilted 2º. The primary tumour was located in hypopharynx,
stage T3 N2 M0. In Figure 13, a CT slice of Patient 4 is shown with the delineated volumes.
Parotid dx
Parotid sin
GTV
PTVB
PTVA
Spinal cord
Spinal cord PRV
Figure 13. A CT slice of Patient 4, displaying GTV, PTVs, spinal cord
(with and without margin) and parotid dx and sin.
Figure 14 shows a second CT slice of patient 4. In this figure three GTVs are shown and
also PTVB, PTVA and PTVA dx. The only OAR in this figure is the spinal cord (with and
without margin).
GTV
PTVB
PTVA dx
PTVA
Spinal cord
Spinal cord PRV
Figure 14. A CT slice of Patient 4, displaying GTV, PTVs and spinal cord.
23
Patient 5
The fifth patient was previously treated in Lund with beam angles 0º, 50º, 100º, 145º,
215º, 260º and 310º, and the collimator tilted 2º. The primary tumour was located in the
tonsil, stage T4 N2 M0. In Figure 15 the delineated volumes are shown, where GTVt and
GTVn are the primary tumour and a regional positive lymph node, respectively.
GTVt
GTVn
PTVB
PTVA
Parotid dx
Parotid sin
Spinal cord
Spinal cord PRV
Figure 15. A CT slice of Patient 5, displaying GTV, PTVs, spinal
cord (with margin) and parotid dx and sin.
24
3.2
OARs included in the optimization
In this study the OARs were limited to the spinal cord, the brainstem and the two
parotid glands. These organs are the most frequently outlined OARs in the head and neck
area used for optimization purposes. There are many other sensitive organs in this region
(e.g. mandible, submandibular glands, larynx, oesophagus entrance, oral cavity, etc.) but we
decided to leave them out in order to be able to make a reasonable comparison between the
optimization techniques. Besides, some of the other OARs may even be enclosed by the
target, e.g. the oral cavity when the target is the base of tongue.
3.3
Treatment planning
The DAHANCA guidelines were used, see Table 1 and Table 2. All treatment plans were
planned with 7 beams in a coplanar arrangement. The main optimization parameters set in
the step-and-shoot IMRT were:
• maximum number of iterations: 40,
• optimization convergence stopping tolerance: 1.10-5,
• maximum number segments: 50.
The optimization dose algorithm applied was the SVD8 (singular value decomposition) dose
engine.
Several different combinations of objectives and/or constrains had to be carried out to
find an acceptable treatment plan. To start with, a treatment plan optimized with physical
dose objectives was performed for each patient. Since physical optimization is the ordinary
way of optimizing, this plan was meant to be the base in the comparison between the
different treatment plans.
Objectives and constraints
It is important to distinguish between objectives and constraints when optimizing. The
constraints are requirements on the treatment plan that must be fulfilled at the end of the
optimization. Objectives on the other hand are tried to be fulfilled as far as possible without
violating the constraints. Since the objectives are not forced to be achieved they can be
weighted against each other. A high weight means more important to be fulfilled than a low.
3.3.1 Physically optimized treatment plans
The process of optimizing with physical dose objectives is a trial and error procedure.
The strategy was to define min and max dose objectives and/or constraints to the target
volumes, see illustration in Figure 16. To fulfil the treatment goals it was also necessary to
introduce uniformity objectives to make a more uniform dose distribution in the target. For
the OARs only max dose and dose-volume objectives were defined. The dose-volume
objectives were of the kind “no more than x % of the volume may receive more than y Gy”.
See Appendix A for more details about the objectives and constraints used in the physically
based optimization. The corresponding DVHs are shown in Appendix B for all patients.
The treatment plan had to be modified several times to find a plan where the defined
treatment goals were met in the best possible way.
8
The SVD (singular value decomposition) is based on an article by Bortfeld et al. 1993. The SVD
dose engine in the research prototype ORBIT Workstation has not been clinically validated.
25
Figure 16. An example of a cumulative dose-volume histogram, with defined
dose-volume and dose objectives for both targets and OARs.
Figure 16 illustrates examples of dose and dose-volume criteria in a physical optimization.
Also the objective function values, [G] in Figure 3, were used when trying to modify the
treatment plan. The function values show how the optimizer distributed the work output
between the different optimization requirements. An objective with a low function value
means that the optimizer doesn’t waste much capacity to fulfil that task and it could
probably be further pressed.
The DVHs of physically based treatment plans for all the patients are shown in
Appendix B.
3.3.2 Biologically optimized treatment plans
After finding an “optimal” physical treatment plan, according to the guidelines given in
Table 1 and Table 2, the optimization was performed with biological models as objectives.
The optimizations using the biological models were limited to the OAR, i.e. the spinal cord,
brainstem and the two parotid glands. Consequently the dose objectives for the target
volumes were defined in the same way in all plans.
EUD optimization parameters
When optimizing with EUD, Eq (9) was used as objectives for the OARs. A maximum
allowed EUD value was defined for each OAR and then the optimizer tried to find a plan
satisfying the given objectives for the OARs, and still keeping the same target dose
coverage on the PTVs. As mentioned before the objectives are possible to weight against
each other. In this optimization however, the highest possible weight was used and from that
condition the EUD was pushed as much as possible, without violating the target objectives.
Since the weight factor was kept constant, the only adjustable parameter was the defined
value of EUDmax. This made the modification of the plans much easier and faster than for
physically based optimization. The procedure of finding the best possible treatment plan
26
was performed using the same evaluation tools as for the physical plans, i.e. objective
function values, DVHs, and max and mean doses.
The tissue specific parameter a in Eq (9) is related to the Lyman model parameter n by a
= 1/n (Wu et al. 2002). The parameter n (Burman et al. 1991) is 0.16 for the brainstem, 0.70
for the parotids, and 0.05 for the spinal cord.
The DVHs of the treatment plans optimized with EUD are shown in Figure B 6 – B 10
in Appendix B.
