scispace - formally typeset

Journal ArticleDOI

Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model

01 Mar 2017-IEEE Transactions on Medical Imaging (IEEE Trans Med Imaging)-Vol. 36, Iss: 3, pp 815-825

TL;DR: Two methods to derive the radiotherapy prescription dose distribution are introduced, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density and it is shown how the method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration.

AbstractIn this article, we propose a proof of concept for the automatic planning of personalized radiotherapy for brain tumors. A computational model of glioblastoma growth is combined with an exponential cell survival model to describe the effect of radiotherapy. The model is personalized to the magnetic resonance images (MRIs) of a given patient. It takes into account the uncertainty in the model parameters, together with the uncertainty in the MRI segmentations. The computed probability distribution over tumor cell densities, together with the cell survival model, is used to define the prescription dose distribution, which is the basis for subsequent Intensity Modulated Radiation Therapy (IMRT) planning. Depending on the clinical data available, we compare three different scenarios to personalize the model. First, we consider a single MRI acquisition before therapy, as it would usually be the case in clinical routine. Second, we use two MRI acquisitions at two distinct time points in order to personalize the model and plan radiotherapy. Third, we include the uncertainty in the segmentation process. We present the application of our approach on two patients diagnosed with high grade glioma. We introduce two methods to derive the radiotherapy prescription dose distribution, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density. We show how our method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration. We further present extensions of the method in order to spare adjacent organs at risk by re-distributing the dose. The presented approach and its proof of concept may help in the future to better target the tumor and spare organs at risk.

Summary (3 min read)

Introduction

  • Previous works on computational growth models for gliomas have focused on reaction-diffusion equations to model cell proliferation and infiltration into surrounding brain tissue [1].
  • In order to account for the infiltrative nature of the tumor, several studies recently proposed to personalize radiotherapy planning based on a computational growth model.
  • They showed that personalizing the delivered dose could improve therapy in terms of days gained by the patients.
  • In the third scenario, the authors include the uncertainty in the segmentation of the abnormality visible on the different MRIs to the personalization strategy.

II. SEGMENTATION SAMPLES

  • The T1Gd abnormality, which is the active part of the tumor, and the larger T2-FLAIR abnormality, which is usually called the edema, were segmented by a clinician.
  • In order to take into account the uncertainty in the segmentation, the authors propose to randomly modify the original clinician segmentations.
  • The samples are efficiently produced on the regular grid using the separability and stationary properties of the squared exponential covariance function (see [18] for details).
  • Segmentation samples for the T1Gd and T2-FLAIR abnormalities at the first and second time points are generated.
  • One could compare the output of the tumor growth model with probabilistic segmentation approaches which have been proposed for glioblastoma [20].

III. TUMOR GROWTH MODEL

  • Below, the authors identify the scalar parameter dw with D. The solution of the reaction-diffusion equation (1) is a tumor cell density u computed over the whole brain domain.
  • The method is based on the assumption that the solution of equation (1) at the first time point has converged to its asymptotic, traveling wave type solution.
  • Thereby, the tumor cell density is propagated outward (and inward), starting from the T1Gd segmentation, and drops approximately exponentially with distance.
  • The reaction-diffusion equation is solved using the Lattice Boltzmann Method [21], [23], [24] which allows for easy parallelization and fast computations.
  • The common approach taken in these works is to add a death term to the reaction-diffusion equation, which allows to model the shrinkage of the tumor due to the therapy.

IV. PERSONALIZATION

  • The personalization of the tumor growth model is combined with a dose response model in order to define the radiotherapy planning.
  • First the authors only use a single time point (the second acquisition) to personalize the model such that the radiotherapy plan will be defined using a single acquisition, similarly to what is being done in clinic.
  • Second the authors use two time points in order to personalize the model.
  • The radiotherapy plan will then be defined on the latest acquisition.
  • Third, the authors use two time points and include the uncertainty in the segmentation.

A. Scenario 1: One time point only

  • The authors further model the prior as log-uniform and independent between the parameters, P (θ) = P (D)P (ρ) (4) The authors sample from the posterior distribution using a Metropolis-Hasting algorithm.
  • Note that this section only uses the initialization algorithm (see Section III) which only depends on the invisibility index λ = √ D/ρ.
  • Note that this section can be related to the method described in [16], where a single time point is used to propose a dose planning.
  • Moreover, the Bayesian methodology allows to take into account the uncertainty in the personalization.

V. RADIOTHERAPY PLANNING

  • The authors detail how they use the personalization of the tumor growth model in order to define the best radiotherapy plan at the time of the second acquisition.
  • The authors start by coupling the growth model with a cell survival model (Section V-A).
  • The authors then detail how to compute the prescription doses in Section V-B, and how to compute the delivered dose in Section V-C.

A. Cell survival

  • Cell survival after irradiation is often modeled using the linear-quadratic model.
  • The authors follow the derivations of [16], and consider the linear approximation of the linear-quadratic model.

B. Prescription Dose Optimization

  • A prescription dose can be defined as the dose minimizing the surviving fraction of tumor cells.
  • The personalization of the tumor growth model provides samples {θl} from the posterior distribution P (θ|S).
  • The probabilistic dose is defined as the dose minimizing the expectation of the surviving fraction of tumor cells.

