Meshless, Bone Remodelling and Bone Regeneration Modelling

  • M. C. Marques
  • Jorge BelinhaEmail author
  • R. Natal Jorge
  • A. F. Oliveira
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 35)


In this chapter, it is presented an extensive bibliographic survey about meshless methods, bone remodelling and bone regeneration modelling. Here, the regeneration and remodelling processes are shown with detail and, in addition, it is presented a description of the mathematical models approaching both regeneration and remodelling processes. Three different classifications of models are presented, the mechanoregulated models, the bioregulated models and the mechanobioregulated models. The literature shows that the combination of remodelling models with meshless techniques allows to numerically achieve more realistic trabecular distributions. Thus, in this chapter, an introduction to meshless methods is presented, with a special focus on radial point interpolation meshless methods, such as the radial point interpolation method (RPIM) and the natural neighbour RPIM (NNRPIM).



The authors truly acknowledge the funding provided by Ministério da Educação e Ciência—Fundação para a Ciência e a Tecnologia (Portugal), under grants SFRH/BD/110047/2015, and by project funding MIT-EXPL/ISF/0084/2017. Additionally, the authors gratefully acknowledge the funding of Project NORTE-01-0145-FEDER-000022—SciTech—Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • M. C. Marques
    • 1
  • Jorge Belinha
    • 2
    Email author
  • R. Natal Jorge
    • 3
  • A. F. Oliveira
    • 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.Faculty of Engineering, Mechanical Engineering DepartmentUniversity of Porto (FEUP)PortoPortugal
  4. 4.Medical Teaching Department—CHP/HSAInstituto de Ciencias Biomédicas Abel Salazar (ICBAS)PortoPortugal

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