NTCP optimization parameters
The NTCP based treatment plans, Eq (5), were performed in the same way as in the
EUD case except that NTCP were used for the OARs. A maximum allowed NTCP was
stated as constraint in the optimization. Since constraints were used it was not possible to
weight NTCP for different OARs against each other. In this method there is therefore only
one parameter to adjust for each OAR, which, again, makes the modification of the plan
much easier than for physically optimized treatment plans. The plans were evaluated in the
same way as for EUD based optimization, i.e. by using function values, DVHs, and max and
mean doses, while keeping the same target dose coverage.
There are some tissue specific parameters needed in the NTCP model; α/β, D50, γ and
the relative seriality parameter s. For late damage to normal tissue the ratio α/β equals
approximately 3 Gy. The numerical values for the other parameters were taken from ÅgrenCronqvist (1995) for the spinal cord (endpoint myelitis9/necrosis10) and brainstem (endpoint
necrosis/infarct), and from Schilstra et al. (2001) for the parotid glands (endpoint
xerostomia grade II), see Table 4.
Table 4. Parameter values used in the NTCP model.
Spinal cord
Brainstem
Parotid gland11
D50 [Gy]
γ
s
68.60
65.10
31.30
1.9
2.4
1.3
4
1
3.8.10-7
The DVHs of the physical and NTCP based treatment plans are shown in Figure B 11 –
B 15 in Appendix B.
3.4
Evaluation of the treatment plans
The two biologically based treatment plans were compared with the physically based
plan one at the time, by merging the DVHs (see figures in Appendix B).
Since the parotid is a parallel organ, the mean doses to this organ were compared. For
the serial organs spinal cord and brainstem on the other hand the “near maximum” doses,
D1%, were compared. D1% means the dose at which only 1% of the volume has a dose equal
or higher than this dose, hence the expression “near maximum” dose.
9
Myelitis means inflammation of the spinal cord.
Necrosis means accidental death of cells and living tissue.
11
The original values for D50 and γ determined by Schilstra et al. (2001) have been converted
(using the LQ model) to be valid for a constant dose per fraction of 2 Gy (K. Eriksson, RaySearch
Laboratories AB, personal communication 2008).
10
27
The third method of evaluation is calculation of NTCP for the OARs. For the physically
and EUD optimized plans these calculations were performed with the ORBIT Workstation,
but also validated for some randomly chosen DVHs.
3.5
Additional investigations
There are a lot of parameters influencing the optimization process. As an additional
investigation, one of these parameters was further investigated, i.e. how the number of beam
segments affects the plans.
3.5.1 Effect of changing number of segments
In all treatment plans performed in this study 50 segments was used in the optimization.
To analyze if the number of segments had any influence on the results, a small test was done.
The treatment plans of patient 3 were repeated with the same parameters as in Table A 7-A
9, but the number of segments was increased to 75, 80 and 100.
28
Chapter 4
Results
DVHs for all treatment plans are presented in Appendix B.
4.1
Evaluation of the treatment plans
The three optimization methods (physical, EUD and NTCP) were evaluated for each
patient.
4.1.1 Target volumes
The “near maximum” and “near minimum” doses to the target volumes were compared
to ensure that the same dose coverage was kept and that the treatment goals, according to
Table 1, was fulfilled for the different treatment plans, see Table 5.
Table 5. D99% and D1% to the target volumes for all treatment plans.
D99% and D1% to target volumes [Gy]
PTVB
D99
Patient 1
Patient 2
Patient 3
Patient 4
Patient 5
PTVA dx
D1
D99
PTVA sin
D1
D99
D1
Physical
65.8
72.7
47.4
57.3
46.2
58.1
EUD
65.7
73.9
46.6
58.0
46.9
58.9
NTCP
65.6
74.6
46.8
58.3
46.7
58.7
Physical
64.6
73.4
45.0
67.0
46.4
54.9
EUD
65.0
73.8
45.0
67.6
46.4
54.8
NTCP
64.5
74.7
44.6
67.0
46.6
54.9
Physical
65.5
74.5
47.1
64.3
46.8
62.5
EUD
65.6
76.0
47.7
64.6
45.4
63.1
NTCP
64.9
75.9
46.9
63.6
46.8
62.1
Physical
65.5
73.9
46.6
63.5
46.4
66.8
EUD
65.3
72.9
46.5
62.8
44.9
66.7
NTCP
64.8
72.8
46.8
61.4
44.7
65.7
Physical
64.2
76.0
43.9
69.0
46.5
54.7
EUD
64.9
75.5
42.5
69.6
46.1
54.7
NTCP
64.2
74.4
42.7
69.8
46.4
54.8
In Table 6 the dose ratios between the biologically and the physically optimized
treatment plans are shown. In some treatment plans the biological optimization gives
slightly higher dose to the target volumes than the physically optimized, and in some the
dose is smaller. The small differences found are assumed to be of no clinical significance.
29
Table 6. D99% and D1% to the target volumes for the biologically optimized treatment plans
relative to the physically optimized plans.
D99% and D1% relative to physically optimized
PTVB
D99
PTVA dx
D1
D99
D1
PTVA sin
D99
D1
Patient 1 EUD
NTCP
0,998
1,017
0,983
1,012
1,015
1,014
0,997
1,026
0,987
1,017
1,011
1,010
Patient 2 EUD
NTCP
1,006
1,005
1,000
1,009
1,000
0,998
0,998
1,018
0,991
1,000
1,004
1,000
Patient 3 EUD
NTCP
1,002
1,020
1,013
1,005
0,970
1,010
0,991
1,019
0,996
0,989
1,000
0,994
Patient 4 EUD
NTCP
0,997
0,986
0,998
0,989
0,968
0,999
0,989
0,985
1,004
0,967
0,963
0,984
Patient 5 EUD
NTCP
1,011
0,993
0,968
1,009
0,991
1,000
1,000
0,979
0,973
1,012
0,998
1,002
30
4.1.2 Parotid glands
Endpoint - xerostomia (grade II)
Mean doses for parotid glands for the different treatment plans were compared, see
Figure 17.
