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A proposed screening algorithm for bone remodelling

Part of: Biology and other natural sciences Physiological, cellular and medical topics Mathematical biology in general

Published online by Cambridge University Press:  23 December 2020

C. F. ARIAS ,
F. BERTOCCHINI ,
M. A. HERRERO ,
J. M. LÓPEZ  and
G. E. OLEAGA Open the ORCID record for G. E. OLEAGA [Opens in a new window]
C. F. ARIAS
Affiliation:
Centro de Investigaciones Biológicas, CSIC, Ramiro de Maeztu 9, 28040 Madrid, Spain
F. BERTOCCHINI
Affiliation:
Centro de Investigaciones Biológicas, CSIC, Ramiro de Maeztu 9, 28040 Madrid, Spain
M. A. HERRERO
Affiliation:
Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain, email: goleaga@ucm.es
J. M. LÓPEZ
Affiliation:
Departamento de Morfología y Biología Celular, Universidad de Oviedo, 33006 Oviedo, Asturias, Spain
G. E. OLEAGA
Affiliation:
Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain, email: goleaga@ucm.es
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Abstract

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One of the most remarkable aspects of human homoeostasis is bone remodelling. This term denotes the continuous renewal of bone that takes place at a microscopic scale and ensures that our skeleton preserves its full mechanical compliance during our lives. We propose here that a renewal process of this type can be represented at an algorithmic level as the interplay of two different but related mechanisms. The first of them is a preliminary screening process, by means of which the whole skeleton is thoroughly and continuously explored. This is followed by a renovation process, whereby regions previously marked for renewal are first destroyed and then rebuilt, in such a way that global mechanical compliance is never compromised. In this work, we pay attention to the first of these two stages. In particular, we show that an efficient screening mechanism may arise out of simple local rules, which at the biological level are inspired by the possibility that individual bone cells compute signals from their nearest local neighbours. This is shown to be enough to put in place a process which thoroughly explores the region where such mechanism operates.

Keywords

Mathematical modelling and simulationbone remodellingbiological algorithmscellular automataosteocytes

MSC classification

Primary: 92-08: Computational methods
Secondary: 92C30: Physiology (general) 92C42: Systems biology, networks 92B25: Biological rhythms and synchronization
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 5: 30th Anniversary Special Issue , October 2021 , pp. 806 - 819
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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