The measurement of backscatter coefficient from a broadband pulse-echo system: a new formulation.

A new formulation for obtaining the absolute backscatter coefficient from pulse-echo measurements is presented. Using this formulation, performing the diffraction correction and system calibration is straightforward. The diffraction correction function for the measurement of backscatter coefficient and the acoustic coupling function for a pulse-echo system are defined. Details of these functions for two very useful cases are presented: a flat disk transducer and a spherically focused transducer. Approximations of these functions are also provided. For a flat disk transducer, the final formulation appears as a modification to the established Sigelmann-Reid formulation. For a focused transducer, the final correction is a weak function of frequency when the scattering volume is near the focal area, rather than the frequency squared dependence proposed by earlier investigators.

Volumetric arterial flow quantification using echo contrast. An in vitro comparison of three ultrasonic intensity methods: radio frequency, video and Doppler.

The two hypotheses presented in this paper are: (1) absolute and relative volumetric flow rates in vessels can be measured by echo contrast time-intensity curves; and (2) echo contrast time-intensity curves generated by different ultrasound backscatter intensity techniques have equivalent capability for flow measurements. A nonpulsatile flow system was built for quantitative ultrasound backscatter measurements from bolus echo contrast injections using two different volumes of mixing. A total of 49 echo contrast bolus injections were made at various flow rates (0.44-2.59 L/min). Ultrasound backscatter time-intensity curves were generated by ultrasound radio frequency, video and Doppler techniques. The rate of backscattered ultrasound intensity washout for each technique (WASHOUT RATE), and relative change in WASHOUT RATE (delta WASHOUT RATE) were compared to the volumetric flow rate (FLOW) and changes in flow rate (delta FLOW), respectively. The relationship between WASHOUT RATE, FLOW and the volume of contrast mixing was studied. A linear relationship was demonstrated between WASHOUT RATE and delta WASHOUT RATE and the corresponding FLOW and delta FLOW by all three methods (r > 0.90 for all comparisons). The WASHOUT RATE was found to depend on the FLOW and the volume of contrast mixing, but the delta WASHOUT RATE was equal to the delta FLOW and independent of the volume of mixing. Time-intensity curves can be generated from different ultrasound backscatter intensity techniques and the WASHOUT RATE correlates well with FLOW. delta FLOW can be determined directly from the corresponding delta WASHOUT RATE. Doppler ultrasound, because of its natural association with the assessment of flow in chambers and vessels, is uniquely suited to assessment of arterial volumetric blood flow in vitro.

Statistics of the physiologic phase of integrated backscatter from canine myocardium with normal and reduced coronary circulation.

The phase, relative to the arterial pressure, of cyclically varying integrated backscatter from canine myocardium was measured at normal and reduced coronary blood flow levels and was found to become more randomized with decreasing flow. The phase, modeled as a von Mises distribution on a unit circle which is very similar to the normal distribution on the line, is characterized by a mean (mu 0) and a concentration or width parameter (kappa). kappa is used to characterize the degree of randomization. The von Mises distribution provides an excellent fit to measured data (p less than 0.01). Hypothesis tests performed on the data for various coronary flow levels indicate that the phase distribution for normal coronary flow level is significantly different from the distributions at other flow levels (p less than 0.05). The results suggest that the parameter kappa may be used for differentiating normal and ischemic myocardium.

Anisotropy of the ultrasonic attenuation in soft tissues: measurements in vitro.

This study was designed to measure the ultrasonic attenuation within phantoms and tissue samples over a broad bandwidth and at many angles of incidence with respect to intrinsic orientations in order to elucidate both the frequency and angular dependence of the attenuation coefficient. Significant angular dependence, or anisotropy, of the attenuation was observed in canine myocardium (maximum to minimum ratio: 2.2 to 1) and a tissue mimicking phantom of oriented graphite fibers in gelatin (max to min: 2 to 1). In control studies, insignificant anisotropy was observed in the attenuation in canine liver samples and phantoms with graphite powder suspended in gelatin. Comparisons of the magnitude of variations of the oriented-fiber phantom to that predicted by a viscous relative motion model are presented.