M ean dose - Parotid glands
60
50
Physical
Mean dose [Gy]
EUD
40
NTCP
30
20
10
0
P1 s
P1 d
P2 s
P2 d
P3 s
P3 d
P4 s
P4 d
P5 s
P5 d
Patient and parotid sin/dx
Figure 17. Mean dose to parotid sin and dx for the different optimization methods (physical, EUD
and NTCP) for each patient.
An improved result was always obtained regarding the mean dose to the parotids when
using biologically based optimization. In Figure 18 the decrease in mean dose to the parotid
glands, using the two biologically-based methods compared to physically-based are shown
for the five patients.
31
Decrease in mean dose - Parotid glands
Decrease in mean dose [%]
50%
40%
EUD based
NTCP based
30%
20%
10%
0%
P1 sin P1 dx P2 sin P2 dx P3 sin P3 dx P4 sin P4 dx P5 sin P5 dx
Patient and parotid sin/dx
Figure 18. Decrease in mean dose to parotid sin and dx for the different optimization methods for
each patient.
The largest decrease in mean dose was obtained with EUD based optimization for
patient 3 for the left parotid, i.e. a decrease of 51%. According to Figure 18 there are no
correlated differences between the two biologically based optimization methods. In some
plans the optimization based on EUD gives a larger decrease in mean dose and in some of
them NTCP is better. Common is the decrease in mean dose to the parotids for all treatment
plans as compared to physically based optimization.
The treatment plans were also compared using NTCP for the OARs. In Figure 19 the
calculated NTCP for parotid sin and dx, respectively, are shown. In this calculation
parameters corresponding to the endpoint “xerostomia grade II” were used, see Table 4.
32
Calculated NTCP (xerostomia grade II) - Parotid glands
100%
90%
80%
NTCP [%]
70%
60%
Physical
50%
EUD
40%
NTCP
30%
20%
10%
0%
P1 s
P1 d
P2 s
P2 d
P3 s
P3 d
P4 s
P4 d
P5 s
P5 d
Patient and parotid sin/dx
Figure 19. NTCP for parotid sin and dx for the different optimization methods
(physical, EUD and NTCP) for each patient.
NTCP for the right parotid was zero for patient 4, therefore this value couldn’t be
calculated for this patient.
4.1.3 Spinal cord and brainstem
For the serially organized OARs, spinal cord and brainstem, the “near maximum” dose
(D1%) was compared for the different optimization methods, see Appendix C.1. For these
two OARs there were no significant differences in D1% using biological optimization
compared to physical.
NTCP were zero with both models and the treatment plans could therefore not be
analyzed in this way for these organs.
33
4.1.4 “Surrounding tissue”
In Table 7 the mean dose to the “surrounding tissue” are shown. It is the volume of the
patient not included in the optimization, i.e. external contour except treatment volumes
(PTV) and OARs (Spinal cord, brainstem and parotid glands).
Table 7. Mean dose to the “surrounding tissue”, i.e. the total head and neck volume except the target
volumes and the OARs.
Mean dose to “Surrounding tissue” [Gy] and its ratio relative to
physically optimized plans
Patient 1
Physical
EUD
NTCP
7.86
7.81
7.87
1.000
0.994
1.001
Patient 2
Physical
EUD
NTCP
6.37
6.53
6.35
1.000
1.025
0.997
Patient 3
Physical
EUD
NTCP
7.03
6.90
6.95
1.000
0.982
0.989
Patient 4
Physical
EUD
NTCP
7.14
7.04
7.11
1.000
0.986
0.996
Patient 5
Physical
EUD
NTCP
9.89
9.82
10.01
1.000
0.993
1.012
The mean dose to the “surrounding tissue” with biological optimization compared to
physical was not changed significantly. For some treatment plans the mean dose increased
slightly with the biological optimization compared to physical, while it decreased for others,
see Table 7.
34
4.2
Additional investigations
4.2.1 Effect of changing number of segments
The treatment plans optimized with different number of segments were compared by the
mean doses to parotids sin and dx, and also the change in calculated NTCP. The mean doses
are displayed in Figure 20 and the differences in calculated NTCP from the NTCP obtained
with 50 segments are shown in Figure 21.
Mean dose - parotid sin and dx
45,0
40,0
Physical sin
35,0
Dose [Gy]
Physical dx
EUD sin
30,0
EUD dx
NTCP sin
25,0
NTCP dx
20,0
15,0
10,0
40
50
60
70
80
90
100
110
# segments
Figure 20. Mean doses to parotids sin and dx respectively, optimized with different number of
segments. Blue means optimized with physical parameters, orange and green means optimized with
biological (EUD and NTCP).
35
Parotids NTCP as a function of beam segments
1,35
1,30
Physical sin
NTCP(x)/NTCP(50)
1,25
Physical dx
EUD sin
1,20
EUD dx
1,15
NTCP sin
NTCP dx
1,10
1,05
1,00
0,95
45
55
65
75
85
95
105
# segments
Figure 21. The figure shows the calculated NTCP for different number of segments relative to NTCP
obtained with 50 segments.
With EUD as optimization parameter, the left parotid couldn’t be analyzed in this way
since NTCP was zero.
36
Chapter 5
Discussion
We have compared optimization with physical and biological constraints/objectives for
some head and neck cancer patients with different diagnoses. For the evaluation mean
doses were compared for the parotid glands due to the parallel structure of this organ. The
“near maximum” dose D1 was used when comparing doses to the serially organized OARs
(spinal cord and brainstem). The doses to the target volumes were compared in terms of D99
and D1, to verify that the same dose coverage was kept, independent of optimization
method. The treatment plans were also evaluated by means of NTCPs for the OARs. NTCP
values were calculated in the Workstation for the physically optimized plans.
A considerable decrease in mean dose to the parotid glands of up to 51% were found
when using biologically compared to physically based optimization while keeping
approximately the same target dose coverage, see Figure 18. According to the guidelines by
DAHANCA (section 2.6.2) the parotid glands should receive a mean dose below 26 Gy. In
the figures in Figure 17 the mean doses to the parotid glands are presented and for at least
one parotid in each patient this dose limit is reached. The dose limit was exceeded when the
target volume overlapped the parotid. In these cases it was considered more important to
cover the target volume than lower the mean dose to parotid. The maximum dose to the
serially organized OARs, spinal cord and brainstem, obtained with biological optimization,
were not significantly different from the maximum dose constraints set in the physical
optimization process, see figures in Appendix C. This may be due to that serially organized
organs have maximum doses as treatment goals, which may be easier to fulfil with physical
optimization than the treatment goal of parotid glands, which is the mean dose.
