Sansalone Vittorio, Gagliardi Davide, Desceliers Christophe, Bousson Valérie, Laredo Jean-Denis, Peyrin Françoise, Haïat Guillaume, Naili Salah
Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France.
Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 5, bd Descartes, 77454, Marne-la-Vallée, France.
Biomech Model Mechanobiol. 2016 Feb;15(1):111-31. doi: 10.1007/s10237-015-0695-8. Epub 2015 Jul 23.
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.
准确可靠地评估骨质量需要能够探测骨微观结构并提供骨力学性能信息的预测方法。多尺度建模与模拟是一种快速且强大的方法，可基于通过基于X射线的方法获得的骨微观结构实验信息来预测骨力学性能。然而，用于检查骨微观结构的实验设备的技术局限性可能会产生模糊的数据，尤其是在体内条件下。影响实验数据（输入）的不确定性可能会质疑模型预测结果（输出）的可靠性。由于输入数据存在不确定性，确定性方法受到限制，因此需要新的建模范式。本文开发了一种新颖的随机多尺度模型，用于估计骨的弹性特性，同时考虑骨成分的不确定性。使用基于连续介质微观力学的多尺度模型计算皮质骨组织的有效弹性特性。将骨成分（胶原蛋白、矿物质和水）的体积分数视为随机变量，其概率描述基于最大熵原理构建。通过分析取自股骨颈下部的人体骨样本，证明了该方法的相关性。使用同步辐射微计算机断层扫描对样本进行成像。从这些图像中提取的哈弗斯孔隙率和组织矿物质密度的三维分布提供了构建体积分数随机模型所需的实验信息。因此，随机多尺度模型在组织尺度上提供了关于骨弹性特性的可靠统计信息（如平均值和置信区间）。此外，还研究了一个更简单的“标称模型”的存在性，该模型考虑了随机模型的主要特征。结果表明这样的模型确实存在，并对其相关性进行了讨论。
