Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale

Sansalone, V.; Naı̈li, S.; Bousson, V.; Bergot, C.; Peyrin, Françoise; Zarka, J.; Laredo, Jean‐Denis; Haïat, Guillaume

doi:10.1016/j.jbiomech.2010.03.034

Cited by 90 publications

(65 citation statements)

References 48 publications

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“…In a recent paper (Sansalone et al 2010) carried out experiments on a specimen of human femoral cortical bone from a 79-year old patient to estimate the average variation of porosity and bone mineral density along the bone radial and axial position via a 3D-image processing method. Each 2D-image, corresponding to the cross-sections in the plane (x 1 , x 2 ), was analyzed identifying regions of interest going from the periosteum to the endosteum.…”

Section: Variation Of Effective Moduli With Cross-sectionmentioning

confidence: 99%

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

Parnell

Vu²,

Grimal³

et al. 2011

Biomech Model Mechanobiol

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We compare theoretical predictions of the effective elastic moduli of cortical bone at both the meso- and macroscales. We consider the efficacy of three alternative approaches: the method of asymptotic homogenization, the Mori-Tanaka scheme and the Hashin-Rosen bounds. The methods concur for specific engineering moduli such as the axial Young's modulus but can vary for others. In a past study, the effect of porosity alone on mesoscopic properties of cortical bone was considered, taking the matrix to be isotropic. Here, we consider the additional influence of the transverse isotropy of the matrix. We make the point that micromechanical approaches can be used in two alternative ways to predict either the macroscopic (size of cortical bone sample) or mesoscopic (in between micro- and macroscales) effective moduli, depending upon the choice of representative volume element size. It is widely accepted that the mesoscale behaviour is an important aspect of the mechanical behaviour of bone but models incorporating its effect have started to appear only relatively recently. Before this only macroscopic behaviour was addressed. Comparisons are drawn with experimental data and simulations from the literature for macroscale predictions with particularly good agreement in the case of dry bone. Finally, we show how predictions of the effective mesoscopic elastic moduli can be made which retain dependence on the well-known porosity gradient across the thickness of cortical bone.

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Section: Variation Of Effective Moduli With Cross-sectionmentioning

confidence: 99%

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

Parnell

Vu²,

Grimal³

et al. 2011

Biomech Model Mechanobiol

Self Cite

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“…These sources were taken into account to develop the computational model of the present system's response. In the context of bone characteristics, the bone remodeling process is rated as highly importance since morphology and microscopic properties change due to the contents of mineralization 10) and biological apatite (BAp). 11) Obviously, the influence of age to the mechanical properties is more significant than the gender in terms of inter-individual differences.…”

Section: Uncertainty Factors To Influence the Effective Propertiesmentioning

confidence: 99%

Uncertainty Modeling in the Prediction of Effective Mechanical Properties Using Stochastic Homogenization Method with Application to Porous Trabecular Bone

Basaruddin

Takano²,

Akiyama³

et al. 2013

Mater. Trans.

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A systematic modeling of uncertainty due to image processing, material characteristics and experimental works was developed in order to propose a novel stochastic image-based multi-scale method for heterogeneous media. The effective mechanical properties with application to three porous trabecular bone models were predicted by introducing the correction factor (¢) to represent the miscellaneous errors or unknown factors. Finally, the probability density was obtained for the effective mechanical properties, which could evaluate the reliability of scattered experimental results. It has been concluded that variation in effective properties of heterogeneous media can be predicted even when only limited measured values are available by using the present extrapolation technique based on verified simulation results.

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“…Recently, a multiscale model based on continuum micromechanics was proposed by our group to estimate the elastic properties of bone tissue (Sansalone et al 2010(Sansalone et al , 2012a. The experimental information was obtained using synchrotron radiation micro-computed tomography (SR-μCT) which provided a 3-D mapping of the HP and TMD with a spatial resolution of about 10 µm.…”

Section: Introductionmentioning

confidence: 99%

Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging

Sansalone

Gagliardi

Desceliers

et al. 2015

Biomech Model Mechanobiol

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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.

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Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale

Cited by 90 publications

References 48 publications

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

Uncertainty Modeling in the Prediction of Effective Mechanical Properties Using Stochastic Homogenization Method with Application to Porous Trabecular Bone

Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging

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