Measurements of ultrasonic phase velocities and attenuation of slow waves in cellular aluminum foams as cancellous bone-mimicking phantoms

Characterization of rigid open-cell foams using direct ultrasonic simulation

An ultrasonic simulation technique based on the direct fluid model is proposed as an alternative to the analogous experimental technique to determine the tortuosity and characteristic lengths for high pore-density foams. It is beneficial as it reduces cost and almost eliminates the signal-to-noise issues encountered in the experiment. The proposed method is demonstrated for periodic microlattices with three different unit-cell configurations, 75%-90% porosity, and a pore size of about 200 microns. The technique is also applicable to high-resolution computed tomography (CT) scans of open-cell foams with a priori unknown microporous structure. An acoustic simulation software, ACTRAN® (Hexagon AB, Stockholm, Sweden), is used to model and perform analysis of the ultrasonic pulse propagation through the foam. Based on through-transmission by foam saturated with two different mediums, the tortuosity, and characteristic lengths are estimated from the high-frequency asymptotic behavior of the square of the propagation index (Nr2) versus the inverse square root of frequency (1/f). The predicted parameters are validated by comparing them with those determined by solving the electric conduction boundary value problem for the same configuration. Further, detailed parametric sensitivity analysis reveals the sensitivity of the Johnson-Champoux-Allard parameters to errors in Nr2 and so the effect of these errors on the acoustic absorption behavior of the rigid porous sample.

Investigation of ultrasonic soft tissue-bone reflection coefficients correlating with curve severity in children with adolescent idiopathic scoliosis

Adolescent idiopathic scoliosis (AIS) is a three-dimensional curvature of spine. Children with AIS and low bone quality have higher chance to get curve progression leading to bigger spinal curvature. In addition, bone quality affects acoustic impedance of bone, thus influencing the reflection coefficient of ultrasound signal from the soft tissue–bone interface. This study aimed to estimate the bone quality of AIS patients based on the reflection coefficients to determine the correlation of the bone quality with curve severity. A simple bone model was used to develop an equation to calculate the reflection coefficient value. Experiments were conducted on five different phantoms. Acrylic was used to design a vertebral shape to study the effect of surface roughness and inclination, including: smooth flat surface (SFS), smooth curved surface (SCS), rough curved surface (RCS), and the rough curved inclined surface (RCIS). A clinical study with 37 AIS patients were recruited. The estimated reflection coefficient values of plate phantoms agreed well with the predicted values and the maximum error was 6.7%. The reflection coefficients measured from the acrylic-water interface for the SFS, SCS, RCS, RCIS (3° and 5°) were 0.37, 0.33, 0.28, (0.23 and 0.12), respectively. The surface roughness and inclination increased the reflection loss. From the clinical data, the average reflection coefficients for children with AIS were 0.11 and 0.07 for the mild curve group and the moderate curve group, respectively. A moderate linear correlation was found between the reflection coefficients and curve severity (r2 = 0.3). Patients with lower bone quality have observed to have larger spinal curvature.

Spatio-Spectral Ultrasound Characterization of Reflection and Transmission Through Bone With Temperature Dependence

Transcranial focused ultrasound (tFUS) is a promising approach for the treatment of neurological disorders. It has proven useful in several clinical applications, with promising outcomes reported in the recent literature. Furthermore, it is currently being investigated in a range of neuromodulation (NM) and ablative applications, including epilepsy. In this application, tFUS access through the temporal window is the key to optimizing the treatment safety and efficacy. Traditional approaches have utilized transducers with low operating frequencies for tFUS applications. Modern array transducers and driving systems allow for more intelligent use of the temporal window by exploiting the spatio-spectral transmission bandwidth to a specified target or targets within the brain. To demonstrate the feasibility of this approach, we have investigated the ultrasound reflection and transmission characteristics for different access points within the temporal window of human skull samples ex vivo. Different transmit-receive (Rx) configurations are used for characterization of the spatio-spectral variability in reflection and transmission through the temporal window. In this article, we show results from a dual-piston transducer set up in the frequency range of 2-7 MHz. Broadband pulses as well as synthesized orthogonal frequency division multiplexed (OFDM) waveforms were used. The latter was used to improve the magnitude and phase measurements in 100-kHz subbands within the 2-7 MHz spectral window. A temperature-controlled water bath was used to characterize the change in reflection and transmission characteristics with temperature in the 25°C-43°C range. The measured values of the complex reflection and transmission coefficients exhibited significant variations with space, frequency, and temperature. On the other hand, the measured transmission phase varied more with location and frequency, with smaller sensitivity to temperature. A measurement-based hybrid angular spectrum (HAS) simulation through the human temporal bone was used to demonstrate the dependence of focusing gain on the skull profile and spatial distribution of change of speed of sound (SOS) at different skull temperatures.

