Optimization methods for high dose rate brachytherapy ... · modulated brachytherapy (EMBT), are...
Transcript of Optimization methods for high dose rate brachytherapy ... · modulated brachytherapy (EMBT), are...
Optimization methods for high dose rate brachytherapytreatment planning
by
Elodie R. Mok Tsze Chung
A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial EngineeringUniversity of Toronto
Copyright c© 2016 by Elodie R. Mok Tsze Chung
Abstract
Optimization methods for high dose rate brachytherapy treatment planning
Elodie R. Mok Tsze Chung
Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
2016
Optimization approaches for treatment planning in two novel high-dose-rate (HDR)
brachytherapy techniques, direction-modulation brachytherapy (DMBT) and energy-
modulated brachytherapy (EMBT), are investigated for cervical cancer and prostate
cancer. Brachytherapy is a form of radiation therapy where a radioactive source is placed
inside the body to irradiate the tumour internally. Conventionally, only one source is used
and it is unshielded, thus providing an isotropic dose distribution. DMBT makes use of
a new shielded applicator that is capable of delivering highly directional radiation distri-
butions. In EMBT, three HDR sources, 192Ir, 60Co, and 169Yb, are used in combination
to provide variety in dose profiles. To investigate the benefit of these two new techniques
over conventional brachytherapy, we use an inverse planning approach to generate the
treatment plans. We model the treatment planning problem as a quadratic program and
use an interior point constraint generation algorithm to generate the treatment plans.
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Acknowledgements
First and foremost, I would like to thank my two supervisors and mentors, Dr. Dionne
Aleman and Dr. William Song for patiently guiding and encouraging me throughout my
entire research. This work would not have been possible without their support and
expertise.
I am grateful to my colleagues and friends from the Medical Operations Research
Laboratory and Sunnybrook Health Sciences Centre for their guidance as I embarked on
my journey at U of T, as well as their insightful ideas and helpful discussions about my
research work. They have helped me overcome many obstacles and I have learned so
much from them.
Lastly, my biggest thanks go to my family for their everlasting love and support from
halfway across the globe. Without them, I would not be the person I am today. As hard
as it was to be away from them, their words of encouragement cheered me through the
hardships of my degree. I would also like to thank Cole for being my rock over the last
two years.
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Contents
1 Introduction 1
1.1 Brachytherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Inverse planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Publications and presentations . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Methodology 9
2.1 Treatment plan evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Optimization model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Interior point constraint generation algorithm . . . . . . . . . . . . . . . 14
3 Direction-modulated brachytherapy 16
3.1 DMBT optimization model . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Energy-modulated brachytherapy 29
4.1 EMBT optimization model . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5 Conclusion 49
Bibliography 51
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List of Tables
3.1 Patient information for cervical cancer cancer . . . . . . . . . . . . . . . 21
3.2 Plan quality comparison between conventional BT and DMBT . . . . . . 22
3.3 Homogeneity index and conformal index for cervical cancer plans . . . . 24
3.4 Computation time for cervical cancer plans . . . . . . . . . . . . . . . . . 26
4.1 HDR source information . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Patient information for prostate cancer . . . . . . . . . . . . . . . . . . . 34
4.3 Clinical protocols for prostate cancer . . . . . . . . . . . . . . . . . . . . 34
4.4 Plan quality summary for the target volume . . . . . . . . . . . . . . . . 35
4.5 Plan quality summary for the OARs . . . . . . . . . . . . . . . . . . . . 36
4.6 Homogeneity index for the prostate cancer plans . . . . . . . . . . . . . . 37
4.7 Conformal index for the prostate cancer plans . . . . . . . . . . . . . . . 38
4.8 Comparison of source combinations to 192Ir plan . . . . . . . . . . . . . . 39
4.9 Treatment time for prostate cancer plans . . . . . . . . . . . . . . . . . . 43
4.10 Breakdown of TRAK for prostate cancer plans . . . . . . . . . . . . . . . 44
4.11 Computation time for prostate cancer plans . . . . . . . . . . . . . . . . 45
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List of Figures
1.1 HDR brachytherapy treatment . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 DTO penalty function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Linear approximations of a convex function . . . . . . . . . . . . . . . . . 14
2.3 morDiRECT evaluation window . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Tandem and ring applicator . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 DMBT tandem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Comparison of tandem design . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Comparison of conventional BT and DMBT plans . . . . . . . . . . . . . 23
3.5 Comparison of plan quality for a representative cervical case . . . . . . . 25
3.6 Computation time for DMBT . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Radial dose functions of 192Ir, 60Co, and 169Yb . . . . . . . . . . . . . . . 32
4.2 Depth dose functions of 192Ir, 60Co, and 169Yb . . . . . . . . . . . . . . . 32
4.3 Comparison of source combinations to 192Ir plan . . . . . . . . . . . . . . 40
4.4 Comparison of plan quality for a representative prostate case without DILs 41
4.5 Comparison of plan quality for a representative prostate case with DILs . 42
4.6 Computation time for EMBT . . . . . . . . . . . . . . . . . . . . . . . . 46
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Chapter 1
Introduction
Cancer is the leading cause of death in Canada [9]. In 2015, the Canadian Cancer Society
estimated 196,900 new cancer diagnoses and 78,000 deaths [10]. There are several ways
to treat cancer, including radiation therapy, chemotherapy, and surgery. In radiation
therapy, high energy radiation is directed to the tumour to kill the cancerous cells. The
goal is to deliver enough radiation to the tumour while minimizing the dose delivered to
the healthy tissues and critical structures surrounding the tumour, known as organs-at-
risk (OARs).
Radiation therapy can be performed externally or internally. In external beam ra-
diation therapy (EBRT), a machine directs beams of radiation from different directions
outside the patient towards the tumour. The radiation must travel through the skin and
healthy tissues before reaching the tumour. In internal radiation therapy, also known as
brachytherapy, radioactive sources are placed inside the body to deliver radiation to the
tumour internally.
1.1 Brachytherapy
Different types of brachytherapy can be defined according to three characteristics. The
first characteristic is the source placement. In intracavitary brachytherapy, the appli-
1
Chapter 1. Introduction 2
cators and the source are placed inside a body cavity near the tumour. This type of
brachytherapy is usually used for the treatment of cervical cancer, where the source is
placed in the vagina. In interstitial brachytherapy, the applicators in which the source
travels are inserted directly into the tumour tissue. Interstitial brachytherapy is com-
monly used to treat prostate or breast cancer. Other types include intralumenal and
intravascular brachytherapy, where the applicators are inserted inside a body lumen (a
tubular-shaped structure) and an artery, respectively.
The second characteristic is the duration of dose delivery. In temporary brachyther-
apy, radioactive sources are temporarily implanted inside the body. The time can range
from a few minutes to several days. On the other hand, in permanent brachytherapy,
small low dose rate radioactive seeds or pellets are permanently placed inside the body
and are left to decay. The radiation will decrease with time until it is insignificant and
the seeds are safe to remain in the body.
The third characteristic is the dose rate, which depends on the energy of the source
being used. Brachytherapy is divided into three modalities: high-dose-rate (HDR), low-
dose-rate (LDR), and pulse-dose-rate (PDR). HDR brachytherapy sources have a dose
rate greater than 12 Gray per hour (Gy/h), while LDR sources have a dose rate smaller
than 2 Gy/h. HDR brachytherapy treatments typically lasts for a few minutes and are
done in one or several sessions, called fractions. In LDR brachytherapy, the radioactive
sources (seeds) are implanted inside the tumour for a few days or permanently. Finally,
in PDR brachytherapy, the treatment is delivered in shorter “pulses”.
HDR brachytherapy offers many advantages. Due to the high dose rate of the source,
the treatment time is very short and can be mainly carried out on an outpatient basis.
Furthermore, it is minimally invasive compared to other treatment types such as surgery.
Unlike EBRT, HDR brachytherapy, as well as LDR and PDR brachytherapy, has the
advantage of reducing the dose delivered outside the tumour. Hence, it allows for higher
amounts of radiation to be prescribed to the tumour with limited exposure of the OARs.
Chapter 1. Introduction 3
HDR brachytherapy is also robust to tumour movement inside the body; since the source
is placed inside or near the tumour, its position relative to the tumour is generally
maintained.
Due to the high radioactivity of the source, usually the isotope Iridum-192 (192Ir),
treatment cannot be done manually and is instead delivered through a technique called
remote afterloading. After the applicators are inserted into the patient (Figure 1.1a),
they are connected to a computer-controlled machine, called an afterloader, using guid-
ing tubes (Figure 1.1b). The source is mounted at the end of a wire which is stored
in a shielded safe within the afterloader. Once the clinical staff leaves the room, the
afterloader is programmed to first send a dummy wire through the applicators to ensure
that the path is unobstructed (Figure 1.1c) and then send the HDR source through the
guiding tubes to pre-determined points in the applicator known as dwell positions (Figure
1.1d). The source sequentially stays at these dwell positions for a pre-specified amount
of time (Figures 1.1e, 1.1f, and 1.1g), known as the dwell time, after which it is pulled
out and returned to the shielded safe (Figure 1.1h).
The treatment potential of two novel HDR brachytherapy techniques are explored
using optimization methods to develop treatment plans. Conventionally, only one HDR
source is used during treatment and it is unshielded. The dose distribution about the
source is thus isotropic. The first technique is called direction modulated brachytherapy
(DMBT) and makes use of a shielded applicator to produce anisotropic dose distributions.
