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First published online July 8, 2016

Modelling of bone fracture healing: influence of gap size and angiogenesis into bioresorbable bone substitute

Yanfei Lu and Tomasz Lekszycki [email protected]View all authors and affiliations

Volume 22, Issue 10

https://doi.org/10.1177/1081286516653272

Abstract

The complex process of bone fracture healing is driven by a set of mechanobiological and biochemical factors. In the present paper, a mathematical model of the angiogenesis effect on bioresorbable bone graft healing is proposed. The synthesis of bone tissue and resorption of bone and bone substitute material are stimulated by adjacent strain energy, and in the meantime regulated by a set of geometry and biochemical factors. The most important new elements included in formulation of this model are the effect of sufficient and insufficient nutrients supply, dependence of actor cell number on pore surface, and dependence of sensor cell number on bone mass.

The proposed mathematical formulation was implemented in FEM software COMSOL. A simple example was selected to perform numerical simulations in order to check the effect of gap size and nutrients diffusion rate on healing process. Values of selected parameters introduced in the proposed model were estimated on the basis of experimental results reported in the literature. Agreement between the results of numerical simulations and experimental studies was observed.

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Mathematics and Mechanics of Solids

Volume 22, Issue 10

Pages: 1997 - 2010

Article first published online: July 8, 2016

Issue published: October 2017

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Yanfei Lu

Warsaw University of Technology, Poland

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Tomasz Lekszycki

Warsaw University of Technology, Poland

International Research Center M&MOCS ’Mathematics and Mechanics of Complex Systems’, Italy

Medical University of Warsaw, Poland

[email protected]

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Notes

Tomasz Lekszycki, Warsaw University of Technology, st. Narbutta 85, 02–524, Warsaw, Poland. Email: [email protected]

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