Mathematical modelling of cartilage and bone defect healing after cell implantation

Abstract

This thesis is concerned with mathematically modelling the regeneration of cartilage and cartilage-bone defects. Defects of the bone-cartilage unit, namely chondral and osteochondral defects, are a leading cause of osteoarthritis, the most common type of arthritis in the UK. These defects can occur through acute trauma, natural wear and tear of the joint, and underlying disease of the bone, and are typically found in the articular joints. Autologous Chondrocyte Implantation (ACI) is the most commonly used cell implantation therapy for treating chondral defects in joints and has good clinical outcomes in osteochondral defects. The procedure begins by inserting chondrocytes into the defect region. The chondrocytes initiate healing by proliferating and depositing extracellular matrix, which allows them to migrate into the defect until it is completely filled with new cartilage. Mesenchymal stem cells (MSCs) can be used instead of chondrocytes with similar long term results. The main
differences between these implantation techniques is observable at early times, as MSCs must first differentiate into chondrocytes before cartilage is formed. For osteochondral defect regeneration, the mechanism behind healing is not fully understood. Though osteochondral defects can spontaneously repair, the tissue is usually fibrous, typically leading to subsequent degradation of the newly regenerated tissue. A recent study in ovine models show osteochondral defects heal by first filling with regenerative cartilage tissue which is subsequently remodelled into bone, replicating the endochondral ossification process.
We refine an existing model of cartilage defect regeneration using ACI to include important regulatory effects of growth factors, FGF-1 (fibroblast growth factor-1) and BMP-2 (bone morphogenetic protein-2). In vitro studies hypothesise these growth factors have a trophic effect on the chondral defect regeneration process. We then model the regeneration of a bone-cartilage defect using ACI in the presence of growth factors to verify the circumstances behind osteochondral healing. To the best of our knowledge, this is the first time this has been modelled for ACI therapy. The mathematical models formulated in this thesis successfully demonstrate the above proposed healing and growth factor mechanisms in chondral and osteochondral defect regeneration. Our key findings indicate a novel cell therapy that combines the ACI and MSC-implantation strategies increases the cartilage tissue formation rate within the first year of healing in chondral defects, regardless of the cell implantation ratio. Additionally, we show that osteochondral defects follow expected regeneration patterns when endochondral ossification is the proposed healing mechanism, under the influence of regulatory growth factors PTHrP (Parathyroid hormone-related protein) and Ihh (Indian hedgehog).
The findnigs of these models enable us to better understand chondral and osteochondral defect regeneration by giving invaluable insight into the healing processes that are occurring, the impact growth factors have on these healing mechanisms, and highlighting the potential for advances of novel cell-based therapies.