# Distribution of elasticity and density in a human femur

Supporting data for the paper entitled “Distribution of mesoscale elastic properties and mass density in the human femoral shaft” published by Daniel Rohrbach, Quentin Grimal, Peter Varga, Francoise Peyrin, Max Langer, Pascal Laugier, and Kay Raum in Connective Tissue Research in 2015 (current status: accepted)**Abstract of paper:**

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C^{micro} of cylindrically shaped samples (diameter: 4.4 mm, N=56) were obtained from cortical regions between 20% and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation DCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM).

Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C^{Meso} were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c_{33} measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft.

Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1-21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R² ≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. The data are suitable as input for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

On this page we provide datasets supporting the results of this paper:

1. microscale elastic maps in femoral cross sections assessed by 50-MHz scanning acoustic microscopy images [LINK Microscale elasticity]

2. mesoscale elasticity in femoral cross sections assessed by homogenization of scanning acoustic microscopy images [LINK Mesoscale elasticity]

3. a 3D surface model of the human femur illustrating the spatial distribution of the parameters assessed in this study [LINK 3D-Model]

The calibrated acoustic impedance images obtained by 50-MHz time-resolved scanning acoustic microscopy and mesoscale parameter maps of the femoral cross sections (derived as explained in the “Parameters derived from cross-sections” part of the Methods section and illustrated in Figures 2 and 3 of the paper) are available here in TIFF format. These images can be viewed with most conventional image viewers. However, the exact quantitative data can be assessed by loading these files into Matlab (The MathWorks Inc., Natick, MA, USA) using the function “read_impedance_map.m” that can also be downloaded from this page.

The 3D femur model (described in the “3D Material Model of the Femoral Shaft” part of the Methods section and shown in Figure 3 of the paper) illustrates the interpolated spatial distribution of the density and elastic information assessed in this study. Please note that this is a surface model, which does not include the endosteal-periosteal variation of these quantities. This data is stored in Ensight Gold format that can be opened and viewed e.g. with the freeware software tool Paraview (Kitware Inc., http://www.paraview.org/). The image “paraview_howto.jpg” illustrates how to proceed after opening the file “femur_model.case” in Paraview: 1) press “Apply”, 2) select parameter, 3) add color bar.

The following parameters are available as scalar fields:

- CtPo_SAM: SAM-based (2D) cortical porosity
- c33_micro: micro-scale (SAM-based) tissue stiffness, axial component (perpendicular to thecross section, equation 1 of the paper)
- Cii_meso: components of the meso-scale (homogenized) transverse isotopic stiffness tensor (equation 11 of the paper), with ii = 33: axial, ii = 11: in-plane, ii = 44: shear, ii = 12, 13: offaxis terms of the stiffness tensor
- AR31_meso: anisotropy ratio (C33/C11) of the meso-scale stiffness tensor (equation 6 of the paper)
- CtPo_SRuCT: synchrotron μCT-based (3D) cortical porosity
- Rho_micro: micro-scale mass density (equation 2 of the paper)
- Rho_meso: meso-scale mass density (equation 4 of the paper)
- DMB: degree of mineralization of bone tissue (SR-μCT-based)
- vBMD: volumetric bone mineral density (equation 3 of the paper)
- Ct.Th: SAM-based cortical thickness

Please note that the original bone surface used for this illustration was acquired in frame of the Living Human Project (www.livinghuman.org) by the Istituto Ortopedico Rizzoli and the Université libre de Bruxelles, and made publicly available through the PhysiomeSpace (www.physiomespace.com) portal of Biomed Town (www.biomedtown.org). Please read document “lhdl_Licence.pdf” about the related* license issues.