The physically and biologically optimized plans were further compared in terms of
NTCP for the parotids (endpoint xerostomia grade II). NTCP was significantly reduced
with the biologically optimized plans, see Figure 19. Spinal cord and brainstem NTCP were
zero with both techniques and could therefore not be analyzed in this way. Even if NTCP is
zero, the dose is not zero, i.e. the dose could in principle be decreased further. This is a
disadvantage when optimizing with the NTCP model. If NTCP already equals zero in an
OAR, the optimizer won’t try any harder to decrease the dose further. This is e.g. the case
for patient 1 optimized with NTCP, see Figure B 11 in Appendix B. The dose to the spinal
cord is lower in the treatment plan optimized with dose objectives than with NTCP
constraints; see Figure C 1 in Appendix C.
Since both biologically based optimization methods decrease the mean dose and NTCP
for parotid glands, while keeping the same target dose coverage, one can suspect that the
decrease in mean dose to parotid and NTCP are probably due to higher dose in some other
volume in the body. A comparison of the mean dose to the volume not included in the
optimization, i.e. external surface (whole head and neck area) except target volumes and
OARs, called “Surrounding tissue”, was done, see Table 7. From the table an average
change in mean dose to surrounding tissue is calculated to 0.2%, i.e. the mean dose is not
significantly changed.
37
It could be argued that both optimization techniques can in principle produce the same
result. Several hours were, however, spent on the physically optimized plans to make them
“optimal” and to meet the dose-volume criteria set for target volumes and OARs in the
optimization process. In the biological optimization the adjustable parameter is only one
(either EUDmax or NTCP) for each OAR, which makes this method much simpler and easy
to apply. The time spent on the biologically optimized plans was far less and hence only
this fact makes this technique interesting and worth pursuing further.
The function values have been useful when evaluating the treatment plans and trying to
find the “optimal” plan. This is a useful tool to see how the optimizer distributes the
capacity between the different objectives. Objectives with low function values could
probably be pressed further.
A disadvantage when optimizing using NTCP is that constraints have to be used. The
reason for not mixing NTCPs and physical functions in the objective function is that they
are mathematically very different. The weights would work differently for the two
objective types. A consequence of this is that the OARs cannot be weighted, which was
possible with both the physically and EUD based optimization since objectives could be
used. The TPS would however allow optimization of a weighted NTCP objective where the
physical functions are treated as constraints.
A limit in this study was that biological optimization was used only for the OARs. If
the guidelines by DAHANCA should be followed the dose to 99% of the target volume
should be within 95%-107% of the prescribed dose. With these kinds of limits it is more
reasonable to use physical optimization parameters on the target volumes, than biological.
The reason is that the TCP model doesn’t have an upper dose limit and because of that, the
dose interval by DAHANCA guidelines would probably be impossible to achieve with only
TCP as optimization parameter. The treatment plans obtained with TCP may be so different
from conventional plans that it may be difficult to judge the quality. If TCP would be used
on the target volumes, it probably would have to be combined with physical max dose
objectives, to avoid too high doses in the target. Too high dose in the target volumes may
cause necrosis to the tumour bed.
In this study there are a lot of other parameters (kept fixed in this study) that probably
can influence the optimization result, e.g. beam angles, collimator angle, max number of
iterations, etc. In this report one parameter was further studied, i.e. the effect of changing
the number of beam segments. The maximum number of segments was increased from 50
to 75, 80 and 100, respectively. In Figure 20 the mean doses to parotid sin and dx are
shown. From the figure one can see that 100 and 75 segments give a slightly higher mean
dose than 50 and 80. The increase is more obvious for the physically optimized treatment
plans than with the biologically. But none of them are clinically significant. The same
tendencies are shown in Figure 21, where the use of 100 segments gives an observable
difference in NTCP compared to 50 segments, especially for the physically optimized
treatment plans.
Another parameter that influences the result is the choice of endpoint in the NTCP
model. Both the optimization with NTCP and the NTCP evaluation will be different with
different endpoints. A more severe endpoint allows for higher doses before the chosen level
of damage will be noticeable.
38
As mentioned earlier, the serially organized organs at risk were delineated both with
and without margins. It may be discussed which of them to use in the biologically based
optimizations. In this study the volumes with included margins are used both in the
optimizations, and also in the calculations of NTCP. On one hand, it may be wrong to
include the margins in the biological optimizations since the parameters are specified for a
specific type of tissue, and this will be violated in the margin.
This study was limited to use biological models only on the OAR, i.e. the target
volumes were optimized with the same criteria in all treatment plans. However, when the
criteria for the OAR are pushed, eventually, the dose coverage to the target volumes will be
too different from that of the completely physically optimized treatment plan. This is one of
the difficulties, and therefore one of the main uncertainties, in this study, to know when the
criteria can’t be pushed further, i.e. how large differences in dose are allowed in the target
volumes to still be able to say that the target dose coverage is kept. In this study this was
determined by looking at the DVHs, and when the variations were too large the biologically
criteria were not pushed further. In Table 5 the “near minimum” (D99%) and “near
maximum” (D1%) to the target volumes are presented. The relative differences in these
doses between the physically and biologically based treatment plans are presented in Table
6. It can be seen that the differences are both decrease and increase of the dose. In future
work of this study, this is definitely something to consider. The expression “keeping the
dose coverage” should probably be more specific.
39
Chapter 6
Conclusions
In working on this study I have come to realize that treatment planning is not an easy
task. You never know when, or even if, you have found the optimal treatment plan. There
are many parameters involved in the process and that is one of the main differences between
physically and biologically based optimization. In dose-volume based optimization there is a
number of adjustable optimization criteria, but in both EUD and NTCP based optimization
there are only one adjustable parameter (EUDmax and NTCPmax, respectively). This means
that physically based optimization is a lot more time-consuming process than biological.
