A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

Abstract

We consider the movement and viability of individual cells in cell colonies. Cell movement is assumed to take place as a result of sensing the strain energy density as a mechanical stimulus. The model is based on tracking the displacement and viability of each individual cell in a cell colony. Several applications are shown, such as the dynamics of filling a gap within a fibroblast colony and the invasion of a cell colony. Though based on simple principles, the model is qualitatively validated by experiments on living fibroblasts on a flat substrate.

Semi-stochastic cell-level computational modelling of cellular forces: application to contractures in burns and cyclic loading

“…Our approach also gives a displacement and stress field over the domain of computation, which can be used to model intercellular contact between cells such that they can form clusters. We have similar simulations on the basis of the strain energy density using simplistic analytic relationships for the displacement over the substrate in Vermolen and Gefen (2013) and Vermolen and Gefen (2012). The present modelling provides a neat mathematical generalisation.…”

“…In two of our modelling studies, we formulated models for cell migration and deformation where only the cell boundary is tracked through its division into nodal points, which are interconnected by springs and connected by springs to the nucleus to model cell stiffness, see for instance Vermolen and Gefen (2012). Although the scope of the present paper is the calculation of cellular forces that are exerted on the extracellular matrix surrounding the cells for a cell-based model where cells are presently treated as equishaped objects, an extension to varying cell shapes is straightforward and is of current research.…”

“…Wiener processes or Brownian motion is described in more detail in Steele (2001). The contact forces have been described in Vermolen and Gefen (2012). Mechanical drag is incorporated by…”

“…This continuous cellular approach was done in earlier studies by Byrne and Drasdo (2009), Groh and Louis (2010) and Neilson et al (2011). Cell-cell contacts in this study will be modelled using the principles outlined in Gefen (2010) and Vermolen and Gefen (2012). We believe that our approach of mechanical boundary forces can also be applied in a cellular Potts framework.…”

Particle methods to solve modelling problems in wound healing and tumor growth

“…Here also cellular automata models are used. Examples are in [7,20,41,49], for tumor-induced angiogenesis we refer to [2];…”