An inverse problem formulation for parameter estimation of a reaction diffusion model of low grade gliomas

TL;DR

This paper introduces a numerical method for estimating tumor growth parameters in low-grade gliomas using reaction-diffusion models, DTI data, and noisy observations, validated through synthetic tests.

Contribution

It develops a constrained optimization approach with a Gauss-Newton algorithm for joint estimation of tumor concentration and diffusion parameters from limited data.

Findings

Effective parameter reconstruction with low noise levels

Robustness demonstrated across monofocal and multifocal cases

Quantified reconstruction errors under varying noise conditions

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 (PDEs). 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 (DTI). 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.