Except the gain in time, an improved result was always obtained regarding the mean
dose and calculated NTCP to the parotids when using biologically based optimization.
However, the number of patients included in this study is limited, and further analyzes
and more patients are needed to be able to determine the impact of biological optimization
in clinical practise. Also the fact that this study only included the head and neck region
implicates that further, similar study is necessary on other parts of the body.
40
Chapter 7
Acknowledgements
I would like to thank my supervisors Per Nilsson, Michael Blomquist and Mikael
Karlsson for their encouragement and guiding during my thesis work. Our discussions have
been vital for this study.
I would also like to express my deepest gratitude to RaySearch Laboratories AB for first
of all letting me use their TPS for this study. Second, a special thanks to Malin Ericsson and
Kjell Eriksson for guiding me in ‘ORBIT Workstation’ and for the quick response of
questions and new versions of the program.
Magnus Jälmbrant deserves to be thanked for the help with several installations of the
TPS, and other computer related issues.
Finally, I would like to thank my classmate Kajsa for listening to all my chatter during
this work and for great support.
Thank you!
41
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43
Appendix A
A.1
Optimization objectives and/or constraints
Patient 1
Physical
ROI
PTVB [Target]
Min dos
[Gy]
Physical
Constraints / objectives
Uniform dose Max dos Max dos volym
[Gy]
[Gy]
[% av vol]
64.60
69.50
71.00
40.00
30.00
45.00
26.00
26.00
Medulla [OAR]
Medulla PRV [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA [Target]
75
35
44
47.50
51.00
53.50
PTVA sin [Target]
47.50
51.00
53.50
weight
950
500
800
1000
100
1000
40
40
950
300
800
950
300
800
Table A 1. The table shows the optimization parameters for the physically based optimization for
patient 1. Cells marked pink means constrains and green means objectives.
EUD
ROI
PTVB [Target]
Min dos
[Gy]
Physical
Constraints / objectives
Uniform dose Max dos
[Gy]
[Gy]
Biological
EUD
[Gy]
a
(a=1/n)
64.60
950
500
800
69.50
71.00
Medulla [OAR]
Medulla PRV [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA [Target]
36.500
21.000
26.000
47.50
51.00
53.50
PTVA sin [Target]
47.50
51.00
53.50
weight
20
1.42857
1.42857
1000
1000
1000
950
300
800
950
300
800
Table A 2. The table shows the optimization parameters for the EUD based optimization for patient 1.
Cells marked pink means constrains and green means objectives.
44
NTCP
ROI
PTVB [Target]
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
Biological
Max
NTCP
64.60
950
500
800
69.50
71.00
Medulla [OAR]
Medulla PRV [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA [Target]
NTCP <0.0000001
NTCP <0.008
NTCP <0.035
47.50
950
300
800
950
300
800
51.00
53.50
PTVA sin [Target]
weight
47.50
51.00
53.50
Table A 3. The table shows the optimization parameters for the NTCP based optimization for patient
1. Cells marked pink means constrains and green means objectives.
Patient 2
Physical
ROI
Medulla [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA-PTVB [Target]
Min dos
[Gy]
Physical
Constraints / objectives
Uniform dose Max dos Max dos volym
[Gy]
[Gy]
[% av vol]
46.00
26.00
26.00
53.50
40
40
950
500
800
950
500
800
72.76
500
800
47.50
51.00
53.50
PVTA sin [Target]
47.50
51.00
PTVB [Target]
50
40
weight
64.60
69.50
Table A 4. The table shows the optimization parameters for the physically based optimization for
patient 2. Cells marked pink means constrains and green means objectives.
45
EUD
ROI
Medulla [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA-PTVB [Target]
Min dos
[Gy]
Physical
Constraints / objectives
Uniform dose Max dos
[Gy]
[Gy]
Biological
EUD
[Gy]
a
(a=1/n)
40.000
20
38.000 1.428571
24.000 1.428571
47.50
53.50
950
500
800
950
500
800
72.76
500
800
51.00
53.50
PVTA sin [Target]
47.50
51.00
PTVB [Target]
weight
64.60
69.50
Table A 5. The table shows the optimization parameters for the EUD based optimization for patient 2.
Cells marked pink means constrains and green means objectives.
NTCP
ROI
Medulla [OAR]
Parotis dx [OAR]
Parotis sin [OAR]
PTVA-PTVB [Target]
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
47.50
weight
53.50
950
500
800
950
500
800
53.50
500
800
53.50
47.50
51.00
PTVB [Target]
Max
NTCP
NTCP <0.000001
NTCP <0.12
NTCP <0.01
51.00
PVTA sin [Target]
Biological
47.50
51.00
Table A 6. The table shows the optimization parameters for the NTCP based optimization for patient
2. Cells marked pink means constrains and green means objectives.
46
Patient 3
Physical
ROI
PTVA sin [Target]
Min
dos
[Gy]
Physical
Constraints / objectives
Uniform
Max
Max dos
dose
dos
volym
[Gy]
[Gy]
[% av vol]
weight
47.50
53.50
950
500
800
950
500
800
72.76
26.00
26.00
41.00
50.00
50.00
55.00
500
800
40
40
1000
1000
1000
1000
51.00
53.50
PTVA dx [Target]
47.50
51.00
PTV [Target]
64.60
69.50
Parotis sin [OAR]
Parotis dx [OAR]
Medulla [OAR]
Medulla PRV [OAR]
Medobl [OAR]
Medobl PRV [OAR]
45
50
Table A 7. The table shows the optimization parameters for the physically based optimization for
patient 3. Cells marked pink means constrains and green means objectives.
