Two-dimension tissue growth model based on circular granular cells for cells with small overlap

TL;DR

This paper presents a two-dimensional tissue growth model using circular granular cells with a spring-dashpot interaction, analyzing growth dynamics, configurations, and conditions for infinite growth without overlap.

Contribution

It introduces a novel 2D tissue growth simulation with explicit and implicit steps, exploring configurations that allow indefinite growth without cell overlap.

Findings

Large cell overlap causes growth termination.

Certain configurations can grow infinitely without overlap.

Growth time increases with cell number, following different asymptotic functions for configurations.

Abstract

Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of interacted cells. Simulation steps must be divided into explicit and implicit ones due to cell growing stage and cell position rearrangement. This division is aimed to avoid simulation problem. Only in the explicit steps time changes is performed. Large cells overlap is chosen as termination condition of tissue growth. Only some cells configuration can growth to infinite time without encountering the large cells overlap. These configurations, and the other also, are presented in this work. Simulation time $t$ increases as cell number $N$ increases due to raise of interaction number between two cells. Linear and network configurations tend to aligned with different asymtotic function, that relates $N$ and $t$, for large $N$.