Mathematical modelling of the distribution of newly formed bone in bone tissue engineering

New bone formation in bone substitutes is usually investigated by histomorphometric global analysis. This study provides a novel mathematical modelling approach of new bone formation in the use of osteoinductive and functionalized biomaterials for bone tissue engineering. We discuss here the repartition and the probability to get new bone formation inside Biphasic Calcium Phosphate (BCP) loaded with autologous osteogenic cells, functionalized with a cyclo RGD peptide, after implantation in rabbits for 2 and 4 weeks. This local analysis allowed us to complement classical global findings and to demonstrate that after 2 weeks of implantation, the probability of new bone formation was significantly higher in RGD-grafted BCP and that new formed bone was largely distributed from the edge to the centre of the implant. While no significant differences were obtained after 4 weeks of implantation between RGD-grafted and non-grafted materials, distribution of new bone formation inside RGD-grafted materials was significantly more homogeneous as demonstrated by our mathematical modelling approach. In conclusion, local analysis of new bone formation inside macroporous substitutes coupled with mathematical modelling constitutes a potential quantitative approach for the evaluation of the osteoconductive and osteoinductive characteristics of such biomaterials.