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A Diffusion Model for Stimulus Propagation in Remodeling Bone Tissues

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Higher Gradient Materials and Related Generalized Continua

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 120))

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Abstract

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.

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Authors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Università di Roma La Sapienza, 18 Via Eudossiana, Rome, Italy

    Ivan Giorgio & Ugo Andreaus

  2. International Research Center for the Mathematics and Mechanics of Complex Systems—M&MoCS, Università dell’Aquila, L’Aquila, Italy

    Ivan Giorgio

  3. NAAM Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Faris Alzahrani & Tasawar Hayat

  4. Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan

    Tasawar Hayat

  5. Faculty of Production Engineering, Warsaw University of Technology, Narbutta 85, 02-524, Warsaw, Poland

    Tomasz Lekszycki

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  1. Ivan Giorgio
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  4. Tasawar Hayat
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  5. Tomasz Lekszycki
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Correspondence to Ivan Giorgio .

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  1. Institut für Mechanik, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Technische Universität Berlin, Institut für Mechanik, Berlin, Germany

    Wolfgang H. Müller

  3. Institut für Mechanik, Technische Universität Berlin, Berlin, Germany

    Bilen Emek Abali

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Giorgio, I., Andreaus, U., Alzahrani, F., Hayat, T., Lekszycki, T. (2019). A Diffusion Model for Stimulus Propagation in Remodeling Bone Tissues. In: Altenbach, H., Müller, W., Abali, B. (eds) Higher Gradient Materials and Related Generalized Continua. Advanced Structured Materials, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-030-30406-5_5

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