Fred Lizzi's statistical framework and the interpretation of ultrasound backscatter from bone.
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Bone and Bones↗
Biomedical subjects
Keith A Wear
Publications and source records attributed to Keith A Wear.
Comparison of measurements of phase velocity in human calcaneus to Biot theory.
Biot's theory for elastic propagation in porous media has previously been shown to be useful for modeling the dependence of phase velocity on porosity in bovine cancellous bone in vitro. In the present study, Biot's theory is applied to measurements of porosity-dependent phase velocity in 53 human calcanea in vitro. Porosity was measured using microcomputed tomography for some samples (n = 23) and estimated based on bone mineral densitometry for the remaining samples (n = 30). The phase velocity at 500 kHz was measured in a water tank using a through-transmission technique. Biot's theory performed well for the prediction of the dependence of sound speed on porosity. The trend was quasilinear, but both the theory and experiment show similar slight curvature. The root mean square error (RMSE) of predicted versus measured sound speed was 15.8 m/s.
Biomechanical Phenomena↗
The dependencies of phase velocity and dispersion on trabecular thickness and spacing in trabecular bone-mimicking phantoms.
Frequency-dependent phase velocity was measured in trabecular-bone-mimicking phantoms consisting of two-dimensional arrays of parallel nylon wires (simulating trabeculae) with thicknesses ranging from 152 to 305 microm and spacings ranging from 700 to 1000 microm. Phase velocity varied approximately linearly with frequency over the range from 400 to 750 kHz. Dispersion was characterized by the slope of a linear least-squares regression fit to phase velocity versus frequency data. The increase in phase velocity (compared with that in water) at 500 kHz was approximately proportional to the (1) square of trabecular thickness, (2) inverse square of trabecular spacing, and (3) volume fraction occupied by nylon wires. The first derivative of phase velocity with respect to frequency was negative and exhibited nonlinear, monotonically decreasing dependencies on trabecular thickness and volume fraction. The dependencies of phase velocity and its first derivative on volume fraction in the phantoms were consistent with those reported in trabecular bone.
Algorithms↗
Interlaboratory comparison of ultrasonic backscatter coefficient measurements from 2 to 9 MHz.
OBJECTIVE: As are the attenuation coefficient and sound speed, the backscatter coefficient is a fundamental ultrasonic property that has been used to characterize many tissues. Unfortunately, there is currently far less standardization for the ultrasonic backscatter measurement than for the other two, as evidenced by a previous American Institute of Ultrasound in Medicine (AIUM)-sponsored interlaboratory comparison of ultrasonic backscatter, attenuation, and speed measurements (J Ultrasound Med 1999; 18:615-631). To explore reasons for these disparities, the AIUM Endowment for Education and Research recently supported this second interlaboratory comparison, which extends the upper limit of the frequency range from 7 to 9 MHz. METHODS: Eleven laboratories were provided with standard test objects designed and manufactured at the University of Wisconsin (Madison, WI). Each laboratory was asked to perform ultrasonic measurements of sound speed, attenuation coefficients, and backscatter coefficients. Each laboratory was blinded to the values of the ultrasonic properties of the test objects at the time the measurements were performed. RESULTS: Eight of the 11 laboratories submitted results. The range of variation of absolute magnitude of backscatter coefficient measurements was about 2 orders of magnitude. If the results of 1 outlier laboratory are excluded, then the range is reduced to about 1 order of magnitude. Agreement regarding frequency dependence of backscatter was better than reported in the previous interlaboratory comparison. For example, when scatterers were small compared with the ultrasonic wavelength, experimental frequency-dependent backscatter coefficient data obtained by the participating laboratories were usually consistent with the expected Rayleigh scattering behavior (proportional to frequency to the fourth power). CONCLUSIONS: Greater standardization of backscatter measurement methods is needed. Measurements of frequency dependence of backscatter are more consistent than measurements of absolute magnitude.
1-Propanol↗
Measurement of dependence of backscatter coefficient from cylinders on frequency and diameter using focused transducers--with applications in trabecular bone.
