An inverse problem formulation for parameter estimation of a reaction diffusion model of low grade gliomas
This work addresses the clinically relevant problem of estimating glioma growth parameters from sparse, noisy medical imaging data, but the method is tested only on synthetic data and is incremental in nature.
The paper presents a numerical scheme for estimating tumor concentration and anisotropic diffusion parameters in a low-grade glioma growth model, achieving reconstruction errors of 5-15% for synthetic data with varying noise levels and detection thresholds.
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.