The study of tumoral cells behaviour through computational models is arising. The movement of these cells is governed by physical laws; therefore, the different forces exerted between them need to be implemented. Nevertheless, biological criteria should be also considered since other factors, as oxygen level or cellular density, are decisive in the real movement. These phenomena are captured by probabilistic models such as the Agent Based Model (ABM). Following this research line, the present paper outlines a numerical model that tries to join both criteria with the aim of reproducing the behaviour of the cells that are part of a brain tumor: Glioblastoma Multiforme (GBM). The study has been carried out by the implementation of the different force equations in a Smoothed-Particle Hydrodynamic (SPH) framework. The SPH method is a meshfree lagrangian method based on the discretization of the study domain into finite particles which carry their own information, as tumoral cells do. Cohesive, viscous and pressure forces have been taking into account. Also, the possible attraction or repulsiveness between cells is considered through the implementation of a mechanical force formulation that combines the Maxwell and KelvinVoigt viscoelastic models. In addition to this forces approach, an energetic model is proposed to consider the results provided by an ABM. It evaluates the energy consumption and the associated extra-force that the cell needs to reach the ABM position, which is considered the biologically optimal one. The model has been tested under different sets of parameters, getting the logical outcome. Successful results have also been found in the evaluation of the energy consumption and, therefore, of the extra-force, finding a formulation that joins both criteria.
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