Next Article in Journal
Quadratic Solid–Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates
Next Article in Special Issue
Hierarchical Characterization and Nanomechanical Assessment of Biomimetic Scaffolds Mimicking Lamellar Bone via Atomic Force Microscopy Cantilever-Based Nanoindentation
Previous Article in Journal
Hot Deformation Behavior and Microstructure Evolution of 14Cr ODS Steel
Previous Article in Special Issue
Influence of Absorbable Calcium Sulfate-Based Bone Substitute Materials on Human Haemostasis—In Vitro Biological Behavior of Antibiotic Loaded Implants
Open AccessArticle

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

Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, University of Tlemcen, Chetouane 13000, Algeria
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
Department of Physical Therapy, College of Staten Island, City University of New York, New York, NY 10314, USA
New York Center for Biomedical Engineering, City College of New York, City University of New York, New York, NY 10031, USA
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;
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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop