title: An inverse problem formulation for parameter estimation of a reaction-diffusion model of low grade gliomas.
abstract: We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor diffusion. We use a constrained optimization formulation with a reaction-diffusion model that results in a system of nonlinear partial differential equations. In our formulation, we estimate the parameters using partially observed, noisy tumor concentration data at two different time instances, along with white matter fiber directions derived from diffusion tensor imaging. The optimization problem is solved with a Gauss-Newton reduced space algorithm. We present the formulation and outline the numerical algorithms for solving the resulting equations. We test the method using a synthetic dataset and compute the reconstruction error for different noise levels and detection thresholds for monofocal and multifocal test cases.
authors.affiliation: Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA. i.amirgh@gmail.com.
authors.forename: Amir
authors.initials: A
authors.lastname: Gholami
authors.affiliation: Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA. andreas@ices.utexas.edu.
authors.forename: Andreas
authors.initials: A
authors.lastname: Mang
authors.affiliation: Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA. biros@ices.utexas.edu.
authors.forename: George
authors.initials: G
authors.lastname: Biros
mesh_terms: D000465:Algorithms; D001932:Brain Neoplasms / Q000473:pathology*; D003198:Computer Simulation; D056324:Diffusion Tensor Imaging; D018450:Disease Progression; D005910:Glioma / Q000473:pathology*; D006801:Humans; D021621:Imaging, Three-Dimensional; D055641:Mathematical Concepts; D008954:Models, Biological; D009361:Neoplasm Invasiveness / Q000473:pathology; D017711:Nonlinear Dynamics
keywords: Glioblastoma multiforme; Glioma; Inverse problems; Parameter estimation; Tumor growth