Simulation of morphogen and tissue dynamics

TL;DR

This paper reviews mathematical models and numerical simulation techniques for morphogen and tissue dynamics during morphogenesis, focusing on PDE systems and methods for static and growing domains.

Contribution

It provides a comprehensive overview of mathematical representations and numerical methods used to simulate morphogen and tissue dynamics in developmental biology.

Findings

Finite element and Lattice Boltzmann methods are key for PDE discretisation.

Numerical techniques like ALE and Diffuse-Domain effectively handle deforming domains.

The chapter offers insights into modeling tissue mechanics during morphogenesis.

Abstract

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focusses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and grow- ing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretisation as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.