Simulating Tumor Growth Using Mathematical And Agent-Based Modeling
Résumé
In this paper, two different approaches for tumor growth modeling are presented and
implemented. In the first part of the paper, a macroscopic approach using a PDE model,
where the tumor is viewed as a cell mass, is implemented using the level-set method to
track the tumor moving boundary in one hand by using Darcy’s law to compute the normal
velocity of the free boundary and on the other hand using the shape optimization to
draw the normal velocity. In the second part of the paper, a microscopic approach, which
focuses on the cellular scale, is presented. A hybrid model using agent-based modeling for
the cell behavior and a PDE for the description of the tumor environment is presented.
A sensitivity analysis is performed on the hybrid model for a better understanding of
its impact on the tumor growth. Numerical experiments are provided for the proposed
approaches.