The second technique, called energy modulated brachytherapy (EMBT), makes use of
three HDR sources, 192Ir, Cobalt-60 (60Co), and Ytterbium-169 (169Yb), in combination.
1.2 Inverse planning
In radiation therapy, including brachytherapy, radiation kills both cancerous and healthy
cells. Therefore, treatments must be designed carefully for each patient to achieve an
Chapter 1. Introduction 4
(a) Applicators inserted in tumour (b) Applicators connected to afterloader
(c) Dummy wire sent through applicators (d) Dwell positions along catheters
(e) HDR source at the first dwell position (f) HDR source at another dwell position
(g) HDR source at the last dwell position (h) HDR source sent back to afterloader
Figure 1.1: HDR brachytherapy treatment procedure (Source: https://www.youtube.
com/watch?v=myxl4HeCcN4)
Chapter 1. Introduction 5
accurate treatment plan and a successful outcome. In brachytherapy, the amount of
radiation delivered by the source from a dwell position is determined by the correspond-
ing dwell time. Therefore, the selection of dwell positions and dwell times, known as
treatment planning, is a critical part of HDR brachytherapy.
Treatment plans are typically generated manually, called forward planning. That
is, the dwell positions and dwell times are iteratively changed until the desired dose
distribution is achieved. The trial-and-error nature of forward planning is time-consuming
and the quality of the treatment plans is heavily dependent on the experience and skill
of the planner.
Alternatively, inverse planning optimization can be used to develop treatment plans to
ensure that the best set of dwell positions and dwell times are selected. Inverse planning
starts with a set of dosimetric criteria and the anatomical information of the patient
obtained from ultrasound (US), computed tomography (CT) or magnetic resonance (MR)
images, and then uses optimization techniques to find the optimal set of dwell positions
and dwell times that satisfies the clinical objectives.
Inverse treatment planning has gained popularity over the last decade [13]. Several
mathematical models and solution techniques have been proposed to optimize brachyther-
apy treatment plans. The optimization techniques can be classified as heuristics or exact
methods. Heuristics produce a solution that is assumed to be “good enough” but can-
not be guaranteed to be optimal. Conversely, exact methods provide certainty in the
optimality of the solution, but may be computationally intensive.
Linear and integer programming are often used to model the brachytherapy treatment
planning problem as they can be solved by exact techniques. Linear programming is
usually used to optimize the dwell times given fixed dwell positions [5, 27, 28, 35]. They
are typically solved using the simplex method [5, 35] or commercial softwares, such as
CPLEX [27, 28]. For interstitial brachytherapy, the need to determine the insertion or
non-insertion of an applicator requires the use of integer programs to model the treatment
Chapter 1. Introduction 6
planning problem. Integer programs and mixed integer programs for brachytherapy have
been solved using branch-and-bound algorithms [41, 42, 76] and commercial softwares
[17, 23].
While these models can be solved exactly to produce an optimal solution, they be-
come increasingly hard to solve as the problem increases in size, especially with in-
teger programs [75]. As an alternative, heuristics can be used in HDR brachyther-
apy optimization. They can further be broken down into stochastic or deterministic
categories. Stochastic heuristics used in brachytherapy include simulated annealing
[15, 30, 32, 37, 43, 44, 74, 77], evolutionary algorithms [38–40, 52, 53, 70], and harmony
search [58]. Deterministic heuristics include gradient methods, such as the projected gra-
dient algorithm [25, 81, 82, 85], the Broyden-Fletcher-Goldberg-Shanno algorithm [54],
or the Fletcher-Reeves-Polak-Ribiere algorithm [54]. Non-gradient methods include the
modified Powell algorithm [54] and an attraction-repulsion model [79].
To combine the guaranteed optimality of an exact method with the speed of a heuris-
tic, we adapt the sector duration optimization (SDO) problem for stereotactic radio-
surgery (SRS) [4, 14, 18–20, 56] for our brachytherapy treatment planning problem. This
model is similar to the fluence map optimization (FMO) problem for intensity-modulated
radiation therapy (IMRT) [1–4, 51, 67–69]. We model the problem as a quadratic pro-
gram and solve it using an interior point constraint generation (IPCG) algorithm, which
was successfully implemented on a SRS inverse planning problem [56]. In SRS, beams
of radiation are directed to a point in the tumour, called an isocenter. Meanwhile in
brachytherapy, radiation diverges from the source at a dwell position. Dwell positions
and dwell times are therefore similar to isocenters and the time of radiation delivery from
the beams in SRS, respectively. Since brachytherapy and SRS are analogous, we expect
the IPCG algorithm to perform well on brachytherapy inverse planning problems.
Chapter 1. Introduction 7
1.3 Contributions
We contribute to the field of brachytherapy by exploring two new forms of treatment
delivery: DMBT for cervical cancer and EMBT for prostate cancer. We show that the
DMBT applicator, with its modulating capacity to produce anisotropic dose profiles,
allows for superior treatment plans compared to conventional brachytherapy. DMBT
especially proves useful in cases where the tumour is asymmetric or extends laterally.
Additionally, we demonstrate that the combination of different HDR sources in EMBT
allows for better OAR sparing without compromising target coverage. With the intro-
duction of afterloaders equipped with additional wires (i.e., capable of handling a second
HDR source) in the market, EMBT is now clinically viable.
We also contribute to the literature on HDR brachytherapy inverse planning. We
use an exact algorithm to solve a dwell time optimization problem to ε-optimality in a
finite number of iterations. This algorithm is able to handle large-scale convex problems,
which is desirable since the DMBT and EMBT problems are more complex than their
conventional counterparts.
1.4 Publications and presentations
The following contributions were made to the literature.
Publications
1. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman,
W. Song. Evaluation of 192Ir, 60Co, and 169Yb sources for high dose rate prostate
brachytherapy inverse planning using an interior point constraint generation algo-
rithm. Work in progress.
Presentations
The underlined text indicate the presenter(s) of the work.
Chapter 1. Introduction 8
1. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman, W.
Song. Evaluation of 192Ir, 60Co, and 169Yb sources for HDR prostate brachyther-
apy using an interior point constraint generation algorithm. INFORMS Annual
Conference, Nashville, TN, November 2016.
2. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman,
W. Song. Evaluation of 192Ir, 60Co, and 169Yb sources for high dose rate prostate
brachytherapy inverse planning using an interior point constraint generation algo-
rithm. AAPM Annual Conference, Washington DC. August 2016.
3. E. Mok Tsze Chung, H. Sagholi, A. Nicolae, M. Davidson, A. Ravi, D. Aleman,
W. Song. Evaluation of 192Ir, 60Co, and 169Yb sources for high dose rate prostate
brachytherapy inverse planning using an interior point constraint generation al-
gorithm. Mechanical and Industrial Engineering Graduate Research Symposium.
University of Toronto, Canada. June 2016.
Chapter 2
Methodology
In our optimization model, we consider every dwell position along the applicator(s) as a
dwell position to be used, thereby ensuring the best possible treatment quality (though
potentially at the expense of treatment time). We then use a dwell time optimization
(DTO) model to optimize the dwell times of each dwell position so that the final dose
distribution meets the clinical objectives as much as possible. Then, we assess the treat-
ment plan quality with common evaluation metrics to determine whether the plans are
clinically acceptable or not.
2.1 Treatment plan evaluation
Once a patient is diagnosed and scheduled for HDR brachytherapy, s/he is imaged using
US, CT or MRI scanners. After the images are obtained, the structures (tumour volume
and surrounding OARs) are contoured by a radiation oncologist. The prescription dose
and the dose thresholds are obtained from the radiation therapist. The structure volumes
are then broken down into 3D pixels, called voxels. Voxels have a size of 1 mm x 1
mm x 1 mm, which depends on the image resolution. The applicators are inserted in
the patient and contoured on the planning scans, after which the location of the dwell
positions relative to the structures are obtained. The corresponding dwell times can then
9
Chapter 2. Methodology 10
be optimized.
The most common method to evaluate a treatment plan is to use the cumulative
dose-volume histogram (DVH) [62]. A DVH shows the percentage of a structure volume
that receives a certain amount of dose or more. The structures can be the target or the
OARs. From the DVH curve, clinically relevant DVH parameters are obtained: (1) Vx,
the structure volume that receives x% of the prescription dose, and (2) Dx, the dose
received by x% of the structure volume. Ideally, 100% of the tumour volume should
receive 100% of the prescription dose (V100 = 100%), while 100% of the OARS should
receive no dose at all. Isodose lines, which are curved lines joining points that receive
the same amount of radiation through the target volume overlaid on structure images,
are also used to assess the plan quality.
There are also a variety of dosimetric indices to assess the quality of a treatment plan.
To measure how well the isodose corresponding to the prescription dose covers the target
volume, we use the conformal index (COIN) [8]. We also use the homogeneity index (HI)
to describe the homogeneity of the dose delivered to the target volume [84]. Both COIN
and HI have an ideal value of 1, with values less than 1 indicating worse conformity and
homogeneity, respectively. COIN and HI are calculated using the following formulas:
COIN =PTVref
PTV× PTVref
BVref
HI =V100 − V150
V100
where PTVref is the target volume that is covered by the prescription dose (100% isodose
line), and BVref is the body volume that receives the prescription dose.
