Joseph J. Hoffman

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.

Cancellous bone fast and slow waves obtained with Bayesian probability theory correlate with porosity from computed tomography

A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R(2) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).

MEASUREMENTS OF ULTRASONIC ATTENUATION PROPERTIES OF MIDGESTATIONAL FETAL PIG HEARTS

The objectives of this study were to measure the relative attenuation properties of the left and right ventricles in fetal pig hearts and to compare the spatial variation in attenuation measurements with those observed in previously published backscatter measurements. Approximately 1.0-mm-thick, short-axis slices of excised, formalin-fixed heart were examined from 15 midgestational fetal pigs using a 50-MHz single-element transducer. Measurements of the attenuation properties demonstrate regional differences in the left and right ventricular myocardium that appear consistent with the previously reported regional differences in apparent integrated backscatter measurements of the same fetal pig hearts. For regions of perpendicular insonification relative to the myofiber orientation, the right ventricular free wall showed larger values for the slope of the attenuation coefficient from 30-60 MHz (1.48 +/- 0.22 dB/(cm x MHz) (mean +/- SD) and attenuation coefficient at 45 MHz (46.3 +/- 7.3 dB/cm [mean +/- SD]) than the left ventricular free wall (1.18 +/- 0.24 dB/(cm x MHz) and 37.0 +/- 7.9 dB/cm (mean +/- SD) for slope of attenuation coefficient and attenuation coefficient at 45 MHz, respectively). This attenuation study supports the hypothesis that intrinsic differences in the myocardium of the left and right ventricles exist in fetal pig hearts at midgestation.

Single mode analysis appears to overestimate the attenuation of human calcaneal bone based on Bayesian-derived fast and slow wave mode analysis

Our laboratory in St. Louis previously demonstrated that a signal transmitted through cancellous bone might be comprised of two interfering (fast and slow wave) modes even though it appears to consist of only a single mode. We also showed that a Bayesian probability technique permits separation of ultrasonic fast and slow waves in cancellous bone even when the modes overlap substantially in time. In this study, the effects of interfering fast and slow waves on measurements of the phase velocity and normalized broadband ultrasonic attenuation were addressed. Ultrasonic measurements were taken on 8 human calcaneal samples in vitro at 9 sites each. The data were analyzed two ways: 1) assuming that the received signal contained only a single wave mode and 2) assuming that the received signal contained both fast and slow wave modes. A Bayesian analysis method was implemented to recover the individual properties of the fast and slow waves. For all eight samples, the phase velocity obtained from the one-mode analysis always lay between the fast and slow wave phase velocities. The overall mean ± SD phase velocities at 500 kHz for the eight samples were (1645 ± 68) m/s, (1523 ± 40) m/s, and (1565 ± 52) m/s for the fast, slow, and one mode waves, respectively. normalized broadband ultrasound attenuationFor all samples, the normalized broadband ultrasound attenuation (nBUA) value obtained from the one-mode analysis was consistently larger than the corresponding values from either the fast or slow waves. The overall mean ± SD normalized broadband ultrasound attenuation for the eight samples for the fast, slow, and single mode waves were (5.6 ±4.0) dB/cm/MHz, (4.1 ± 3.0) dB/cm/MHz, and (19.3 ± 8.2) dB/cm/MHz, respectively. Microarchitectural parameters were also measured using microCT. The phase velocities and nBUAs for both the fast and slow waves showed moderate inverse correlations with porosity and trabecular spacing (r = -0.70 to -0.93).

Effective-medium theory of elastic waves in random networks of rods.

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.

Characterization of the fast wave in cancellous bone using the Bayesian probability theory approach

Bayesian probability approach with a simple model was introduced for the analysis of two wave propagation phenomenon in the cancellous bone. The fast and slow waves could be estimated from the experimentally observed wave. The reproduced wave made by these estimated fast and slow waves was compared with the initial experimental wave using a wavelet technique. The high frequency component of the reproduced wave corresponded to the slow wave and showed similar temporal-frequency characteristics of the experimental wave. The low frequency component of the reproduced wave, however, showed a small difference from the experimental wave. Although the model used in this study was very simple and still incomplete, the estimation of two waves was relatively good. Introduction of more appropriate model will bring us better estimation of the two wave propagation.

Bayesian-derived fast and slow waves correlate with porosity obtained from microCT

It has previously been shown by our laboratory that Bayesian probability theory permits separation of ultrasonic fast and slow waves in cancellous bone even when the modes overlap substantially in time. The goal of the current study was to determine whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity. The Bayesian technique was applied to data from cancellous bone samples from 8 human heels insonified with a broadband 500 kHz ultrasound pulse in the medial/lateral direction. The phase velocity (SOS), slope of attenuation (nBUA), and relative amplitude were determined for both the fast and slow waves. The porosity of the samples was measured by X-ray microCT. The phase velocity and slope of attenuation for both the fast and slow wave modes showed an inverse correlation with porosity. The fast wave amplitude decreased with increasing porosity. Conversely, the slow wave amplitude increased with increasing porosity. These r...

Direct comparison of single mode versus fast and slow wave modes analyses of calcaneal bone data

Background: We previously demonstrated that a signal transmitted through cancellous bone might be comprised of two interfering (fast and slow wave) modes even though it appears to consist of only a single mode. Objective: The goal of this study was to compare the results of single mode analysis and two mode analysis to quantify the effects of interfering waves on the measured speed of sound (SOS) and broadband ultrasound attenuation (BUA). Methods: A series of human calcaneal samples (bone volume fractions = 0.09 to 0.21) were measured medial-laterally using 500kHz broadband focused transducers. Phase velocity was determined by phase spectroscopy and attenuation was determined by log-spectral subtraction. The original radiofrequency signal and the Bayesian-separated fast and slow wave radiofrequency signals were analyzed. Results: For each of the specimens, the slope of attenuation determined by single mode analysis was larger than that for either the fast or slow wave, and the speed of sound determined b...

Determining the attenuation of overlapping fast and slow waves in cancellous bone using Bayesian techniques

The effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels farther into the sample. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance.

Development of myocardial tissue-mimicking phantoms exhibiting a range of lipid concentrations comparable to that observed in obese subjects

Studies have demonstrated an increased myocardial lipid accumulation in obese subjects and suggest that this may contribute to the pathogenesis of heart failure. Development of echocardiographic-based methods to assess the level of myocardial lipid content may provide a useful tool for the clinical management of these patients. The goal of this study was to develop a series of myocardial tissue-mimicking phantoms exhibiting a range of oil concentrations comparable to the lipid levels reported in the hearts of obese subjects and determine if these levels can be differentiated using ultrasonic measurements over a clinically-relevant frequency range. A series of gelatin-based ultrasonic tissue-mimicking phantoms was constructed containing 0% (n=8), 0.5% (n=5), 1% (n=5), 2% (n=5), and 4% (n=6) suspensions of olive oil by volume. Ultrasonic measurements of the speed of sound, frequency dependence of the attenuation coefficient, apparent integrated backscatter, and the magnitude and frequency dependence of the backscatter coefficient were performed at room temperature on the phantoms over a bandwidth ranging from 3 to 9 MHz. Results of this study suggest that the increased lipid levels observed in the hearts of obese subjects may produce corresponding increases in measured ultrasonic backscatter levels over the clinically-relevant 3 to 4 MHz frequency range. Hence, development of echocardiographic-based methods to assess myocardial lipid content and its change with therapeutic intervention may be feasible.