Delaunay-Object-Dynamics: cell mechanics with a 3D kinetic and dynamic weighted Delaunay-triangulation

Abstract

Mathematical methods in Biology are of increasing relevance for understanding the control and the dynamics of biological systems with medical relevance. In particular, agent-based methods turn more and more important because of fast increasing computational power which makes even large systems accessible. An overview of different mathematical methods used in Theoretical Biology is provided and a novel agent-based method for cell mechanics based on Delaunay-triangulations and Voronoi-tessellations is explained in more detail: The Delaunay-Object-Dynamics method. It is claimed that the model combines physically realistic cell mechanics with a reasonable computational load. The power of the approach is illustrated with two examples, avascular tumor growth and genesis of lymphoid tissue in a cell-flow equilibrium.