The treatment time is an important factor to consider in evaluating a treatment plan,
since longer treatment times mean that the patient needs to stay in the brachytherapy
unit and under anaesthesia for longer. Treatment time is assumed to be a linear sum
of the individual dwell times. This definition is not entirely accurate because transition
Chapter 2. Methodology 11
time between dwell positions is not accounted for. However, the dwell positions are
evenly spaced and hence the transition time should remain constant across plans, and
can therefore be ignored for comparison purposes.
2.2 Optimization model
Similar to existing optimization models for IMRT [1–4, 51, 67–69] and SRS [4, 14, 18–
20, 56], we formulate the brachytherapy treatment planning problem as a quadratic
program that minimizes the sum of penalties incurred by deviating from the desired
dose per voxel. The only constraints are that the dwell times must be non-negative
and bounded. Quadratic programs generally reflect clinical attitudes towards overdose
and underdose, i.e., small deviations are more acceptable than large deviations [3, 69].
The DTO model is a basic formulation for brachytherapy treatments using conventional
applicators and only one HDR source.
Define P as the set of all possible dwell positions along the applicator(s), S as the set
of structures, and Vs as the voxels in structure s ∈ S. The set S consists of the target(s)
and all or a subset of the OARs surrounding the target. The decision variables are xi,
the dwell time at dwell position i ∈ P . The dose delivered to voxel j in structure s, zjs,
is calculated as
zjs =∑i∈P
Dijsxi ∀j ∈ Vs,∀s ∈ S (2.1)
where Dijs is the amount of dose delivered from dwell position i to voxel j in structure
s per unit time. These dose coefficients were obtained using the Monte Carlo N-Particle
(MCNP) code [22] to simulate the dose distributions around the source in water. All
recommendations of the AAPM TG-43 [55, 66] and AAPM-ESTRO [60] reports for HDR
brachytherapy sources were considered in the simulation.
Each voxel is assigned a penalty for any overdose or underdose it receives. The
Chapter 2. Methodology 12
T_u T_oz
js
Fs(z
js)
Figure 2.1: The penalty function of the DTO problem is convex and non-smooth. Notethat no penalty is incurred between the lower and upper dose thresholds, Tu and To.
penalties are weighted according to the structure to which the voxel belongs so that
some structures have a higher priority than others. Additionally, some structures may
benefit from an underdose but not an overdose. For example, the penalty weight for
underdosing an OAR could be zero. To this end, the penalties for an underdose may be
different from the penalties for an overdose. The penalty function for voxel j in structure
s is
Fs(zjs) =1
|Vs|[ws(zjs − T s)
2+ + ws(T s − zjs)2+] (2.2)
where (·)+ is max{0, ·}; ws and ws are the overdose and underdose penalties for structure
s ∈ S, respectively; and T s and T s are the upper and lower dose thresholds for structure
s ∈ S, respectively. These dose thresholds provide flexibility to the model: If zjs lies
between T s and T s, then there is no penalty. The penalty function is normalized with
respect to the number of voxels in the structure to remove any bias towards structure
size. Figure 2.1 illustrates the shape of Fs.
Chapter 2. Methodology 13
The DTO model is then to minimize the total penalty over all voxels:
minimize∑s∈S
∑j∈Vs
Fs(zjs) (DTO)
subject to zjs =∑i∈P
Dijsxi ∀j ∈ Vs,∀s ∈ S
0 ≤ xi ≤ tmax ∀i ∈ P
where tmax is the upper bound on the dwell times.
Since the penalty functions Fs are convex, the DTO model can be reformulated as
a semi-infinite linear optimization (SILO) problem and solved using an interior point
constraint generation (IPCG) algorithm developed by Oskoorouchi et al. [56]. A SILO
problem is an optimization problem in which there is an infinite number of variables or
an infinite number of constraints, but not both. Our DTO-SILO problem has a linear
objective and infinitely many linear constraints:
minimize δ (DTO-SILO)
subject to∑s∈S
∑j∈Vs
Fs(zjs) ≤ δ
zjs =∑i∈P
Dijsxi ∀j ∈ Vs,∀s ∈ S
0 ≤ xi ≤ tmax ∀i ∈ P
The infinite number of constraints come from the constraints used to approximate the
convex functions Fs(zjs), as shown in Figure 2.2.
A graphical user interface (GUI) called morDiRECT (the Medical Operations Reseach
Laboratory’s Display for Ranking and Evaluating Customized Treatments) [65] was used
to generate treatment plans with ranges of parameter values automatically (Figure 2.3).
The best plan was then chosen for each patient according to target coverage and OAR
Chapter 2. Methodology 14
Figure 2.2: Linear approximations (blue) of a convex function (black)
sparing. morDiRECT is a multi-criteria decision support system that allows the decision-
maker to easily generate and choose a high-quality plan without the iterative process
of identifying suitable model parameters, which is a common characteristic of inverse
treatment planning in brachytherapy.
2.3 Interior point constraint generation algorithm
The IPCG algorithm was developed to solve a similar model for a SRS inverse planning
problem [4, 14, 56]. The algorithm is guaranteed to find an ε-optimal solution, unlike
heuristics and gradient descent methods, and it was shown to converge to an ε-optimal
solution in a finite number of iterations. For simplicity, we only present the main idea
of the IPCG algorithm. The theoretical aspects and mathematical proofs behind the
algorithm can be found in Oskoorouchi et al. [56].
We start with a simpler version of the original problem that only considers a small
subset of the constraints, called the reduced problem. An optimal solution to the reduced
problem is found and multiple constraints violated by that optimal solution are identified.
Chapter 2. Methodology 15
Figure 2.3: morDiRECT’s evaluation window
These constraints are added to the reduced problem and at the same time, the barrier
function is updated by reducing the barrier parameter. The feasibility of the solution
is then recovered, and an optimal solution is found for the new reduced problem. The
process is repeated until the duality gap is within ε distance, that is, the solution is
ε-optimal.
Chapter 3
Direction-modulated brachytherapy
Using conventional intracavitary applicators, such as the tandem and ring applicator
(Figure 3.1), with isotropic sources limits the maximal dose delivered to the tumour,
especially in cases where the target volume is laterally extended or non-symmetric. To
prevent the overdose of OARs, parts of the target volume must be underdosed, leading
to less conformal plans.
To address the lack of shielded intrauterine tandem applicators for cervical cancer
brachytherapy and build on the concept of anisotropic dose profiles [15], a novel tandem
applicator, called the DMBT tandem (Figure 3.2), was proposed that is able to produce
anisotropic dose distributions [25]. The tandem can generate directional radiation dose
profiles through its intelligent shielding design to achieve superior target coverage (Figure
3.3). DMBT was theoretically studied on rectal cancer [81, 82], breast cancer [83], and
cervical cancer [25, 26, 71–73].
The DMBT tandem is symmetric along the transverse and longitudinal axes. It has
six peripheral holes of width 1.3 mm grooved along a non-magnetic tungsten alloy (95%
tungsten, 3.5% nickel, and 1.5% copper, ρ = 18 g/cm3), enclosed in a 0.3 mm thick
plastic sheath. The DMBT tandem diameter is no larger than 6 mm, the dimension
of a conventional tandem. Thus, it can be readily used with existing tandem-and-ring
16
Chapter 3. Direction-modulated brachytherapy 17
Tandem
Ring
Interstitial/needles(optional)
Figure 3.1: Tandem and ring applicator. The HDR source can travel through the ringand the tandem. (Adapted from Viswanathan et al. [80])
Figure 3.2: DMBT tandem (Source: Han et al. [26])
applicators. Furthermore, the paramagnetic tungsten alloy renders the DMBT tandem
MRI-safe.
The high density of the tungsten alloy allows the rod to be used as a shield to block
part of the radiation. With the grooves equally spaced at 60◦, highly directional beams
of radiation can be delivered in six different directions, which is a sharp contrast to the
near-circular, or isotropic, dose distribution obtained from a conventional tandem that
has no shielding.
To evaluate the modulating capacity of the DMBT tandem, we use our inverse plan-
ning approach to develop treatment plans for both conventional brachytherapy (conven-
Chapter 3. Direction-modulated brachytherapy 18
6.0 mm
(a) Conventional tandem
60°
6.0 mm
1.3mm
(b) DMBT tandem
(c) Isotropic dose distribution fromconventional tandem
(d) Anisotropic dose distribution fromDMBT tandem
Figure 3.3: Cross-sections of conventional and DMBT tandems
Chapter 3. Direction-modulated brachytherapy 19
tional BT) and DMBT for cervical cancer, and then compare the plan quality. We use
the DTO formulation to model the conventional BT problem and then solve it using the
IPCG algorithm.
3.1 DMBT optimization model
The optimization model for DMBT is a slight modification of the DTO model. In addition
to the parameters previously defined, let C be the set of channels grooved along the
tandem applicator, where |C| = 6. The dwell positions (in the ring and in the tandem)
are fixed to the positions used in the clinical treatments. The decision variables for
DMBT-DTO are xic, the dwell time at dwell position i ∈ P in channel c ∈ C, as opposed
to xi for conventional brachytherapy. The dose delivered to voxel j in structure s, zjs, is
calculated as
zjs =∑c∈C
∑i∈P
Dicjsxic ∀j ∈ Vs,∀s ∈ S (3.1)
where Dicjs is the amount of dose delivered from dwell position i to voxel j in structure
s per unit time along channel c.
Using the same penalty function Fs(zjs) (Equation 2.2), the DMBT-DTO problem is
then
minimize∑s∈S
∑j∈Vs
Fs(zjs) (DMBT-DTO)
subject to zjs =∑c∈C
∑i∈P
Dicjsxic ∀j ∈ Vs,∀s ∈ S
0 ≤ xic ≤ tmax ∀i ∈ P, ∀c ∈ C
where tmax is the upper bound on the dwell times.
