Incorporating domain growth into hybrid methods for reaction-diffusion systems

TL;DR

This paper extends hybrid reaction-diffusion modeling methods to account for domain growth, enabling accurate multiscale simulations of biological and physical phenomena involving expanding spatial domains.

Contribution

The authors develop and detail three hybrid methods for reaction-diffusion systems on growing domains, filling a gap in existing static domain approaches.

Findings

Methods accurately model reaction-diffusion systems on growing domains.

Algorithms enable practical implementation of the hybrid methods.

The approaches are unbiased and effective across multiple systems.

Abstract

Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth is an important process for embryonic growth and wound healing. There are many numerical modelling frameworks capable of simulating such systems on growing domains, however each of these may be well suited to different spatial scales and particle numbers. Recently, spatially extended hybrid methods on static domains have been produced in order to bridge the gap between these different modelling paradigms in order to represent multiscale phenomena. However, such methods have not been developed with domain growth in mind. In this paper, we develop three hybrid methods on growing domains, extending three of the prominent static domain hybrid methods. We also provide detailed algorithms to allow others to employ them. We demonstrate that the methods are able to accurately model three representative reaction-diffusion systems accurately and without bias.