Mussel-Inspired Adhesive Double-Network Hydrogel for Intraoral Ultrasound Imaging

Periodontal diseases could be diagnosed through intraoral ultrasound imaging with the advantages of simple operation procedures, low cost, and low safety risks. A couplant is normally placed between transducers and tissues for better ultrasound image quality. If applied intraorally, the couplants should possess good stability in water and robust mechanical properties, as well as strong adhesiveness to transducers and tissues. However, commercial couplants, such as Aquaflex (AF) cannot fulfill these requirements. In this work, inspired by the mussel adhesion mechanism, we reported a poly(vinyl alcohol)-polyacrylamide-polydopamine (PVA-PAM-PDA) hydrogel synthesized by incorporating PDA into the PAM-PVA double-network for intraoral ultrasound imaging. The hydrogel maintains good stability in water as well as exceptional mechanical properties and can adhere to different substrates (i.e., metal, glass, and porcine skin) without losing the original adhesion strength after multiple adhesion-strip cycles. Besides, when applied to porcine mandibular incisor imaging, the PVA-PAM-PDA hydrogel possesses good image quality for diagnosis as AF does. This work provides practical insights into the fabrication of multifunctional hydrogel-based interfaces between human tissues and medical devices for disease diagnosis applications.

Relationships of the ultrasonic backscatter measurements with the bone mineral density and the microarchitectural parameters in bovine trabecular bone in vitro

Relationships of the backscatter coefficient (BC), the apparent integrated backscatter (AIB), and the integrated reflection coefficient (IRC) with the bone mineral density (BMD) and the microarchitectural parameters were investigated in 28 bovine femoral trabecular bone samples. The BC was highly correlated with the BMD and the microarchitectural parameters (R = -0.66 to 0.71). In contrast, the AIB and the IRC exhibited high correlations with the BMD and the bone volume fraction (R = -0.68 to 0.77) and relatively lower correlations with the remaining microarchitectural parameters (R = -0.62 to 0.60). The multiple regression models yielded the adjusted squared correlation coefficients of 0.54-0.76.

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.

Bayesian inference of a human bone and biomaterials using ultrasonic transmitted signals

Ultrasonic techniques could be good candidates to aid the assessment of osteoporosis detection, due to their non-intrusiveness and low cost. While earlier studies made use of the measured ultrasonic phase velocity and attenuation inside the bone, very few have considered an inverse identification of both the intrinsic pore microstructure and the mechanical properties of the bone, based on Biot's model. The main purpose of this work is to present an in vitro methodology for bone identification, adopting a statistical Bayesian inference technique using ultrasonic transmitted signals, which allows the retrieval of the identified parameters and their uncertainty. In addition to the bone density, Young's modulus and Poisson's ratio, the bone pore microstructure parameters (porosity, tortuosity, and viscous length) are identified. These additional microstructural terms could improve the knowledge on the correlations between bone microstructure and bone diseases, since they provide more information on the trabecular structure. In general, the exact properties of the saturating fluid are unknown (bone marrow and blood in the case of bone study) so in this work, the fluid properties (water) are identified during the inference as a proof of concept.

