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Advisor(s)
Abstract(s)
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 reactiondiffusion 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
Description
Keywords
Integration points Influence domains Meshless methods Cell proliferation Numerical simulation
Citation
Publisher
Elsevier