A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes.

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429-1450, 2018), Vermolen and Gefen (BMM 12:301-323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340-348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.