SIMULATION OF GROWTH AND DIVISION OF 3D CELLS BASED ON FINITE ELEMENT METHOD

Abstract

Adequate proliferating model including each cell's growth and division in 3D is key for the simulation of tissue growth in early stages as embryo, avascular tumor and so on. This paper proposed a novel model to perform the simulation based on a nonlinear finite element method. With the mechanism of cellular growth controlled by total energy of volume and surface of cells, the surface of each cell is divided by triangular elements and the nodal displacements determine the variation of the cellular surface and volume uniquely when cells grow. The nonlinear finite element equations of nodal displacements were deduced by the minimum energy increment in each growth's step. Further, by using the volume-based algorithm to determine cellular division and the modified penalty function method, the nonlinear procedure of the cellular proliferation (growth-division-regrowth) was solved. The numerical results show that the method can simulate both tissue and tissue's every cell well in each growth-division step, and will do great help to model the growth of varied tissues in their early stages.