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A hybrid bioregulatory model of angiogenesis during bone fracture healing

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Abstract

Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.

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Author notes

  1. Véronique Peiffer

    Present address: Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

  2. Alf Gerisch

    Present address: Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, 64293, Darmstadt, Germany

  3. Liesbet Geris

    Present address: Biomechanics Research Unit, Université de Liège, Bât. B52/3 Génie biomécanique, chemin des Chevreuils 1, 4000, Liège, Belgium

Authors and Affiliations

  1. Division of Production Engineering, Machine design and Automation, Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300B, 3001, Leuven, Belgium

    Véronique Peiffer & Dirk Vandepitte

  2. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle, Saale, Germany

    Alf Gerisch

  3. Division of Biomechanics and Engineering Design, Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300C, PB 2419, 3001, Leuven, Belgium

    Hans Van Oosterwyck & Liesbet Geris

  4. Prometheus, Division of Skeletal Tissue Engineering, K.U. Leuven, Herestraat 48, 3000, Leuven, Belgium

    Hans Van Oosterwyck & Liesbet Geris

Authors
  1. Véronique Peiffer
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  2. Alf Gerisch
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  3. Dirk Vandepitte
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  4. Hans Van Oosterwyck
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  5. Liesbet Geris
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Correspondence to Véronique Peiffer or Liesbet Geris.

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Peiffer, V., Gerisch, A., Vandepitte, D. et al. A hybrid bioregulatory model of angiogenesis during bone fracture healing. Biomech Model Mechanobiol 10, 383–395 (2011). https://doi.org/10.1007/s10237-010-0241-7

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  • DOI: https://doi.org/10.1007/s10237-010-0241-7

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