Biomechanics Lab

Mathematical model of cartilage-bone defect healing

Head of Research: Dr. Jan Herman Kuiper – Orthopaedic InterventionsCollaborators: Mr Andrew Barnett, Dr Kelly Campbell, Ms Taya Chapman, Dr Caroline Dover, Mr Pete Gallacher, Dr Shailesh Naire, Mr Simon Pickard, Dr Nikhil Sharma

Our hospital has been at the forefront of cell therapy in orthopaedics. We are leading a number of clinical trials in this area and have collected a large amount of clinical data. Cartilage defect patients are treated using Autologous Chondrocyte Implantation, whereby cartilage cells (chondrocytes) are isolated from a small biopsy and expanded in our OsCell cell manufacturing facility, eventually yielding between 1 and 20 million cells. These cartilage cells are implanted into the defect, after which new cartilage grows over time.

Most of our patients who receive cell therapy have defects so deep that they also include the bone underneath the cartilage. Rather than cartilage defects, they are cartilage-bone defects, but the treatment works for them as well. However, instead of a deeper defect filled with only cartilage, these patients’ defects fill with new bone and new cartilage, restoring the original tissue. It is amazing that implanting cartilage cells can achieve this result: a bone-cartilage tissue with just the right amount of cartilage on top. The whole process seems very similar to what happens in the growth plate in children and adolescents.

To find out if this might be true and what might control the thickness of the cartilage layer, we formulated a mathematical model based on relatively simple rules that describe several processes that must take place. Our model describes processes such as cell proliferation, migration, differentiation and death, production of cartilage and bone, cartilage calcification, diffusion of nutrients and signalling proteins and the influence of these proteins on the cells, all expressed as mathematical equations. We then used the model to find out how cartilage-bone defects heal after implanting chondrocytes at the bottom of the defect and what controls the thickness of the cartilage tissue.

Our model predicted that the defect first fills completely with cartilage, taking around 12 months. Next, at the bottom of the defect chondrocytes begin to swell (hypertrophy) and the cartilage around them starts to calcify, after which bone cells were predicted to move in and form new bone. This process was predicted to move as a traveling wave towards the surface of the defect but to stop when around 3mm of cartilage was left at the surface, with a thin layer of calcified cartilage between cartilage and bone. The thickness of the remaining cartilage and the timing of the calcification process depended mainly on specific properties of parathyroid hormone-related protein (PTHrP), a signalling molecule produced by chondrocytes close to the cartilage surface. We think that our model can be helpful in translating between animal models and human patients and in understanding the repair process at a fundamental level.