An ultrasonic pulse was generated with a Panametrics 5800 Pulser/Receiver operating in pitch/catch mode and sent to the transmit transducer. The through-transmitted signal was received by the receive transducer, amplified by the Panametrics 5800, and digitized with a Tektronix 2430A (Tektronix, Beaverton, OR) oscilloscope. The pulser/receiver settings were optimized to provide sufficient dynamic range over the usable bandwidth of the measurement system for all angles of insonification relative to the predominant fiber orientation.

The velocity of sound in the specimen (V_specimen) at angle, θ , is obtained by Eq. (1):

Myocardial specimen thickness can be measured by first determining the distance between the transducers using the known speed of sound in water and the measured time-of-flight of an ultrasonic pulse transmitted through water (without the myocardial specimen). Then with the myocardial specimen inserted, for each angle of rotation, the part of the total path length occupied by water is determined by making time-of-flight measurements of the reflected ultrasound from the transmitting transducer to the front wall and separately from the receiving transducer to the back wall of the tissue. This approach overcomes a difficulty described in previous studies from this laboratory in making time-of-flight measurements of the back wall from pulse/echo through the attenuating specimen in which “attenuation of the signal caused a weakened back wall echo to be returned, thereby making it difficult to distinguish the specular echo surface phenomenon from the backscatter in bulk” (Verdonk et al., 1992). By subtracting the part of the total path length occupied by water from the distance between the two transducers, the thickness of the specimen could then be determined at each angle of rotation. As described, this technique would require separate pulse/echo measurements at each angle of rotation for both the front wall and the back wall of the myocardial specimen. Because measurements can be time-sensitive, the following technique was used, in practice, to eliminate the need for two sets of pulse/echo measurements: Timing mark measurements for front and back wall echoes were made relative to a reference (the cylindrical plastic coupling of known thickness into which the plastic mount of the myocardial specimen was fit). The thickness of the specimen at angle θ then equals the thickness of the reference minus the difference between the front walls of the reference and the specimen at angle θ , minus the difference between the front walls of the reference and specimen at angle θ + 180°. By this relative approach, any slight precession in the measurement assembly would be intrinsically compensated because it would presumably act on both the plastic coupling and the myocardial specimen.

For calculations of the thickness of myocardial specimens using this technique, we used a 31 mm diameter plastic (Delrin) coupling as a reference as shown in Fig. 1. The difference in arrival times between the signal reflected back from the plastic coupling reference and that reflected back from the tissue specimen, (Δ t_{front wall} (θ)), was calculated for each angle of rotation for the front wall. Measurements of the time differences were repeated upon rotation by 180° which corresponds to measurements of the time differences for the back wall at angle θ (Δ t_{back wall} (θ)). Myocardial specimen thickness as a function of angle of rotation, L_specimen (θ), was then calculated by

in which V_water is the speed of sound in water, and L_reference (θ) is the known thickness of the plastic coupling reference which was measured ultrasonically.

Previous measurements from this laboratory on formalin-fixed human myocardial tissue (at 5 MHz and 18.1° ± 1.2°C) demonstrated a clear anisotropy of ultrasonic velocity with maxima for insonification parallel to the predominant direction of myofibers and minima for perpendicular insonification (Verdonk et al., 1992). As described in the Appendix, when these data were reanalyzed using the approach of the current study in order to minimize the error in measurement introduced by specimen attenuation on timing mark determination, identical magnitudes of the anisotropy of velocity were determined between the formalin-fixed human myocardium of that study and the formalin-fixed ovine myocardium of the present study. Overall values of ultrasonic velocity for that study were lower than results for the current study and other studies as seen in Table I. We have observed a decrease in the measured speed of sound in formalin-fixed myocardial tissue as a function of time in the water bath before measurements are made. This decrease appears to be on the order of 10 m/s after approximately 3 hours and 20 m/s after approximately 15 hours. Measurements in the current study were made within 5 to 10 minutes of immersion in the water bath. However, if specimens were left in the water for long amounts of time prior to measurement, this may partially explain the lower overall values of velocity in the previous study. In addition, it should be noted that the formalin-fixed human myocardial measurements were performed on seven tissue specimens from six explanted human hearts obtained from patients who had undergone heart transplantation for ischemic cardiomyopathy. “Grossly normal myocardial segments, distant from regions of infarction, were selected for investigation” (Verdonk et al., 1992). A detailed comparison of the results obtained from the seriously compromised hearts of that study with the results of the present study may not be appropriate.

This work was supported, in part, by NIH R37 HL40302. The authors gratefully acknowledge Star Packing Company, St. Louis, MO for providing ovine and bovine myocardial tissues. These investigations benefited substantially from the very careful studies conducted by Edward Verdonk when he was a member of this Laboratory.

Previous work from this laboratory has employed a timing mark detection algorithm which searched for a fixed percentage (15%) of the baseline-to-peak voltage levels of the magnitude of the analytic signal of the radiofrequency trace (Verdonk et al., 1992). With measurements using this technique in formalin-fixed human myocardium, the authors reported that “Complications introduced by the anisotropy of attenuation were a potential source of systematic error in our measurements of the anisotropy of velocity. The low-pass filtering effect exhibited by soft tissues can confound timing measurements by changing the pulse shape as the wideband ultrasonic signal propagates through the sample” (Verdonk et al., 1992). While that work reported a clear anisotropy of velocity in myocardial tissue with maximal velocity along the myofibers, they suggested that potential errors in the measured values of velocity introduced by the anisotropy of attenuation (with that technique) would require future consideration (Verdonk et al., 1992). This Appendix explores these potential errors and suggests a method for minimizing the effects of attenuation on measurements of velocity in soft tissues (in this case myocardium).

