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

TL;DR

This paper develops a comprehensive mathematical framework linking discrete and continuous models of tissue growth, incorporating phenotypic diversity and viscoelastic properties, with implications for understanding complex biological tissues.

Contribution

It introduces a novel viscoelastic tissue growth model derived from the limit of infinite phenotypes with fixed viscosity, unifying multiple modeling approaches.

Findings

Derived a continuous phenotype model from discrete subpopulations.

Established the relationship between viscoelastic and Darcy-type models.

Provided a unified framework connecting four tissue growth models.

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.