Mathematical modeling and experimental validation of cancer cell migration in a three-dimensional tumor matrix

Understanding the processes and mechanisms of cancer cell migration and metastasis are critical to the fields of oncology and drug design. However, little is known about the controlling factors that influence cell migration and metastasis especially under complex micro-environmental conditions. The focus of this research is to study cell migration phenomena in response to two major factors - chemotaxis and durotaxis. The effects of other control parameters, such as fluid flow rates and concentration of nutrients, are also investigated using a simulated three-dimensional cell culture system. The simulation is based on a two-scale approach by solving coupled partial differential equations involving the Stokes-Brinkman equation with continuous stress at the interface between the porous media and the channel for the fluid flow profile in the system, the convection-diffusion equation for the distribution of nutrients, and the Newtonian formulation of motion for tumor cells. The simulation results show very good agreement with experimental data from literature and our collaborative lab at Virginia Tech. Three applications of the developed cell migration model were used to investigate the capabilities of the model in more complex biological systems. These applications include cell migration at a different spatial scale, cell migration in a more biologically relevant complex vasculature, and cell migration in a standardized model of a whole prostate gland. The simulation results demonstrate that the model is capable of predicting, to a certain extent, cell migration velocities in those different cases. The significance of this research is to provide some clue and insight for further investigation in the processes of cancer metastasis.