Alterations of structure and density of cortical bone are associated with fragility fractures and can be assessed in vivo in humans at the tibia. Bone remodeling deficits in aging women have been recently linked to an increase in size of cortical pores. In this ex vivo study, we characterized the cortical microarchitecture of 19 tibiae from human donors (aged 69 to 94 years) to address, whether this can reflect impairments of the mechanical competence of the proximal femur, i.e., a major fracture site in osteoporosis. Scanning acoustic microscopy (12 μm pixel size) provided reference microstructural measurements at the left tibia, while the bone vBMD at this site was obtained using microcomputed tomography (microCT). The areal bone mineral density of both left and right femoral necks (aBMD neck ) was measured by dual‐energy X‐ray absorptiometry (DXA), while homogenized nonlinear finite element models based on high-resolution peripheral quantitative computed tomography provided hip stiffness and strength for one-legged standing and sideways falling loads. Hip strength was associated with aBMD neck (r = 0.74 to 0.78), with tibial cortical thickness (r = 0.81) and with measurements of the tibial cross-sectional geometry (r = 0.48 to 0.73) of the same leg. Tibial vBMD was associated with hip strength only for standing loads (r = 0.59 to 0.65). Cortical porosity (Ct.Po) of the tibia was not associated with any of the femoral parameters. However, the proportion of Ct.Po attributable to large pores (diameter > 100 μm) was associated with hip strength in both standing (r = -0.61) and falling (r = 0.48) conditions. When added to aBMD neck , the prevalence of large pores could explain up to 17% of the femur ultimate force. In conclusion, microstructural characteristics of the tibia reflect hip strength as well as femoral DXA, but it remains to be tested whether such properties can be measured in vivo.

Cortical pores are determinants of the elastic properties and of the ultimate strength of bone tissue. An increase of the overall cortical porosity (Ct.Po) as well as the local coalescence of large pores cause an impairment of the mechanical competence of bone. Therefore, Ct.Po represents a relevant target for identifying patients with high fracture risk. However, given their small size, the in vivo imaging of cortical pores remains challenging. The advent of modern high-resolution peripheral quantitative computed tomography (HR-pQCT) triggered new methods for the clinical assessment of Ct.Po at the peripheral skeleton, either by pore segmentation or by exploiting local bone mineral density (BMD). In this work, we compared BMD-based Ct.Po estimates with high-resolution reference values measured by scanning acoustic microscopy. A calibration rule to estimate local Ct.Po from BMD as assessed by HR-pQCT was derived experimentally. Within areas of interest smaller than 0.5 mm, our model was able to estimate the local Ct.Po with an error of 3.4%. The incorporation of the BMD inhomogeneity and of one parameter from the BMD distribution of the entire scan volume led to a relative reduction of the estimate error of 30%, if compared to an estimate based on the average BMD. When applied to the assessment of Ct.Po within entire cortical bone cross-sections, the proposed BMD-based method had better accuracy than measurements performed with a conventional threshold-based approach.

Summary The estimation of cortical thickness (Ct.Th) and porosity (Ct.Po) at the tibia using axial transmission ultrasound was successfully validated ex vivo against site-matched micro-computed tomography. The assessment of cortical parameters based on full-spectrum guided-wave analysis might improve the prediction of bone fractures in a cost-effective and radiation-free manner. Purpose Cortical thickness (Ct.Th) and porosity (Ct.Po) are key parameters for the identification of patients with fragile bones. The main objective of this ex vivo study was to validate the measurement of Ct.Po and Ct.Th at the tibia using a non-ionizing, low-cost, and portable 500-kHz ultrasound axial transmission system. Additional ultrasonic velocities and site-matched reference parameters were included in the study to broaden the analysis. Methods Guided waves were successfully measured ex vivo in 17 human tibiae using a novel 500-kHz bi-directional axial transmission probe. Theoretical dispersion curves of a transverse isotropic free plate model with invariant matrix stiffness were fitted to the experimental dispersion curves in order to estimate Ct.Th and Ct.Po. In addition, the velocities of the first arriving signal ( υ FAS ) and A 0 mode ( υ A0 ) were measured. Reference Ct.Po, Ct.Th, and vBMD were obtained from site-matched micro-computed tomography. Scanning acoustic microscopy (SAM) provided the acoustic impedance of the axial cortical bone matrix. Results The best predictions of Ct.Po (R 2 = 0.83, RMSE = 2.2%) and Ct.Th (R 2 = 0.92, RMSE = 0.2 mm, one outlier excluded) were obtained from the plate model. The second best predictors of Ct.Po and Ct.Th were vBMD (R 2 = 0.77, RMSE = 2.6%) and υ A0 (R 2 = 0.28, RMSE = 0.67 mm), respectively. Conclusions Ct.Th and Ct.Po were accurately predicted at the human tibia ex vivo using a transverse isotropic free plate model with invariant matrix stiffness. The model-based predictions were not further enhanced when we accounted for variations in axial tissue stiffness as reflected by the acoustic impedance from SAM. Electronic supplementary material The online version of this article (10.1007/s11657-019-0578-1) contains supplementary material, which is available to authorized users.

