Tumor ablation due to inhomogeneous -- anisotropic diffusion in generic 3-dimensional topologies

Abstract: We derive a full 3-dimensional (3-D) model of inhomogeneous -- anisotropic diffusion in a tumor region coupled to a binary population model. The diffusion tensors are acquired using Diffusion Tensor Magnetic Resonance Imaging (DTI) from a patient diagnosed with glioblastoma multiform (GBM). Then we numerically simulate the full model with Finite Element Method (FEM) and produce drug concentration heat maps, apoptosis regions, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists.