Dean Ta

Measurement of the Dispersion and Attenuation of Cylindrical Ultrasonic Guided Waves in Long Bone

Osteoporotic bones are likely to have less cortical bone than healthy bones. The velocities of guided waves propagating in a long cylindrical bone are very sensitive to bone properties and cortical thickness (CTh). This work studies the dispersion and attenuation of ultrasonic guided waves propagating in long cylindrical bone. A hollow cylinder filled with a viscous liquid was used to model the long bone and then to calculate the theoretical phase and group velocities, as well as the attenuation of the waves. The generation and selection of guided wave modes were based on theoretical dispersive curves. The phase velocity and attenuation of cylindrical guided wave modes, such as L(0,1), L(0,2) and L(0,3), were measured in bovine tibia using angled beam transducers at various propagation distances ranging from 75 to 160 mm. The results showed that the phase velocity of the L(0,2) guided wave mode decreased with an increase in CTh. The attenuation of the low cylindrical guided wave modes was a nonlinear function that increased with propagation distance and mode order. The L(0,2) mode had a different attenuation for each CTh. The experimental results were in good agreement with the predicted values. Cylindrical guided waves of low-frequency and low-order have been shown to demonstrate more dispersion and less attenuation and should, therefore, be used to evaluate long bone.

Mode separation of Lamb waves based on dispersion compensation method.

Ultrasonic Lamb modes typically propagate as a combination of multiple dispersive wave packets. Frequency components of each mode distribute widely in time domain due to dispersion and it is very challenging to separate individual modes by traditional signal processing methods. In the present study, a method of dispersion compensation is proposed for the purpose of mode separation. This numerical method compensates, i.e., compresses, the individual dispersive waveforms into temporal pulses, which thereby become nearly un-overlapped in time and frequency and can thus be extracted individually by rectangular time windows. It was further illustrated that the dispersion compensation also provided a method for predicting the plate thickness. Finally, based on reversibility of the numerical compensation method, an artificial dispersion technique was used to restore the original waveform of each mode from the separated compensated pulse. Performances of the compensation separation techniques were evaluated by processing synthetic and experimental signals which consisted of multiple Lamb modes with high dispersion. Individual modes were extracted with good accordance with the original waveforms and theoretical predictions.

Multiridge-based analysis for separating individual modes from multimodal guided wave signals in long bones

Quantitative ultrasound has great potential for assessing human bone quality. Considered as an elastic waveguide, long bone supports propagation of several guided modes, most of which carry useful information, individually, on different aspects of long bone properties. Therefore, precise knowledge of the behavior of each mode, such as velocity, attenuation, and amplitude, is important for bone quality assessment. However, because of the complicated characteristics of the guided waves, including dispersion and mode conversion, the measured signal often contains multiple wave modes, which yields the problem of mode separation. In this paper, some novel signal processing approaches were introduced to solve this problem. First, a crazy-climber algorithm was used to separate time-frequency ridges of individual modes from time-frequency representations (TFR) of multimodal signals. Next, corresponding time domain signals representing individual modes were reconstructed from the TFR ridges. It was found that the separated TFR ridges were in agreement with the theoretical dispersion, and the reconstructed signals were highly representative of the individual guided modes as well. The validations of this study were analyzed by simulated multimodal signals, with or without noise, and by in vitro experiments. Results of this study suggest that the ridge detection and individual reconstruction method are suitable for separating individual modes from multimodal signals. Such a method can improve the analysis of skeletal guided wave signals by providing accurate assessment of mode-specific ultrasonic parameters, such as group velocity, and indicate different bone quality properties.

Analysis of frequency dependence of ultrasonic backscatter coefficient in cancellous bone

The ultrasonic scattering mechanism in cancellous bone is investigated theoretically and a model describing the frequency dependence of ultrasonic scattering from cancellous bone is presented. The ultrasonic backscatter coefficient (BSC) of bovine tibiae, human calcanei in vitro and in vivo, were measured and discussed. The data of BSC were also fitted by polynomial. The results demonstrate that BSC is a nonlinear function of frequency and increases with frequency. A good agreement was obtained between BSC values from theory and experiment. Also, the high correlation coefficient between BSC and bone mineral density was obtained, r=0.85+/-0.07 (mean+/-SD) (n=15, p<0.001). Based on the values of BSC, the status of cancellous bone and the degree of osteoporotic fracture risk may be assessed.

Analysis of Superimposed Ultrasonic Guided Waves in Long Bones by the Joint Approximate Diagonalization of Eigen-matrices Algorithm

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones.

