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arXiv · 2409.02904

From Finite to Continuous Phenotypes in (Visco-)Elastic Tissue Growth Models

Tomasz Dębiec·Mainak Mandal·Markus Schmidtchen
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Abstract

In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by phenotype-dependent growth rates and collective population pressure, governed by Brinkman's law. We examine two primary objectives: the joint limit where viscosity tends to zero while the number of species approaches infinity, yielding an inviscid Darcy-type model with a continuous phenotype variable, and the continuous phenotype limit where the number of species becomes infinite with a fixed viscosity, resulting in a novel viscoelastic tissue growth model. In this sense, this paper provides a comprehensive framework that elucidates the relationships between four different modelling paradigms in tissue growth.

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Tomasz Dębiec, Mainak Mandal, Markus Schmidtchen. 2024-09-04. From Finite to Continuous Phenotypes in (Visco-)Elastic Tissue Growth Models. https://arxiv.org/abs/2409.02904

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