A mathematical framework to study the effects of growth factor influences on fracture healing

During fracture healing, multipotential stem cells differentiate into speci alized cells responsible for producing the different tissues involved in th e bone regeneration process. This cell differentiation has been shown to be regulated by locally expressed growth factors. The details of their regula tory mechanisms need to be understood. In this work, we present a two-dimen sional 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; me senchymal cell, chondrocyte and osteoblast proliferation and differentiatio n, and extracellular matrix synthesis and degradation over time. The effect s of two generic growth factors on cell differentiation are based on the ex perimentally studied chondrogenic and osteogenic effects of bone morphogene tic proteins-2 and 4 and transforming growth factor-beta -1, respectively. The model successfully simulates the progression of healing and predicts th at the rate of osteogenic growth factor production by osteoblasts and the d uration of the initial release of growth factors upon injury are particular ly important parameters for complete ossification and successful healing. T his temporo-spatial model of fracture healing is the first model to conside r the effects of growth factors. It will help us understand the regulatory mechanisms involved in bone regeneration and provides a mathematical framew ork with which to design experiments and understand pathological conditions . (C) 2001 Academic Press.