While osteoporosis assessment has long focused on the characterization of trabecular bone, the cortical bone micro-structure also provides relevant information on bone strength. This numerical study takes advantage of ultrasound multiple scattering in cortical bone to investigate the effect of pore size and pore density on the acoustic diffusion constant. Finite-difference time-domain simulations were conducted in cortical microstructures that were derived from acoustic microscopy images of human proximal femur cross sections and modified by controlling the density (Ct.Po.Dn) ∈[5−25] pore/mm2 and size (Ct.Po.Dm) ∈[30−100] μm of the pores. Gaussian pulses were transmitted through the medium and the backscattered signals were recorded to obtain the backscattered intensity. The incoherent contribution of the backscattered intensity was extracted to give access to the diffusion constant D. At 8 MHz, significant differences in the diffusion constant were observed in media with different porous micro-architectures. The diffusion constant was monotonously influenced by either pore diameter or pore density. An increase in pore size and pore density resulted in a decrease in the diffusion constant (D =285.9Ct.Po.Dm−1.49, R2=0.989 , p=4.96×10−5,RMSE=0.06; D=6.91Ct.Po.Dn−1.01, R2=0.94, p=2.8×10−3 , RMSE=0.09), suggesting the potential of the proposed technique for the characterization of the cortical microarchitecture.

Multi-channel pulse-echo ultrasound using linear arrays and single-channel data acquisition systems opens new perspectives for the evaluation of cortical bone. In combination with spectral backscatter analysis, it can provide quantitative information about cortical microstructural properties. We present a numerical study, based on the finite-difference time-domain (FDTD) method, to estimate the backscatter cross-section of randomly distributed circular pores in a bone matrix. A model that predicts the backscatter coefficient using arbitrary pore diameter distributions was derived. In an ex-vivo study on 19 human tibia bones (6 males, 13 females, 83.7 ± 8.4 years), multidirectional ultrasound backscatter measurements were performed using an ultrasound scanner equipped with a 6-MHz 128-element linear array with sweep motor control. A normalized depth-dependent spectral analysis was performed to derive backscatter and attenuation coefficients. Site-matched reference values of tissue acoustic impedance Z, cortical thickness Ct.Th, pore density Ct.Po.Dn, porosity Ct.Po and characteristic parameters of the pore diameter (Ct.Po.Dm) distribution were obtained from 100-MHz scanning-acoustic microscopy images. Proximal femur areal bone mineral density (aBMD), stiffness S and ultimate force Fu from the same donors were available from a previous study. All pore structure and material properties could be predicted using linear combinations of backscatter parameters with median to high accuracy (0.28  adjusted R²  0.59). The combination of cortical thickness and backscatter parameter provided similar or better prediction accuracies than aBMD. For the first time, a method for the non-invasive assessment of the pore diameter distribution in cortical bone by ultrasound is proposed. The combined assessment of cortical thickness, sound velocity, and pore size distribution in a mobile, non-ionizing measurement system could have a major impact to prevent osteoporotic fractures.

Bone extravascular matrix (EVM) elasticity at several tens micrometer scale plays a key role in the mechanical behavior of bone at different length scales with implications on bone biology through mechanotransduction.The elastic properties of cortical bone EVM have been evaluated by several experimental methods, including nanoindentation, scanning acoustic microscopy (SAM) and mechanical testing on µm sized bone specimens.Nevertheless, these methods hardly give access to elastic anisotropy. In this work, we propose a novel inverse homogenization method to evaluate the anisotropic elastic properties of cortical bone EVM based on the transverse isotropic elastic tensor of millimeter-sized bone specimens measured by using resonant ultrasound spectroscopy and Fast Fourier Transform homogenization method. With the inverse homogenization method, the anisotropic EVM stiffness constants were evaluated on 50 human femoral cortical bone specimens from an elderly group. To our knowledge, this is the first time that the whole set of the EVM stiffness tensor is evaluated on the same specimen and on a large number of samples. Further comparison with the results from SAM and the degree of mineralization of bone (DMB) showed the potential of this method. Empirical laws between DMB and EVM anisotropic stiffness constants were also provided for the first time. With the anisotropic elasticity evaluated by the proposed method, more accurate models can be developed to better understand bone mechanics and biology, such as mechanotransduction.

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published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User