A mathematical model of cartilage regeneration after cell therapy

Autologous Chondrocyte Implantation (ACI) is a cell-based therapy used mainly for the treatment of chondral defects in the knee. It involves surgically inserting isolated chondrocytes or mesenchymal stem cells (MSCs), previously expanded in culture, into the defect region. These chondrocytes then proliferate and migrate in the process forming extracellular matrix (ECM) and new cartilage. In the case of MSCs, the process of forming new cartilage is initiated only after differentiation of the stem cells into chondrocytes. Many details of the repair process following insertion in humans are unknown. To enable better understanding of the repair process, we present a mathematical model of cartilage regeneration after cell therapy. The key mechanisms involved in the regeneration process are simulated by modelling cell migration, proliferation and differentiation, nutrient diffusion and depletion, and ECM synthesis and degradation at the defect site, both spatially and temporally. The model successfully simulates the progression of cartilage regeneration. The model predicts a time frame of about 18months for the defect to reach full maturation which corresponds with results from clinical studies and demonstrates that cartilage regeneration is a slow process. Moreover, the model also suggests that regeneration using stem cells alone is no better than that using chondrocytes. The stem cells need to first differentiate into chondrocytes before forming ECM and new cartilage, a process that is initiated only after the stem cell density exceeds a threshold value. Furthermore, with chondrocytes alone, the matrix seems to develop from the subchondral bone interface as compared to the normal cartilage interface, in the case of stem cells alone. The influence of initial conditions and parameters, such as the initial cell seeding densities and cell proliferation rates, is shown to not significantly influence the general evolution characteristics other than accelerating the initial growth process. The model presented here is a first approach towards better understanding of cartilage regeneration after cell therapy techniques.