VI. RESULTS

  • The authors first present the results for one high grade glioma patient.
  • For scenarios 2 and 3, 2000 samples are drawn from the posterior distribution, leading to an acceptance rate of 60%.
  • Including the second time point, and the uncertainty in the segmentation, increases the uncertainty in the invisibility index.
  • Those two figures highlights the two sources of uncertainty for scenario 3: the segmentation, and the tumor infiltration.
  • This can be more clearly observed by looking at the dose volume histograms on Figure 15.

VII. DISCUSSION

  • Extensions of the model could be considered in order to include the noise level σ, the thresholds τ1, and τ2, as free parameters of the model.
  • This level of noise allows to explore the parameter space, and to focus on a region of interest which is in accordance with the lowest distances found.
  • It was set manually after a few experiments.
  • The authors did not include it in this study for several reasons.
  • Second, this adds complexity and increases the computational cost of the method.

VIII. CONCLUSION

  • The authors presented the proof of concept for a method combining a computational model of tumor growth with a dose response model in order to optimize radiotherapy planning, which takes into account the uncertainty in the model parameters and the clinical segmentations.
  • In the third one, the authors include uncertainty in the segmentation process.
  • The MAP dose minimizes surviving tumor cells after irradiation of the most probable situation, while the probabilistic dose allows one to take into account the uncertainty by minimizing the expected surviving tumor cells.
  • To that end, the model should be extended in order to take into account the complex therapy the patient is undergoing.
  • Finally, it should be investigated if more conformal dose delivery techniques such as proton therapy lead to IMRT planning more conformal to the prescribed dose.

Did you find this useful? Give us your feedback

...read more

Content maybe subject to copyright    Report

HAL Id: hal-01403847
https://hal.inria.fr/hal-01403847
Submitted on 27 Nov 2016
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Personalized Radiotherapy Planning Based on a
Computational Tumor Growth Model
Matthieu Lê, Hervé Delingette, Jayashree Kalpathy-Cramer, Elizabeth R
Gerstner, Tracy Batchelor, Jan Unkelbach, Nicholas Ayache
To cite this version:
Matthieu Lê, Hervé Delingette, Jayashree Kalpathy-Cramer, Elizabeth R Gerstner, Tracy Batche-
lor, et al.. Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model.
IEEE Transactions on Medical Imaging, Institute of Electrical and Electronics Engineers, 2016, pp.11.
�10.1109/TMI.2016.2626443�. �hal-01403847�

JOURNAL SUBMISSION 1
Personalized Radiotherapy Planning
Based on a Computational Tumor Growth Model
Matthieu L
ˆ
e
1
, Herv
´
e Delingette
1
, Jayashree Kalpathy-Cramer
2
, Elizabeth R. Gerstner
3
,
Tracy Batchelor
3
, Jan Unkelbach
4
, Nicholas Ayache
1
Abstract—In this article, we propose a proof of concept
for the automatic planning of personalized radiotherapy for
brain tumors. A computational model of glioblastoma growth
is combined with an exponential cell survival model to describe
the effect of radiotherapy. The model is personalized to the
magnetic resonance images (MRIs) of a given patient. It takes
into account the uncertainty in the model parameters, together
with the uncertainty in the MRI segmentations. The computed
probability distribution over tumor cell densities, together with
the cell survival model, is used to define the prescription
dose distribution, which is the basis for subsequent Intensity
Modulated Radiation Therapy (IMRT) planning. Depending on
the clinical data available, we compare three different scenarios to
personalize the model. First, we consider a single MRI acquisition
before therapy, as it would usually be the case in clinical routine.
Second, we use two MRI acquisitions at two distinct time points in
order to personalize the model and plan radiotherapy. Third, we
include the uncertainty in the segmentation process. We present
the application of our approach on two patients diagnosed with
high grade glioma. We introduce two methods to derive the
radiotherapy prescription dose distribution, which are based on
minimizing integral tumor cell survival using the maximum a
posteriori or the expected tumor cell density. We show how our
method allows the user to compute a patient specific radiotherapy
planning conformal to the tumor infiltration. We further present
extensions of the method in order to spare adjacent organs at
risk by re-distributing the dose. The presented approach and its
proof of concept may help in the future to better target the tumor
and spare organs at risk.
Index Terms—Radiotherapy planning, computational tu-
mor growth model, personalization, uncertainty, segmentation,
glioblastoma
I. INTRODUCTION
H
IGH grade glioma is one of the most common and
aggressive types of primary brain tumors. The treatment
of high grade glioma usually involves resection when possible,
followed by concurrent chemotherapy and radiotherapy.
Previous works on computational growth models for
gliomas have focused on reaction-diffusion equations to model
cell proliferation and infiltration into surrounding brain tis-
sue [1]. The model has been extended to model response
to chemotherapy, surgical resection, and radiotherapy. For
instance, a sink term can be added to the reaction-diffusion
1
Asclepios Project, Inria Sophia Antipolis, France.
2
Martinos Center for Biomedical Imaging, Harvard-MIT Division of Health
Sciences and Technology, Charlestown, MA, USA.
3
Department of Neurology, Massachusetts General Hospital, Boston, MA,
USA.
4
Department of Radiation Oncology, Massachusetts General Hospital and
Harvard Medical School, Boston, MA, USA.
Figure 1. The clinical segmentation of the T1Gd abnormality (Top, orange
line) is used to define the clinical target volume (CTV, white dashed line) as a
2 cm expansion of the segmentation. In clinical settings, 60 Gy is prescribed
to the CTV. We propose to personalize the prescription dose (Bottom) to
account for tumor infiltration and segmentation uncertainty.
equation in order to model the impact of chemo or radio-
therapy [2], [3]. The resection of a brain tumor can also be
modeled by deleting the tumor cells in the resected region
[4], [5]. More advanced therapy schedules using for instance
anti-angiogenic drugs can also be studied with more complex
models [6], [7], [8].
In this article, we provide proof of concept of a method
for the automatic planning of personalized radiotherapy for
glioblastoma (Figure 1). The beneficial impact of radiotherapy
for glioblastoma patients has been clearly demonstrated [9],
[10]. However, its planning is made difficult by the infiltrative
nature of the disease, and the uncertainty in delineating the
abnormality in Magnetic Resonance Images (MRI). To account
for the tumor infiltration, a margin of 1 to 3 cm is added to the
abnormality visible on MRI to define the clinical target volume
(CTV) [11] (Figure 1). The exact extent of this margin is left
at the discretion of the clinician.

