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.

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.

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.

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.

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.