Importance of patient DTI's to accurately model glioma growth using the reaction diffusion equation

Stretton, Erin; Geremia, Ezequiel; Menze, Bjoern; Delingette, Hervé; Ayache, Nicholas

doi:10.1109/isbi.2013.6556681

Cited by 11 publications

(11 citation statements)

References 7 publications

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“…In the case of GBM growth modeling, it is clinically admitted that tumor cells have higher motility in white matter, compared to gray matter. Some work has been conducted to relate the diffusion tensor D to DTI -see [28], [29] for a detailed discussion. In this work, for simplification, we follow [21], and 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, and d w a scalar parametrizing the diffusion tensor.…”

Section: A the Reaction-diffusion Modelmentioning

confidence: 99%

MRI Based Bayesian Personalization of a Tumor Growth Model

Le¹,

Delingette²,

Kalpathy–Cramer

et al. 2016

IEEE Trans. Med. Imaging

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The mathematical modeling of brain tumor growth has been the topic of numerous research studies. Most of this work focuses on the reaction-diffusion model, which suggests that the diffusion coefficient and the proliferation rate can be related to clinically relevant information. However, estimating the parameters of the reaction-diffusion model is difficult because of the lack of identifiability of the parameters, the uncertainty in the tumor segmentations, and the model approximation, which cannot perfectly capture the complex dynamics of the tumor evolution. Our approach aims at analyzing the uncertainty in the patient specific parameters of a tumor growth model, by sampling from the posterior probability of the parameters knowing the magnetic resonance images of a given patient. The estimation of the posterior probability is based on: 1) a highly parallelized implementation of the reaction-diffusion equation using the Lattice Boltzmann Method (LBM), and 2) a high acceptance rate Monte Carlo technique called Gaussian Process Hamiltonian Monte Carlo (GPHMC). We compare this personalization approach with two commonly used methods based on the spherical asymptotic analysis of the reaction-diffusion model, and on a derivative-free optimization algorithm. We demonstrate the performance of the method on synthetic data, and on seven patients with a glioblastoma, the most aggressive primary brain tumor. This Bayesian personalization produces more informative results. In particular, it provides samples from the regions of interest and highlights the presence of several modes for some patients. In contrast, previous approaches based on optimization strategies fail to reveal the presence of different modes, and correlation between parameters.

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Section: A the Reaction-diffusion Modelmentioning

confidence: 99%

MRI Based Bayesian Personalization of a Tumor Growth Model

Le¹,

Delingette²,

Kalpathy–Cramer

et al. 2016

IEEE Trans. Med. Imaging

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“…14, 15 Taking into account that brain tumor cells are generally assumed to diffuse toward regions of lower cellular density 2, 5 and invade the surrounding tissue by moving along white matter tracts, 1 the diffusion tensor acquired by DTI has been used to describe the diffusion of tumor cells as well. 10, 11…”

Section: Diffusion Tensor Imagingmentioning

confidence: 99%

In SilicoNeuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

Αντωνόπουλος

Stamatakos

2015

Cancer Inform

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Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided.

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“…The Fisher Kolmogorov (FK) Model: The Fisher Kolmogorov (FK) equation is a type of reaction-diffusion model, which has been used extensively in tumor growth modeling [32,21,31,4,12,16,20,10,11,26,27]. In our work, we use the following formulation:…”

Section: Preprocessing Of Datamentioning

confidence: 99%

“…Advances have been made in integrating a more precise anatomy in the atlas. Whereas the very first templates in the nineties were built from a 2D CT scan [35,6,33], just outlining the brain surface and the ventricles, more recent works are based on 3D-MRI atlases of CSF, grey matter and white matter [28], and eventually including detailed white matter architecture via DTI sequences [12,3,27,26]. CSF spaces are of utmost importance for achieving realistic glioma growth patterns, as they constitute anatomical barriers that cannot be crossed by tumor cells (a statement that is implemented in the model by a no flux boundary condition).…”

Section: Introductionmentioning

confidence: 99%

Expert-validated CSF segmentation of MNI atlas enhances accuracy of virtual glioma growth patterns

et al. 2014

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Biomathematical modeling of glioma growth has been developed to optimize treatments delivery and to evaluate their efficacy. Simulations currently make use of anatomical knowledge from standard MRI atlases. For example, cerebrospinal fluid (CSF) spaces are obtained by automatic thresholding of the MNI atlas, leading to an approximate representation of real anatomy. To correct such inaccuracies, an expert-revised CSF segmentation map of the MNI atlas was built. Several virtual glioma growth patterns of different locations were generated, with and without using the expert-revised version of the MNI atlas. The adequacy between virtual and radiologically observed growth patterns was clearly higher when simulations were based on the expert-revised atlas. This work emphasizes the need for close collaboration between clinicians and researchers in the field of brain tumor modeling.

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Importance of patient DTI's to accurately model glioma growth using the reaction diffusion equation

Cited by 11 publications

References 7 publications

MRI Based Bayesian Personalization of a Tumor Growth Model

MRI Based Bayesian Personalization of a Tumor Growth Model

In SilicoNeuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

Expert-validated CSF segmentation of MNI atlas enhances accuracy of virtual glioma growth patterns

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