JOURNAL SUBMISSION 2
Figure 2. Summary of the method: the segmentation of the tumor on the different MRIs is used to personalize the tumor growth model. This is combined
with a dose response model to define the prescription dose. Finally, the delivered dose is optimized using 9 equally spaced coplanar photon beams. The color
code indicates which data is used for the different scenarios: one or two MRI acquisition at two different time points, the clinical segmentations or plausible
samples to take into account the segmentation uncertainty.
Figure 3. First time point on the left, second time point on the right. (Top)
The proliferative rim is outlined in orange on the T1Gd MRI. (Middle Top)
The edema is outlined in red on the T2-FLAIR MRI. The edema encloses
the proliferative rim. (Middle Bottom) Tumor cell density computed with the
reaction-diffusion model. The black (resp. white) line is the threshold values
τ
1
(resp. τ
2
) corresponding to the T1Gd (resp. T2-FLAIR) abnormality.
(Bottom) Comparison between the clinician segmentation and the contours
from the model.
In order to account for the infiltrative nature of the tumor,
several studies recently proposed to personalize radiotherapy
planning based on a computational growth model. Corwin et
al. [12], [13] personalized spherically symmetric doses based
on a 1D reaction-diffusion tumor growth model using the
T1Gd and T2-FLAIR abnormalities radius as observations
[14], [15]. In this framework, they showed that personalizing
the delivered dose could improve therapy in terms of days
gained by the patients. However, this spherically symmetric
assumption prevents taking into account boundaries of the
tumor progression such as the ventricles. Unkelbach et al.
[16], [17] studied the optimization of the radiotherapy planning
based on a tumor growth model in order to automatically
define realistic 3D prescription dose distributions, taking into
account the natural boundaries and privileged pathways of the
tumor progression. The proposed planning was personalized
to the patients geometry, but without personalizing the tumor
growth model parameters.
In this article, we extend previous works by personalizing
a 3D tumor growth model in order to define radiotherapy
prescription doses. This allows one to automatically compute
realistic 3D prescription doses conformal to the tumor infiltra-
tion (see Figure 1). Moreover, we study the impact of taking
into account the uncertainty in the different inputs of the model
(segmentations and model parameters). We use a tumor growth
model based on a reaction diffusion equation, which models
the infiltrative spread of tumor cells in the surrounding white
and gray matter. A Bayesian approach is taken to estimate
the posterior distribution over the model parameters based
on the MRIs of the patient. A recently proposed method to
sample plausible image segmentations is used to incorporate
uncertainty in the segmentation of the tumor in the MR
images [18]. The tumor growth model is then combined
with an exponential cell survival model to describe the effect
of radiotherapy. The probability distribution over tumor cell
densities, together with the cell survival model, is used to
define the prescription dose distribution, which is the basis
for subsequent Intensity Modulated Radiation Therapy (IMRT)
planning. The scope of this paper is the personalization of
radiotherapy planning. As such, we focus on patients which
were not treated with surgical resection. The proposed model
could however be extended in order to included the impact of
such therapy following the developments done in [4], [5].

