Attenuation Coefficient Slope Research Articles

The effect of windowing on spectral estimation of echoes scattered by a random medium

In executing spectral analysis of echoes scattered by a random medium, a window is generally applied to an echo signal. Spatial resolving power to characterize the random medium is improved by shortening the window length. But it is difficult to shorten the window length arbitrarily since, in the conventional method, the shorter the window length, the more severely the spectrum is distorted. This article shows that the spectrum distorted by the window can be expressed as a convolution of the spectrum of echoes that would be obtained from a spatially truncated thin layer of the random medium with the spectrum of the window function. Consequently, it can be corrected by a deconvolution operation, and by the fact that the spectral estimation over a wide frequency range can be carried out even using a window of shorter length. The effects of the deconvolution are first demonstrated by computer simulation where a random signal is used as the echo signal. The effects can be seen more clearly in the measurement of attenuation coefficient slope obtained by the ratio of two spectra that are subjected to different attenuation. Finally, the applicability of this method is shown by the experiments where the attenuation coefficient slope of an agar block is measured using the window of various lengths.

Influence of pathological state on the acoustic attenuation coefficient slope of liver

The acoustic attenuation coefficient slope (beta) of liver was estimated in vivo from the spectral difference of returned echoes. beta of normal young subjects was lower than that of older subjects (mean: 0.340 vs 0.418 dB/cm.MHz). Limited fluid withdrawal from the body by haemodialysis did not affect beta. In alcoholic liver disease beta was related to the amount of fat and of fibrous tissue in liver biopsy specimens. High values of beta were observed as soon as the degree of steatosis exceeded 5 vol%. There was a similar increase of beta in the presence of fibrous interlobular septa. In normal liver beta was related to the amount of triglycerides in the liver specimen.

Estimating Reflected Ultrasound Spectra from Quantized Signals

Quantization errors are inevitably introduced whenever analog-to-digital conversion of data is employed. The effect of these errors on estimating power spectra from ultrasound signals reflected from within the body is examined. Reflected data were simulated by convolving a pulse sequence with a filter model of the random reflectors encountered within the liver. The data were then quantized with an N-bit quantizer model, with 1 N 8, multiplied by a Hamming data window and used to estimate the power spectrum. For typical diagnostic signals reflected from 1 cm of tissue, the results indicate that the quantization errors limit the frequency range over which unbiased estimates of the spectra are observed for N 8. For N 8, the sidelobes in the Hamming window spectrum limit this range. To illustrate the implication of these results, the problem of estimating the slope of the acoustic attenuation coefficient, denoted by s, for liver tissue from reflected ultrasound signals is examined. Three sestimators are considered: 1) a new correlation method, 2) a zero-crossing count analysis, and 3) the slope of the log-spectral difference. The simulated results indicate under which conditions a particular sestimator should be employed.

Diffraction effects in reflected ultrasound spectral estimates.

This paper explores the effect of diffraction on estimates of the spectra of signals reflected from interfaces located at a given range from the transducer. When an ultrasound pulse is transmitted into a medium, the power spectra of reflected signals vary as a function of range from the transducer. These spectral changes are caused by diffraction effects, due to the finite-sized aperture, and by the properties of the medium. When the properties of the medium are to be determined from the backscattered signals, the diffraction effects tend to mask these properties, especially in the near field. Estimates of the diffraction effects are determined by accurately estimating the reflected signal spectra at a set of ranges from the transducer. The observed signals are reflections from media that are composed of randomly distributed scatterers and have a linear-with-frequency attenuation. The two random media considered are the in vivo liver and a tissue-equivalent phantom. The results indicate that the diffraction effects produce a high-frequency enhancement in the reflected spectra which diminishes with range. Similar results are observed for the reflections from plane and randomly roughened surfaces located at the same ranges. Simulated results using a transducer model verify the plane surface results. The effect of diffraction is examined in the clinical problem of estimating the slope of the acoustic attenuation coefficient of the in vivo liver. Diffraction introduces a bias into the observed slope estimate. The bias is a function of the range interval over which the reflected data are acquired.

Estimation of the slope of the acoustic attenuation coefficient

In this paper, a theoretical framework is developed which removes the Gaussian assumption commonly used in ultrasonic attenuation estimation based on mean frequency shift. The theory is developed for general non-Gaussian spectra and for media whose attenuation coefficient is nonlinear with frequency. Then, a linear approximation in the estimation of the attenuation coefficient's slope is examined. It is shown that the error due to the linear approximation is negligibly small.

Estimation of the slope of the acoustic attenuation coefficient.

In this paper, a theoretical framework is developed which removes the Gaussian assumption commonly used in ultrasonic attenuation estimation based on mean frequency shift. The theory is developed for general non-Gaussian spectra and for media whose attenuation coefficient is nonlinear with frequency. Then, a linear approximation in the estimation of the attenuation coefficient's slope is examined. It is shown that the error due to the linear approximation is negligibly small.

Estimation of ultrasonic attenuation and mean backscatterer size via digital signal processing.

