Turning Gels into Cartilage:
Modeling Tissue Regeneration in Cell-Seeded Scaffolds
Department of Mathematics
North Carolina State University
Articular cartilage is the hydrated biological soft tissue that lines surfaces of bones in joints such as the knee, shoulder and hip. Unlike most other tissues, cartilage is avascular (no blood vessels) and aneural (no nerve endings). When the tissue is healthy, it is in a state of homeostasis in which synthesis and degradation of its extracellular matrix (ECM) constituents such as collagen and proteoglycan are in balance. This balance is maintained by a population of cells (chondrocytes) that are sparsely distributed within the ECM, and can regulate their metabolic activity by detecting changes in their external biophysical environment. Remarkably, when cartilage cells are seeded into a hydrogel scaffold in vitro, they detect “foreign” features of their local environment and initiate biosynthetic activity in an attempt to reproduce native ECM. Progression of this process to the point of complete matrix regeneration depends on several characteristics of the in vitro experiment. Among these factors are biophysical properties of the hydrogel material (e.g. mechanical stiffness, diffusivities), nutrient absorption and matrix reaction rates associated with chondrocyte metabolism, and mechanisms of cross-linking in assembly of ECM from its underlying constituents.
In this project, the team will develop mathematical models for time and spatially varying biophysical interactions between a single cartilage cell and an encapsulating hydrogel scaffold material. The starting point will be a reaction-diffusion system of PDEs that models progression of tissue regeneration relative to an equilibrium state that represents cellular homeostasis in healthy cartilage ECM. While there are several biophysical factors to consider in model development, a primary aim is to compute “regeneration” times required to turn over a specified volume of hydrogel material into newly synthesized tissue that mimics native cartilage ECM.