A Multiscale Finite Element Model for Avascular Tumor Growth

Abstract

There are many mathematical models or chemical models available to describe the avascular tumor growth. However, few of them take into account the necessary physical growth for the avascular tumor. In this paper, we proposed a multiscale finite element model that spans three distinct scales for the avascular tumor growth. At the extracellular microenvironment level, we proposed a new set of piecewise reaction diffusion equations to describe the extracellular microenvironment of the tumor growth. At the intracellular cycle level, we proposed a cell cycle control factor to model the key role that played by the G1-S phase transition. At the cellular level, we introduced the proposed cell cycle control factor to combine the extracellular microenvironment, the intracellular cycle and the cellular cycle into the total energy equations to form our finite element cellular model. Experiments were performed to simulate the growth of EMT6/Ro mouse mammary cell under three different kinds of initial chemical concentrations. Results showed that the proposed approach outperformed the baseline approach in terms of tumor cell number and tumor cell volume.