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Mathematical Modelling of Spatio-temporal Cell Dynamics Observed During Bone Remodelling

  • Madalena M. A. Peyroteo
  • Jorge BelinhaEmail author
  • Susana Vinga
  • R. Natal Jorge
  • Lúcia Dinis
Chapter
  • 32 Downloads
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 35)

Abstract

Bone is an active tissue capable to adapt its activity according to external stimuli. The consequent changes in mass, composition and shape are a result of this remodelling process, in which old bone is continuously replaced by new tissue. In order to mathematically describe this remodelling process, several mathematical models have been proposed. In this chapter, a novel model simulating the biological events that occur during bone remodelling is presented, based on Komarova’s (Bone 33:206–215, 2003 [1]) and Ayati’s (Biol Direct 5:28, 2010 [2]) models. Also, a thorough temporal and spatial analysis is performed using numerical methods, namely the finite element method (FEM), the radial point interpolation method (RPIM) and the natural neighbour radial point interpolation method (NNRPIM), being the last two meshless approaches. Results show that the combination of this model with distinct numerical approaches allows an accurate reproduction of the biological event, as described in the literature. Besides this, although all numerical techniques have been successfully applied, better quality results have been obtained with the NNRPIM.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Madalena M. A. Peyroteo
    • 1
  • Jorge Belinha
    • 2
    Email author
  • Susana Vinga
    • 3
  • R. Natal Jorge
    • 4
  • Lúcia Dinis
    • 4
  1. 1.Institute of Mechanical Engineering and Industrial Management (INEGI)PortoPortugal
  2. 2.Department of Mechanical Engineering, School of EngineeringPolytechnic of Porto (ISEP)PortoPortugal
  3. 3.Institute of Mechanical Engineering (IDMEC), ISTLisbonPortugal
  4. 4.Faculty of Engineering, Mechanical Engineering DepartmentUniversity of Porto (FEUP)PortoPortugal

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