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

Yanfei Lu , Tomasz Lekszycki


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.
Author Yanfei Lu IMP
Yanfei Lu,,
- The Institute of Mechanics and Printing
, Tomasz Lekszycki IMP
Tomasz Lekszycki,,
- The Institute of Mechanics and Printing
Journal seriesMathematics and Mechanics of Solids, ISSN 1081-2865, e-ISSN 1741-3028
Issue year2017
Publication size in sheets0.65
Keywords in EnglishBone fracture, tissue, bone substitute, modelling, FEM, computer simulation
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 15-02-2018, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 15-02-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.953 (2) - 2016=2.113 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.