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

Erdi Kara

Aminur Rahman*

Eugenio Aulisa

Souparno Ghosh

  • Department of Mathematics and Statistics, Texas Tech University, Lubbock TX

  • Department of Applied Mathematics, University of Washington, Seattle WA

  • Department of Mathematics and Statistics, Texas Tech University, Lubbock TX

  • Department of Statistics, University of Nebraska - Lincoln, Lincoln NB

  • *arahman2@uw.edu
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Phys. Rev. E 102, 062425 – Published 30 December, 2020

DOI: https://doi.org/10.1103/PhysRevE.102.062425

Abstract

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, 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.

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Phys. Rev. E 102, 062425– Published 30 December, 2020
  • Received 6 January 2020
  • Revised 28 May 2020
  • Accepted 23 November 2020
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