Modeling tumor transport and growth with poroelastic biopolymer networks

Abstract

The mechanical properties of the extracellular matrix (ECM) regulate tumor growth and invasion in the tumor microenvironment. Models of biopolymer networks have been used to investigate the impact of elasticity and viscoelasticity of ECM on tumor behavior. Under tumor compression, these networks also show poroelastic behavior that is governed by the resistance to water flow through their pores. This work investigates the hypothesis that stress-dependent transport properties of biopolymer networks regulate tumor growth. Here, alginate hydrogels are used as a model ECM system with tunable ionic and hybrid ionic/covalent crosslinking. Hydrogel stiffness, viscoelasticity, and stress relaxation behavior were characterized using stepwise axial compression. Among these properties, we find poroelastic fluid outflow dominates ECM stress relaxation, as the measured water flux was significantly affected under compression. Continuum mechanics-based modeling was developed to formulate and calculate the chemical potential gradients of water (solvent) in the hydrogels under compression. This framework was extended into an advection-diffusion framework to quantify growth factor (solute) distribution under varying strengths of stress and diffusion indexed by the relative strength of convective to diffusive transport, characterized by the Péclet number. An agent-based computational simulation showed that the Péclet numbers based on our experimental timescales strongly influenced tumor growth over longer, more physiologic timescales. Together, these results highlight the important role of water flux and transport in three-dimensional biopolymer networks.