Chapter 3. Direction-modulated brachytherapy 20
3.2 Results
Twenty-seven clinical cervical cancer cases obtained from Aarhus University Hospital
(Aarhus, Denmark) are studied retrospectively. The target volume and the OARs (blad-
der, rectum, and sigmoid) were contoured on T2w MR images and treatment plans were
generated using the BrachyVisionTM (Varian Medical Systems, Palo Alto, CA, USA)
treatment planning system. The prescription dose was 15 Gy or 17.5 Gy. All patients
were treated using a tandem and ring applicator and an 192Ir pulsed-dose-rate source,
with source strength normalized to one Curie (Ci). The results can be converted back to
match a 10 Ci source, which is typical in HDR brachytherapy. The clinical details of the
cases are shown in Table 3.1.
To ensure that any improvement solely resulted from the modulating capacity of the
DMBT tandem, the ring was left untouched in both the conventional BT and DMBT
setup and only the tandem was replaced. To evaluate the quality of treatment plans, all
plans were normalized to receive their respective clinical target volume D90 values. D2cc,
the dose to the hottest 2 cm3 of the structure volume, was calculated for the three OARs,
as well as COIN and HI.
On average, DMBT improved the sparing of all three OARs (Table 3.2). The per-
cent improvement in OAR D2cc is illustrated in Figure 3.4. The dose delivered to the
bladder, rectum, and sigmoid was reduced by 6.4%, 12.5%, and 2.6%, respectively. The
corresponding maximum decrease was 17.2%, 43.3%, and 16.7%, respectively. In 23 out
of 27 cases (85%), DMBT plans were superior to the conventional BT plans for all three
OARs.
The COIN and HI values are shown in Table 3.3. In terms of conformity, 25 of 27
(92.5%) DMBT plans are more conformal than the conventional BT plans. The mean
COIN values for conventional BT and DMBT plans were 0.47 ± 0.07 (mean ± standard
deviation) and 0.55 ± 0.08, respectively. With regards to homogeneity, the DMBT plans
and conventional BT plans exhibit no clear relationship, but they are comparable on
Chapter 3. Direction-modulated brachytherapy 21
Table 3.1: Patient information
Number of dwell positions
Patient ID Target vol. (cc) Conventional BT DMBT Rx dose (Gy)
1 12.2 27 67 17.5
2 14.0 29 79 15.0
3 16.1 29 79 17.5
4 16.8 27 67 17.5
5 17.8 34 94 15.0
6 19.6 29 79 15.0
7 19.9 31 91 17.5
8 21.1 27 67 17.5
9 21.6 34 94 17.5
10 22.0 31 91 17.5
11 22.1 31 91 17.5
12 22.4 31 91 15.0
13 22.4 28 88 17.5
14 22.5 31 91 17.5
15 24.6 34 94 17.5
16 25.0 32 82 15.0
17 28.0 31 91 15.0
18 28.5 34 94 15.0
19 30.7 29 79 15.0
20 31.8 29 79 17.5
21 35.6 31 91 17.5
22 36.1 33 103 17.5
23 38.5 38 118 15.0
24 38.8 34 94 17.5
25 49.6 30 80 15.0
26 54.5 36 106 15.0
27 81.1 38 118 15.0
Mean 28.6 31 89 16.4
Stdev 14.6 3 13 1.3
Chapter 3. Direction-modulated brachytherapy 22
Table 3.2: OAR dose metrics for the conventional BT plans and the DMBT plans. Anegative value (shaded) means that the DMBT plan improves on the conventional BTplan. The maximum decrease is bolded.
D2cc Bladder (Gy) D2cc Rectum (Gy) D2cc Sigmoid (Gy)
Patient
ID
Conventional
BTDMBT % Diff
Conventional
BTDMBT % Diff
Conventional
BTDMBT % Diff
1 8.6 8.2 -4.8 6.8 5.9 -13.2 11.1 10.8 -2.3
2 6.6 6.5 -0.5 4.4 4.0 -9.8 7.5 7.1 -4.8
3 13.2 13.7 3.5 10.7 9.8 -8.4 7.4 7.6 3.2
4 13.3 12.8 -3.6 10.1 8.6 -14.9 12.9 12.9 0.6
5 11.9 10.9 -8.9 4.5 4.0 -11.5 11.2 9.9 -11.0
6 6.6 6.1 -7.2 7.6 7.2 -5.7 9.7 9.0 -7.3
7 13.5 13.2 -2.5 4.6 4.5 -2.5 9.1 9.7 6.7
8 7.5 6.5 -13.8 8.3 6.9 -16.7 7.2 6.7 -6.0
9 13.6 12.8 -5.9 4.4 4.1 -7.5 8.3 8.2 -1.1
10 11.7 9.8 -15.9 9.0 7.3 -19.3 6.5 6.4 -2.4
11 13.0 13.0 -0.2 7.7 7.1 -8.1 13.3 13.4 0.6
12 9.5 8.3 -12.5 9.7 7.1 -27.2 8.8 7.9 -10.6
13 11.5 10.4 -9.6 11.1 9.3 -16.8 11.2 11.4 1.3
14 11.5 11.4 -1.5 6.4 5.9 -8.2 12.3 11.4 -7.4
15 6.4 5.3 -17.1 4.1 3.5 -16.6 11.3 11.3 -0.5
16 9.8 9.3 -5.3 6.2 5.8 -6.2 11.6 12.0 3.4
17 9.1 8.1 -11.0 4.0 3.5 -13.3 10.0 9.7 -2.8
18 12.2 12.1 -0.6 7.8 6.5 -16.4 11.6 11.9 2.2
19 8.2 6.8 -17.2 6.4 5.1 -19.9 11.3 10.8 -4.4
20 12.4 11.7 -6.2 8.0 7.9 -2.0 6.6 6.7 1.6
21 12.4 10.8 -13.1 8.5 4.8 -43.3 11.9 9.9 -16.7
22 11.3 11.2 -1.0 4.9 4.9 0.2 11.6 12.0 3.7
23 13.0 12.9 -0.7 6.8 6.4 -6.3 9.8 10.2 4.5
24 9.8 9.4 -4.5 8.4 6.6 -21.0 16.9 16.9 0.0
25 14.4 13.9 -3.4 9.3 8.9 -4.4 7.5 6.7 -10.5
26 11.4 11.1 -2.1 6.1 5.8 -5.5 12.8 11.7 -8.1
27 13.9 12.9 -7.3 11.0 9.4 -14.1 8.3 8.3 -1.0
Mean 11 10.3 -6.4 7.3 6.3 -12.5 10.3 10 -2.6
Stdev 2.4 2.6 5.7 2.2 1.9 9 2.4 2.5 5.6
Chapter 3. Direction-modulated brachytherapy 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27−50
−40
−30
−20
−10
0
10
Case number
Pe
rce
nt
ch
an
ge
Bladder Rectum Sigmoid
Figure 3.4: Pairwise difference between the conventional BT and DMBT plans for all 27cases
.
average. The mean HI was of 0.31 ± 0.08 for the conventional BT plans and 0.30 ± 0.06
for the DMBT plans.
The DVH and isodose lines for a representative case (Patient 4) are shown in Figure
3.5 to illustrate the benefits of the DMBT tandem. The DVHs (Figure 3.5a) show that the
target receives the required prescription dose in both plans while the dose to the three
OARs decreases in the DMBT plans. The corresponding slices (Figure 3.5b) further
illustrate the OAR sparing, as well as the superior conformity of the DMBT plans.
The average IPCG computation time for conventional BT plans was 0.4 min for a
mean of 31 dwell positions and 1.1 min for a mean of 89 dwell positions for DMBT plans
(Table 3.4). As expected, the DMBT computation times are consistently longer than
their corresponding conventional BT times since the number of variables increases when
the DMBT tandem applicator is used. Figure 3.6 shows that the computation time is
quadratic with the number of dwell positions, despite the exponential complexity of the
algorithm [18].
Chapter 3. Direction-modulated brachytherapy 24
Table 3.3: Homogeneity index and conformal index. The better index value is shaded.
HI COIN
Patient IDConventional
BTDMBT
Conventional
BTDMBT
1 0.30 0.31 0.42 0.49
2 0.30 0.25 0.43 0.45
3 0.16 0.15 0.42 0.41
4 0.23 0.20 0.39 0.46
5 0.24 0.25 0.46 0.55
6 0.33 0.34 0.40 0.44
7 0.14 0.14 0.50 0.44
8 0.42 0.35 0.42 0.48
9 0.33 0.35 0.44 0.53
10 0.30 0.29 0.46 0.56
11 0.38 0.41 0.47 0.53
12 0.27 0.26 0.33 0.47
13 0.33 0.33 0.42 0.58
14 0.27 0.28 0.42 0.45
15 0.28 0.28 0.47 0.59
16 0.33 0.38 0.47 0.57
17 0.27 0.28 0.48 0.57
18 0.27 0.28 0.49 0.58
19 0.28 0.30 0.43 0.58
20 0.33 0.35 0.62 0.65
21 0.29 0.25 0.42 0.58
22 0.34 0.43 0.57 0.67
23 0.26 0.26 0.51 0.54
24 0.36 0.37 0.53 0.65
25 0.33 0.35 0.60 0.67
26 0.41 0.48 0.53 0.66
27 0.35 0.37 0.55 0.73
Mean 0.30 0.31 0.47 0.55
Stdev 0.06 0.08 0.07 0.08
Chapter 3. Direction-modulated brachytherapy 25
0 20 40 60 80 100 120 140 160 180 200 220 2400
10
20
30
40
50
60
70
80
90
100
Percent dose (%)
Pe
rce
nt
vo
lum
e (
%)
HRCTVBladder
RectumSigmoid
(a) Dose-volume histogram
(b) Slices with 100% and 50% isodose lines
Figure 3.5: Comparison between a conventional BT plan (dashed lines) and a DMBTplan (solid lines) for a representative case.
