M5 mesoscopic and macroscopic models for mesenchymal motion

Abstract

In this paper mesoscopic (individual based) and macroscopic (population based) models for mesenchymal motion of cells in fibre networks are developed. Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fibre networks, for example the invasion of tumor metastases through collagen networks. The movement of cells is guided by the directionality of the network and in addition, the network is degraded by proteases.The main results of this paper are derivations of mesoscopic and macroscopic models for mesenchymal motion in a timely varying network tissue. The mesoscopic model is based on a transport equation for correlated random walk and the macroscopic model has the form of a drift-diffusion equation where the mean drift velocity is given by the mean orientation of the tissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. The transport equation as well as the drift-diffusion limit are coupled to a differential equation that describes the tissue changes explicitly, where we distinguish the cases of directed and undirected tissues. As a result the drift velocity and the diffusion tensor are timely varying. We discuss relations to existing models and possible applications.

A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

“…Particular questions include how migration direction or strong/weak activities of proteolysis can be affected by the detailed structure of key structural components, such as collagen fibers, of the ECM. While there are models of polymer networks such as collagen (Stein et al 2011), and macroscopic models of cells moving through the ECM (Hillen 2006;Hillen et al 2010;Preziosi and Vitale 2011), much remains to be done. The approach in Stein et al (2011) and Preziosi and Vitale (2011), as well as the current hybrid approach, may be useful in understanding the detailed mechanical interaction between a cell and fiber structure in order to better understand how migration can be controlled.…”

A Multiscale Modeling Approach to Glioma Invasion with Therapy

“…Here the turning kernel K accounting for such influences is taken for simplicity to be of the form (see [30]…”

The impact of adhesion on cellular invasion processes in cancer and development

“…Dallon et al 1999;McDougall et al 2006) and continuous approaches (e.g. Dallon & Sherratt 2000;Hillen 2006;Painter 2009) indicate that it forms a powerful mechanism for generating "cellular highways", i.e. paths in the matrix along which cells preferentially migrate.…”