JOURNAL SUBMISSION 3
In this article, we consider three different scenarios. In
the first one, we only consider a single MRI acquisition of
the T1Gd and T2-FLAIR MRI before therapy planning. This
scenario is the closest to the clinical setting where radiotherapy
planning is usually based on a single MRI acquisition. In the
second, we consider two MRI acquisition at two time points
for a total of four MRIs: the T1Gd and T2-FLAIR at the first
and second time point (see Figure 3). In the third scenario, we
include the uncertainty in the segmentation of the abnormality
visible on the different MRIs to the personalization strategy.
The second and third scenarios are proofs of concept of a
method to include additional information to the personalized
therapy pipeline. We acknowledge that patients are usually
subject to therapy between the two time points, and as such,
the growth model personalization is biased by the impact of
therapy. Note however that if the therapy does not result in a
decrease of the tumor volume, its impact is implicitly taken
into account in the personalization of the growth parameter.
Based on those different scenarios, we propose three prin-
cipled approaches to compute the prescription dose. First, we
minimize the surviving fraction of tumor cells after irradiation
for the most probable tumor cell density. Second, we minimize
the expected survival fraction tumor cells after irradiation.
Third, we present an approach to correct the prescription dose
to take into account the presence of adjacent organs at risk.
The generation of different plausible segmentations based
on the clinical ones is presented in Section II. The forward
model of tumor growth is presented in Section III. The
personalization method for the three different scenarios is
presented in Section IV. The three principled approach for
the personalization of the dose response model to define the
prescription dose and the IMRT is detailed in Section V. A
summary of the method is illustrated in Figure 2. To our
knowledge, this is the first work that uses a personalized model
of brain tumor growth taking into account the uncertainty in
tumor growth parameters and the clinician’s segmentations in
order to optimize radiotherapy planning.
II. SEGMENTATION SAMPLES
The T1Gd abnormality, which is the active part of the tumor,
and the larger T2-FLAIR abnormality, which is usually called
the edema, were segmented by a clinician. In order to take
into account the uncertainty in the segmentation, we propose
to randomly modify the original clinician segmentations. The
method is based on [18], where samples of such segmentations
are generated from a high dimensional Gaussian process,
as the zero crossing of a level function. The samples are
efficiently produced on the regular grid using the separability
and stationary properties of the squared exponential covariance
function (see [18] for details). The samples take into account
the image intensity information using the signed geodesic
distance as the mean of the Gaussian process.
Segmentation samples for the T1Gd and T2-FLAIR abnor-
malities at the first and second time points are generated. Let
S
0
i
denote the clinical segmentations for the T1Gd and T2-
FLAIR abnormalities at the first and second time points, where
the index i = 1, ..., 4 refers to the 4 available images (see
Figure 3). Let S
i
=
S
k
i
k=1,...,K
denote sets of K plausible
segmentations per modality and time point, where each S
k
i
is
a plausible sample from S
0
i
, the i-th clinician segmentation.
Figure 4 shows examples of such samples for K = 5. The
samples automatically respect the boundaries of the tumor
progression such as the ventricles, because of the presence
of large intensity gradients. The five presented samples per
abnormality correspond to an average DICE of 87%, which is
comparable to the inter-expert DICE measured in the BraTS
Challenge for brain tumors delineation [19]. Comparing the
output of the forward tumor growth model with these plausible
noisy segmentations allows to include the uncertainty of the
original clinician segmentations.
Note that other approaches could allow the handling of
segmentation uncertainty. For instance, one could compare the
output of the tumor growth model with probabilistic segmen-
tation approaches which have been proposed for glioblastoma
[20].
III. TUMOR GROWTH MODEL
The tumor growth model is based on the reaction-diffusion
equation,
u
t
= (D.u)
| {z }
Diffusion
+ ρu(1 u)
| {z }
Logistic Proliferation
(1)
Du.
n
= 0 (2)
Equation (1) describes the spatio-temporal evolution of the
tumor cell density u, which infiltrates neighboring tissues with
a diffusion tensor D, and proliferates with a net proliferation
rate ρ. Equation (2) enforces Neumann boundary conditions
on the brain domain . Following [21], we define the diffusion
tensor as D = d
w
I in the white matter, and D = d
w
/10 I in
the gray matter, where I is the 3x3 identity matrix. Below, we
identify the scalar parameter d
w
with D.
The solution of the reaction-diffusion equation (1) is a
tumor cell density u computed over the whole brain domain.
However, parts of the brain that glioblastomas usually do not
invade were excluded from the tumor simulation such as the
CSF or the cerebellum. In order to relate the tumor cell density
u to the MRIs, the frontier of the visible abnormalities is
assumed to correspond to a threshold value of the tumor cell
density u. We note τ
1
the value of the tumor cell density u
corresponding to the frontier of the T1Gd abnormality, and
τ
2
the value corresponding to the frontier of the T2-FLAIR
abnormality (see Figure 3).
The initialization of the tumor cell density u(t = t
1
, x) at
the time of the first acquisition is of particular importance, as it
impacts the rest of the simulation. In this work, the tumor tail
extrapolation algorithm described in [22] is used. The method
is based on the assumption that the solution of equation
(1) at the first time point has converged to its asymptotic,
traveling wave type solution. Thereby, the tumor cell density
is propagated outward (and inward), starting from the T1Gd
segmentation, and drops approximately exponentially with
distance. The steepness of the falloff, i.e. the distance at which
the cell density drops by a factor 1/e is given by the invisibility

