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

Subramanian, Shashank; Scheufele, Klaudius; Mehl, Miriam; Biros, George

doi:10.1088/1361-6420/ab649c

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

Journal Article · Wed Feb 26 00:00:00 EST 2020 · Inverse Problems

DOI:https://doi.org/10.1088/1361-6420/ab649c· OSTI ID:1803775

^[1]; Scheufele, Klaudius ^[2]; Mehl, Miriam ^[2]; Biros, George ^[1]

Univ. of Texas, Austin, TX (United States). Oden Inst. for Computational Engineering and Sciences
Univ. Stuttgarg (Germany). Inst. for Parallel and Distributed Systems

In this work, 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.

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Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR); National Institutes of Health (NIH); National Science Foundation (NSF)

Grant/Contract Number:: SC0019393; R01NS042645-14; CCF-1817048; CCF-1725743; FA9550-17-1-0190

OSTI ID:: 1803775

Journal Information:: Inverse Problems, Vol. 36, Issue 4; ISSN 0266-5611

Publisher:: IOPscienceCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (2)

Image-Driven Biophysical Tumor Growth Model Calibration Scheufele, Klaudius; Subramanian, Shashank; Mang, Andreas SIAM Journal on Scientific Computing, Vol. 42, Issue 3 https://doi.org/10.1137/19m1275280	journal	January 2020
Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect Subramanian, Shashank; Scheufele, Klaudius; Himthani, Naveen arXiv https://doi.org/10.48550/arxiv.2006.09932	preprint	January 2020

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