Estimation of Cortical Bone Microstructure From Ultrasound Backscatter.

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 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 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.

BMD-based assessment of local porosity in human femoral cortical bone.

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 mm2, 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.

Tailoring the excitation of fundamental flexural guide waves in coated bone by phase-delayed array: two-dimensional simulations.

The fundamental flexural guided wave (FFGW) enables ultrasonic assessment of cortical bone thickness. In vivo, it is challenging to detect this mode, as its power ratio with respect to disturbing ultrasound is reduced by soft tissue covering the bone. A phase-delayed ultrasound source is proposed to tailor the FFGW excitation in order to improve its power ratio. This situation is analyzed by 2D finite-element simulations. The soft tissue coating (7-mm thick) was simulated as a fluid covering an elastic plate (bone, 2-6 mm thick). A six-element array of emitters on top of the coating was excited by 50-kHz tone bursts so that each emitter was appropriately delayed from the previous one. Response was recorded by an array of receivers on top of the coating, 20-50 mm away from the closest emitter. Simulations predicted that such tailored/phase-delayed excitations should improve the power ratio of FFGW by 23 ± 5 dB, independent of the number of emitters (N). On the other hand, the FFGW magnitude should increase by 5.8 ± 0.5 dB for each doubling of N. This suggests that mode tailoring based on phase-delayed excitation may play a key role in the development of an in vivo FFGW assessment.

Photo-acoustic excitation and optical detection of fundamental flexural guided wave in coated bone phantoms.

Photo-acoustic (PA) imaging was combined with skeletal quantitative ultrasound (QUS) for assessment of human long bones. This approach permitted low-frequency excitation and detection of ultrasound so as to efficiently receive the thickness-sensitive fundamental flexural guided wave (FFGW) through a coating of soft tissue. The method was tested on seven axisymmetric bone phantoms, whose 1- to 5-mm wall thickness and 16-mm diameter mimicked those of the human radius. Phantoms were made of a composite material and coated with a 2.5- to 7.5-mm layer of soft material that mimicked soft tissue. Ultrasound was excited with a pulsed Nd:YAG laser at 1064-nm wavelength and received on the same side of the coated phantom with a heterodyne interferometer. The FFGW was detected at 30-kHz frequency. Fitting the FFGW phase velocity by the FLC(1,1) tube mode provided an accurate (9.5 ± 4.0%) wall thickness estimate. Ultrasonic in vivo characterization of cortical bone thickness may thus become possible.

Assessment of the fundamental flexural guided wave in cortical bone by an ultrasonic axial-transmission array transducer.

The fundamental flexural guided wave (FFGW), as modeled, for example, by the A0 Lamb mode, is a clinically useful indicator of cortical bone thickness. In the work described in this article, we tested so-called multiridge-based analysis, based on the crazy climber algorithm and short-time Fourier transform, for assessment of the FFGW component recorded by a clinical array transducer featuring a limited number of elements. Methods included numerical finite-element simulations and experiments in bone phantoms and human radius specimens (n = 41). The proposed approach enabled extraction of the FFGW component and determination of its group velocity. This group velocity was in good agreement with theoretical predictions and possessed reasonable sensitivity to cortical width (r(2) = 0.51, p < 0.001) in the in vitro experiments. It is expected that the proposed approach enables related clinical application. Further work is still needed to analyze in more detail the challenges related to the impact of the overlying soft tissue.

Modeling the impact of soft tissue on axial transmission measurements of ultrasonic guided waves in human radius.

Recent in vitro and simulation studies have shown that guided waves measured at low ultrasound frequencies (f=200 kHz) can characterize both material properties and geometry of the cortical bone wall. In particular, a method for an accurate cortical thickness estimation from ultrasound velocity data has been presented. The clinical application remains, however, a challenge as the impact of a layer of soft tissue on top of the bone is not yet well established, and this layer is expected to affect the dispersion and relative intensities of guided modes. The present study is focused on the theoretical modeling of the impact of an overlying soft tissue. A semianalytical method and finite-difference time domain simulations were used. The models developed were shown to predict consistently real in vivo data on human radii. As a conclusion, clinical guided wave data are not consistent with in vitro data or related in vitro models, but use of an adequate in vivo model, such as the one introduced here, is necessary. A theoretical model that accounts for the impact of an overlying soft tissue could thus be used in clinical applications.

Assessment of the cortical bone thickness using ultrasonic guided waves: modelling and in vitro study.

Determination of cortical bone thickness is warranted, e.g., for assessing the level of endosteal resorption in osteoporosis or other bone pathologies. We have shown previously that the velocity of the fundamental antisymmetric (or flexural) guided wave, measured for bone phantoms and bones in vitro, correlates with the cortical thickness significantly better than those by other axial ultrasound methods. In addition, we have introduced an inversion scheme based on guided wave theory, group velocity filtering and 2-D fast Fourier transform, for determination of cortical thickness from the measured velocity of guided waves. In this study, the method was validated for tubular structures by using numerical simulations and experimental measurements on tube samples. In addition, 40 fresh human radius specimens were measured. For tubes with a thin wall, plate theory could be used to determine the wall thickness with a precision of 4%. For tubes with a wall thicker than 1/5 of the outer radius, tube theory provided the wall thickness with similar accuracy. For the radius bone specimens, tube theory was used and the ultrasonically-determined cortical thickness was found to be U-Th = 2.47 mm +/- 0.66 mm. It correlated strongly (r(2) = 0.73, p < 0.001) with the average cortical thickness, C-Th = 2.68 +/- 0.53 mm, and the local cortical thickness (r(2) = 0.81, p < 0.001), measured using peripheral quantitative computed tomography. We can conclude that the guided-wave inversion scheme introduced here is a feasible method for assessing cortical bone thickness.

Thickness sensitivity of ultrasound velocity in long bone phantoms.

One approach to bone disease diagnosis such as osteoporosis is to measure the velocity of ultrasound propagating axially along long bones. In this study, the variation in velocity as a function of radial position was assessed using two polyvinyl chloride (PVC) bone phantoms with cross-sectional geometry similar to the human tibia but differing in medullary cavity diameter. Two ultrasonometers were used: these were a commercial device operating at a relatively high frequency (HF) of 1.25 MHz and a prototype low frequency (LF) device operating at approximately 200 kHz. The LF measurements showed a larger variation with radial position, with changes in velocity of up to 20% occurring around the phantom compared with changes of only 4% at most for HF. The LF velocity correlated strongly with local thickness (r(2) = 0.81) but HF velocity did not. The results demonstrate that LF measurements have a greatly enhanced thickness sensitivity. Using LF, it may therefore be possible to assess bone thickness as a function of radial position and hence to determine the distribution of bone around the long axis.