Pulsed vibro-acoustic method for assessment of osteoporosis & osteopenia: A feasibility study on human subjects

In this paper we propose a new non-invasive ultrasound method, pulsed vibro-acoustic, for evaluating osteoporotic and osteopenic bone in humans. Vibro-acoustic method uses acoustic radiation force (ARF) to stimulate bone and the resulting acoustic signal can be used to characterize bone. The resulting acoustic signal is collected by a hydrophone at the skin surface. Wave velocity and numbers of intrinsic modes are used for analysis. Wave velocity is estimated using the received signal and maximum power mode of the decomposed signal is estimated using variational mode composition from different push points of ARF based on the cross-correlation method. A total of 27 adult volunteers, including healthy and those diagnosed with osteopenia and osteoporosis, were tested. Results of pulsed vibro-acoustic test on tibia of volunteers showed that healthy group could be differentiated from osteoporosis or osteopenia (p < 2 × 10^-5). The results of our study support the feasibility of pulsed vibro-acoustic method for measuring mechanical properties of bone and the potential clinical utility of the proposed method for assessment of bone health.

Correlations of the frequency dependence of the ultrasonic backscatter coefficient with the bone volume fraction and the trabecular thickness in bovine trabecular bone: Application of the binary mixture model

The ultrasonic backscatter coefficient and the exponent n (frequency dependence of the backscatter coefficient) were measured in 24 bovine femoral trabecular bone samples. The binary mixture model for ultrasonic scattering from trabecular bone was applied to predict the variations of the ultrasound parameters with the bone volume fraction (BV/TV) and the trabecular thickness (Tb.Th) in trabecular bone. The backscatter coefficient exhibited significant, positive correlations with the BV/TV (R = 0.82) and the Tb.Th (R = 0.79). In contrast, the exponent n was found to be significantly, negatively correlated with the BV/TV (R = -0.77) and the Tb.Th, (R = -0.71).

Characterization of a polymer, open-cell rigid foam that simulates the ultrasonic properties of cancellous bone

Materials that simulate the ultrasonic properties of tissues are used widely for clinical and research purposes. However, relatively few materials are known to simulate the ultrasonic properties of cancellous bone. The goal of the present study was to investigate the suitability of using a polymer, open-cell rigid foam (OCRF) produced by Sawbones^®. Measurements were performed on OCRF specimens with four different densities. Ultrasonic speed of sound and normalized broadband ultrasonic attenuation were measured with a 0.5 MHz transducer. Three backscatter parameters were measured with a 5 MHz transducer: apparent integrated backscatter, frequency slope of apparent backscatter, and normalized mean of the backscatter difference. X-ray micro-computed tomography was used to measure the microstructural characteristics of the OCRF specimens. The trabecular thickness and relative bone volume of the OCRF specimens were similar to those of human cancellous bone, but the trabecular separation was greater. In most cases, the ultrasonic properties of the OCRF specimens were similar to values reported in the literature for cancellous bone, including dependence on density. In addition, the OCRF specimens exhibited an ultrasonic anisotropy similar to that reported for cancellous bone.

Development of an Estimation Instrument of Acoustic Lens Properties for Medical Ultrasound Transducers

In medical ultrasound transducers, the transmission mode (pass-through) approach has been used to estimate the characteristics of the acoustic lens. However, it is difficult to measure the acoustic lens properties with high precision because of human, systemic, or mechanical measurement errors. In this paper, we propose a low-cost estimation instrument for acoustic lens properties connected with a customized database. In the instrument, three-axis and one-axis transmitting and material fixtures accurately align the transmitting and receiving transducers separately. Through the developed instrument, we obtained a precise standard deviation of the attenuation coefficient and velocity of the acoustic lens material of 0.05 dB/cm and 2.62 m/s, respectively. Additionally, the simultaneous alignment between the fixtures is controllable with developed programs, thus generating very accurate information of the acoustic lens about the testing ultrasound transducer. In our instrument, the database could support users in managing the result data efficiently. User programs developed using LabVIEW provide the capability to obtain precise values of the attenuation coefficient and velocity, which represent the fundamental material characteristics of the acoustic lens of the medical ultrasound transducers. The developed review program of the customized database can also search the acoustic lens information and store the experimental results.