EUD
ROI
Physical
Biological
Constraints / objectives
Min dos Uniform dose Max dos EUD
a
[Gy]
[Gy]
[Gy]
[Gy] (a=1/n)
PTVA sin [Target]
47.50
PTVA dx [Target]
47.50
PTV [Target]
64.60
950
500
800
950
500
800
51.00
53.50
51.00
53.50
69.50
15
41
1.429
1.429
500
800
1000
1000
36
20
1000
32
6.25
1000
72.76
Parotis sin [OAR]
Parotis dx [OAR]
Medulla [OAR]
Medulla PRV [OAR]
Medobl [OAR]
Medobl PRV [OAR]
weight
Table A 8. The table shows the optimization parameters for the EUD based optimization for patient 3.
Cells marked pink means constrains and green means objectives.
47
NTCP
ROI
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
PTVA sin [Target]
47.50
PTVA dx [Target]
47.50
PTV [Target]
64.60
Biological
Max
NTCP
weight
53.50
950
500
800
950
500
800
72.76
500
800
51.00
53.50
51.00
69.50
NTCP < 0.02
NTCP < 0.60
Parotis sin [OAR]
Parotis dx [OAR]
Medulla [OAR]
Medulla PRV [OAR]
Medobl [OAR]
Medobl PRV [OAR]
NTCP <0.00001
NTCP < 0.000001
Table A 9. The table shows the optimization parameters for the NTCP based optimization for patient
3. Cells marked pink means constrains and green means objectives.
Patient 4
Physical
ROI
Min dos
[Gy]
PTVB [Target]
64.60
Physical
Constraints / objectives
Uniform dose Max dos Max dos volym
[Gy]
[Gy]
[% av vol]
69.00
72.76
PTVA-PTVB [Target]
47.50
PTVA dx [Target]
47.50
53.50
53.50
40.00
20.00
43.00
48.00
parotis sin [OAR]
parotis dx [OAR]
Medulla [OAR]
Medulla porv [OAR]
medobl [OAR]
medobl porv [OAR]
28
30
weight
500
800
950
500
950
800
50
40
1000
1000
Table A 10. The table shows the optimization parameters for the physically based optimization for
patient 4. Cells marked pink means constrains and green means objectives.
48
EUD
ROI
PTVB [Target]
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
Biological
EUD
[Gy]
a
(a=1/n)
weight
64.60
69.00
22
12
1.428571
1.428571
500
800
950
500
950
800
1000
1000
40
20
1000
11
6.25
1000
72.76
PTVA-PTVB [Target]
47.50
PTVA dx [Target]
47.50
53.50
53.50
parotis sin [OAR]
parotis dx [OAR]
Medulla [OAR]
Medulla porv [OAR]
medobl [OAR]
medobl porv [OAR]
Table A 11. The table shows the optimization parameters for the EUD based optimization for patient
4. Cells marked pink means constrains and green means objectives.
NTCP
ROI
PTVB [Target]
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
Biological
EUD
[Gy]
a
(a=1/n)
weight
64.60
69.00
500
800
950
500
950
800
72.76
PTVA-PTVB [Target]
47.50
PTVA dx [Target]
47.50
53.50
53.50
parotis sin [OAR]
parotis dx [OAR]
Medulla [OAR]
Medulla porv [OAR]
medobl [OAR]
medobl porv [OAR]
NTCP
NTCP
<0.004
<0.000001
NTCP
< 0.002
NTCP
< 0.000001
Table A 12. The table shows the optimization parameters for the NTCP based optimization for
patient 4. Cells marked pink means constrains and green means objectives.
49
Patient 5
Physical
ROI
Min dos
[Gy]
Parotid sin [OAR]
Parotid dx [OAR]
Spinal Cord [OAR]
porvspinal [OAR]
Brain Stem [OAR]
porvhjrns [OAR]
PTVA-PTVB [Target]
48.00
PTVAsin [Target]
47.50
PTVB [Target]
64.60
Physical
Constraints / objectives
Uniform dose Max dos Max dos volym
[Gy]
[Gy]
[% av vol]
30.00
50.00
43.00
48.00
52.00
58.00
50
55
weight
50
40
1000
53.50
1000
1000
950
500
950
800
72.76
700
800
53.50
69.50
Table A 13. The table shows the optimization parameters for the physically based optimization for
patient 5. Cells marked pink means constrains and green means objectives.
Physical
Constraints / objectives
EUD
ROI
Min
dos
[Gy]
Parotid sin [OAR]
Parotid dx [OAR]
Spinal Cord [OAR]
porvspinal [OAR]
Brain Stem [OAR]
porvhjrns [OAR]
PTVA-PTVB [Target]
48.00
PTVAsin [Target]
47.50
PTVB [Target]
64.60
Uniform dose
[Gy]
Biological
Max dos
[Gy]
EUD
[Gy]
a
(a=1/n)
weight
27
57
1.4285714
1.4285714
1000
1000
38
20
1000
39
6.25
53.50
1000
950
500
950
800
72.76
700
800
53.50
69.50
Table A 14. The table shows the optimization parameters for the EUD based optimization for patient
5. Cells marked pink means constrains and green means objectives.
50
NTCP
ROI
Parotid sin [OAR]
Parotid dx [OAR]
Spinal Cord [OAR]
porvspinal [OAR]
Brain Stem [OAR]
porvhjrns [OAR]
PTVA-PTVB [Target]
Physical
Constraints / objectives
Min dos Uniform dose Max dos
[Gy]
[Gy]
[Gy]
48.00
47.50
PTVB [Target]
64.60
Max NTCP
NTCP
NTCP
< 0.16
< 0.8
NTCP
<0.003
NTCP
<0.004
weight
53.50
950
500
950
800
72.76
700
800
53.50
PTVAsin [Target]
Biological
69.50
Table A 15. The table shows the optimization parameters for the NTCP based optimization for
patient 5. Cells marked pink means constrains and green means objectives.
51
Appendix B
B.1
DVHs - only physical optimization parameters
Patient 1
DVH Patient 1 - Physical
100
90
80
GTV
Spinal cord
Volume [%]
70
Spinal cord PRV
60
Parotid dx
50
Parotid sin
PTVB
40
PTVA dx
30
PTVA sin
Surrounding tissue
20
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 1. The figure illustrates the DVH of the physically based treatment plan for patient 1. Treatment
volumes are coloured in red and pink, and OAR yellow/orange and green.
