Point Forces and Their Alternatives in Cell-Based Models for Skin Contraction

Peng, Qiyao and Vermolen, Fred (2020) Point Forces and Their Alternatives in Cell-Based Models for Skin Contraction. In: Numerical Mathematics and Advanced Applications, ENUMATH 2019 : European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4. Springer, Cham, pp. 763-771. ISBN 9783030558734

Abstract

We consider a cell-based approach in which the balance of momentum is used to predict the impact of cellular forces on the surrounding tissue. To this extent, the elasticity equation and Dirac Delta distributions are combined. In order to avoid the singularity caused by Dirac Delta distribution, alternative approaches are developed and a Gaussian distribution is used as a smoothed approach. Based on the application that the pulling force is pointing inward the cell, the smoothed particle approach is probed as well. In one dimension, it turns out that the aforementioned three approaches are consistent. For two dimensions, we report a computational consistence between the direct and smoothed particle approach.