JOURNAL SUBMISSION 4
index λ =
p
D . By construction of the initialization, the
T1Gd abnormality falls exactly on the threshold τ
1
of the
tumor cell density at the first time point.
The reaction-diffusion equation is solved using the Lattice
Boltzmann Method [21], [23], [24] which allows for easy
parallelization and fast computations. On a 1mm×1mm×1mm
resampled MRI, simulating 30 days of growth takes approxi-
mately 50 seconds on a 2.3Ghz 50 core machine.
Note that this model is an approximation of the complex
growth of the disease. For instance, it could be extended
in order to include mass effect [25], or a more detailed
description of the disease [6]. In other works, this model
has been extended to model different types of therapy such
as resection [26], [5], chemotherapy [2], or anti-angiogenic
therapy [7]. The common approach taken in these works is
to add a death term to the reaction-diffusion equation, which
allows to model the shrinkage of the tumor due to the therapy.
It was also shown in [27] that the personalized parameters
of a reaction-diffusion model were good predictors of certain
mutations status of the patient.
IV. PERSONALIZATION
The personalization of the tumor growth model is combined
with a dose response model in order to define the radiotherapy
planning. We compare three different scenarios. First we only
use a single time point (the second acquisition) to personalize
the model such that the radiotherapy plan will be defined using
a single acquisition, similarly to what is being done in clinic.
Second we use two time points in order to personalize the
model. The radiotherapy plan will then be defined on the latest
acquisition. Third, we use two time points and include the
uncertainty in the segmentation.
A. Scenario 1: One time point only
In this section, we are interested in the posterior probability
of the model parameter θ = (D, ρ), knowing the clinical
segmentations S
0
3
on the T1Gd and S
0
4
on the T2-FLAIR at
the second time point. To cast the problem in a probabilis-
tic framework, we follow the Bayes rule: P (θ|S
0
3
, S
0
4
)
P (S
0
3
, S
0
4
|θ) P (θ). The likelihood is modeled as
P (S
0
3
, S
0
4
|θ) exp
H(D, ρ, S
0
3
, S
0
4
)
2
σ
2
(3)
where H(D, ρ, S
0
3
, S
0
4
) is the 95th percentile of the symmet-
ric Hausdorff distance between the border of the segmentation
S
0
4
, and the isoline at τ
2
of the simulated tumor cell density
u using (D, ρ), and initialized with the segmentation S
0
3
.
We further model the prior as log-uniform and independent
between the parameters,
P (θ) = P (D)P (ρ) (4)
We sample from the posterior distribution using a
Metropolis-Hasting algorithm. Note that this section only
uses the initialization algorithm (see Section III) which only
depends on the invisibility index λ =
p
D. Note that this
section can be related to the method described in [16], where a
single time point is used to propose a dose planning. However,
Unkelbach et al. [16] use a nominal value of the invisibility
index whereas it is personalized in this scenario. Moreover,
the Bayesian methodology allows to take into account the
uncertainty in the personalization.
B. Scenario 2: Two time points
In this section, we are interested in the posterior probability
of the model parameter θ = (D, ρ), knowing the clinical
segmentations S
0
i
for i = 1, 2, 3, 4 on the T1Gd and T2-FLAIR
at the first and second time point respectively. In this case, the
likelihood is model as
P ({S
0
i
}
i=1,2,3,4
|θ) exp
1
σ
2
P
4
i=2
H
i
(D, ρ, S
0
1
, S
0
i
)
3
!
2
(5)
where H
i
(D, ρ, S
0
1
, S
0
i
) is the 95th percentile of the sym-
metric Hausdorff distance between the border of the segmen-
tation S
0
i
for i = 2, 3, 4, and the isoline of the simulated
tumor cell density u using (D, ρ), and initialized with the
segmentation S
0
1
. We model the prior as described in Section
IV-A.
We sample from the posterior distribution using the Gaus-
sian Process Hamiltonian Monte Carlo (GPHMC) algorithm
first described by [28], and used for tumor growth personal-
ization in [21].
C. Scenario 3: Two time points and segmentation uncertainty
In this section, we want to include the uncertainty in the
segmentation to the personalization process. We denote the set
of plausible segmentations by S = {S
i
}
i=1,2,3,4
(see Section
II). We introduce the random variables Z
i
= (Z
i1
, ..., Z
iK
)
for i = 1, 2, 3, 4, which are one-hot binary vectors where
P (Z
ij
= 1|S) P (S
j
i
), and Z
il
= 0 for l 6= j when Z
ij
= 1.
The random variable Z
i
is a measure of the plausibility
of the samples: P (Z
i
) =
Q
K
i=1
P (Z
ij
= 1)
Z
ij
. We are
interested in the posterior probability of the model parameter
θ = (D, ρ, Z
1
, Z
2
, Z
3
, Z
4
), knowing the observations S. We
model the likelihood as
P (S|θ) exp
1
σ
2
P
4
i=2
H
i
(D, ρ, Z
1
, Z
i
)
3
!
2
(6)
where H
i
(D, ρ, Z
1
, Z
i
) is the 95th percentile of the sym-
metric Hausdorff distance between the border of the segmen-
tation indexed by Z
i
, and the isolines of the simulated tumor
cell density u using (D, ρ), and initialized with the contour
selected with Z
1
. We model the prior independent between
the parameters, log-uniform for D and ρ, and uniform for Z
i
(i.e. P (Z
ij
= 1) = 1/K),
P (θ) = P (D)P (ρ)
4
Y
i=1
P (Z
i
) (7)

