Triphasic mixture model of cell-mediated enzymatic degradation of hydrogels - Vernerey, Franck J. (2011)
In order to engineer living tissue equivalents, a critical component is designing scaffolds, such as hydrogels, whose degradation kinetics can match that of matrix production by cells. However, cell-mediated enzymatic degradation of a hydrogel is highly complex and nonlinear process that is challenging to comprehend based solely on experimental observations. To address this issue, this study presents a triphasic mixture model of the enzyme/hydrogel system, that consists of a solid polymer network, water and enzyme. Based on mixture theory, rubber elasticity theory and the Michaelis-Menton kinetics for degradation, the model naturally incorporates a strong coupling between gel mechanical properties, the kinetics of degradation and the transport of enzyme through the gel. The model is then used to investigate the particular problem of a single spherical enzyme-producing cell, embedded in a spherical hydrogel domain, for which the governing equations can be cast within the cento-symmetric assumptions. The governing equations are subsequently solved using an implicit nonlinear finite element procedure in order to obtain the evolution of enzyme concentration and gel degradation through time and space. The model shows that two regimes of degradation behavior exist, whereby degradation is dominated either by diffusion or dominated by reaction kinetics. Depending on the enzyme properties and the initial hydrogel design, the temporal and spatial changes in gel cross-linking are dramatically impacted, a feature that is likely to strongly affect new tissue development.