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- W2276300890 abstract "INTRODUCTION: Angiogenesis is a key process in bone regeneration and bone engineering. Impaired angiogenesis may lead to non-union in the case of bone fractures. In this study we present a novel, mathematical model of bone regeneration in which angiogenesis has been explicitly implemented. Its relevance for bone engineering is demonstrated by applying it to the study of atrophic non-union. METHODS: The model is based on [1], in which a bioregulatory model for fracture healing was developed. This model expresses the change of a number of continuum-type variables – growth factor concentrations, cell densities and matrix densities – as a function of time and spatial coordinates. Mathematical expressions for (the rate of) cell migration, proliferation, differentiation, growth factor and matrix synthesis were formulated and made dependent on local matrix density and/or growth factor concentration, leading to a coupled system of non-linear partial differential equations. We extended the model, a.o. with expressions for angiogenesis and its relation with bone forming processes. Vascular growth factor density, endothelial cell concentration and vascular matrix density were defined as additional variables, and were related to processes (by modulating and/or adding terms to the equations), like chemotaxis, osteogenic differentiation and chondrocyte hypertrophy. Model equations were implemented in a customised finite volume code [2]. A simplified geometrical domain of a fracture callus, based on [3], was constructed (fig. 1)." @default.
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- W2276300890 date "2008-01-01" @default.
- W2276300890 modified "2023-09-26" @default.
- W2276300890 title "A mathematical model of bone regeneration including angiogenesis: relevance for tissue engineering strategies" @default.
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