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Open AccessArticle

A Novel Multiscale Mathematical Model for Building Bone Substitute Materials for Children

1
Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, University of Tlemcen, Chetouane 13000, Algeria
2
Université de Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, F-69622 Villeurbanne CEDEX, France; Inria Team Dracula, Inria Grenoble Rhône-Alpes Center, 69100 Villeurbanne CEDEX, France
3
Department of Physical Therapy, College of Staten Island, City University of New York, New York, NY 10314, USA
4
New York Center for Biomedical Engineering, City College of New York, City University of New York, New York, NY 10031, USA
5
Nanoscience Initiative, Advance Science Research Center, City University of New York, New York, NY 10031, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Materials 2018, 11(6), 1045; https://doi.org/10.3390/ma11061045
Received: 30 April 2018 / Revised: 10 May 2018 / Accepted: 12 May 2018 / Published: 20 June 2018
(This article belongs to the Special Issue Bone Substitute Materials)
Bone is an engineering marvel that achieves a unique combination of stiffness and toughness exceeding that of synthesized materials. In orthopedics, we are currently challenged for the child population that needs a less stiff but a tougher bone substitute than adults. Recent evidence suggests that the relationship between inter-molecular connections that involve the two main bone building blocks, TropoCollagen molecules (TC) and carbonated Hydroxyapatite (cAp), and bone macroscopic mechanical properties, stiffness and toughness, are key to building bone substitute materials for children. The goal of our study is to establish how inter-molecular connections that occur during bone mineralization are related to macroscopic mechanical properties in child bones. Our aim is to link the biological alterations of the TC-cAp self assembly process happening during bone mineralization to the bone macroscopic mechanical properties’ alterations during aging. To do so, we have developed a multiscale mathematical model that includes collagen cross links (TC–TC interface) from experimental studies of bone samples to forecast bone macroscopic mechanical properties. Our results support that the Young’s modulus cannot be a linear parameter if we want to solve our system. In relation to bone substitute material with innovative properties for children, our results propose values of several biological parameters, such as the number of crystals and their size, and collagen crosslink maturity for the desired bone mechanical competence. Our novel mathematical model combines mineralization and macroscopic mechanical behavior of bone and is a step forward in building mechanically customized biomimetic bone grafts that would fit children’s orthopedic needs. View Full-Text
Keywords: mathematical model; mechanical behavior; children’s bone grafts mathematical model; mechanical behavior; children’s bone grafts
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MDPI and ACS Style

Chekroun, A.; Pujo-Menjouet, L.; Berteau, J.-P. A Novel Multiscale Mathematical Model for Building Bone Substitute Materials for Children. Materials 2018, 11, 1045.

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