Simulation of Cell Proliferation Using a Meshless Tool

Abstract

To preserve the haemostasis of the body, a balance between cell formation and cell death has to be maintained. Thus, when necessary, cells divide into two new ones through a complex and controlled process that is mainly dependent on the availability of oxygen and glucose. Numerical methods have been used to study and solve several problems in science and engineering. Regarding biomechanics and the study of cells, these methods were already combined with distinct formulations. Within these methods, it is possible to highlight the meshless methods, which are a novel and efficient approach that emerged as an alternative to traditional methods. However, the available literature is not yet as extensive as these last ones. The aim of this work is to simulate the process of cell proliferation resorting to a new algorithm. This was based on a phenomenological growth law proposed by the authors, dependent on the presence of oxygen and glucose and solved by a meshless method (Radial Point Interpolation Method). In the end, the algorithm leads to satisfactory and coherent results. It was capable of simulating cell proliferation, under different concentration of oxygen and glucose, as expected. Furthermore, the RPIM proved to be a viable option to solve this problem since the results obtained were adequate.