Fig. A1 depicts three representative through-transmitted radiofrequency traces. The water reference trace (top panel) occurs later in time than either of the myocardial specimen traces, indicating the slower speed of sound in water compared to that in myocardial tissue. The earliest myocardial specimen trace in time corresponds to parallel insonification (bottom panel) and the later one corresponds to perpendicular insonification (middle panel). The effects of attenuation (weaker pulse amplitude and changed pulse shape compared to the water reference trace) are most apparent for parallel insonification. While clearly still experiencing attenuation, the trace corresponding to perpendicular insonification appears more “water-like” in shape. Previous work by Wear has examined the effects of frequency-dependent attenuation and dispersion on measurements of velocity in which a specific timing marker (e.g., a zero-crossing, maximum, or minimum) is designated for the specimen and the reference waveforms (Wear, 2000). In the case of sufficiently weakly dispersive media, like myocardium, the effect of dispersion on the received signal is not significant. (Previous studies in this laboratory have predicted a 2.5 m/s difference for phase velocities at 1 and 9 MHz for perpendicular insonification in freshly excised canine myocardium (O'Donnell et al., 1981; Waters et al., 2003; Waters et al., 2000).) The study by Wear showed that for media that exhibit a frequency-dependent attenuation, the pulse spreads over time and the magnitude of the estimate of the difference in arrival times between the specimen and the reference depends on the point in the waveform that is analyzed (Wear, 2000). Similarly, the calculated time difference (and resulting calculated velocity) depends on the choice of percentage of magnitude of the analytic signal when using that technique for timing mark detection. Furthermore, when comparing results in which the attenuation varies (here as a consequence of changing angle of insonification relative to the predominant direction of the myofibers), the measured anisotropy of velocity also depends on that choice. Table II shows results of calculation of the anisotropy of velocity for specific percentages of the magnitude of analytic signal for a representative specimen. The measured anisotropy of velocity is seen to increase with decreasing choice of percentage. This effect on measured velocity indicates that this method of velocity determination is biased because of changing pulse shape resulting from the frequency-dependent effects of attenuation. Similarly to what was shown by Wear for timing mark detection using a particular marker on the radiofrequency waveform (Wear, 2000), a timing mark detection algorithm based on percentage of analytic signal appears to be more strongly affected by certain frequency components of the specimen trace because it only takes into account a certain point on the corresponding analytic signal which has been shown to depend on the attenuation of the specimen.

In order to facilitate an objective measure of timing differences that would reflect all present frequency components and, as a consequence, be less dependent on the effects of changing pulse shape resulting from attenuation in the specimen, we determined differences in signal arrival times by cross-correlation of the specimen and water reference through-transmitted radiofrequency signals. Use of the radiofrequency trace (rather than the analytic signal) includes all measured information for use in determining timing marks. The work by Wear observed that when using a zero crossing method of timing mark detection, errors in group velocity estimates are minimized when the zero crossing marker is chosen near the center of the waveform (Wear, 2000). Furthermore, that study demonstrated that in media such as myocardium that have a faster speed of sound than in water, the effects of attenuation caused calculated velocities to be increasingly too high as timing marks were chosen nearer the leading edge of the waveforms and they were, correspondingly, increasingly too low as timing marks were chosen nearer the trailing edge of the waveforms (Wear, 2000). Because the effects of pulse spreading due to attenuation appear to have an approximately symmetric effect on velocity estimates for points nearer the leading edge of the waveform compared to points nearer the trailing edge of the waveform (Wear, 2000), this suggests that determining timing differences from radiofrequency trace correlation, which uses all points of the waveform in determining timing differences, may yield results closer to those obtained from timing mark choices nearer the center of the waveform and thus with minimized errors as a result of the effects of attenuation. Table II shows results of calculated anisotropy of velocity using radiofrequency trace correlation for comparison to results of specific choices of percentage of magnitude analytic signal for the representative specimen. In addition, results from radiofrequency trace correlation are seen to agree with results using a zero crossing method of timing mark detection as employed in the Mol and Breddels work (Mol and Breddels, 1982).

In order to compare current measurements of velocity made with the radiofrequency cross-correlation method for timing mark detection with previous measurements from this laboratory (Verdonk et al., 1992) that employed 15% of the magnitude of analytic signal for timing mark detection, we analyzed our current data on formalin-fixed lamb myocardial specimens and also reanalyzed the historical data on formalin-fixed human myocardial specimens using both methods. Measured mean values of the anisotropy were in good agreement between the two data sets (22 m/s for the current lamb myocardial data compared to 19 m/s for the previous human myocardial data using 15% analytic signal for timing mark detection, and 12 m/s for current lamb myocardial data compared to 12 m/s for previous human myocardial data using cross-correlation of the radiofrequency traces for timing mark detection). The larger measured anisotropy of velocity observed when using a percentage analytic signal method for timing mark detection would be expected because of the larger attenuation for parallel compared to perpendicular insonification and corresponding dependence of this method on pulse shape which is affected by changing attenuation in the rotating specimens. For these reasons, timing mark detection based on cross-correlation of the radiofrequency traces may be a preferable choice for measurements of velocity in weakly dispersive specimens that exhibit attenuation different from the reference medium and for specimens that exhibit an anisotropy of velocity. In addition, the cross-correlation of radiofrequency traces method of timing mark detection is more straightforward and less arbitrary than that based on a percentage of the magnitude of analytic signal.