Chapter 3. Direction-modulated brachytherapy 26
Table 3.4: Computation time in minutes for the conventional BT and DMBT plans
Conventional BT DMBT
Patient ID # dwell positions Comp. time # dwell positions Comp. time
1 27 0.29 67 0.70
2 29 0.29 79 0.68
3 29 0.38 79 1.00
4 27 0.45 67 1.02
5 34 0.50 94 1.46
6 29 0.34 79 0.82
7 31 0.55 91 1.42
8 27 0.30 67 0.71
9 34 0.52 94 1.32
10 31 0.26 91 0.61
11 31 0.28 91 0.80
12 31 0.36 91 0.89
13 28 0.32 88 0.95
14 31 0.36 91 0.92
15 34 0.43 94 1.06
16 32 0.37 82 0.90
17 31 0.29 91 0.80
18 34 0.68 94 1.56
19 29 0.48 79 1.17
20 29 0.29 79 0.74
21 31 0.39 91 1.15
22 33 0.46 103 1.62
23 38 0.45 118 1.42
24 34 0.52 94 1.40
25 30 0.36 80 0.97
26 36 0.54 106 1.82
27 38 0.48 118 1.48
Mean 31 0.41 89 1.09
Stdev 3 0.11 13 0.34
Chapter 3. Direction-modulated brachytherapy 27
0 20 40 60 80 100 1200
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Number of dwell positions
Co
mp
uta
tio
n t
ime
(m
in)
Conventional BT DMBT Best fit: Quadratic
Figure 3.6: Computation time for DMBT as a function of number of dwell positions.
3.3 Discussion
Treatment planning for cervical cancer can be challenging, especially with the presence
of asymmetric or bulky tumours. We have shown that the DMBT tandem, with its
ability to generate highly directional beams of radiation, allows for clinically significant
reduction in dose to the OARs without compromising the target coverage. Furthermore,
the results are independent of the tumour size. The dose homogeneity is maintained
from the conventional BT plans to the DMBT plans, while conformity is significantly
improved clinically in the DMBT plans. Since a prototype has already been constructed,
the next step is to obtain approval for DMBT clinical trials.
Our results also indicate that the inverse planning approach used in SRS [4, 14, 56]
can be successfully implemented in HDR brachytherapy. High quality treatment plans
were obtained in less than two minutes. While these times are comparable to, say,
simulated annealing run times previously used in brachytherapy inverse planning [43],
we are able to guarantee the optimality of our results. If the planner is not satisfied
Chapter 3. Direction-modulated brachytherapy 28
with the plan obtained, new plans can be quickly generated within a few minutes. To
avoid such situations, we used morDiRECT [65] as a complementary tool to choose the
best treatment plans according to our criteria. The short computation time of the IPCG
algorithm is advantageous when running several trials through morDiRECT.
3.4 Conclusion
We investigated the dosimetric benefits of DMBT on 27 cervical cancer cases with differ-
ent tumour sizes. The DMBT plans achieved lower OAR doses than the conventional BT
plans while maintaining similar target coverage. An alternative interpretation of these
results is that for the same OAR exposure to radiation, the dose to the target can be
safely escalated, thus potentially improving tumour control and treatment outcome.
In terms of algorithm performance, we showed that a quadratic penalty optimiza-
tion approach combined with IPCG [56], similar to approaches in radiosurgery inverse
planning [4, 14, 18–20, 56], performs well for HDR brachytherapy inverse planning prob-
lems. Good quality treatment plans were generated within a few minutes of run time.
Additionally, the treatment time obtained were all clinically acceptable.
Chapter 4
Energy-modulated brachytherapy
The radionuclides 192Ir and 60Co are commonly used as sources in HDR brachytherapy,
but other nuclides, such as 169Yb, have also been previously used as HDR sources [50].
While the use of these individual radionuclides as HDR sources has been studied, the use
of two or more radionuclides in combination, or EMBT, has yet to be investigated on
prostate cancer. If used together, the different dose profiles of these radioactive sources
can potentially improve OAR sparing. The dosimetric benefits of EMBT were successfully
investigated on cervical cancer using 192Ir, 60Co, and 169Yb [71, 73]. A quadratic penalty
model (with same penalty for overdose and underdose of a structure) and a projected
gradient algorithm [25] were used to develop the treatment plans for single- and dual-
source combinations and only the DMBT tandem was used (instead of the conventional
tandem). Since the DMBT tandem alone allows for superior plan quality, we assess the
potential advantages of EMBT only on prostate cancer. Furthermore, we also consider
using all three sources in combination.
Recently, in addition to irradiating the whole prostate gland, regions of the prostate
with the highest tumour concentration have been prescribed higher doses [29]. These
regions are called dominant intraprostatic lesions (DILs) and they are now a new focus
of HDR prostate brachytherapy [29]. The expectation is that recurrence is less likely to
29
Chapter 4. Energy-modulated brachytherapy 30
happen when DILs are identified and boosted [33]. EMBT may allow safer dose escalation
to the DILs while limiting the dose to the OARs.
192Ir is the most common radioactive source for HDR brachytherapy [64, 78]. Due to
its high specific activity, which is defined as the rate at which unstable nuclei decay per
unit mass, the radioactive source can be made small enough to be inserted in the body
while keeping a significantly high activity, which is essential for HDR purposes. However,
the source has a short half-life of 74 days, which means that it needs to be replaced every
three to four months to maintain acceptable treatment times.
60Co sources are now commercially available in the same geometric dimensions as
192Ir, and are comparable with 192Ir with respect to clinical aspects for HDR prostate
brachytherapy [31, 64, 78]. However, 60Co’s longer half-life of approximately five years
means that it does not need to be replaced frequently, leading to fewer source exchanges.
Thus, 60Co has a lower operating cost, and can be a cheaper alternative for developing
countries [7, 64]. 169Yb, with a half-life of 32 days, has also been investigated as a potential
HDR source [11, 47, 59]. It has been shown to be at least equivalent to 192Ir in terms of
dosimetry [36, 45, 46], with reduced radiation protection and shielding requirements due
to its lower energy [24].
Afterloaders that can handle two sources, such as the Multisource R© afterloader from
Eckert & Ziegler BEBIG [16], have already been introduced on the market. However,
such afterloaders cannot handle both sources at the same time [57]. Recently, a new
afterloader capable of handling two different sources simultaneously was proposed by
Elekta (Flexitron R©, Elekta Brachytherapy, Veenendaal, The Netherlands). Furthermore,
the machine is equipped to handle 192Ir, 60Co, or 169Yb. We therefore investigate the
dosimetric benefits of EMBT for every possible combination of 192Ir, 60Co, and 169Yb,
and then compare treatment quality to the 192Ir-only plan. The DTO model is used in
combination with the IPCG algorithm to generate the single-source plans.
Chapter 4. Energy-modulated brachytherapy 31
Table 4.1: HDR source information
Source Model ManufacturerLength
(mm)
Diameter
(mm)
Energy
(keV)
Activity
(Ci)
Half-life
(days)
192IrmicroSelectron
v2Nucletron 4.5 0.9 380 10 73.83
60Co Co0.A86Eckert & Ziegler
BEBIG5.0 1.0 1250 2 1925.00
169Yb 4140Implant Sciences
Corporation4.8 0.9 93 10 32.02
4.1 EMBT optimization model
Based on the DTO model, we formulate the EMBT-DTO problem as follows. In addition
to the previously defined parameters, let R be the set of sources, where |R| = 3 in our
study. The dwell positions, evenly spaced at intervals (which vary per case), are fixed
to the positions used in the clinical treatments.The decision variables are xir, the dwell
time of source r ∈ R at dwell position i ∈ P . The dose delivered to voxel j in structure
s, zjs, is calculated as
zjs =∑r∈R
∑i∈P
Dirjsxir ∀j ∈ Vs,∀s ∈ S (4.1)
where Dirjs is the amount of dose delivered from dwell position i to voxel j in structure
s per unit time from source r. Details about the sources are shown in Table 4.1. Their
radial and depth dose functions are plotted against the distance from the middle of each
source in Figures 4.1 and 4.2, respectively.
Chapter 4. Energy-modulated brachytherapy 32
0 2 4 6 8 100.7
0.8
0.9
1
1.1
1.2
Distance (cm)
Radia
l dose function
Ir−192
Co−60
Yb−169
Figure 4.1: Radial dose function of 192Ir, 60Co, and 169Yb normalized at 1 cm.
0 2 4 6 8 10
10−2
10−1
100
Distance (cm)
De
pth
do
se
Ir−192
Co−60
Yb−169
Figure 4.2: Depth dose function of 192Ir, 60Co, and 169Yb normalized at 1 cm.
