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

TL;DR

This paper develops a reaction-diffusion mathematical model to study the spread and control of cartilage lesions caused by injury, highlighting the potential therapeutic role of anti-inflammatory cytokine erythropoietin (EPO).

Contribution

It introduces a novel reaction-diffusion model incorporating cytokine interactions and cell states to simulate cartilage injury and repair mechanisms.

Findings

Model captures spatial lesion development and abatement.

EPO shown to have anti-inflammatory effects in vitro.

EPO may prevent chondrocyte apoptosis and modulate response to inflammation.

Abstract

Injuries to articular cartilage result in the development of lesions that form on the surface of the cartilage. Such lesions are associated with articular cartilage degeneration and osteoarthritis. The typical injury response often causes collateral damage, primarily an effect of inflammation, which results in the spread of lesions beyond the region where the initial injury occurs. We present a minimal mathematical model based on known mechanisms to investigate the spread and abatement of such lesions. In particular we represent the "balancing act" between pro-inflammatory and anti-inflammatory cytokines that is hypothesized to be a principal mechanism in the expansion properties of cartilage damage during the typical injury response. We present preliminary results of in vitro studies that confirm the anti-inflammatory activities of the cytokine erythropoietin (EPO). We assume that the diffusion of cytokines determine the spatial behaviour of injury response and lesion expansion so that a reaction-diffusion system involving chemical species and chondrocyte cell state population densities is a natural way to represent cartilage injury response. We present computational results using the mathematical model showing that our representation is successful in capturing much of the interesting spatial behaviour of injury associated lesion development and abatement in articular cartilage. Further, we discuss the use of this model to study the possibility of using EPO as a therapy for reducing the amount of inflammation induced collateral damage to cartilage during the typical injury response. The mathematical model presented herein suggests that not only are anti-inflammatory cytokines, such as EPO necessary to prevent chondrocytes signaled by pro-inflammatory cytokines from entering apoptosis, they may also influence how chondrocytes respond to signaling by pro-inflammatory cytokines.