Figures (18)
Citations
More filters

Journal ArticleDOI
TL;DR: The experimental results demonstrate that the proposed edge-aware generative adversarial networks (Ea-GANs) outperform multiple state-of-the-art methods for cross-modality MR image synthesis in both qualitative and quantitative measures.
Abstract: Magnetic resonance (MR) imaging is a widely used medical imaging protocol that can be configured to provide different contrasts between the tissues in human body. By setting different scanning parameters, each MR imaging modality reflects the unique visual characteristic of scanned body part, benefiting the subsequent analysis from multiple perspectives. To utilize the complementary information from multiple imaging modalities, cross-modality MR image synthesis has aroused increasing research interest recently. However, most existing methods only focus on minimizing pixel/voxel-wise intensity difference but ignore the textural details of image content structure, which affects the quality of synthesized images. In this paper, we propose edge-aware generative adversarial networks (Ea-GANs) for cross-modality MR image synthesis. Specifically, we integrate edge information, which reflects the textural structure of image content and depicts the boundaries of different objects in images, to reduce this gap. Corresponding to different learning strategies, two frameworks are proposed, i.e., a generator-induced Ea-GAN (gEa-GAN) and a discriminator-induced Ea-GAN (dEa-GAN). The gEa-GAN incorporates the edge information via its generator, while the dEa-GAN further does this from both the generator and the discriminator so that the edge similarity is also adversarially learned. In addition, the proposed Ea-GANs are 3D-based and utilize hierarchical features to capture contextual information. The experimental results demonstrate that the proposed Ea-GANs, especially the dEa-GAN, outperform multiple state-of-the-art methods for cross-modality MR image synthesis in both qualitative and quantitative measures. Moreover, the dEa-GAN also shows excellent generality to generic image synthesis tasks on benchmark datasets about facades, maps, and cityscapes.

84 citations


Cites background from "Personalized Radiotherapy Planning ..."

  • ...For example, multi-modality MR images have been collectively utilized to study the neuroanatomy of human brains for disease diagnosis [3] or therapy planning [4]....

    [...]


Journal ArticleDOI
01 Oct 2019
TL;DR: The opportunities of a model‐based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.
Abstract: Increasing knowledge of intertumor heterogeneity, intratumor heterogeneity, and cancer evolution has improved the understanding of anticancer treatment resistance. A better characterization of cancer evolution and subsequent use of this knowledge for personalized treatment would increase the chance to overcome cancer treatment resistance. Model-based approaches may help achieve this goal. In this review, we comprehensively summarized mathematical models of tumor dynamics for solid tumors and of drug resistance evolution. Models displayed by ordinary differential equations, algebraic equations, and partial differential equations for characterizing tumor burden dynamics are introduced and discussed. As for tumor resistance evolution, stochastic and deterministic models are introduced and discussed. The results may facilitate a novel model-based analysis on anticancer treatment response and the occurrence of resistance, which incorporates both tumor dynamics and resistance evolution. The opportunities of a model-based approach as discussed in this review can be of great benefit for future optimizing and personalizing anticancer treatment.

30 citations


Cites methods from "Personalized Radiotherapy Planning ..."

  • ...This model structure was also recently used to investigate the personalization of radiotherapy strategy for brain cancer patients.(66) Setting f (c (x,t))= ⋅c (x,t), a similar model structure was also used to simulate the growth of glioblastoma based on previous reported parameters estimated from patients and estimated the survival times of patients under different parameter settings....

    [...]


Journal ArticleDOI
TL;DR: The ultimate goal of the work is the design of inversion methods that integrate complementary data, and rigorously follow mathematical and physical principles, in an attempt to support clinical decision making, which requires reliable, high-fidelity algorithms with a short time-to-solution.
Abstract: PDE-constrained optimization problems find many applications in medical image analysis, for example, neuroimaging, cardiovascular imaging, and oncologic imaging. We review the related literature and give examples of the formulation, discretization, and numerical solution of PDE-constrained optimization problems for medical imaging. We discuss three examples. The first is image registration, the second is data assimilation for brain tumor patients, and the third is data assimilation in cardiovascular imaging. The image registration problem is a classical task in medical image analysis and seeks to find pointwise correspondences between two or more images. Data assimilation problems use a PDE-constrained formulation to link a biophysical model to patient-specific data obtained from medical images. The associated optimality systems turn out to be sets of nonlinear, multicomponent PDEs that are challenging to solve in an efficient way. The ultimate goal of our work is the design of inversion methods that integrate complementary data, and rigorously follow mathematical and physical principles, in an attempt to support clinical decision making. This requires reliable, high-fidelity algorithms with a short time-to-solution. This task is complicated by model and data uncertainties, and by the fact that PDE-constrained optimization problems are ill-posed in nature, and in general yield high-dimensional, severely ill-conditioned systems after discretization. These features make regularization, effective preconditioners, and iterative solvers that, in many cases, have to be implemented on distributed-memory architectures to be practical, a prerequisite. We showcase state-of-the-art techniques in scientific computing to tackle these challenges.

23 citations


Cites background or methods from "Personalized Radiotherapy Planning ..."

