A Mathematical Framework to Study the Effects of Growth Factor Influences on Fracture Healing

During fracture healing, multipotential stem cells differentiate into specialized cells responsible for producing the different tissues involved in the bone regeneration process. This cell differentiation has been shown to be regulated by locally expressed growth factors. The details of their regulatory mechanisms need to be understood. In this work, we present a two-dimensional mathematical model of the bone healing process for moderate fracture gap sizes and fracture stability. The inflammatory and tissue regeneration stages of healing are simulated by modeling mesenchymal cell migration; mesenchymal cell, chondrocyte and osteoblast proliferation and differentiation, and extracellular matrix synthesis and degradation over time. The effects of two generic growth factors on cell differentiation are based on the experimentally studied chondrogenic and osteogenic effects of bone morphogenetic proteins-2 and 4 and transforming growth factor- β -1, respectively. The model successfully simulates the progression of healing and predicts that the rate of osteogenic growth factor production by osteoblasts and the duration of the initial release of growth factors upon injury are particularly important parameters for complete ossification and successful healing. This temporo-spatial model of fracture healing is the first model to consider the effects of growth factors. It will help us understand the regulatory mechanisms involved in bone regeneration and provides a mathematical framework with which to design experiments and understand pathological conditions.