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Multichannel 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 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 (six 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 a median to high accuracy (0.28 ≤ adjusted R 2 ≤ 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 noninvasive 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, nonionizing measurement system could have a major impact on preventing osteoporotic fractures.

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/mm 2 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 , R 2 =0.989 , p=4.96×10 -5 ,RMSE=0.06; D=6.91Ct.Po.Dn -1.01 , R 2 =0.94, p=2.8×10 -3  , RMSE=0.09), suggesting the potential of the proposed technique for the characterization of the cortical microarchitecture.

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 (aBMDneck) 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 aBMDneck (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 aBMDneck, 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., Competing Interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: GI and KR have the patent "CortBS: Ultrasonic method for determining pore dimensions in cortical bone" pending. JB reports grants and personal fees from Eli Lilly, Amgen and Will Pharma, outside the submitted work. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

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 2 , 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., (Copyright © 2018 Elsevier Inc. All rights reserved.)