  • ...They have been used to (i) study tumor growth patterns in individual patients [45, 127, 135, 167, 189], (ii) extrapolate the physiological boundary of tumors [113, 148], (iii) or study the effects of clinical intervention [116, 117, 139, 164, 169, 191, 203]....

    [...]

  • ...finite-difference approximations to the gradient [101], or tackle the parameter estimation problem within a Bayesian framework [48, 91, 116, 117, 122, 123, 138, 154] (see Rem....

    [...]

  • ...A common assumption in many models is that the rate of migration depends on the tissue composition; typically, it is modeled to be faster in white than in gray matter [116, 117, 189]....

    [...]

  • ...such example is to relate (manual) segmentations of imaging abnormalities to a detection thresholds for the computed population density of cancerous cells [70, 89, 116, 117, 127, 133, 191]....

    [...]


Book ChapterDOI
TL;DR: This chapter will focus on introducing typical CNNs and GANs models for medical image synthesis, and elaborate the recent work about low-dose to high-dose PET image synthesisation, and cross-modality MR images synthesis, using these models.
Abstract: Medical images have been widely used in clinics, providing visual representations of under-skin tissues in human body. By applying different imaging protocols, diverse modalities of medical images with unique characteristics of visualization can be produced. Considering the cost of scanning high-quality single modality images or homogeneous multiple modalities of images, medical image synthesis methods have been extensively explored for clinical applications. Among them, deep learning approaches, especially convolutional neural networks (CNNs) and generative adversarial networks (GANs), have rapidly become dominating for medical image synthesis in recent years. In this chapter, based on a general review of the medical image synthesis methods, we will focus on introducing typical CNNs and GANs models for medical image synthesis. Especially, we will elaborate our recent work about low-dose to high-dose PET image synthesis, and cross-modality MR image synthesis, using these models.

22 citations


Journal ArticleDOI
Abstract: In this paper we present a method for simultaneously segmenting brain tumors and an extensive set of organs-at-risk for radiation therapy planning of glioblastomas. The method combines a contrast-adaptive generative model for whole-brain segmentation with a new spatial regularization model of tumor shape using convolutional restricted Boltzmann machines. We demonstrate experimentally that the method is able to adapt to image acquisitions that differ substantially from any available training data, ensuring its applicability across treatment sites; that its tumor segmentation accuracy is comparable to that of the current state of the art; and that it captures most organs-at-risk sufficiently well for radiation therapy planning purposes. The proposed method may be a valuable step towards automating the delineation of brain tumors and organs-at-risk in glioblastoma patients undergoing radiation therapy.

17 citations


References
More filters

Journal ArticleDOI
Abstract: In this paper we report the set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences Twenty state-of-the-art tumor segmentation algorithms were applied to a set of 65 multi-contrast MR scans of low- and high-grade glioma patients—manually annotated by up to four raters—and to 65 comparable scans generated using tumor image simulation software Quantitative evaluations revealed considerable disagreement between the human raters in segmenting various tumor sub-regions (Dice scores in the range 74%–85%), illustrating the difficulty of this task We found that different algorithms worked best for different sub-regions (reaching performance comparable to human inter-rater variability), but that no single algorithm ranked in the top for all sub-regions simultaneously Fusing several good algorithms using a hierarchical majority vote yielded segmentations that consistently ranked above all individual algorithms, indicating remaining opportunities for further methodological improvements The BRATS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource

2,695 citations


Journal ArticleDOI
01 Jan 2015
TL;DR: The set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences are reported, finding that different algorithms worked best for different sub-regions, but that no single algorithm ranked in the top for all sub-Regions simultaneously.
Abstract: In this paper we report the set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences. Twenty state-of-the-art tumor segmentation algorithms were applied to a set of 65 multi-contrast MR scans of low- and high-grade glioma patients - manually annotated by up to four raters - and to 65 comparable scans generated using tumor image simulation software. Quantitative evaluations revealed considerable disagreement between the human raters in segmenting various tumor sub-regions (Dice scores in the range 74-85%), illustrating the difficulty of this task. We found that different algorithms worked best for different sub-regions (reaching performance comparable to human inter-rater variability), but that no single algorithm ranked in the top for all subregions simultaneously. Fusing several good algorithms using a hierarchical majority vote yielded segmentations that consistently ranked above all individual algorithms, indicating remaining opportunities for further methodological improvements. The BRATS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource.

1,367 citations


"Personalized Radiotherapy Planning ..." refers result in this paper

  • ...The five presented samples per abnormality correspond to an average DICE of 87%, which is comparable to the inter-expert DICE measured in the BraTS Challenge for brain tumors delineation [19]....

    [...]


Journal ArticleDOI
Abstract: The method of lattice Boltzmann equation (LBE) is a kinetic-based approach for fluid flow computations. This method has been successfully applied to the multi-phase and multi-component flows. To extend the application of LBE to high Reynolds number incompressible flows, some critical issues need to be addressed, noticeably flexible spatial resolution, boundary treatments for curved solid wall, dispersion and mode of relaxation, and turbulence model. Recent developments in these aspects are highlighted in this paper. These efforts include the study of force evaluation methods, the development of multi-block methods which provide a means to satisfy different resolution requirement in the near wall region and the far field and reduce the memory requirement and computational time, the progress in constructing the second-order boundary condition for curved solid wall, and the analyses of the single-relaxation-time and multiple-relaxation-time models in LBE. These efforts have lead to successful applications of the LBE method to the simulation of incompressible laminar flows and demonstrated the potential of applying the LBE method to higher Reynolds flows. The progress in developing thermal and compressible LBE models and the applications of LBE method in multi-phase flows, multi-component flows, particulate suspensions, turbulent flow, and micro-flows are reviewed.