52
Patient 2
DVH Patient 2 - Physical
100
90
80
70
GTV
Volume [%]
Spinal cord PRV
60
Parotid dx
Parotid sin
50
PTVA-PTVB
PTV sin
40
PTVB
30
Surrounding tissue
20
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 2. The figure illustrates the DVH of the physically based treatment plan for patient 2. Treatment
volumes are coloured in red and pink, and OAR yellow/orange and green.
53
Patient 3
DVH Patient 3 - Physical
100
90
80
PTVB
PTVA dx
Volume [%]
70
PTVA sin
GTVn1+2
60
GTVt
Spinal cord
50
Spinal cord PRV
40
Brain stem
30
Parotid dx
20
Surrounding tissue
Brain stem PRV
Parotid sin
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 3. The figure illustrates the DVH of the physically based treatment plan for patient 3. Treatment
volumes are coloured in red and pink, and OAR yellow/orange and green.
54
Patient 4
DVH Patient 4 - Physical
100
90
PTVB
PTVA dx
80
PTVA-PTVB
Volume [%]
70
GTVn1
GTVn2
60
GTVt
Spinal cord
50
Spinal cord PRV
40
Brain stem
Brain stem PRV
30
Parotid dx
20
Parotid sin
Surrounding tissue
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 4. The figure illustrates the DVH of the physically based treatment plan for patient 4. Treatment
volumes are coloured in red and pink, and OAR yellow/orange and green.
55
Patient 5
DVH Patient 5 - Physical
100
90
80
GTVn
GTVt
70
PTVB
Volume [%]
PTVA-PTVB
60
PTVA sin
Spinal cord
50
Spinal cord PRV
Brain stem
40
Brain stem PRV
Parotid dx
30
Parotid sin
20
Surrounding tissue
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 5. The figure illustrates the DVH of the physically based treatment plan for patient 5. Treatment
volumes are coloured in red and pink, and OAR yellow/orange and green.
56
B.2
DVHs - EUD opt. parameters on OAR versus physical
Patient 1
DVH Patient 1 - Physical vs. EUD
100
90
Spinal cord (EUD)
Spinal cord PTV (EUD)
80
Parotid dx (EUD)
Parotid sin (EUD)
Volume [%]
70
PTVB (EUD)
PTVA dx (EUD)
60
PTVA sin (EUD)
Spinal cord
50
Spinal cord PRV
Parotid dx
40
Parotid sin
PTVB
30
PTVA dx
20
PTVA sin
Surrounding tissue (EUD)
10
Surrounding tissue
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 6. The figure illustrates the DVH of the physically and EUD based treatment plan for patient 1.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
57
Patient 2
DVH Patient 2 - Physical vs. EUD
100
Spinal cord PRV (EUD)
90
Parotid dx (EUD)
Parotid sin (EUD)
80
PTVA-PTVB (EUD)
Volume [%]
70
PTVA sin (EUD)
PTVB (EUD)
60
Surrounding tissue (EUD)
Spinal cord PRV
50
Parotid dx
40
Parotid sin
PTVA-PTVB
30
PTVA sin
20
PTVB
Surrounding tissue
10
0
0
20
40
60
80
Dose [Gy]
Figure B 7. The figure illustrates the DVH of the physically and EUD based treatment plan for patient 2.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
58
Patient 3
DVH Patient 3 - Physical vs. EUD
100
PTVB
PTVA dx
90
PTVA sin
Spinal cord
80
Spinal cord PRV
Brain stem
70
Brain stem PRV
Volume [%]
Parotid dx
60
Parotid sin
Surrounding tissue
PTV (EUD)
50
PTVA dx (EUD)
PTVA sin (EUD)
40
Spinal cord (EUD)
Spinal cord PRV (EUD)
30
Brain stem (EUD)
Brain stem PRV (EUD)
20
Parotid dx (EUD)
Parotid sin (EUD)
Surrounding tissue (EUD)
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 8. The figure illustrates the DVH of the physically and EUD based treatment plan for patient 3.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
59
Patient 4
DVH Patient 4 - Physical vs. EUD
PTVB
100
PTVA dx
PTVA-PTVB
90
Spinal cord
Spinal cord PRV
80
Brain stem
Brain stem PRV
Volume [%]
70
Parotid dx
Parotid sin
60
Surrounding tissue
PTVB (EUD)
50
PTVA dx (EUD)
PTVA-PTVB (EUD)
40
Spinal cord (EUD)
Spinal cord PRV (EUD)
30
Brain stem (EUD)
Brain stem PRV (EUD)
20
Parotid dx (EUD)
Parotis sin (EUD)
10
Surrounding tissue (EUD)
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 9. The figure illustrates the DVH of the physically and EUD based treatment plan for patient 4.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
60
Patient 5
DVH Patient 5 - Physical vs. EUD
100
PTVB
PTVA-PTVB
90
PTVA sin
Spinal cord
80
Spinal cord PRV
Brain stem
Brain stem PRV
70
Volume [%]
Parotid dx
Parotid sin
60
Surrounding tissue
PTVB (EUD)
50
PTVA-PTVB (EUD)
PTVA sin (EUD)
Spinal cord (EUD)
40
Spinal cord PRV (EUD)
Brain stem(EUD)
30
Brain stem PRV (EUD)
Parotid dx (EUD)
Parotid sin (EUD)
20
Surrounding tissue (EUD)
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 10. The figure illustrates the DVH of the physically and EUD based treatment plan for patient 5.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
61
B.3
DVHs - NTCP opt. parameters on OAR versus physical
Patient 1
DVH Patient 1 - Physical vs. NTCP
100
Spinal cord
90
Spinal cord PRV
Parotid dx
80
Parotid sin
PTVB
70
Volume [%]
PTVA dx
60
PTVA sin
Spinal cord (NTCP)
50
Spinal cord PRV (NTCP)