Sampling frequency of the electrocardiogram for spectral analysis of the heart rate variability.

The R-R interval measurement from digitized electrocardiograms (ECG) contains an error due to the finite sampling frequency which may jeopardize the beat-to-beat analysis of the heart rate. In this paper, we develop a model to describe and quantitate this error. The "measured" R-R interval is modeled as the sum of the "true" R-R interval and of the error of measurement. The first and second order statistics of the error are computed in order to investigate its influence on the heart rate variability (HRV) power spectrum. They are found to be only functions of the ECG sampling frequency and, in particular, the power spectrum of the error contributes an additive high-pass filter-like term (colored noise) to the power spectrum of the HRV. The accuracy of the model is tested via a simulation procedure. The model indicates that the relative balance between the HRV and the error power spectra is important and should be checked before any variability analysis on the heart rate. This balance may be favorable to the error when 1) the sampling frequency of the ECG is too low, and/or 2) the variability of the heart rate is too little. In these cases, the HRV spectrum analysis may not give reliable results. Two tests are proposed in order to evaluate the error influence either in specific frequency bands or in the total frequency range.

Anisotropy of the ultrasonic backscatter of myocardial tissue: I. Theory and measurements in vitro.

This research addresses the variations in the ultrasonic backscatter from specimens consisting of a suspension of approximately aligned cylindrical scatterers in a fluid medium as a function of the angle of propagation in the sample. Predictions of the angular dependence of backscatter based on the time-domain Born approximation described by Rose and Richardson [J. H. Rose and J. M. Richardson, J. Nondestr. Eval. 3, 45-53 (1982)] were compared with experimental measurements of the backscatter from both tissue-mimicking phantoms consisting of graphite fibers suspended in gelatin and from canine myocardial tissue. The angular dependence of the backscatter was predicted and measured to be maximum for propagation perpendicular to the cylinder axes and minimum for propagation parallel to the axes. Maximum to minimum (i.e., perpendicular to parallel) changes in the integrated backscatter were predicted to be between 5 and 10 dB in the phantom. The corresponding quantity measured in both the phantom and in canine myocardial tissue was approximately 6 dB.

Anisotropy of the ultrasonic backscatter of myocardial tissue: II. Measurements in vivo.

The purpose of this investigation was to determine the angular dependence of the backscatter from canine myocardial tissue in vivo and to compare it with the variation of backscatter over the cardiac cycle that has been recognized and reported previously. The backscatter was measured from regions of left ventricular wall in canine hearts in which the fibers of the muscle lay parallel to the surface of the heart and were oriented predominantly in a circumferential fashion. Because of technical considerations, the angle of insonification was varied systematically through two cycles in which the angle relative to the muscle fiber axes ranged from 60 degrees-120 degrees. Backscatter was maximum at angles of interrogation perpendicular to the myocardial fibers and minimum at those most acute (60 degrees) relative to the orientation of the fibers. The previously observed variation of integrated backscatter over the heart cycle was evident at each angle of interrogation. At end systole, the average maximum-to-minimum angular variation of integrated backscatter as 5.0 +/- 0.4 dB. At end diastole, the average maximum-to-minimum angular variation was 3.2 +/- 0.4 dB. Thus, even though angular dependence of the backscatter from tissues with directionally oriented structures is substantial, the anisotropy does not account for cardiac-cycle-dependent variation of backscatter. Accordingly, the angular dependence should be incorporated in approaches to quantitative tissue characterization with ultrasound.

Changes in ultrasonic attenuation and backscatter of muscle with state of contraction.