Chapter 4. Energy-modulated brachytherapy 33
Using the same penalty function Fs(zjs) (Equation 2.2), the EMBT-DTO problem is
minimize∑s∈S
∑j∈Vs
Fs(zjs) (EMBT-DTO)
subject to zjs =∑r∈R
∑i∈P
Dirjsxir ∀j ∈ Vs,∀s ∈ S
0 ≤ xir ≤ tmax ∀i ∈ P, ∀r ∈ R
where tmax is the upper bound on the dwell times.
4.2 Results
We test our approach retrospectively on 12 anonymized HDR prostate cases treated at
the Odette Cancer Centre, Sunnybrook Health Sciences Centre (Toronto, ON, Canada)
(Table 4.2). The structures (prostate, DILs, urethra, and rectum) were contoured on
the planning scans and treatment plans were generated using the Oncentra Brachy R©
(Nucletron, Veenendaal, The Netherlands) treatment planning system. For planning
purposes, the cases were separated into two groups: Group A patients have the prostate
as the main target volume, while Group B patients have DILs as secondary targets in
addition to the prostate. DILs are prescribed 150% of the prescription dose. All patients
were treated with the Nucletron microSelectron HDR-version 2 (mHDR-V2) 192Ir source
and followed the clinical protocol shown in Table 4.3.
The plans were separated into three categories: (1) single-source with Co, Ir, and Yb
individually; (2) double-source with the pairs Co-Ir, Co-Yb, and Ir-Yb; and (3) triple-
source with Co-Ir-Yb (assuming future developments in afterloader technology allows for
triple-source delivery). There were a total of seven treatment plans per patient. For fair
comparison, all plans were normalized to the clinical prostate V100 and where applicable,
the clinical DIL V150. In addition to reporting the DVH parameters presented in Table
4.3, COIN and HI are also calculated.
Chapter 4. Energy-modulated brachytherapy 34
Table 4.2: Patient information. Group A patients have the prostate as main targetvolume, and Group B patients have DILs as secondary targets.
Group Patient IDTarget vol.
(cc)
#
Applicators
# Dwell
positions
Rx dose
(Gy)
A
1 24.3 12 165 15.0
2 28.2 12 152 13.5
3 28.7 12 257 15.0
4 34.7 16 189 15.0
5 35.4 16 226 15.0
6 39.6 12 283 15.0
7 40.9 12 166 15.0
8 53.6 16 233 19.0
Mean 38.1
Stdev 11.4
B
9 22.0 16 231 19.0
10 25.5 16 350 19.0
11 34.1 16 447 19.0
12 40.7 16 330 19.0
Mean 30.6
Stdev 8.5
Table 4.3: Clinical protocols
Target DILs Urethra Rectum
V100 ≥ 95 % V150 = 100 % Dmax ≤ 130 % Dmax ≤ 90 %
V150 < 35 % - D10 ≤ 110 % V80 ≤ 0.5 cc
V200 < 12 % - - -
Chapter 4. Energy-modulated brachytherapy 35
Table 4.4: Average values ± standard deviation of target DVH parameters and indices.Group A patients have the prostate as main target volume, and Group B patients haveDILs as secondary targets.
Group Plan V150 (%) V200 (%) HI COIN
A
Clinical 37.6 ± 3.4 11.6 ± 2.5 0.61 ± 0.04 0.74 ± 0.04
Ir 27.3 ± 4.4 11.9 ± 2.1 0.72 ± 0.05 0.78 ± 0.03
Co 29.1 ± 4.5 12.8 ± 2.3 0.70 ± 0.05 0.78 ± 0.03
Yb 24.8 ± 4.6 10.5 ± 1.9 0.75 ± 0.05 0.79 ± 0.03
Co-Ir 29.8 ± 4.3 13.2 ± 2.2 0.70 ± 0.05 0.77 ± 0.03
Co-Yb 29.0 ± 4.2 13.0 ± 2.2 0.70 ± 0.05 0.78 ± 0.03
Ir-Yb 26.7 ± 4.0 11.6 ± 2.1 0.73 ± 0.04 0.77 ± 0.04
Co-Ir-Yb 28.6 ± 4.1 12.4 ± 2.2 0.71 ± 0.04 0.77 ± 0.02
B
Clinical 34.1 ± 3.2 9.7 ± 2.2 0.65 ± 0.04 0.58 ± 0.04
Ir 32.1 ± 2.6 13.7 ± 0.6 0.66 ± 0.05 0.75 ± 0.06
Co 33.7 ± 3.9 14.8 ± 1.6 0.65 ± 0.05 0.74 ± 0.05
Yb 30.9 ± 1.7 12.8 ± 0.6 0.68 ± 0.04 0.76 ± 0.06
Co-Ir 33.9 ± 3.5 14.8 ± 1.4 0.64 ± 0.05 0.74 ± 0.06
Co-Yb 33.9 ± 3.5 14.6 ± 1.2 0.64 ± 0.05 0.74 ± 0.06
Ir-Yb 31.9 ± 2.9 13.7 ± 0.8 0.66 ± 0.05 0.75 ± 0.06
Co-Ir-Yb 33.5 ± 3.8 14.6 ± 1.3 0.65 ± 0.04 0.73 ± 0.05
On average, treatment plans generated from all combinations achieve the clinical
objectives for both targets (Table 4.4) and OARs (Table 4.5). As expected, Group B
patients have higher V150 and V200 values than Group A patients due to the presence of
DILs. Additionally, source combinations that include 60Co generate plans with higher
V150 and V200 values than the conventional Ir-only plans, due to the higher energy of 60Co.
Yb-only plans have the lowest V150 and V200 values since 169Yb has the lowest energy.
The HI and COIN values are presented in Tables 4.6 and 4.7, respectively. The column
with the heading “Clinical 192Ir” shows the clinical treatment values. With the exception
of Patient 12, all optimized Ir-only plans have better HI values than the clinical Ir plans.
Source combinations that include 60Co generate plans that are slightly less homogeneous
Chapter 4. Energy-modulated brachytherapy 36
Table 4.5: Average values ± standard deviation of OARs DVH parameters. Group Apatients have the prostate as main target volume, and Group B patients have DILs assecondary targets.
Urethra Rectum
Group Plan Dmax (%) D10 (%) Dmax (%) V80 (cc)
A
Clinical 123.9 ± 6.9 116.4 ± 0.5 88.2 ± 10.2 0.2 ± 0.2
Ir 125.6 ± 8.7 112.1 ± 2.2 83.8 ± 8.9 0.3 ± 0.5
Co 127.2 ± 9.8 111.7 ± 2.9 83.6 ± 8.5 0.2 ± 0.2
Yb 130.0 ± 8.7 113.8 ± 2.7 84.5 ± 8.1 0.4 ± 0.7
Co-Ir 124.2 ± 7.0 111.2 ± 3.0 83.5 ± 9.7 0.4 ± 0.6
Co-Yb 124.8 ± 6.3 110.7 ± 1.9 83.6 ± 9.6 0.5 ± 0.7
Ir-Yb 123.6 ± 5.4 110.9 ± 1.9 83.7 ± 8.5 0.2 ± 0.2
Co-Ir-Yb 122.6 ± 6.3 109.5 ± 1.2 82.8 ± 8.7 0.2 ± 0.2
B
Clinical 121.5 ± 1.9 116.0 ± 1.0 85.0 ± 2.8 0.1 ± 0.1
Ir 121.8 ± 7.8 112.9 ± 5.7 88.7 ± 7.7 0.4 ± 0.6
Co 118.6 ± 8.0 110.8 ± 6.5 85.3 ± 7.2 0.2 ± 0.3
Yb 121.6 ± 9.9 114.4 ± 6.8 90.7 ± 8.1 0.6 ± 0.7
Co-Ir 117.5 ± 9.1 111.1 ± 6.5 84.9 ± 8.0 0.2 ± 0.3
Co-Yb 117.6 ± 8.2 110.8 ± 6.2 85.3 ± 7.0 0.2 ± 0.3
Ir-Yb 119.5 ± 7.1 112.2 ± 4.8 88.0 ± 8.7 0.4 ± 0.5
Co-Ir-Yb 118.0 ± 8.6 110.9 ± 6.4 84.7 ± 6.6 0.2 ± 0.3
Chapter 4. Energy-modulated brachytherapy 37
Table 4.6: Homogeneity index. Any metric in the inverse plans that achieved a bettervalue than the clinical Ir-only plans and the inverse Ir-only plans are bolded and shaded,respectively.
GroupPatient
ID
Clinical
IrIr Yb Co Co-Ir Co-Yb Ir-Yb Co-Ir-Yb
Inverse
plan
range
A
1 0.66 0.72 0.72 0.68 0.69 0.68 0.72 0.69 [0.68, 0.72]
2 0.60 0.72 0.73 0.69 0.69 0.70 0.72 0.69 [0.69, 0.73]
3 0.66 0.74 0.79 0.75 0.75 0.75 0.77 0.76 [0.74, 0.79]
4 0.58 0.77 0.80 0.75 0.74 0.75 0.77 0.75 [0.74, 0.80]
5 0.65 0.73 0.75 0.71 0.69 0.71 0.73 0.71 [0.69, 0.75]
6 0.57 0.61 0.65 0.61 0.60 0.61 0.64 0.62 [0.60, 0.65]
7 0.59 0.73 0.75 0.71 0.71 0.70 0.71 0.70 [0.70, 0.75]
8 0.62 0.74 0.77 0.73 0.71 0.73 0.75 0.74 [0.71, 0.77]
Mean 0.61 0.72 0.75 0.70 0.70 0.70 0.73 0.71
Stdev 0.04 0.05 0.05 0.05 0.05 0.05 0.04 0.04
B
9 0.67 0.67 0.68 0.66 0.66 0.66 0.67 0.66 [0.66, 0.68]
10 0.67 0.67 0.68 0.64 0.64 0.64 0.67 0.65 [0.64, 0.68]
11 0.60 0.70 0.70 0.70 0.69 0.69 0.70 0.70 [0.69, 0.70]
12 0.65 0.64 0.66 0.61 0.61 0.61 0.64 0.61 [0.61, 0.66]
Mean 0.65 0.67 0.68 0.65 0.65 0.65 0.67 0.65
Stdev 0.04 0.02 0.01 0.04 0.03 0.03 0.03 0.04
than Ir plans, which is expected since Co plans have larger hotspots. On the other hand,
Yb-only plans are more homogeneous than Ir-only plans since they have smaller hotspots.