Relationships of linear and nonlinear ultrasound parameters with porosity and trabecular spacing in trabecular-bone-mimicking phantoms

The speed of sound (SOS), the normalized broadband ultrasound attenuation (nBUA), and the nonlinear parameter (B/A) were measured in 18 trabecular-bone-mimicking phantoms consisting of water-saturated aluminum foams. The strong slow wave and the very weak fast wave were consistently observed in the signals transmitted through all of the phantoms. It was found that the SOS increased as the porosity and the trabecular spacing increased. In contrast, both the nBUA and the B/A showed opposite dependences on the porosity and the trabecular spacing. All three ultrasound parameters exhibited high correlation coefficients with the porosity and the trabecular spacing.

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.

Basic study for ultrasound-based navigation for pedicle screw insertion using transmission and backscattered methods

The purpose of this study was to understand the acoustic properties of human vertebral cancellous bone and to study the feasibility of ultrasound-based navigation for posterior pedicle screw fixation in spinal fusion surgery. Fourteen human vertebral specimens were disarticulated from seven un-embalmed cadavers (four males, three females, 73.14 ± 9.87 years, two specimens from each cadaver). Seven specimens were used to measure the transmission, including tests of attenuation and phase velocity, while the other seven specimens were used for backscattered measurements to inspect the depth of penetration and A-Mode signals. Five pairs of unfocused broadband ultrasonic transducers were used for the detection, with center frequencies of 0.5 MHz, 1 MHz, 1.5 MHz, 2.25 MHz, and 3.5 MHz. As a result, good and stable results were documented. With increased frequency, the attenuation increased (P<0.05), stability of the speed of sound improved (P<0.05), and penetration distance decreased (P>0.05). At about 0.6 cm away from the cortical bone, warning signals were easily observed from the backscattered measurements. In conclusion, the ultrasonic system proved to be an effective, moveable, and real-time imaging navigation system. However, how ultrasonic navigation will benefit pedicle screw insertion in spinal surgery needs to be determined. Therefore, ultrasound-guided pedicle screw implantation is theoretically effective and promising.

Dependences of ultrasonic properties on frequency and trabecular spacing in trabecular-bone-mimicking phantoms

The dependences of ultrasonic properties on the frequency and the trabecular spacing were investigated in 20 trabecular-bone-mimicking phantoms consisting of cellular copper foams. The strong slow waves were consistently observed in the signals transmitted through all of the phantoms. The frequency-dependent phase velocity and attenuation coefficient of the slow wave were measured at frequencies from 0.7 to 1.3 MHz. The phase velocity decreased approximately linearly with increasing frequency while the attenuation coefficients increased with increasing frequency. The phase velocity increased monotonically with increasing trabecular spacing from 1337 to 2931 μm while the attenuation coefficient decreased with increasing spacing.

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.

Time-domain separation of interfering waves in cancellous bone using bandlimited deconvolution: simulation and phantom study

In through-transmission interrogation of cancellous bone, two longitudinal pulses ("fast" and "slow" waves) may be generated. Fast and slow wave properties convey information about material and micro-architectural characteristics of bone. However, these properties can be difficult to assess when fast and slow wave pulses overlap in time and frequency domains. In this paper, two methods are applied to decompose signals into fast and slow waves: bandlimited deconvolution and modified least-squares Prony's method with curve-fitting (MLSP + CF). The methods were tested in plastic and Zerdine(®) samples that provided fast and slow wave velocities commensurate with velocities for cancellous bone. Phase velocity estimates were accurate to within 6 m/s (0.4%) (slow wave with both methods and fast wave with MLSP + CF) and 26 m/s (1.2%) (fast wave with bandlimited deconvolution). Midband signal loss estimates were accurate to within 0.2 dB (1.7%) (fast wave with both methods), and 1.0 dB (3.7%) (slow wave with both methods). Similar accuracies were found for simulations based on fast and slow wave parameter values published for cancellous bone. These methods provide sufficient accuracy and precision for many applications in cancellous bone such that experimental error is likely to be a greater limiting factor than estimation error.

