Mathematical model for cartilage tissue-growth using a quadriphasic mixture and finite element analysis.

摘要

Despite tremendous advances in the field of tissue engineering, a number of obstacles is still hindering its successful translation to the clinic. One of these challenge has been to design cell-laden scaffolds that can provide an appropriate environment for cells to successfully synthesize new tissue while providing a mechanical support that can resist physiological loads at the early stage of in-situ implementation. A solution to this problem has been to balance tissue growth and scaffold degradation by creating new hydrogel systems that possess both hydrolytic and enzymatic degradation behaviors. Very little is known however, about the complex behavior of these systems, which emphasis the need for a rigorous mathematical approach that can eventually assist and guide experimental advances. This paper introduces a mathematical and numerical formulation based on mixture theory, to describe the degradation, swelling and transport of extra-cellular matrix (ECM) molecules released by cartilage cells (chondrocytes) in within a hydrogel scaffold. The model particularly investigates the relative roles of hydrolytic and enzymatically on ECM diffusion and its impact on the evolution of the scaffold's mechanical integrity. Numerical results based on finite element show that if properly tuned, enzymatic degradation differs from hydrolytic degradation in that it can create a degradation front that is key to maintaining scaffold stiffness while allowing ECM deposition. This results therefore suggest a possible hydrogel design space to enable successful "in-situ" cartilage tissue engineering.