Technical Report: Modelling Multiple Cell Types with Partial Differential Equations

TL;DR

This paper discusses modeling multiple cell types using partial differential equations, addressing challenges in representing tissue dynamics, cell differentiation, and hypertrophic volume changes in reaction-advection-diffusion systems.

Contribution

It introduces methods to incorporate delayed cell differentiation and hypertrophic volume changes into PDE models for multiple cell types.

Findings

Modeling of multiple cell types with PDEs is feasible with added differentiation dynamics.

Delayed differentiation impacts tissue patterning and cell volume.

The approach enhances understanding of complex tissue behaviors.

Abstract

Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly. However, in case of multiple cell types it is not always straight forward to integrate a continuous description of the tissue dynamics. Here, we discuss (delayed) differentiation of cells into different cell types and hypertrophic cell volume change upon differentiation.