For the COIN, with the exception of Patients 5 and 7, all optimized Ir-only plans have
superior values than the clinical Ir-only plans. All Group B patients benefit from an
improvement in conformity across all plans, while most of Group A plans have a better
COIN value than the one obtained in the clinic.
It is clear that using dual or triple sources result in more OAR sparing (Table 4.8).
The improvement is further illustrated in Figure 4.3. For Group A patients, 60Co is
comparable to 192Ir except for the urethral Dmax. However, Yb-only plans have larger
doses to the OARs, especially the urethra. In the dual-source category for Group A, the
Ir-Yb plans have the lowest dose to the urethra, whereas the pair Co-Ir spares the rectum
the most compared to 192Ir. In the same group, the combination Co-Ir-Yb has the largest
Chapter 4. Energy-modulated brachytherapy 38
Table 4.7: Conformal index. Any metric in the inverse plans that achieved a bettervalue than the clinical Ir-only plans and the inverse Ir-only plans are bolded and shaded,respectively.
GroupPatient
ID
Clinical
IrIr Yb Co Co-Ir Co-Yb Ir-Yb Co-Ir-Yb
Inverse
plan
range
A
1 0.75 0.81 0.85 0.81 0.79 0.82 0.81 0.80 [0.79, 0.85]
2 0.69 0.76 0.78 0.73 0.75 0.76 0.77 0.76 [0.73, 0.78]
3 0.71 0.79 0.78 0.81 0.80 0.76 0.79 0.76 [0.76, 0.81]
4 0.72 0.79 0.77 0.79 0.72 0.75 0.78 0.77 [0.72, 0.79]
5 0.79 0.76 0.81 0.76 0.78 0.80 0.79 0.80 [0.76, 0.81]
6 0.80 0.80 0.81 0.79 0.79 0.78 0.69 0.75 [0.69, 0.81]
7 0.78 0.74 0.76 0.75 0.73 0.75 0.76 0.75 [0.73, 0.76]
8 0.71 0.81 0.78 0.80 0.80 0.78 0.80 0.78 [0.78, 0.81]
Mean 0.74 0.78 0.79 0.78 0.77 0.78 0.77 0.77
Stdev 0.04 0.03 0.03 0.03 0.03 0.03 0.04 0.02
B
9 0.52 0.67 0.67 0.67 0.67 0.67 0.67 0.67 [0.67, 0.67]
10 0.57 0.81 0.81 0.79 0.82 0.82 0.82 0.80 [0.79, 0.82]
11 0.60 0.77 0.77 0.73 0.73 0.74 0.76 0.73 [0.73, 0.77]
12 0.62 0.76 0.77 0.75 0.74 0.74 0.76 0.73 [0.73, 0.77]
Mean 0.58 0.75 0.76 0.74 0.74 0.74 0.75 0.73
Stdev 0.04 0.06 0.06 0.05 0.06 0.06 0.06 0.05
Chapter 4. Energy-modulated brachytherapy 39
Table 4.8: Average difference of OARs DVH parameters between Ir plans and proposedplans. A negative value (shaded) means that the plan improves on the Ir plan. Themaximum decrease is bolded. Group A patients have the prostate as main target volume,and Group B patients have DILs as secondary targets.
Urethra Rectum
Group Plan Dmax (%) D10 (%) Dmax (%) V80 (%)
A
Yb 4.39 ± 3.25 1.70 ± 2.07 0.71 ± 4.56 0.37 ± 0.84
Co 1.57 ± 5.30 -0.35 ± 1.92 -0.16 ± 3.03 -0.28 ± 0.64
Co-Ir -1.36 ± 4.08 -0.82 ± 1.74 -0.28 ± 4.26 -0.28 ± 0.58
Co-Yb -0.77 ± 2.79 -1.32 ± 1.11 -0.21 ± 2.15 -0.23 ± 0.62
Ir-Yb -1.97 ± 3.61 -1.18 ± 2.21 -0.12 ± 2.23 -0.14 ± 0.61
Co-Ir-Yb -3.03 ± 4.77 -2.58 ± 1.48 -1.00 ± 1.39 -0.23 ± 0.66
B
Yb -0.21 ± 3.77 1.47 ± 1.30 2.03 ± 0.54 0.37 ± 0.39
Co -3.24 ± 2.91 -2.09 ± 1.25 -3.38 ± 2.78 -0.57 ± 0.73
Co-Ir -4.29 ± 4.74 -1.85 ± 2.01 -3.76 ± 1.76 -0.59 ± 0.75
Co-Yb -4.20 ± 5.16 -2.10 ± 1.66 -3.41 ± 1.77 -0.57 ± 0.78
Ir-Yb -2.29 ± 2.13 -0.66 ± 1.07 -0.63 ± 1.19 -0.11 ± 0.19
Co-IrYb -3.79 ± 3.85 -2.03 ± 1.07 -3.94 ± 1.82 -0.67 ± 0.74
decrease in dose to both the urethra and the rectum. For Group B patients, plans from
all source combinations, except Yb-only plans, have lower doses to both OARs compared
to Ir-only plans.
DVHs and isodose lines illustrate the improvement in plan quality between a multi-
souce plan and an Ir-only plan for representative patients without DILs (Figure 4.4) and
with DILs (Figure 4.5). In both DVHs (Figures 4.4a and 4.5a), the target receives the
required prescription dose while the rectal and urethral doses are clearly reduced. The
corresponding slices (Figures 4.4b and 4.5b) further illustrate the dose reduction to the
OARs in the Co-Ir plans.
The activity of the sources is normalized to what is currently commercially available
to show real treatment times. The treatment times for the 192Ir and 169Yb single-source
plans are within an acceptable window ranging from 8 to 18 min, which is typical for HDR
Chapter 4. Energy-modulated brachytherapy 40
Yb Co Co−Ir Co−Yb Ir−Yb Co−Ir−Yb−4
−3
−2
−1
0
1
2
3
4
5
Source combination
Perc
enta
ge d
iffe
rence
Urethra DmaxUrethra D10
Rectum DmaxRectum V80
(a) Group A
Yb Co Co−Ir Co−Yb Ir−Yb Co−Ir−Yb−5
−4
−3
−2
−1
0
1
2
3
Source combination
Perc
enta
ge d
iffe
rence
Urethra Dmax
Urethra D10
Rectum Dmax
Rectum V80
(b) Group B
Figure 4.3: Pairwise difference between an Ir-plan and the proposed plans
Chapter 4. Energy-modulated brachytherapy 41
0 20 40 60 80 100 120 140 160 180 200 220 2400
10
20
30
40
50
60
70
80
90
100
Percent dose (%)
Perc
ent volu
me (
%)
Prostate
Urethra
Rectum
(a) Dose-volume histogram
(b) Slices with 150%, 100% and 50% isodose lines
Figure 4.4: Comparison between an Ir plan (dashed) and a Co-Ir (solid) plan for arepresentative case without DILs.
Chapter 4. Energy-modulated brachytherapy 42
0 20 40 60 80 100 120 140 160 180 200 220 2400
10
20
30
40
50
60
70
80
90
100
Percent dose (%)
Perc
ent volu
me (
%)
Prostate
DIL
Urethra
Rectum
(a) Dose-volume histogram
(b) Slices with 150%, 100% and 50% isodose lines
Figure 4.5: Comparison between an Ir plan (dashed) and a Co-Ir (solid) plan for arepresentative case with DILs.
Chapter 4. Energy-modulated brachytherapy 43
Table 4.9: Treatment time in minutes. Group A patients have the prostate as maintarget volume, and Group B patients have DILs as secondary targets.
GroupPatient
IDIr Yb Co Co-Ir Co-Yb Ir-Yb Co-Ir-Yb
A
1 8 8 51 49 50 8 50
2 8 8 55 46 45 8 45
3 9 10 58 55 56 9 52
4 10 11 65 63 63 10 65
5 10 10 68 62 61 10 60
6 11 12 74 60 64 13 60
7 11 12 76 68 69 11 67
8 17 18 112 110 109 16 110
Mean 10 11 70 64 65 11 64
Stdev 3 3 19 20 20 3 20
B
9 12 13 83 80 80 12 80
10 17 18 115 106 103 17 100
11 16 17 109 102 95 16 109
12 14 15 98 98 97 14 98
Mean 15 16 101 97 94 15 97
Stdev 2 2 14 11 10 2 12
prostate brachytherapy (Table 4.9). The treatment times for plans with 60Co are higher
since the activity of the radionuclide was normalized to 2 Ci. To evaluate the contribution
of each source towards the final dose delivered, a metric called total reference air kerma
(TRAK) is calculated. TRAK is the product of the source strength and irradiation time
and it represents the total dose accumulated at a distance of 1 m from the source [61].
