Coupling brain-tumor biophysical models and diffeomorphic image registration

Scheufele, Klaudius; Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George; Mehl, Miriam

doi:10.1016/j.cma.2018.12.008

Cited by 38 publications

(71 citation statements)

References 67 publications

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“…This can be inaccurate for very large tumors. We are currently working on incorporating the ideas presented here with our previous work [56], in which we coupled diffeomorphic image registration with tumor inversion for this purpose. described in [45], which yields optimal theoretical guarantees on convergence rates for quadratic mismatch functions.…”

Section: Limitationsmentioning

confidence: 99%

“…This is primarily due to the rich initial conditions produced by the L 2 solver which impedes its ability to predict the correct reaction scaling using our method. We note that if the reaction scaling is known beforehand, the L 2 solver can potentially have better performance (see [16,56] for similar synthetic experiments). This problem is magnified for larger tumors (AT-C2 and AT-C3) where the predicted reaction coefficient shows about 66% and 54% relative error in the L 2 solver for the two test-cases respectively (as compared to around 15% and 1% error with sparsity constraints).…”

Section: Test Casementioning

confidence: 99%

“…Setup: Since we do not have access to the healthy patient brain, we cannot resort to direct inversion of model parameters. There have been many approaches in literature (see [16,56] for a comprehensive review) to approximate the healthy brain through methods such as diffeomorphic image registration and registration-tumor coupled optimization formulations. While such techniques are necessary to capture the healthy patient brain, we do not pursue them since this test-case is intended to primarily serve as an illustration.…”

Section: Real Tumor (Rt) Test-casementioning

confidence: 99%

“…This is ultimately more useful for tumor growth understanding and prediction. We emphasize that approaches like a coupled image registration and tumor inversion formulation are necessary for access to a more informative healthy patient (see [56] for more details). Our plan is to conduct a systematic study of the solver considering hundreds of cases.…”

Section: Fig 46mentioning

confidence: 99%

“…Now we discuss, in some detail, attempts to reconstruct the initial condition of the tumor using a single scan. In our previous works [15,56], we employed an L 2 regularization scheme for c(x, 0) and we inverted for κ assuming known ρ. We used reduced-space parallel algorithms allowing for the calibration of highly complex tumor shapes in reasonable time.…”

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confidence: 99%

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Where did the tumor start? An inverse solver with sparse localization for tumor growth models

et al. 2020

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We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of Magnetic Resonance Imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver. Related work.Although there has been a lot of work on forward problems for tumor growth, there has been less work on inverse problems. The latter has different aspects. The first is the underlying biophysical model. The second is the inverse problem setup, observation operators and the existence of scans at multiple points, the noise models, inversion parameters and constraints. And the third one is the solution algorithm.Regarding the underlying model, like us, most researchers focus on parameter calibration of a handful of model parameters using single-species reaction-diffusion equations [7,22,24,28,33,39,51,58,59]. While more complex models describing processes like mass effect, angiogenesis and chemotaxis [23,26,48,54,60] exist, they have not been considered for calibration due to theoretical and computational challenges. However, several groups, including ours, are working to address these challenges.Regarding the inverse problem setup, in most studies t...

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Section: Limitationsmentioning

confidence: 99%

Section: Test Casementioning

confidence: 99%

Section: Real Tumor (Rt) Test-casementioning

confidence: 99%

Section: Fig 46mentioning

confidence: 99%

mentioning

confidence: 99%

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Where did the tumor start? An inverse solver with sparse localization for tumor growth models

et al. 2020

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Towards Model-Based Characterization of Biomechanical Tumor Growth Phenotypes

Abler

Büchler

Rockne

2019

Lecture Notes in Computer Science

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Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect

Subramanian

Scheufele

Himthani

et al. 2020

Medical Image Computing and Computer Assisted Intervention – MICCAI 2020

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We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing tumor, which on its own is an important radiographic feature but its automatic quantification remains an open problem. In particular, we calibrate a partial differential equation (PDE) tumor growth model that captures mass effect, parameterized by a single scalar parameter, tumor proliferation, migration, while localizing the tumor initiation site. The single-scan calibration problem is severely ill-posed because the precancerous, healthy, brain anatomy is unknown. To address the ill-posedness, we introduce an ensemble inversion scheme that uses a number of normal subject brain templates as proxies for the healthy precancer subject anatomy. We verify our solver on a synthetic dataset and perform a retrospective analysis on a clinical dataset of 216 glioblastoma (GBM) patients. We analyze the reconstructions using our calibrated biophysical model and demonstrate that our solver provides both global and local quantitative measures of tumor biophysics and mass effect. We further highlight the improved performance in model calibration through the inclusion of mass effect in tumor growth models-including mass effect in the model leads to 10% increase in average dice coefficients for patients with significant mass effect. We further evaluate our model by introducing novel biophysics-based features and using them for survival analysis. Our preliminary analysis suggests that including such features can improve patient stratification and survival prediction.Index Terms-tumor growth model personalization, inverse problem, mass effect, glioblastoma (Preprint submitted to IEEE Transactions on Medical Imaging) I. INTRODUCTIONComputational oncology is an emerging field that attempts to integrate biophysical models with imaging with the goal of assisting image analysis in a clinical setting. Typically, the integration is accomplished by calibrating PDE model parameters from images. A significant challenge in brain tumors, and in particular, GBMs, is the single-scan calibration, that becomes even harder in the presence of mass effect. However, modeling provides the capability for automatic quantification of mass effect along with additional biomarkers related to

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Coupling brain-tumor biophysical models and diffeomorphic image registration

Cited by 38 publications

References 67 publications

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

Towards Model-Based Characterization of Biomechanical Tumor Growth Phenotypes

Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect

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