Analysis of Apparent Integrated Backscatter Coefficient and Backscattered Spectral Centroid Shift in Calcaneus in vivo for the Ultrasonic Evaluation of Osteoporosis

The purposes of our study were to evaluate the correlation among apparent integrated backscatter coefficient (AIB), spectral centroid shift (SCS) of ultrasonic backscatter signals and bone mineral density (BMD) and to examine the effectiveness of ultrasound variables as predictors of osteoporosis. A total of 1011 persons aged 21-80 y old were included. All study participants underwent BMD measurements of the lumbar spine (LSBMD) and the femoral neck (FNBMD). The participants also underwent calcaneal measurements to determine AIB and SCS with central frequencies of 3.5 (one transducer) and 5.0 MHz (the other transducer). AIB decreased with age and was positively correlated with BMD, while SCS increased with age and was negatively correlated with BMD. The correlation coefficient of SCS with LSBMD and FNBMD at 3.5 MHz was -0.72 and -0.70, respectively. The correlation coefficient at 5.0 MHz was -0.75 and -0.74, respectively. The correlation coefficient of AIB with LSBMD and FNBMD at 3.5 MHz was 0.65 and 0.63. The correlation coefficient at 5.0 MHz was 0.59 and 0.55, respectively. The correlation between SCS and BMD was significantly better than the correlation between AIB and BMD. Using receiver operating characteristic analysis, a significant difference was found between the areas under the curve for SCS and AIB at 3.5 MHz (0.781 vs. 0.715, respectively, p < 0.05), as well as at 5.0 MHz (0.782 vs. 0.709, respectively, p < 0.05). The optimum T-score threshold for SCS was -1.3 for both transducers. The sensitivity and specificity of SCS at 3.5 MHz and 5.0 MHz for the optimum threshold were 64%, 85%, 63% and 86%, respectively. In conclusion, the correlations among the ultrasound parameters and BMDs are strong. SCS performs better than AIB in differentiating patients with osteoporosis. Ultrasound variables may be taken into consideration as predictors of osteoporosis in the future considering its portability.

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

The water-saturated aluminum foams with an open network of interconnected ligaments were investigated by ultrasonic transmission technique for the suitability as cancellous bone-mimicking phantoms. The phase velocities and attenuation of nine samples covering three pores per inch (5, 10, and 20 PPI) and three aluminum volume fractions (5, 8, and 12% AVF) were measured over a frequency range of 0.7-1.3 MHz. The ligament thickness and pore sizes of the phantoms and low-density human cancellous bones are similar. A strong slow wave and a weak fast wave are observed for all samples while the latter is not visible without significant amplification (100x). This study reports the characteristics of slow wave, whose speeds are less than the sound speed of the saturating water and decrease mildly with AVF and PPI with an average 1469 m/s. Seven out of nine samples show positive dispersion and the rest show minor negative dispersion. Attenuation increases with AVF, PPI, and frequency except for the 20 PPI samples, which exhibit non-increasing attenuation level with fluctuations due to scattering. The phase velocities agree with Biots porous medium theory. The RMSE is 16.0 m/s (1%) at n = 1.5. Below and above this value, the RMSE decreases mildly and rises sharply, respectively.

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch.

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R=1.00, P<0.0004).

Simplified inverse filter tracking algorithm for estimating the mean trabecular bone spacing

Ultrasonic backscatter signals provide useful information relevant to bone tissue characterization. Trabecular bone microstructures have been considered as quasi-periodic tissues with a collection of regular and diffuse scatterers. This paper investigates the potential of a novel technique using a simplified inverse filter tracking (SIFT) algorithm to estimate mean trabecular bone spacing (MTBS) from ultrasonic backscatter signals. In contrast to other frequency-based methods, the SIFT algorithm is a time-based method and utilizes the amplitude and phase information of backscatter echoes, thus retaining the advantages of both the autocorrelation and the cepstral analysis techniques. The SIFT algorithm was applied to backscatter signals from simulations, phantoms, and bovine trabeculae in vitro. The estimated MTBS results were compared with those of the autoregressive (AR) cepstrum and quadratic transformation (QT) . The SIFT estimates are better than the AR cepstrum estimates and are comparable with the QT values. The study demonstrates that the SIFT algorithm has the potential to be a reliable and robust method for the estimation of MTBS in the presence of a small signal-to-noise ratio, a large spacing variation between regular scatterers, and a large scattering strength ratio of diffuse scatterers to regular ones.

The relationship between ultrasonic backscatter and trabecular anisotropic microstructure in cancellous bone

To investigate the relationship between ultrasonic backscatter and trabecular microstructure, ultrasonic backscatter measurements were performed on cylindrical bovine cancellous bone samples in vitro. The backscatter signals from different specimen angles were obtained by rotating the specimen at various central frequencies. The backscatter signal varied a lot as the specimen angle changed. The main trabecular alignment (MTA) orientation was estimated by the maximum of signal energy and integrated reflection coefficient, or the minor axis of fitted ellipse for apparent integrated backscatter and the backscattered spectrum centroid frequency versus specimen angle. The degree of anisotropy (DA) was estimated by the eccentricity of the fitted ellipse with highly significant correlations. The MTA orientation and DA value estimation method proposed in this study is useful for ultrasonic cancellous bone assessment.