Simulate Computation And Parallel Research Of Tumor Growth Based On FEM

Today, cancer has become one of the world’s highest morbidity and mortalitydiseases. The difficulty of cancer treatment lies in the unclear internal mechanism andprocess of tumor growth. Thus the modeling of tumor growing essential mechanismhas become one of the most active research areas.Studying the tumor cell’sbehaviourat cellular level is important for understanding how genes, proteins and cells affecttumor growth. However, most of the current cell-based models treat cells as2Dlattices or simple particles, which isn’t the realistic shape of cells.This paper presents a3D growth model of avascular tumor cells based on thefinite element method (FEM), which enables us to model cells and tumors complexityboundaries. The model provides conditions for future analysis of the behavior andforce between tumor cells in cellular level.In this paper, we focus on the simulate computation and parallel research of themodel. The original cell is a sphere composed of triangular mesh. The cell growthfollows the total energy equation, combine with the finite element method we canderived the growth nonlinear equation. To solve such nonlinear equation, we proposethe penalty function with equality constraint based on the optimization method toprevent the situation that the iteration doesn’t converge. According to thecharacteristics of the FEM model, a cell division algorithm based on breadth firstsearch is designed to simulate the cell division. The size and shape of the surfacemesh will change with tumor growth, which may affect the accuracy of calculation, soa series of mesh processing algorithms will be used to optimize the grids. In order toaccommodate large-scale simulations, we design a MPI-based parallel framework andverify its feasibility and scalability through cluster. The result showed that the parallelframework gets a good acceleration effect.The simulation system is developed on Linux platform with C++. Through thesimulation, we obtain the image of a multiple-cells tumor and the cell growth curve.The numerical results showed that the FEM tumor growth model and relatedalgorithms may overcome the strong nonlinearity of the cell’s deformation in growth and division, and are prediction of the cell’s growth and division in3D, which hasgreat potential in the study of cellular interaction in cell’s level.