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Injuries to articular cartilage result in the development of lesions thatform on the surface of the cartilage. Such lesions are associated witharticular cartilage degeneration and osteoarthritis. The typical injuryresponse often causes collateral damage, primarily an effect of inflammation,which results in the spread of lesions beyond the region where the initialinjury occurs. We present a minimal mathematical model based on knownmechanisms to investigate the spread and abatement of such lesions. Inparticular we represent the "balancing act" between pro-inflammatory andanti-inflammatory cytokines that is hypothesized to be a principal mechanism inthe expansion properties of cartilage damage during the typical injuryresponse. We present preliminary results of in vitro studies that confirm theanti-inflammatory activities of the cytokine erythropoietin (EPO). We assumethat the diffusion of cytokines determine the spatial behaviour of injuryresponse and lesion expansion so that a reaction-diffusion system involvingchemical species and chondrocyte cell state population densities is a naturalway to represent cartilage injury response. We present computational resultsusing the mathematical model showing that our representation is successful incapturing much of the interesting spatial behaviour of injury associated lesiondevelopment and abatement in articular cartilage. Further, we discuss the useof this model to study the possibility of using EPO as a therapy for reducingthe amount of inflammation induced collateral damage to cartilage during thetypical injury response. The mathematical model presented herein suggests thatnot only are anti-inflammatory cytokines, such as EPO necessary to preventchondrocytes signaled by pro-inflammatory cytokines from entering apoptosis,they may also influence how chondrocytes respond to signaling bypro-inflammatory cytokines.

Reaction-Diffusion-Delay Model for EPO/TNF-$\alpha$? Interaction in Articular Cartilage Lesion Abatement