1. From Finite to Continuous Phenotypes in (Visco-)Elastic Tissue Growth Models
- Author
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Dębiec, Tomasz, Mandal, Mainak, and Schmidtchen, Markus
- Subjects
Mathematics - Analysis of PDEs ,35K57, 47N60, 35B45, 35K55, 35K65, 35Q92 - 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.
- Published
- 2024