A Three-Phase Model for Tumor Cell Migration

Abstract

Flow of interstitial fluid (IF) has proven to have a significant effect on the migration of cancer cells through tissue due to the tumor cells ability to sense flow by secreting chemokines that convect in the flow direction (autologous chemotaxis). It has become increasingly popular to model this (and other) phenomena using multiphase models based on e.g. Darcy's law, the Brinkman equation or more general mixture theory approaches.

Recent experimental work suggests that fibroblast cells present in vivo might influence the ability of cancer cells to invade the surrounding tissue. The objective of this thesis is to expand a two-fluid model used to investigate autologous chemotaxis of cancer cells to a three-phase model where also the effect of the fibroblasts can be accounted for.

First, relevant experimental results will be analyzed, followed by a general model formulation using mass and momentum balance based on mixture theory. The approach is inspired by that of modeling hydrocarbon flow in underground reservoirs. Finally, we will implement a numerical solution for a simplified 1-D version of the model and compare the simulated output to experimental results to elucidate some of the mechanism(s) behind fibroblast-enhanced tumor cell invasion. Special focus we will be on investigating the fibroblasts ability to remodel the ECM and also viscous coupling between cells and fibroblasts.