Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T04:43:25.315Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Check for updates
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

References

Office of the Surgeon General (US). Bone health and osteoporosis: A report of the surgeon general. Rockville (MD): Office of the Surgeon General (US); 2004. Available from: https://www.ncbi.nlm.nih.gov/books/NBK45513/Google Scholar
Arias, C. F., Herrero, M. A., Echeverri, L. F., Oleaga, G. E., & López, J. M. (2018). Bone remodeling: A tissue-level process emerging from cell-level molecular algorithms. PloS One, 13(9), e0204171.CrossRefGoogle ScholarPubMed
Bezanson, J., Edelman, A., Karpinski, S. & Shah, V. B. (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1), 65–98.CrossRefGoogle Scholar
Crockett, J. C., Rogers, M. J., Coxon, F. P., Hocking, L. J. & Helfrich, M. H. (2011) Bone remodelling at a glance. J. Cell Sci. 124, 991–998.CrossRefGoogle ScholarPubMed
Dallas, S. L., Prideaux, M. & Bonewald, L. F. (2013) The osteocyte: An endocrine cell … and more. Endocr. Rev. 34(5), 658–690.CrossRefGoogle Scholar
Deutsch, A. & Dormann, S. (2017) Cellular Automaton Modeling of Biological Pattern Formation, Birkhäuser Ed. Basel.CrossRefGoogle Scholar
Echeverri, L. F., Herrero, M. A., López, J. M. & Oleaga, G. E. (2015) Early stages of bone fracture healing: Formation of a fibrin collagen scaffold in the fracture hematoma. Bull. Math. Biol. 77, 156–183.CrossRefGoogle ScholarPubMed
Eriksen, E. F. (2010) Cellular mechanisms of bone remodeling. Rev. Endocr. Metab. Disord. 4(11), 219–227.CrossRefGoogle Scholar
Garca-Aznar, J. M., Rueberg, T. & Doblaré, M. (2005) A bone remodelling model coupling microdamage growth and repair by 3d BMU activity. Biomech. Model Mechanobiol. 4, 147–167.CrossRefGoogle Scholar
Gardner, M. (1970) Mathematical games - the fantastic combinations of John Conway’s new solitary game life. Sci. Am. 223, 120–123.CrossRefGoogle Scholar
George, D., Allena, R. & Remond, Y. (2018) A multiphysics stimulus for continuum mechanics bone remodelling. Math. Mech. Complex Syst. 6(4), 307–319.CrossRefGoogle Scholar
Giorgio, I., dell’Isola, F., Andreaus, U., Alzahrani, F., Hayat, T. & Lekszycki, T. (2019) On mechanically driven biological stimulus for bone remodelling as a diffusive phenomenon. Biomech. Model. Mechanobiol. 18(6), 1617–1663.CrossRefGoogle ScholarPubMed
Graham, J. M., Ayati, B. P., Holstein, S. A. & Martin, J. A. (2013) The role of osteocytes in targeted bone remodeling: A mathematical model. PLoS One 8(5), e63884.CrossRefGoogle ScholarPubMed
Hadkidakis, D. J. & Androulakis, I. I. (2006) Bone remodeling. Ann. N. Y. Acad. Sci. 1092(1), 385–396.CrossRefGoogle Scholar
Hattner, R., Epker, B. N. & Frost, H. M. (1965) Suggested sequential mode of control of changes in cell behaviour in adult bone remodelling. Nature 206(4983), 489–490.CrossRefGoogle ScholarPubMed
Husain, A. & Jeffries, M. A. (2017) Epigenetics and bone remodeling. Curr. Osteoporos Rep. 15(5), 450–458.CrossRefGoogle ScholarPubMed
Kenkre, J. S. & Basset, J. H. D. (2018) The bone remodeling cycle. Ann. Clin. Biochem. 55(3), 308–327.CrossRefGoogle Scholar
Köhn-Luque, A., de Back, W., Starruß, J., Mattiotti, A., Deutsch, A., Pérez-Pomares, J. M. & Herrero, M. A. (2011) Early embryonic vascular patterning by matrix-mediated paracrine signalling: A mathematical model study. PLoS ONE 6(9), e24175.CrossRefGoogle ScholarPubMed
Komarova, S. V., Smith, R. J., Dixon, S. J., Sims, S. M. & Wahl, L. M. (2003) Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone 33(2), 206–15.CrossRefGoogle ScholarPubMed
MacArthur, B. D., Please, C. P., Taylor, M. & Oreffo, R. O. C. (2004) Mathematical modelling of skeletal repair. Biochem. Biophys. Res. Commun. 313, 825–833.CrossRefGoogle ScholarPubMed
Martnez-Reina, J., Reina, I., Domnguez, J. & Garca-Aznar, J. M. (2014) A bone remodelling model including the effect of damage on the steering of BMUs. J. Mech. Behav. Biomed. Math. 32, 99–112.CrossRefGoogle Scholar
Noble, B. S. (2008) The osteocyte lineage. Arch. Biochem. Biophys. 473, 106–111.CrossRefGoogle ScholarPubMed
Parfitt, A. M. (2002) Targeted and nontargeted bone remodeling: relationship to basic multicellular unit origination and progression. Bone 30, 5–7.CrossRefGoogle ScholarPubMed
Park-Min, K. H. (2018) Mechanisms involved in normal and pathological osteoclastogenesis. Cell Mol. Life Sci. 75(14), 2519–2528.CrossRefGoogle ScholarPubMed
Prisby, R. D. (2017) Mechanical, hormonal and metabolic influences on blood vessels, blood flow and bone. J. Endocrinol. 235(3), R77–R100.CrossRefGoogle ScholarPubMed
Robling, A., Castillo, A. & Turner, C. (2006) Biomechanical and molecular regulation of bone remodeling. Ann. Rev. Biomed. Eng. 8, 455–98.CrossRefGoogle ScholarPubMed
Ross, D. S., Mehta, K. & Cabal, A. (2017) Mathematical model of bone remodeling captures the antiresorptive and anabolic actions of various therapies. Bull. Math. Biol. 79, 117–142.CrossRefGoogle ScholarPubMed
Rucci, N. (2008) Molecular biology of bone remodelling. Clin. Cases Miner Bone Metab. 5(1), 49–56.Google ScholarPubMed
Ryser, M. D., Komarova, S. V. & Nigam, N. (2010) The cellular dynamics of bone remodeling: A mathematical model. SIAM J. Appl. Math. 70(6), 1899–1921.CrossRefGoogle Scholar
Siddiqui, J. A. & Partridge, N. C. (2016) Physiological bone remodeling: Systemic regulation and growth factor involvement. Physiology (Bethesda) 31(3), 233–245.Google ScholarPubMed
Sims, N. A. & Martin, T. J. (2014) Coupling the activities of bone formation and resorption: A multitude of signals within the basic multicellular unit. BoneKEy Rep. 3, 481.CrossRefGoogle ScholarPubMed
Zaidi, M. (2007) Skeletal remodeling in health and disease. Nat. Med. 13, 791–801.CrossRefGoogle ScholarPubMed