The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis

Novel nomograms for predicting the risk of low distal bone strength: development and validation in a Chinese population-based observational study

BACKGROUND

This study aims to develop nomogram models based on the speed of sound (SOS) measurements results along with demographic information to predict the risk of low bone strength (LBS) of radius appropriate to the Chinese population of a broad age spectrum.

METHODS

A population-based cross-sectional study was conducted in 5 outpatient clinics located in Zhejiang, the southern part of China. A total of 38,699 participants from 2013 to 2017 were included. Baseline measurements included SOS of the distal radius and clinical risk factor evaluation. Logistic regression models were used to evaluate prognosis and identify independent predictive factors, which were then utilized to establish nomograms for predicting the low bone strength of radius. The discrimination and calibration of nomograms were validated using the calibration plots, the decision curve analysis (DCA), and the receiver operating characteristics curve (ROC).

RESULTS

A total of 19,845 of the 38,904 participants ranged in age from 10 to 88 years were selected in this process. LBP nomogram model 1 was constructed based on age, weight, height, BMI, and gender. LBP nomogram model 2 was constructed based on age, height, BMI, and gender. The AUCs for model 1 and model 2 were 0.838 (95% CI: 0.832-0.844) and 0.837 (95% CI: 0.831-0.843), respectively. High-quality calibration plots and DCA in nomogram models were noticed, indicated that the constructed nomogram models were clinically useful.

CONCLUSIONS

Our study demonstrates that the nomograms established in this study could effectively evaluate the high-risk population groups of distal radius fracture in China.

Radiation Characteristics of Cranial Leaky Lamb Waves

We numerically and experimentally investigate the dispersion properties of leaky Lamb waves in the cranial bone. Cranial Lamb waves leak energy from the skull into the brain when propagating at speeds higher than the speed of sound in the surrounding fluid. The understanding of their radiation mechanism is significantly complicated by the geometric and mechanical characteristics of the cortical tables and the trabecular bone (diploë). Toward such understanding, we here analyze the sub-1.0 MHz radiation angle dispersion spectrum of porous bone phantoms and parietal bone geometries obtained from μ CT scans. Our numerical results show that, when diploic pores are physically modeled, leakage angles computed from time transient finite-element analyses correspond to those predicted by an equivalent three-layered fluid-loaded waveguide model. For the bone geometries analyzed, two main leaky branches are observed in the near-field dispersion spectrum: a fast wave radiated at small angles, which is related to the fastest fundamental Lamb mode supported by the cranial bone, and a slower wave radiated at larger angles. This observation is also confirmed by experimental tests carried out on an immersed parietal bone.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Comparison between the gold standard DXA with calcaneal quantitative ultrasound based-strategy (QUS) to detect osteoporosis in an HIV infected cohort

Introduction

Osteoporosis represents one of the most frequent comorbidity among HIV patients. The current standard method for osteoporosis diagnosis is dual-energy X-ray absorptiometry. Calcaneal quantitative ultrasound can provide information about bone quality. The aims of this study are to compare these two methods and to evaluate their ability to screen for vertebral fracture.

Methods

This cross-sectional study was conducted in HIV patients attending the Clinic of Infectious and Tropical Diseases of Brescia during 2014 and who underwent lumbar/femoral dual-energy X-ray absorptiometry, vertebral fracture assessment and calcaneal quantitative ultrasound. The assessment of osteoporosis diagnostic accuracy was performed for calcaneal quantitative ultrasound and for vertebral fracture comparing them with dual-energy X-ray absorptiometry.

Results

We enrolled 73 patients and almost 48% of them had osteoporosis with at least one of the method used. Vertebral fracture were present in 27.4%. Among patients with normal bone measurements, we found vertebral fracture in proportion between 10% and 30%. If we used calcaneal quantitative ultrasound method and/or X-ray as screening, the percentages of possible savable dual-energy X-ray absorptiometry ranged from 12% to 89% and misclassification rates ranged from 0 to 24.6%. A combined strategy, calcaneal quantitative ultrasound and X-Ray, identified 67% of patients with low risk of osteoporosis, but 16.4% of patients were misclassified.

