Simulating Tumor Growth Using Mathematical And Agent-Based Modeling

In this paper, two different approaches for tumor growth modeling are presented andimplemented. 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 totrack the tumor moving boundary in one hand by using Darcy's law to compute the normalvelocity of the free boundary and on the other hand using the shape optimization todraw the normal velocity. In the second part of the paper, a microscopic approach, whichfocuses on the cellular scale, is presented. A hybrid model using agent-based modeling forthe 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 ofits impact on the tumor growth. Numerical experiments are provided for the proposedapproaches.