Mathematical modeling of fracture healing: coupling between mechanics, angiogenesis and osteogenesis

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 and angiogenesis is explicitly incorporated. To illustrate the added value of such a framework, a coupled mechanobioregulatory model was proposed. This model was based on a previously developed bioregulatory model [1], using a simple coupling between mechanics and biology whereby certain parameters of the bioregulatory model were made dependent on local mechanical stimuli. As a first example, in this study, the proliferation of osteoblasts and endothelial cells were made dependent on the local fluid flow [2]. Various loading situations, ranging from non-loading to overloading, were simulated. Simulations of adverse mechanical circumstances predicted the formation of avascular nonunions, a result that was corroborated by various experimental observations.
This model allows testing various hypotheses concerning the nature of the mechanical stimulus influencing the healing process, as well as the most important cellular processes
influenced by mechanical loading. It is one of the first models that provides an explicit coupling between mechanical and angiogenic factors. As both factors have been identified to play a key role in the occurrence of delayed and nonunions, the model allows to further explore their etiology and treatment.