Conclusions

We observed that patients with osteoporosis determined by calcaneal quantitative ultrasound and/or dual-energy X-ray absorptiometry have higher probability to undergo vertebral fracture, but neither of them can be used for predicting vertebral fracture. Use of calcaneal quantitative ultrasound for screening is a reasonable alternative of dual-energy X-ray absorptiometry since our study confirm that none strategy is clearly superior, but both screen tools must be always completed with X-ray.

Comparison of Bone Mineral Density by Dual-Energy X-Ray Absorptiometry and Bone Strength by Speed-of-Sound Ultrasonography in Adults With Gaucher Disease

Patients with the lysosomal disorder Gaucher disease (GD) are at risk of osteoporosis and/or avascular necrosis, but to date, no adequate biomarkers are available to ascertain individual predilections. Bone mineral density by dual-energy X-ray absorptiometry (DXA) has traditionally been used to monitor trends. With the availability of a speed-of-sound (SOS) ultrasonography to assess bone strength/elasticity, we aimed to ascertain whether these modalities are complimentary or comparable so SOS, with no radiation risk, might be used more routinely as a potential biomarker. A prospective comparative study in adult GD patients undergoing routine follow-up of bone mineral density T- and Z-scores at forearm (FA), femoral neck, and lumbar spine, and SOS Z-scores at FA was initiated. Interpretation was by qualitative categorization of Z-scores. The kappa measure of agreement beyond chance was calculated between pairs of measurements and the McNemar test was then applied. This noninterventional trial (ClinicalTrials.gov Identifier: NCT02067247) was approved by the institutional ethics committee. There were 89 patients (ages 21-78 years, 61% female, 62% common Ashkenazi genotype, 18% splenectomized, and 18% with avascular necrosis/fractures). When comparing Z-scores at FA by DXA and SOS, only 39.3% correlated, while the remaining results were in disagreement; no trend was noted. Similarly, when comparing Z-scores at the femoral neck by DXA with those at FA by SOS, 44.9% of the results were in agreement; no trend was noted; and Z-scores at the lumbar spine by DXA with FA by SOS, 46% were in agreement and no trend was noted. DXA at the 3 sites did not track in the same direction or the same magnitude of difference with SOS at FA in adult patients with GD. Due to the fundamental differences between the 2 measurements and their clinical correlates, plus the lack of long-term follow-up to assess outcome, the potential added value of the measurements at the FA by SOS in patients with GD awaits further studies.

Micro-scale finite element modeling of ultrasound propagation in aluminum trabecular bone-mimicking phantoms: A comparison between numerical simulation and experimental results

The present study investigated the accuracy of micro-scale finite element modeling for simulating broadband ultrasound propagation in water-saturated trabecular bone-mimicking phantoms. To this end, five commercially manufactured aluminum foam samples as trabecular bone-mimicking phantoms were utilized for ultrasonic immersion through-transmission experiments. Based on micro-computed tomography images of the same physical samples, three-dimensional high-resolution computational samples were generated to be implemented in the micro-scale finite element models. The finite element models employed the standard Galerkin finite element method (FEM) in time domain to simulate the ultrasonic experiments. The numerical simulations did not include energy dissipative mechanisms of ultrasonic attenuation; however, they expectedly simulated reflection, refraction, scattering, and wave mode conversion. The accuracy of the finite element simulations were evaluated by comparing the simulated ultrasonic attenuation and velocity with the experimental data. The maximum and the average relative errors between the experimental and simulated attenuation coefficients in the frequency range of 0.6-1.4 MHz were 17% and 6% respectively. Moreover, the simulations closely predicted the time-of-flight based velocities and the phase velocities of ultrasound with maximum relative errors of 20 m/s and 11 m/s respectively. The results of this study strongly suggest that micro-scale finite element modeling can effectively simulate broadband ultrasound propagation in water-saturated trabecular bone-mimicking structures.