Parotid dx (NTCP)
40
Parotid sin (NTCP)
PTVB (NTCP)
30
PTVA dx (NTCP)
20
PTVA sin (NTCP)
Surrounding tissue
10
Surrounding tissue (NTCP)
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 11. The figure illustrates the DVH of the physically and NTCP based treatment plan for patient 1.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
62
Patient 2
DVH Patient 2 - Physical vs. NTCP
100
90
Spinal cord PRV
80
Parotid dx
Parotid sin
Volume [%]
70
PTVA dx
PTVA sin
60
PTVB
Surrounding tissue
50
Spinal cord PRV (NTCP)
Parotid dx (NTCP)
40
Parotid sin (NTCP)
30
PTVA dx (NTCP)
20
PTVB (NTCP)
PTVA sin (NTCP)
Surrounding tissue (NTCP)
10
0
0
10
20
30
40
50
60
70
Dose [Gy]
Figure B 12. The figure illustrates the DVH of the physically and NTCP based treatment plan for patient 2.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
63
Patient 3
DVH Patient 3 - Physical vs. NTCP
100
PTVB
PTVA dx
90
PTVA sin
Spinal cord
80
Spinal cord PRV
Brain stem
70
Brain stem PRV
Volume [%]
Parotid dx
60
Parotid sin
Surrounding tissue
PTV NTCP
50
PTVA dx NTCP
PTVA sin NTCP
40
Spinal cord NTCP
Spinal cord PRV NTCP
30
Brain stem NTCP
Brain stem PRV NTCP
20
Parotid dx NTCP
Parotid sin NTCP
Surrounding tissue NTCP
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 13. The figure illustrates the DVH of the physically and NTCP based treatment plan for patient 3.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
64
Patient 4
DVH Patient 4 - Physical vs. NTCP
PTVB
100
PTVA dx
PTVA-PTVB
90
Spinal cord
Spinal cord PRV
80
Brain stem
Brain stem PRV
Volume [%]
70
Parotid dx
Parotid sin
60
Surrounding tissue
PTVB (NTCP)
50
PTVA dx (NTCP)
40
PTVA-PTVB (NTCP)
30
Spinal cord PRV (NTCP)
20
Brain stem PRV (NTCP)
10
Parotis sin (NTCP)
Spinal cord (NTCP)
Brain stem (NTCP)
Parotid dx (NTCP)
Surrounding tissue (NTCP)
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 14. The figure illustrates the DVH of the physically and NTCP based treatment plan for patient 4.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green.
65
Patient 5
DVH Patient 5 - Physical vs. NTCP
100
PTVB
PTVA-PTVB
90
PTVA sin
Spinal cord
80
Spinal cord PRV
Brain stem
70
Brain stem PRV
Volume [%]
Parotid dx
Parotid sin
60
Surrounding tissue
PTVB (NTCP)
50
PTVA-PTVB (NTCP)
PTVA sin (NTCP)
Spinal cord (NTCP)
40
Spinal cord PRV (NTCP)
Brain stem (NTCP)
30
Brain stem PRV (NTCP)
Parotid dx (NTCP)
20
Parotid sin (NTCP)
Surrounding tissue (NTCP)
10
0
0
10
20
30
40
50
60
70
80
Dose [Gy]
Figure B 15. The figure illustrates the DVH of the physically and NTCP based treatment plan for patient 5.
Treatment volumes are coloured in red and pink, and OAR yellow/orange and green
66
Appendix C
C.1
Mean doses, D99 and D1 to OAR
Patient 1
Patient 1 - Dose to OAR
45.00
40.00
35.00
Mean dose Parotid sin
Dose [Gy]
30.00
Mean dose Parotid dx
25.00
D99 Spinal cord
20.00
D1 Spinal cord
15.00
Mean dose Surr. tissue
10.00
5.00
0.00
Physical
EUD
NTCP
Plan type
Figure C 1. The figure shows mean doses for parotid sin and dx and D99 and D1 for spinal cord and
brainstem for the different optimization methods for patient 1.
Patient 2
Patient 2 - Dose to OAR
45.00
40.00
Dose [Gy]
35.00
Mean dose Parotid sin
30.00
Mean dose Parotid dx
25.00
D99 Spinal cord
20.00
D1 Spinal cord
15.00
Mean dose Surr. tissue
10.00
5.00
0.00
Physical
EUD
NTCP
Plan type
Figure C 2. The figure shows mean doses for parotid sin and dx and D99 and D1 for spinal cord and
brainstem for the different optimization methods for patient 2.
67
Patient 3
Patient 3 - Dose to OAR
50.00
Dose [Gy]
45.00
40.00
Mean dose Parotid sin
35.00
Mean dose Parotid dx
D99 Spinal cord
30.00
D1 Spinal cord
25.00
D99 Brainstem
20.00
D1 Brainstem
15.00
Mean dose Surr.tissue
10.00
5.00
0.00
Physical
EUD
NTCP
Plan type
Figure C 3. The figure shows mean doses for parotid sin and dx and D99 and D1 for spinal cord and
brainstem for the different optimization methods for patient 3.
Patient 4
Patient 4 - Dose to OAR
50.00
Dose [Gy]
45.00
40.00
Mean dose Parotid sin
35.00
Mean dose Parotid dx
D99 Spinal cord
30.00
D1 Spinal cord
25.00
D99 Brainstem
20.00
D1 Brainstem
15.00
Mean dose Surr.tissue
10.00
5.00
0.00
Physical
EUD
NTCP
Plan type
Figure C 4. The figure shows mean doses for parotid sin and dx and D99 and D1 for spinal cord and
brainstem for the different optimization methods for patient 4.
68
Patient 5
Patient 5 - Dose to OAR
60.00
55.00
Dose [Gy]
50.00
45.00
Mean dose Parotid sin
40.00
Mean dose Parotid dx
35.00
D99 Spinal cord
30.00
D1 Spinal cord
25.00
D99 Brainstem
20.00
D1 Brainstem
15.00
Mean dose Surr.tissue
10.00
5.00
0.00
Physical
EUD
NTCP
Plan type
Figure C 5. The figure shows mean doses for parotid sin and dx and D99 and D1 for spinal cord and
brainstem for the different optimization methods for patient 5.
69