Simulation of glioblastoma growth using a 3D multispecies tumor model with mass effect

TL;DR

This paper introduces a comprehensive 3D multispecies tumor model coupled with linear elasticity to simulate glioblastoma growth and its mechanical effects on brain tissue, validated through MRI-like image simulations.

Contribution

It presents a novel coupled PDE and elasticity model with an operator-splitting scheme for realistic glioblastoma growth simulation.

Findings

Successfully simulates MRI-like glioblastoma structures

Captures tumor-induced brain deformation

Demonstrates model's potential for clinical imaging analysis

Abstract

In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme observed in magnetic resonance imaging (MRI) scans. These include enhancing and necrotic tumor structures, brain edema and the so called "mass effect", that is, the deformation of brain tissue due to the presence of the tumor. The multispecies model accounts for proliferating, invasive and necrotic tumor cells as well as a simple model for nutrition consumption and tumor-induced brain edema. The coupling of the model with linear elasticity equations with variable coefficients allows us to capture the mechanical deformations due to the tumor growth on surrounding tissues. We present the overall formulation along with a novel operator-splitting scheme with components that include linearly-implicit preconditioned elliptic solvers, and semi-Lagrangian method for advection. Also, we present results showing simulated MRI images which highlight the capability of our method to capture the overall structure of glioblastomas in MRIs.