Quantitative Model Explaining the Competition Between Calcium Phosphate Resorption and Bone Formation in Sheep Model

The biocompatibility of bioresorbable ceramics is critically influenced by the interplay between ceramic resorption and bone formation. This study presents a mathematical framework to quantitatively model the competition between these processes using beta-tricalcium phosphate (β-TCP) as a model system. Such a framework incorporates the paracrine and autocrine signaling interactions among osteoblasts and osteoclasts. While analysing in vivo data (sheep model), the temporal dynamics of bone formation and ceramic resorption are evaluated. The model predictions align closely with the experimental results, capturing key biophysical mechanisms. Apart from fitting with empirical models, the bone growth kinetics data of the published studies follow Hill's model closely, which is regarded as the foundation of quantitative pharmacology. While analysing its physiological relevance, the parametric sensitivity analysis reveals the dominant influence of osteoclast removal rates and specific signaling pathways (osteoblast-to-osteoblast and osteoblast-to-osteoclast) on bone growth. The competition between bone growth and β-TCP resorption leads to a cross-over at 6 weeks, which correlates well with the time period to produce the half-of-the-maximum bone growth as per Hill's model. These findings provide insights into optimising the design of bioresorbable ceramics for clinical applications, emphasising the tailoring of resorption rates to support bone growth, in vivo.