Biochemomechanical poroelastic theory of avascular tumor growth. (September 2016) - Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao; Gao, Huajian
Abstract: Tumor growth is a complex process involving genetic mutations, biochemical regulations, and mechanical deformations. In this paper, a thermodynamics-based nonlinear poroelastic theory is established to model the coupling among the mechanical, chemical, and biological mechanisms governing avascular tumor growth. A volumetric growth law accounting for mechano-chemo-biological coupled effects is proposed to describe the development of solid tumors. The regulating roles of stresses and nutrient transport in the tumor growth are revealed under different environmental constraints. We show that the mechano-chemo-biological coupling triggers anisotropic and heterogeneous growth, leading to the formation of layered structures in a growing tumor. There exists a steady state in which tumor growth is balanced by resorption. The influence of external confinements on tumor growth is also examined. A phase diagram is constructed to illustrate how the elastic modulus and thickness of the confinements jointly dictate the steady state of tumor volume. Qualitative and quantitative agreements with experimental observations indicate the developed model is capable of capturing the essential features of avascular tumor growth in various environments. Graphical Abstract: Highlights: A thermodynamics-based nonlinear poroelastic model of developing avascular tumors. Coupling among mechanical, chemical, and biological mechanisms in tumor growth. Nutrient transport and stresses regulate the anisotropic growth and layered structure. The theory reproduces the experiments of tumor growth under different confinements.