Two-scale Moving Boundary Dynamics of Cancer Invasion:Heterotypic Cell Populations Evolution in Heterogeneous ECM

This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.

Mesenchymal Motion Models in One Dimension

Abstract: Mesenchymal motion denotes a form of cell movement through tissue, which can be observed for certain cancer metastasis. In [11], a mathematical model for this form of movement was introduced. In the current paper we present a comprehensive analysis of the one dimensional mesenchymal motion model. We establish the global existence of classical solutions and rigorously carry out the parabolic limit of the model. We discuss the stationary solutions, prove the existence of travelling wave solutions, and we use numerical simulations to illustrate the results. Finally, we discuss the biological implications of the results