Simulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis

TL;DR

This paper compares two computational methods, ALE and Phase-Field, for simulating lung branching morphogenesis, highlighting the advantages of the Phase-Field approach in handling complex tissue growth.

Contribution

It introduces a Phase-Field implementation for simulating organogenesis and provides a detailed comparison with the traditional ALE method.

Findings

Phase-Field method avoids mesh deformation issues.

Phase-Field allows for more complex and extended simulations.

Comparison shows advantages of Phase-Field over ALE in lung development modeling.

Abstract

During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung development can be recapitulated by a receptor-ligand based Turing model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE) framework for solving the receptor-ligand Turing model on growing lung domains. However, complex mesh deformations which occur during lung growth severely limit the number of branch generations that can be simulated. A new Phase-Field implementation avoids mesh deformations by considering the surface of the modelling domains as interfaces between phases, and by coupling the reaction-diffusion framework to these surfaces. In this paper, we present a rigorous comparison between the Phase-Field approach and the ALE-based simulation.