A Diffusion Model for Stimulus Propagation in Remodeling Bone Tissues

  • Ivan GiorgioEmail author
  • Ugo Andreaus
  • Faris Alzahrani
  • Tasawar Hayat
  • Tomasz Lekszycki
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 120)


The mechanically driven biological stimulus in bone tissues regulates and controls the action of special cells called osteoblasts and osteoclasts. Different models have been proposed to describe the important and not yet completely understood phenomena related to this ‘feedback’ process. In Lekszycki and dell’Isola (2012) an integro-differential system of equations has been studied to describe the remodeling process in reconstructed bones where the biological stimulus in a given instant t depends on the deformation state of the tissue at the same instant. Instead biological knowledge suggests that the biological stimulus, once produced, is ‘diffused’ in bone tissue to reach the target cells. In this paper, we propose a model for de-scribing biological stimulus diffusion in remodeling tissues in which diffusive time dependent phenomena are taken into account. Some preliminary numerical simulations are presented which suggest that this model is promising and deserves further investigations.


Mechanical–biological coupling Bone functional adaptation Growth and resorption processes Bone remodeling 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ivan Giorgio
    • 1
    • 2
    Email author
  • Ugo Andreaus
    • 1
  • Faris Alzahrani
    • 3
  • Tasawar Hayat
    • 3
    • 4
  • Tomasz Lekszycki
    • 5
  1. 1.Department of Structural and Geotechnical EngineeringUniversità di Roma La SapienzaRomeItaly
  2. 2.International Research Center for the Mathematics and Mechanics of Complex Systems—M&MoCS, Università dell’AquilaL’AquilaItaly
  3. 3.NAAM Research Group, Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  5. 5.Faculty of Production EngineeringWarsaw University of TechnologyWarsawPoland

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