Simulation of the cancer cell growth and their invasion into healthy tissues using local radial basis function method

Abstract

Applying mathematical models to simulate dynamic biological processes has been a common practice for a long time. In recent decades, cancer research has also adopted this approach to understand how cancer cell populations grow and spread. This study focuses on a mathematical model that uses a system of PDEs to explain the time-dependent reaction–diffusion interaction among cancer cells, extracellular matrix, and matrix degradation enzymes. We use a computational method that involves the discrete Galerkin technique by employing local radial basis functions (LRBFs) as its basis to approximate the behavior of cancer cells as they grow and invade neighboring healthy tissues. This novel approach employs a smaller set of nodes to approximate the solution, instead of considering all data in the given domain of the cancer growth model. Utilizing locally supported radial basis functions, this method significantly reduces the computational volume required, in contrast to globally supported radial basis functions. Finally, we provide experimental examples to validate and illustrate the effectiveness of this new scheme in modeling the growth and behavior of cancer cells at different stages.