title: Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging.
abstract: Accurate and reliable assessment of bone quality requires predictive methods which could probe bone microstructure and provide information on bone mechanical properties. Multiscale modelling and simulation represent a fast and powerful way to predict bone mechanical properties based on experimental information on bone microstructure as obtained through X-ray-based methods. However, technical limitations of experimental devices used to inspect bone microstructure may produce blurry data, especially in in vivo conditions. Uncertainties affecting the experimental data (input) may question the reliability of the results predicted by the model (output). Since input data are uncertain, deterministic approaches are limited and new modelling paradigms are required. In this paper, a novel stochastic multiscale model is developed to estimate the elastic properties of bone while taking into account uncertainties on bone composition. Effective elastic properties of cortical bone tissue were computed using a multiscale model based on continuum micromechanics. Volume fractions of bone components (collagen, mineral, and water) were considered as random variables whose probabilistic description was built using the maximum entropy principle. The relevance of this approach was proved by analysing a human bone sample taken from the inferior femoral neck. The sample was imaged using synchrotron radiation micro-computed tomography. 3-D distributions of Haversian porosity and tissue mineral density extracted from these images supplied the experimental information needed to build the stochastic models of the volume fractions. Thus, the stochastic multiscale model provided reliable statistical information (such as mean values and confidence intervals) on bone elastic properties at the tissue scale. Moreover, the existence of a simpler "nominal model", accounting for the main features of the stochastic model, was investigated. It was shown that such a model does exist, and its relevance was discussed.
authors.affiliation: Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France. vittorio.sansalone@u-pec.fr.
authors.forename: Vittorio
authors.initials: V
authors.lastname: Sansalone
authors.affiliation: Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France.
authors.forename: Davide
authors.initials: D
authors.lastname: Gagliardi
authors.affiliation: Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 5, bd Descartes, 77454, Marne-la-Vallée, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Desceliers
authors.affiliation: Sorbonne Paris Cité, UMR CNRS 7052 B2OA, Université Paris Diderot, 10, avenue de Verdun, 75010, Paris, France.
authors.forename: Valérie
authors.initials: V
authors.lastname: Bousson
authors.affiliation: Sorbonne Paris Cité, UMR CNRS 7052 B2OA, Université Paris Diderot, 10, avenue de Verdun, 75010, Paris, France.
authors.forename: Jean-Denis
authors.initials: JD
authors.lastname: Laredo
authors.affiliation: CREATIS, INSERM U1044, UMR CNRS 5220, INSA Lyon, Université de Lyon, 69621, Villeurbanne Cedex, France.|ESRF, BP 220, 38043, Grenoble Cedex, France.
authors.forename: Françoise
authors.initials: F
authors.lastname: Peyrin
authors.affiliation: Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Haïat
authors.affiliation: Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France.
authors.forename: Salah
authors.initials: S
authors.lastname: Naili
mesh_terms: D000368:Aged; D000465:Algorithms; D015519:Bone Density / Q000502:physiology; D000071538:Cortical Bone / Q000033:anatomy & histology / Q000502:physiology*; D004548:Elasticity; D020342:Finite Element Analysis; D006253:Haversian System / Q000502:physiology; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008954:Models, Biological; D016062:Porosity; D013269:Stochastic Processes
keywords: Continuum micromechanics; Cortical bone; Elastic properties; Haversian porosity; MaxEnt principle; Microstructure; Multiscale modelling; SR-CT imaging; Stochastic modelling; Tissue mineral density; Uncertainty quantification