The backscattered rf signals from the lungs of fetal sheep during their last trimester of development were digitized and processed in an attempt to correlate ultrasonic parameters with measured functional parameters related to lung maturation. The broadband, post- TGC , rf signal of a commercial B-mode ultrasonic scanner was digitized at a sampling rate of 25 MHz. Sorting excluded data from regions of rib shadowing and other nonlung structures from analysis. The sorted data were used to estimate the slope of the ultrasonic attenuation coefficient with respect to frequency via linear regression on the average difference of the logarithm of power spectra from separated data segments. The power spectra were also corrected for attenuation, averaged and used to compute the power cepstrum of the backscattered signal which can be related to mean backscatterer radius. Results are presented for eight fetal sheep.

Estimation of ultrasonic attenuation and mean backscatterer size via digital signal processing

The backscattered rf signals from the lungs of fetal sheep during their last trimester of development were digitized and processed in an attempt to correlate ultrasonic parameters with measured functional parameters related to lung maturation. The broad-band, post-TGC, rf signal of a commercial B-mode ultrasonic scanner was digitized at a sampling rate of 25 MHz. Sorting excluded data from regions of rib shadowing and other nonlung structures from analysis. The sorted data were used to estimate the slope of the ultrasonic attenuation coefficient with respect to frequency via linear regression on the average difference of the logarithm of power spectra from separated data segments. The power spectra were also corrected for attenuation, averaged and used to compute the power cepstrum of the backscattered signal which can be related to mean backscatterer radius. Results are presented for eight fetal sheep.

Processing of diagnostic ultrasound signals

Ultrasound signals reflected from the human liver contain significant information about its condition. Several techniques have been developed to process such signals. In this paper, two approaches are described for estimating the slope of the acoustic attenuation coefficient, denoted by β, which provides important cues about the condition of diffuse liver disease. The first is a nonparametric approach which determines the β value from the slope of log periodogram differences. The second is a parametric approach which requires a Gaussian-shaped spectrum and determines the β value from s shift in the spectral center-frequency. A zero-crossing count procedure allows the parametric approach to be implemented with minimal hardware and in real-time. Simulated and actual signals illustrate the two approaches.

A beam corrected estimation of the frequency dependent attenuation of biological tissues from backscattered ultrasound

A practical and highly accurate method of estimation of the frequency-dependent slope of the acoustic attenuation coefficient, α 1, using backscattered ultrasound energy is presented. The influence of the focused ultrasound beam is experimentally measured and a simple method for incorporating the field effects in the estimate of α 1 is described. The accuracy of the estimate of α 1 in vitro which appears to be of the order of 10 percent, demonstrates the feasibility of in vivo applications of the technique.

A beam corrected estimation of the frequency dependent attenuation of biological tissues from backscattered ultrasound.

A practical and highly accurate method of estimation of the frequency-dependent slope of the acoustic attenuation coefficient, alpha 1, using backscattered ultrasound energy is presented. The influence of the focused ultrasound beam is experimentally measured and a simple method for incorporating the field effects in the estimate of alpha 1 is described. The accuracy of the estimate of alpha 1 in vitro which appears to be of the order of 10 percent, demonstrates the feasibility of in vivo applications of the technique.

Comparison of spectral-shift and spectral-difference methods for estimating acoustic attenuation coefficient slopes: Roman Kuc, Departments of Electrical Engineering and Diagnostic Radiology, Yale University, New Haven, CT 06520

Comparison of spectral-shift and spectral-difference methods for estimating acoustic attenuation coefficient slopes: Roman Kuc, Departments of Electrical Engineering and Diagnostic Radiology, Yale University, New Haven, CT 06520

Variation of acoustic attenuation coefficient slope estimates for in vivo liver.

Characterization of diffuse alcoholic disease is being attempted by estimating the slope of the acoustic attenuation coefficient with frequency, a parameter denoted by beta, from reflected ultrasound signals. The ultrasound signals reflected from within the body are distorted by the non-ideal properties of tissues. Two distorting mechanisms are considered: the propagation through nonhomogeneous media and the reflection from irregularly shaped interfaces. The mechanisms are modeled as random filters and their effect on estimating the value of beta are considered. The variances of three beta estimators are derived from the model. Clinical results on normals and patients with alcoholic liver disease are presented to verify the model.

Oil-in-gelatin dispersions for use as ultrasonically tissue-mimicking materials.

A form of tissue-mimicking material is reported in which oil droplets are dispersed in a water-based gelatin. Broad ranges of ultrasonic parameters, including speed of sound, attenuation coefficient, density and backscatter level, exist for this material. Very important, the attenuation coefficients are nearly proportional to the frequency as in the case of mammalian tissue and the available attenuation coefficient slopes span the range of mammalian tissues. The available range of slopes is 0.1 dB/cm/MHz through at least 2.0 dB/cm/MHz. The available speeds of sound range from a minimum below that of mammalian fat (approximately 1460 m/s) to a maximum above the accepted average for human tissue (154o m/s). Densities available range from below that of fat (approximately 0.92 gm/cm3) through about 1.00 gm/cm3. Backscatter levels are easily made negligible compared to clinical levels and compared to those exhibited in previously reported tissue-mimicking materials in which the suspended particles are solid (Madsen et al. 1978; Burlew et al., 1980). Addition of solid or hollow glass scatterers allows backscatter levels to be made comparable to those clinically observed.