Accelerating Parameter Inference in Diffusion-Reaction Models of Glioblastoma Using Physics-Informed Neural Networks

Abstract

Glioblastoma is an aggressive brain tumor with cells that infiltrate and proliferate rapidly into surrounding brain tissue. Current mathematical models of glioblastoma growth capture this behavior using partial differential equations (PDEs) that are simulated via numerical solvers—a highly-efficient im-plementation can take about 80 seconds to complete a single forward evaluation. However, clinical applications of tumor modeling are often framed as inverse problems that require sophisticated numerical methods and, if implemented naively, can lead to prohibitively long runtimes that render them inadequate for clinical settings. Recently, physics-informed neural networks (PINNs) have emerged as a novel method in scientific machine learning for solving nonlinear PDEs. Compared to traditional solvers, PINNs leverage unsupervised deep learning methods to minimize residuals across mesh-free domains, enabling greater flexibility while avoiding the need for complex grid constructions. Here, we describe and implement a general method for solving time-dependent diffusion-reaction PDE models of glioblastoma and inferring biophysical parameters from numerical data via PINNs. We evaluate the PINNs over patient-specific geometries, accounting for individual variations with diffusion mobilities derived from pre-operative MRI scans. Using synthetic data, we demonstrate the performance of our algorithm in patient-specific geometries. We show that PINNs are capable of solving parameter inference inverse problems in approximately one hour, expediting previous approaches by 20–40 times owing to the robust interpolation capabilities of machine learning algorithms. We anticipate this method may be sufficiently accurate and efficient for clinical usage, potentially rendering personalized treatments more accessible in standard-of-care medical protocols.