Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are included. Mechanics and biology are coupled by making certain parameters of a previously established bioregulatory model dependent on local mechanical stimuli. To illustrate the potential added value of such a framework, this coupled model was applied to investigate whether local mechanical stimuli influencing only the angiogenic process can explain normal healing as well as overload-induced nonunion development. Simulation results showed that mechanics acting directly on angiogenesis alone was not able to predict the formation of overload-induced nonunions. However, the direct action of mechanics on both angiogenesis and osteogenesis was able to predict overload-induced nonunion formation, confirming the hypotheses of several experimental studies investigating the interconnection between angiogenesis and osteogenesis. This study shows that mathematical models can assist in testing hypothesis on the nature of the interaction between biology and mechanics.