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Computational simulation of cellular proliferation using a meshless method

Barbosa, M.I.A. ; Belinha, J. ; Jorge, R.M. Natal ; Carvalho, A.X.

Computer methods and programs in biomedicine, 2022-09, Vol.224, p.106974-106974, Article 106974 [Periódico revisado por pares]

Elsevier B.V

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  • Título:
    Computational simulation of cellular proliferation using a meshless method
  • Autor: Barbosa, M.I.A. ; Belinha, J. ; Jorge, R.M. Natal ; Carvalho, A.X.
  • Assuntos: Cell proliferation ; Influence domains ; Integration points ; Meshless methods ; Numerical simulation
  • É parte de: Computer methods and programs in biomedicine, 2022-09, Vol.224, p.106974-106974, Article 106974
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: •Simulation of cell proliferation using a new phenomenological law solved by the Radial Point Interpolation Method (RPIM), a meshless method.•Description of the RPIM.•Description of the proposed algorithm.•Numerical analyses of the optimal number of integration points per integration cell and of the number of nodes for each influence-domain, two parameters that affect that accuracy of the RPIM. 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. 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. 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. 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.
  • Editor: Elsevier B.V
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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