813 citations


"Personalized Radiotherapy Planning ..." refers methods in this paper

  • ...The reaction-diffusion equation is solved using the Lattice Boltzmann Method [21], [23], [24] which allows for easy parallelization and fast computations....

    [...]


Journal ArticleDOI
TL;DR: CERR provides a powerful, convenient, and common framework which allows researchers to use common patient data sets, and compare and share research results.
Abstract: A software environment is described, called the computational environment for radiotherapy research (CERR, pronounced "sir"). CERR partially addresses four broad needs in treatment planning research: (a) it provides a convenient and powerful software environment to develop and prototype treatment planning concepts, (b) it serves as a software integration environment to combine treatment planning software written in multiple languages (MATLAB, FORTRAN, C/C++, JAVA, etc.), together with treatment plan information (computed tomography scans, outlined structures, dose distributions, digital films, etc.), (c) it provides the ability to extract treatment plans from disparate planning systems using the widely available AAPM/RTOG archiving mechanism, and (d) it provides a convenient and powerful tool for sharing and reproducing treatment planning research results. The functional components currently being distributed, including source code, include: (1) an import program which converts the widely available AAPM/RTOG treatment planning format into a MATLAB cell-array data object, facilitating manipulation; (2) viewers which display axial, coronal, and sagittal computed tomography images, structure contours, digital films, and isodose lines or dose colorwash, (3) a suite of contouring tools to edit and/or create anatomical structures, (4) dose-volume and dose-surface histogram calculation and display tools, and (5) various predefined commands. CERR allows the user to retrieve any AAPM/RTOG key word information about the treatment plan archive. The code is relatively self-describing, because it relies on MATLAB structure field name definitions based on the AAPM/RTOG standard. New structure field names can be added dynamically or permanently. New components of arbitrary data type can be stored and accessed without disturbing system operation. CERR has been applied to aid research in dose-volume-outcome modeling, Monte Carlo dose calculation, and treatment planning optimization. In summary, CERR provides a powerful, convenient, and common framework which allows researchers to use common patient data sets, and compare and share research results.

796 citations


"Personalized Radiotherapy Planning ..." refers methods in this paper

  • ...[29] J. O. Deasy, A. I. Blanco, and V. H. Clark, “CERR: A computational environment for radiotherapy research,” Med....

    [...]

  • ...Dose-calculation is performed using the software CERR [29]....

    [...]


Journal ArticleDOI
15 Feb 1981-Cancer
TL;DR: Patients in Group 3 deteriorated faster than patients in Groups 1 and 2, and Bleomycin had no positive or negative influence on survival.
Abstract: In a controlled, prospective, randomized investigation, started in 1974, 118 patients with supratentorial astrocytoma Grade III--IV were divided into three groups. Groups 1 and 2 received 45 Gy postoperatively to the whole supratentorial brain. Bleomycin in 15-mg doses and a total dose of 180 mg or placebo was given intravenously three times a week, one hour prior to radiotherapy, during weeks 1, 2, 4 and 5. Group 3 received conventional care but no radiotherapy or chemotherapy. Median survival rates of patients were 10.8 months in Groups 1 and 2, and 5.2 months in Groups 3, a statistically significant difference. With regard to performance, the patients in Group 3 deteriorated faster than patients in Groups 1 and 2. Bleomycin had no positive or negative influence on survival.

395 citations


"Personalized Radiotherapy Planning ..." refers background in this paper

  • ...The beneficial impact of radiotherapy for glioblastoma patients has been clearly demonstrated [9], [10]....

    [...]


Related Papers (5)
Frequently Asked Questions (2)
Q1. What have the authors contributed in "Personalized radiotherapy planning based on a computational tumor growth model" ?

In this article, the authors propose a proof of concept for the automatic planning of personalized radiotherapy for brain tumors. First, the authors consider a single MRI acquisition before therapy, as it would usually be the case in clinical routine. The authors present the application of their approach on two patients diagnosed with high grade glioma. The authors introduce two methods to derive the radiotherapy prescription dose distribution, which are based on minimizing integral tumor cell survival using the maximum a posteriori or the expected tumor cell density. The authors show how their method allows the user to compute a patient specific radiotherapy planning conformal to the tumor infiltration. The authors further present extensions of the method in order to spare adjacent organs at risk by re-distributing the dose. 

The authors presented the proof of concept for a method combining a computational model of tumor growth with a dose response model in order to optimize radiotherapy planning, which takes into account the uncertainty in the model parameters and the clinical segmentations. In the second one, the authors use two time points in order to personalize the model and plan radiotherapy. In the future, the inclusion of the fractionation scheme of the delivered dose could be optimized. To that end, the model should be extended in order to take into account the complex therapy the patient is undergoing.