A theory for the elastic scattering response from a cylinder insonified by a plane wave was previously derived by Faran. In the present paper, the empirical relationship between Faran's theory and measurements of backscatter coefficient from cylindrical targets using focused transducers is investigated. Experimental measurements of dependence of backscatter coefficient on frequency and diameter for nylon wires are reported. It is found that, under certain conditions (including weak, incoherent scattering), backscatter coefficient measurements from collections of cylindrical scatterers may be meaningfully compared with Faran's model predictions. At low frequencies, the theory and experimental measurements exhibit similar dependences on frequency and diameter, provided that the scatterers are not too densely packed. At higher frequencies, the fine structure of Faran's predictions becomes difficult to reproduce experimentally with a focused transducer. Implications regarding applications to characterization of trabecular bone are discussed.
Bone and Bones↗
Characterization of trabecular bone using the backscattered spectral centroid shift.
Ultrasonic attenuation in bone in vivo is generally measured using a through-transmission method at the calcaneus. Although attenuation in calcaneus has been demonstrated to be a useful predictor for osteoporotic fracture risk, measurements at other clinically important sites, such as hip and spine, could potentially contain additional useful diagnostic information. Through-transmission measurements may not be feasible at these sites due to complex bone shapes and the increased amount of intervening soft tissue. Centroid shift from the backscattered signal is an index of attenuation slope and has been used previously to characterize soft tissues. In this paper, centroid shift from signals backscattered from 30 trabecular bone samples in vitro were measured. Attenuation slope also was measured using a through-transmission method. The correlation coefficient between centroid shift and attenuation slope was -0.71. The 95% confidence interval was (-0.86, -0.47). These results suggest that the backscattered spectral centroid shift may contain useful diagnostic information potentially applicable to hip and spine.
Algorithms↗
Autocorrelation and cepstral methods for measurement of tibial cortical thickness.
Cortical thickness of the tibia is related to stress fracture risk and overall skeletal status. Two methods are proposed for estimating tibial cortical thickness based on power spectra of ultrasonic echoes containing reflections from front and back surfaces of the cortex. The locations of the peaks in the autocorrelation function and the cepstrum are related to cortical thickness. Data were acquired on plastic plates in order to validate the methodology. These data indicate high correlations between estimated and true thickness with correlation coefficients r = 0.99, (95% confidence interval: 0.993-1.00) for the autocorrelation method and r = 0.99 (95% CI: 0.996-1.00) for the cepstral method. Data on six tibia samples in vitro indicate correlation coefficients of r = 0.92 (95% CI: 0.72-1.00) for the autocorrelation method and r = 0.85 (95% CI: 0.62-0.94) for the cepstral method. Estimates of precisions of the two methods were 0.3 +/- 0.1 mm (autocorrelation method) and 0.5 +/- 0.2 mm (cepstral method). One measurement in a human volunteer in vivo demonstrated clinical feasibility of the measurement and good agreement with cortical thickness assessed using peripheral quantitative computed tomography (QCT). This technology offers the promise of an inexpensive, fast, portable, simple, nonionizing technique for assessing skeletal status.
Algorithms↗
The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results.
Trabecular thickness within cancellous bone is an important determinant of osteoporotic fracture risk. Noninvasive assessment of trabecular thickness potentially could yield useful diagnostic information. Faran's theory of elastic scattering from a cylindrical object immersed in a fluid has been used to predict the dependence of ultrasonic backscatter on trabecular thickness. The theory predicts that, in the range of morphological and material properties expected for trabecular bone, the backscatter coefficient at 500 kHz should be approximately proportional to trabecular thickness to the power of 2.9. Experimental measurements of backscatter coefficient were performed on 43 human calcaneus samples in vitro. Mean trabecular thicknesses on the 43 samples were assessed using micro computed tomography (CT). A power law fit to the data showed that the backscatter coefficient empirically varied as trabecular thickness to the 2.8 power. The 95% confidence interval for this exponent was 1.7 to 3.9. The square of the correlation coefficient for the linear regression to the log transformed data was 0.40. This suggests that 40% of variations in backscatter may be attributed to variations in trabecular thickness. These results reinforce previous studies that offered validation for the Faran cylinder model for prediction of scattering properties of cancellous bone, and provide added evidence for the potential diagnostic utility of the backscatter measurement.
Calcaneus↗
The effect of trabecular material properties on the frequency dependence of backscatter from cancellous bone.
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Acoustics↗
A Gaussian framework for modeling effects of frequency-dependent attenuation, frequency-dependent scattering, and gating.
For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.
Agar↗