Dependences of quantitative ultrasound parameters on frequency and porosity in water-saturated nickel foams

The frequency-dependent phase velocity, attenuation coefficient, and backscatter coefficient were measured from 0.8 to 1.2 MHz in 24 water-saturated nickel foams as trabecular-bone-mimicking phantoms. The power law fits to the measurements showed that the phase velocity, the attenuation coefficient, and the backscatter coefficient were proportional to the frequency with exponents n of 0.95, 1.29, and 3.18, respectively. A significant linear correlation was found between the phase velocity at 1.0 MHz and the porosity. In contrast, the best regressions for the normalized broadband ultrasound attenuation and the backscatter coefficient at 1.0 MHz were obtained with the polynomial fits of second order.

Feasibility of bone assessment with ultrasonic backscatter signals in neonates

The objective of this study was to assess the value of ultrasonic backscatter signals and the backscatter coefficient (BSC) in the analysis of bone status in neonates and to analyze the relationships between the BSC and gestational age, birth weight, length, head circumference and gender. A total of 122 neonates participated in the study, including 83 premature infants and 39 full-term infants. Their BSCs were measured by ultrasound after birth. The results revealed a significant correlation between the BSC and gestational age (R = 0.47, p < 0.001), birth weight (R = 0.47, p < 0.0001) and length at birth (R = 0.43, p < 0.001) at a frequency of 5.0 MHz. This study suggests that the use of ultrasonic backscattering and the BSC is feasible for assessment of the bone status of neonates.

Estimation of fast and slow wave properties in cancellous bone using Prony's method and curve fitting

The presence of two longitudinal waves in poroelastic media is predicted by Biot's theory and has been confirmed experimentally in through-transmission measurements in cancellous bone. Estimation of attenuation coefficients and velocities of the two waves is challenging when the two waves overlap in time. The modified least squares Prony's (MLSP) method in conjuction with curve-fitting (MLSP + CF) is tested using simulations based on published values for fast and slow wave attenuation coefficients and velocities in cancellous bone from several studies in bovine femur, human femur, and human calcaneus. The search algorithm is accelerated by exploiting correlations among search parameters. The performance of the algorithm is evaluated as a function of signal-to-noise ratio (SNR). For a typical experimental SNR (40 dB), the root-mean-square errors (RMSEs) for one example (human femur) with fast and slow waves separated by approximately half of a pulse duration were 1 m/s (slow wave velocity), 4 m/s (fast wave velocity), 0.4 dB/cm MHz (slow wave attenuation slope), and 1.7 dB/cm MHz (fast wave attenuation slope). The MLSP + CF method is fast (requiring less than 2 s at SNR = 40 dB on a consumer-grade notebook computer) and is flexible with respect to the functional form of the parametric model for the transmission coefficient. The MLSP + CF method provides sufficient accuracy and precision for many applications such that experimental error is a greater limiting factor than estimation error.

Relationships of quantitative ultrasound parameters with cancellous bone microstructure in human calcaneus in vitro

Ultrasound parameters (attenuation, phase velocity, and backscatter), bone mineral density (BMD), and microarchitectural features were measured on 29 human cancellous calcaneus samples in vitro. Regression analysis was performed to predict ultrasound parameters from BMD and microarchitectural features. The best univariate predictors of the ultrasound parameters were the indexes of bone quantity: BMD and bone volume fraction (BV/TV). The most predictive univariate models for attenuation, phase velocity, and backscatter coefficient yielded adjusted squared correlation coefficients of 0.69-0.73. Multiple regression models yielded adjusted correlation coefficients of 0.74-0.83. Therefore attenuation, phase velocity, and backscatter are primarily determined by bone quantity, but multiple regression models based on bone quantity plus microarchitectural features achieve slightly better predictive performance than models based on bone quantity alone.

Correlations of group velocity, phase velocity, and dispersion with bone density in bovine trabecular bone

The present study investigated the correlations of the group velocity, the phase velocity, and the velocity dispersion with the apparent bone density in bovine trabecular bone in vitro. The phase velocity exhibited the negative dispersion, consistent with the behavior in human trabecular bone. The group and the phase velocities were found to increase with increasing apparent bone density, respectively, exhibiting similar high correlations of r=0.94 and 0.96. The negative dispersion rate exhibited a decreasing dependence on the apparent bone density, with a significant correlation of r=-0.86.