We use TRAK since it is independent of source strength or source activity. Sources with
higher energy have a larger contribution to the total dose delivered (Table 4.10). In
particular, 60Co contributes the most to the total dose delivered, especially for Group B
cases.
The mean computation time is 4 min for an average of 505 dwell positions (Table
Chapter 4. Energy-modulated brachytherapy 44
Table 4.10: TRAK breakdown (%) for each multi-source plan. Group A patients have theprostate as main target volume, and Group B patients have DILs as secondary targets.The largest contributions are shaded.
GroupPatient
IDCo-Ir Co-Yb Ir-Yb Co-Ir-Yb
60Co 192Ir 60Co 169Yb 192Ir 169Yb 60Co 192Ir 169Yb
A
1 87 13 100 0 85 15 97 1 2
2 77 23 74 26 79 21 76 2 21
3 92 8 86 14 88 12 75 1 24
4 86 14 87 13 96 4 96 0 3
5 90 10 89 11 90 10 88 0 11
6 73 27 77 23 81 19 65 6 30
7 79 21 86 14 74 26 80 0 20
8 97 3 92 8 96 4 96 0 4
Mean 85 15 86 14 86 14 84 2 14
Stdev 8 8 8 8 8 8 12 2 11
B
9 96 4 96 4 93 7 96 0 4
10 91 9 87 13 86 14 84 0 16
11 92 8 81 19 80 20 73 0 27
12 100 0 100 0 100 0 100 0 0
Mean 95 5 91 9 90 10 88 0 12
Stdev 4 4 8 8 8 8 12 0 12
Chapter 4. Energy-modulated brachytherapy 45
Table 4.11: Computation time in minutes. Group A patients have the prostate as maintarget volume, and Group B patients have DILs as secondary targets.
GroupPatient
IDIr Yb Co Co-Ir Co-Yb Ir-Yb Co-Ir-Yb
A
1 0.5 0.5 0.5 1.5 1.3 1.3 2.5
2 0.3 0.5 0.3 1.3 1.0 1.0 2.0
3 1.0 1.1 1.4 2.9 2.9 3.0 7.5
4 0.6 0.6 0.6 1.6 1.7 1.8 3.6
5 0.8 0.9 0.9 2.3 2.4 2.3 4.9
6 1.2 1.2 1.3 3.7 3.6 6.5 10.1
7 0.6 0.6 0.6 1.6 1.8 1.5 3.2
8 1.2 1.0 1.0 3.1 3.5 3.1 6.6
Mean 0.8 0.8 0.8 2.2 2.3 2.6 5.0
Stdev 0.3 0.3 0.4 0.9 1.0 1.8 2.8
B
9 1.4 1.5 1.3 1.9 1.9 3.1 4.4
10 2.8 2.5 2.5 6.2 6.4 7.2 12.3
11 4.0 4.3 4.1 10.2 9.6 10.8 19.3
12 2.3 2.3 2.3 5.9 6.0 5.5 10.4
Mean 2.6 2.6 2.5 6.0 6.0 6.7 11.6
Stdev 1.1 1.2 1.1 3.4 3.2 3.2 6.1
4.11). In multi-source plans, the number of dwell positions increases by a factor equal
to the number of sources used. As with DMBT, the computation time is quadratic with
the number of dwell positions (Figure 4.6). Our results align with Ghaffari [18] who
reported that the IPCG algorithm converges comparably with polynomial algorithms
despite its exponential complexity. The addition of dwell positions in the multi-source
configurations increases the complexity of the problem, and thus the improvement in
plan quality is obtained at the cost of larger computation time. Still, even for 1,400
dwell positions, computation time is under 25 minutes.
Chapter 4. Energy-modulated brachytherapy 46
0 500 1000 15000
5
10
15
20
25
30
Number of dwell positions
Co
mp
uta
tio
n t
ime
(m
in)
Ir
Co
Yb
Co−Ir
Co−Yb
Ir−Yb
Co−Ir−Yb
Best fit: Quadratic
Figure 4.6: Computation time for EMBT as a function of number of dwell positions.
4.3 Discussion
The introduction of dual-source afterloaders can revolutionize the field of HDR brachyther-
apy. The afterloaders can be exploited in two ways. First, two 192Ir sources can be used
simultaneously to reduce treatment time, if only one type of radionuclide were to be
used. Second, different radionuclides can be used simultaneously or sequentially during
treatment.
When comparing single-source plans, two conclusions are drawn. First, our results
agree with the literature that 60Co is at least equivalent to 192Ir with respect to clinical
aspects [31, 64, 78]. For boost cases, 60Co actually outperforms 192Ir. This behaviour
can be attributed to the dose profile of 60Co. With the faster fall-off of 60Co’s radial and
depth dose profiles, the OARs can be better spared. Second, in Yb-plans, doses to the
OARs are higher compared to 192Ir, which contradicts the findings of Lymperopoulou
et al. [45] and Krishnamurthy et al. [36]. This increase can also be explained by the
higher depth dose of 169Yb. Because higher doses are delivered by 169Yb compared to
Chapter 4. Energy-modulated brachytherapy 47
192Ir for the same distance, more dose is delivered to the OARs.
In EMBT plans, it is possible to spare the OARs while maintaining the same target
coverage with multi-source brachytherapy. On average, dual- and triple-source combina-
tions outperform their individual single sources, as expected. In particular, cases with
DILs benefit the most from energy-modulation. The combinations Co-Ir and Co-Yb are
comparable, but both are superior to the Ir-Yb pair. These results are particularly in-
teresting given that boosting the DILs results in lower recurrence probability and better
treatment outcome [6, 21, 34, 48, 49, 63].
If all radionuclides are normalized to 10 Ci, there is no large difference in terms of
treatment time among the treatment plans, with a slight increase when multiple sources
are used. Furthermore, the number and location of the active dwell positions (dwell time
> 0 seconds) do not change significantly across the plans. One important point to note
is that we assume that the sources are used sequentially during treatment. Should the
sources be used concurrently, treatment times would be greatly reduced but inter-seed
attenuation would have to be accounted for [12].
EMBT is still in its infancy and more theoretical studies need to be carried out. While
some of the dosimetric improvements are very small for regular prostate cases, they show
a positive trend that can be more thoroughly explored. More clinical scenarios must
be tested in order to find the ideal use of multi-source brachytherapy and selection of
HDR sources. From a feasibility perspective, using three sources is not yet possible. We
therefore propose the dual use of 60Co and 192Ir for EMBT.
4.4 Conclusion
We retrospectively investigated the dosimetric benefits of a novel brachytherapy technique
called EMBT with three different HDR sources, 192Ir, 60Co, and 169Yb. On average, the
plans generated from all source combinations satisfied the clinical protocols, showing
Chapter 4. Energy-modulated brachytherapy 48
that EMBT is viable. Our results show that HDR prostate brachytherapy benefits from
dose reduction to the OARs when multiple sources are used, while keeping similar target
coverage. Cases with DILs benefit the most from EMBT. From a practical point of view,
we propose the dual use of 60Co and 192Ir. As with DMBT, we also show that our inverse
planning approach is effective for HDR brachytherapy.
Chapter 5
Conclusion
The HDR brachytherapy forward planning process is time-consuming and heavily relies
on the planner’s expertise, which can vary from one planner to another. Since several
cancer patients are treated in one day, the treatment planning process should be faster
and the quality of the treatment plans more consistent. Our inverse planning approach
has solved some of these problems. We have shown that the mathematical framework used
in SRS and IMRT can be successfully applied to HDR brachytherapy. The DTO model
and its modified versions are solved to ε-optimality by the IPCG algorithm [56] within
a few minutes. The resulting treatment plans satisfy the clinical objectives while having
acceptable treatment times. This fast and automated framework to generate treatment
plans relieves the load of the planners and allows for more plans to be generated within
a certain time frame.
Two novel brachytherapy techniques, DMBT and EMBT, were evaluated. They may
improve treatment outcome and save lives by providing superior plan quality than con-
ventional brachytherapy treatments. We showed that DMBT, which makes use of a
shielded tandem applicator, allows for more OAR sparing while keeping the same target
coverage, homogeneity, and conformity. The next step is to use the DMBT tandem in
clinical trials.
49
Chapter 5. Conclusion 50
We also investigated the effectiveness of EMBT using 192Ir, 60Co, and 169Yb. Our
results showed that multi-source combinations were, on average, as good or better than
their individual building blocks, as expected. Cases with DILs benefited the most from
EMBT in terms of OAR sparing. With the introduction of new dual-source afterloaders
on the market, EMBT is clinically viable. Our hypothetical study shows that EMBT is
a promising treatment modality, and should be investigated for other cancer sites and
different radionuclides.
There are several extensions to this work. In terms of the mathematical model, the
dwell positions can be optimized in addition to the dwell times. We can approach the
problem as a two-stage optimization problem, where the location of the dwell positions
are selected first, followed by the optimization of the dwell times. Alternatively, both
types of variables can be optimized at the same time in a mixed integer programming
problem. Another extension is the incorporation of a penalty term in the objective
function to lower the treatment time. For example, the penalty term could be the sum
of the dwell times. Regarding the selection of model parameters, machine learning could
be used to identify patient clusters that would match a single set of penalty weights.
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