Contributions of Pore Volume Fraction and Mineralized Matrix Elasticity to Millimeter-Scale Cortical Bone Elastic Coefficients

Mathilde Granke, Quentin Grimal, Amena Saıed, Pascal Laugier, Françoise Peyrin, Alf Gerisch, and Kay Raum


bone, homogenization, effective properties, cortical, anisotropy, porosity


At the millimeter scale, cortical bone is considered to be a mineralized matrix pervaded by roughly cylindrical pores. In a former study we measured the vascular porosity and the millimeter scale elasticity of 21 human cortical bone samples (10 donors). We found that the porosity (pore volume fraction) accounts for a large part, but not all, of the elasticity variations. In the present work, we revisit the data and try to determine which characteristics of the pore network or of the mineralized matrix have an influence on the millimeter-scale elasticity. Apparent elasticity predictions obtained with (1) an analytical model with idealized pore shapes and (2) a finite element model accounting for some details of the pore network, are compared to experimental values. The main finding is that for a fixed porosity, the specific distribution of the pores play a minor role in the elasticity values. In contrast, relatively small variations of the mineralized matrix elasticity (±5%) have a measurable impact on millimeter-scale elasticity. The results of this study will serve as a guideline to build sample-specific cortical bone models. This will be of interest to analyze the structure-function relationship in bone and to design bone mimicking materials.

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