We have previously demonstrated that backscatter (uncompensated for attenuation) of canine myocardium varies systematically throughout the cardiac cycle and in relation to regional contractile performance. To elucidate these phenomena under conditions independent of blood flow and complex myofibrillar architecture, we measured attenuation with a phase-insensitive receiver and backscatter over a wide range of frequencies in an intermittently tetanized (10 stimulations), isolated frog gastrocnemius preparation (n = 12 muscles). Muscle contraction, as compared with relaxation, was associated with increased values of slope of attenuation (0.78 +/- 0.04 vs 0.58 +/- 0.03 dB/(cm MHz); p less than 0.001) and increased values of integrated backscatter (-29.5 +/- 0.9 vs -35.5 +/- 0.8 dB; p less than 0.005). Differences in attenuation and backscatter diminished with the number of muscle stimulations (as the muscle fatigued). Thus, quantitative ultrasonic indices of skeletal muscle vary systematically with the contractile performance of the tissue. Extrapolation of these results to cardiac muscle suggests that the sensitivity of these indices to contractile function of muscle may provide an approach for noninvasive assessment of intrinsic properties of myocardium that determines its performance.

Effects of coronary artery occlusion and reperfusion on cardiac cycle-dependent variation of myocardial ultrasonic backscatter.

We have recently reported a systematic variation in integrated ultrasonic backscatter throughout the cardiac cycle in canine hearts. This study was performed to determine whether the pattern of such variation is modified systematically by ischemia. Measurements of integrated ultrasonic backscatter in selected regions of normal, ischemic, and reperfused hearts were compared in view of known differences in systolic function of myocardium in each of these regions. Integrated ultrasonic backscatter (3-7 MHz) gated to the first derivative of left ventricular pressure was measured at the apex, midwall, and base in 10 dogs and at the apex before and during transient ischemia and reperfusion in four dogs. Quantitative integrated ultrasonic backscatter was referenced to a steel reflector. Cyclic variation of integrated ultrasonic backscatter was greatest at the apex [peak to trough variation 5.5 +/- 0.9 dB (mean +/- SE)] with the maximum near end diastole (-52.9 +/- 0.9 dB) and minimum near end systole (-58.4 +/- 1.0 dB). Variation at the apex (5.5 +/- 0.9 dB) and the midwall (4.3 +/- 0.8 dB) was greater than at the base (0.5 +/- 1.0 dB) (P less than 0.01 for either region compared with base). Left anterior descending coronary occlusion for 10 minutes in four of 10 dogs reduced variation at the apex to 0.4 +/- 1.5 dB (P less than 0.02 compared with preocclusion). Reperfusion for 2 hours restored apical cyclic variation to 3.9 +/- 1.7 dB, i.e., to values not significantly different from those before occlusion.(ABSTRACT TRUNCATED AT 250 WORDS)

Regional differences in the cyclic variation of myocardial backscatter that parallel regional differences in contractile performance.

Previous reports from our laboratory indicate that ultrasonic backscatter from myocardium exhibits a cyclic variation during the cardiac cycle that is reduced sharply by ischemia, a process which impairs both systolic contraction and diastolic relaxation. These results suggest that the cyclic variation of backscatter may be related to the cyclic variation of the contractile performance of the myocardium. Because contractile performance of the left ventricle is known to exhibit regional variability, the present study was undertaken to determine whether such regional differences in contractile performance are paralleled by differences in the magnitude of the cyclic variation of ultrasonic backscatter. Measurements obtained from representative zones of three regions of the hearts of ten open-chest dogs indicate that the magnitude of the cyclic pattern of variation of backscatter parallels the regional differences in contractile performance throughout the left ventricle with the maximum variation (5.5 +/- 0.9 dB peak-to-peak amplitude) occurring at the apex, intermediate values (4.3 +/- 0.8 dB) at the midwall, and minimum (0.5 +/- 1.0 dB) at the base. These results suggest that the ultrasonic backscatter may be sensitive to the regional myocardial contractile performance.