- Changyu Liu, Huiling Li, Alexander Hauptmann, Cong Li. 2014. Modeling Physical and Chemical Growths of Avascular Tumor. Abstract: Due to the avascular tumor growths were a complex activities that involved a chemical process and a physical process, a Finite Element Method (FEM) based mixture model was proposed in this paper. For the chemical process, the FEM was used to solve the reaction diffusion equations of three chemicals, which are the oxygen, glucose and GIF, under several specified boundary conditions. For the physical process, the FEM was used to solve the total energy equations which can be uniquely calculated as a function of the nodal displacements in the tumor. In each simulation step, we minimize the energy increment for all the tumor cells. The experiment results demonstrated that the proposed approach is quite efficient for the modeling of avascular tumor growth.
