Modelado de la dinámica celular utilizando celdas de Voronoi Modeling cell dynamics using Voronoi cells

Abstract

In this work, a geometric model is presented to describe cellular dynamics using Voronoi cells. The conditions under which these cells, constructed from nuclei of cell within a compact domain and modeled as Voronoi cells, converge in the Kuratowski and Hausdorff sense, are studied. To this end, the displacement of a cell is formalized as a sequence of sites converging to a final position, and it is shown that the corresponding cells converge topologically. Cell division (mitosis) is modeled as the addition of a new site, while death is represented by weighted cells, increasing that weight progressively until the cell is nullified. The results allow for the establishment of precise mathematical criteria to simulate cellular dynamics in a stable manner. This approach provides a formal basis for the study of biological processes using tools from linear analysis theory. Examples of the simulation implemented in the two-dimensional plane are presented.