Computationally modelling cell proliferation: A review.

Cell proliferation is vital for the development and homeostasis of the human body. For such to occur, cells go through the cell cycle during which they replicate their genetic material and ultimately complete cellular division, when one cell divides into two new cells with equal genetic material. However, if there are some errors or abnormalities during the cell cycle that disrupt the balance between cell death and proliferation, severe problems can occur, such as tumour development, which is currently one of the leading causes of death in the world. Nowadays, mathematical and computational models are used to understand and study several biological mechanisms and processes, namely cellular proliferation. Over the last forty-five years, several models have attempted to describe cell proliferation and its regulation. Due to the complexity of the process, numerous assumptions and simplifications have been considered. This work presents a review of some of these models, focusing mainly on mammalian or generic eukaryotic models. Previously published continuum, discrete and hybrid approaches are presented and compared, in order to understand and highlight the relevance and capabilities of these models, their shortcomings and future challenges.

Computational simulation of cellular proliferation using a meshless method.

BACKGROUND AND OBJECTIVE: During cell proliferation, cells grow and divide in order to obtain two new genetically identical cells. Understanding this process is crucial to comprehend other biological processes. Computational models and algorithms have emerged to study this process and several examples can be found in the literature. The objective of this work was to develop a new computational model capable of simulating cell proliferation. This model was developed using the Radial Point Interpolation Method, a meshless method that, to the knowledge of the authors, was never used to solve this type of problem. Since the efficiency of the model strongly depends on the efficiency of the meshless method itself, the optimal numbers of integration points per integration cell and of nodes for each influence-domain were investigated. Irregular nodal meshes were also used to study their influence on the algorithm. METHODS: For the first time, an iterative discrete model solved by the Radial Point Interpolation Method based on the Galerkin weak form was used to establish the system of equations from the reaction-diffusion integro-differential equations, following a new phenomenological law proposed by the authors that describes the growth of a cell over time while dependant on oxygen and glucose availability. The discretization flexibility of the meshless method allows to explicitly follow the geometric changes of the cell until the division phase. RESULTS: It was found that an integration scheme of 6 × 6 per integration cell and influence-domains with only seven nodes allows to predict the cellular growth and division with the best balance between the relative error and the computing cost. Also, it was observed that using irregular meshes do not influence the solution. CONCLUSIONS: Even in a preliminary phase, the obtained results are promising, indicating that the algorithm might be a potential tool to study cell proliferation since it can predict cellular growth and division. Moreover, the Radial Point Interpolation Method seems to be a suitable method to study this type of process, even when irregular meshes are used. However, to optimize the algorithm, the integration scheme and the number of nodes inside the influence-domains must be considered.