A μCT-based investigation of the influence of tissue modulus variation, anisotropy and inhomogeneity on ultrasound propagation in trabecular bone

Ultrasound propagation is widely used in the diagnosis of osteoporosis by providing information on bone mechanical quality. When it loses calcium, the tissue properties will first decrease. However, limited research about the influence of tissue properties on ultrasound propagation have been done due to the cumbersome experiment. The goal of this study was to explore the relationships between tissue modulus (Es) and speed of sound (SOS) through numerical simulations, and to study the influence of Es on the acoustical behavior in characterizing the local structural anisotropy and inhomogeneity. In this work, three-dimensional finite element (FE) simulations were performed on a cubic high-resolution (15μm) bovine trabecular bone sample (4×4×4mm(3), BV/TV=0.18) mapped from micro-computed tomography. Ultrasound excitations of 50kHz, 500kHz and 2MHz were applied in three orthogonal axes and the first arriving signal (FAS) was collected to quantify wave velocity. In this study, a strong power law relationship between Es and SOS was measured with estimated exponential index β=2.08-3.44 for proximal-distal (PD), anterior-posterior (AP) and medial-lateral (ML), respectively (all R(2)>0.95). For various Es, a positive dispersion of sound speed with respect to sound frequency was observed and the velocity dispersion magnitude (VDM) was measured. Also, with Es=15GPa in three orientations, the SOS in PD axis is 2009±120m/s, faster than that of AP (1762±106m/s) and ML (1798±132m/s) (f=2MHz) directions. Besides, the standard deviation of SOS increases with the sound frequency and the Es in all directions except for that at 50kHz. For the mechanical properties, the apparent modulus with certain Es was highest in the longitudinal direction compared with the transverse directions. It indicates that the tissue modulus combining with anisotropy and inhomogeneity has great influence on ultrasound propagation. Simulation results agree well with theoretical and experimental results.

Quantitative ultrasound measurements at the heel: improvement of short- and mid-term speed of sound precision

Calcaneal quantitative ultrasound can be used to predict osteoporotic fracture risk, but its ability to monitor therapy is unclear possibly because of its limited precision. We developed a quantitative ultrasound device (foot ultrasound scanner) that measures the speed of sound at the heel with the aim of minimizing common error sources like the position and penetration angle of the ultrasound beam, as well as the soft tissue temperature. To achieve these objectives, we used a receiver array, mechanics to adjust the beam direction and a foot temperature sensor. In a group of 60 volunteers, short-term precision was evaluated for the foot ultrasound scanner and a commercial device (Achilles Insight, GE Medical, Fairfield, CT, USA‎). In a subgroup of 20 subjects, mid-term precision (1-mo follow-up) was obtained. Compared with measurement of the speed of sound with the Achilles Insight, measurement with the foot ultrasound scanner reduced precision errors by half (p < 0.05). The study indicates that improvement of the precision of calcaneal quantitative ultrasound measurements is feasible.

The finite element method for micro-scale modeling of ultrasound propagation in cancellous bone

Quantitative ultrasound for bone assessment is based on the correlations between ultrasonic parameters and the properties (mechanical and physical) of cancellous bone. To elucidate the correlations, understanding the physics of ultrasound in cancellous bone is demanded. Micro-scale modeling of ultrasound propagation in cancellous bone using the finite-difference time-domain (FDTD) method has been so far utilized as one of the approaches in this regard. However, the FDTD method accompanies two disadvantages: staircase sampling of cancellous bone by finite difference grids leads to generation of wave artifacts at the solid-fluid interface inside the bone; additionally, this method cannot explicitly satisfy the needed perfect-slip conditions at the interface. To overcome these disadvantages, the finite element method (FEM) is proposed in this study. Three-dimensional finite element models of six water-saturated cancellous bone samples with different bone volume were created. The values of speed of sound (SOS) and broadband ultrasound attenuation (BUA) were calculated through the finite element simulations of ultrasound propagation in each sample. Comparing the results with other experimental and simulation studies demonstrated the capabilities of the FEM for micro-scale modeling of ultrasound in water-saturated cancellous bone.