Abstract
Mitchell, Gary F., Marc A. Pfeffer, Peter V. Finn, and Janice M. Pfeffer. Comparison of techniques for measuring pulsewave velocity in the rat. J. Appl. Physiol. 82(1): 203–210, 1997.—We evaluated methods for measuring average and regional pulsewave velocity along the full length of the aorta in 18moold etheranesthetized male spontaneously hypertensive rats. Cathetertip manometers were placed in the ascending and descending thoracic aorta via the right carotid and left femoral arteries, respectively. As the distal catheter was withdrawn at 1cm intervals, the relationship between distal catheter insertion distance and distance between transducers was determined from the intercept of the insertion distance vs. transmission delay regression line. Methods that assessed the foottofoot time delay between pressures accurately predicted the separation between catheters (measured distance of 14.3 cm; intercept of 14.0 ± 0.5 cm;P = not significant) were highly reproducible (coefficient of variation of 2.3% for repeated measurements) and showed minimal variability (range 509 ± 30 to 600 ± 29 cm/s) along the full length of the aorta. Methods that made use of the pressurepressure transfer function were spatially (range of values along the aorta 367 ± 17 to 722 ± 39 cm/s) and temporally more variable, especially during vasoconstriction with methoxamine, due to the effects of reflected waves.
 aorta
 hemodynamics
 blood pressure
 computer analysis
 Fourier analysis
normal aging results in breakdown of the elastic elements of the conduit vessels, leading to an increase in pulsewave velocity and premature return of the reflected pressure wave to the proximal aorta in systole (11, 21, 22). The resulting late systolic augmentation of the aortic pressure wave increases the pulsatile load on the left ventricle and contributes to left ventricular hypertrophy even after controlling for mean arterial pressure (6, 24, 31). This process is exacerbated by the presence of hypertension (26) or a diet high in sodium (5) and may be reversible with some forms of antihypertensive treatment (9, 23, 25, 29) or by salt restriction (4). Because hypertension has a cumulative timedependent effect on the breakdown of the elastic elements of the aorta, an assessment of pulsewave velocity (2) or of the effects of increased pulsewave velocity on proximal aortic pressure waveform (7) may provide an index of the duration and severity of hypertension.
To measure pulsewave velocity, it is necessary to measure two pressures with highfidelity transducers a known distance apart and to accurately determine the time delay between the recorded pressure waveforms. However, reflected waves modify the pressure waveform as it moves distally through the arterial system, making measurement of the time delay difficult. In the frequency domain, reflected waves create frequencydependent discrepancies between true phase velocity (c _{ph}), which is determined by the intrinsic properties of the arterial wall and blood, and measured or apparent phase velocity (c _{app}) (8, 10,27, 28). Numerous criteria for averagingc _{app} across a range of frequencies or harmonics have been proposed (10, 13, 14). The resultant meanc _{app}(c _{ a̅ p̅ p̅ }) should approximatec _{ph}. In the time domain, foottofoot pulsewave velocity (c _{ff}) has been shown to approximatec _{ph} (10). However, modification of the advancing pressure wave by reflections complicates definition of the “foot” of the waveform. Evaluating the precise curvilinear distance between pressure transducers is also difficult, especially in small animals where arterial size limits the use of multisensor catheters with transducers mounted a known distance apart. In the present study, we evaluated a new technique for determining the curvilinear distance between the pressure transducers. We also evaluated four techniques for determining the time delay between simultaneously recorded waveforms. Our goals were to establish a robust method for assessing pulsewave velocity and to assess the regional variability in pulsewave velocity along the aorta in the rat.
METHODS
Study animals. Experiments were performed on 18moold etheranesthetized male spontaneously hypertensive rats obtained from colonies that were bred and maintained in our animal facility. Complete regional analysis of pulsewave velocity using the pullback procedure described below was performed in seven animals. Reproducibility of pulsewave velocity measurement techniques at baseline and in response to vasodilation and vasoconstriction was assessed in a total of 13 animals.
Hemodynamic preparation. The 2Fr cathetertip pressure transducers used in this study (model SPR407, Millar Instruments) were calibrated against a mercury manometer. Before each study, the transducers were balanced and then maintained in a 37°C water bath for ≥1 h to confirm stability of the zero baseline. Atmospheric zeroes were recorded for each study immediately before insertion and after removal of the pressure transducers. The femoral pressure catheter was marked at 1cm intervals along its distal 20 cm starting from the center of the pressure transducer. After induction of anesthesia with ether, a tracheotomy was performed and the animal was connected to a rodent respirator for maintenance of ventilation and ether anesthesia. The right jugular vein was cannulated to allow for intravenous infusions. The right carotid and left femoral arteries were cannulated with 2Fr cathetertip pressure transducers. The tip of the carotid catheter was advanced into the ascending aorta. The femoral catheter was advanced to the 12cm mark, placing its pressure transducer in the proximal descending thoracic aorta ∼2 cm distal to the proximal aortic pressure transducer. Once animals were fully instrumented, an incremental pullback of the femoral pressure catheter was performed, with proximal and distal pressures recorded at 1cm intervals starting at 12 cm and pulling back to the 3cm point, which placed the transducer at approximately the level of the aortic bifurcation. The catheter was then returned to the 5cm point (2 cm proximal to the aortic bifurcation) for the remainder of the study. This pullback information, obtained over the course of ∼2 min, was used to calculate pulsewave velocity and the distance between the two transducers as detailed below.
After the pullback procedure, a midline thoracotomy was performed and a flow probe was placed around the ascending aorta. The location of the tip of the proximal aortic pressure transducer was visually confirmed and adjusted to be 1–2 mm distal to the downstream edge of the electromagnetic flow probe to avoid interference with the flow measurements. Any necessary adjustments in the location of the proximal transducer were considered in subsequent calculations. To assess repeatability of pulsewave velocity determinations, four baseline recordings were taken over a period of 10–12 min, during which time the animals were hemodynamically stable. Subsequently, a graded infusion of the vasodilator sodium nitroprusside (0.5–30 μg/min) was administered to reduce mean arterial pressure into the lowtonormal range (75–100 mmHg). After return of arterial pressure to baseline, a graded infusion of methoxamine (20–1,600 μg ⋅ kg^{−1} ⋅ min^{−1}) was titrated to produce a rise in mean arterial pressure first into the moderately (135–175 mmHg) and then into the markedly (175–215 mmHg) hypertensive ranges. Steadystate recordings at each of these three data points were made 1 min after initiation of each new dosage level of nitroprusside and methoxamine. At the completion of each study, the final distance between the proximal and distal pressure transducers was determined by measuring the length of a segment of polyethylene tubing that was inserted into the proximal aorta at the level of the proximal transducer and advanced antegrade to the level of the distal pressure transducer.
Data analysis. All hemodynamic data were recorded on an FM data recorder (model XR310, TEAC) for later analysis. Waveforms were digitized at 1,000 samples/s by using a 12bit simultaneously sampling analogtodigital converter and analyzed on a microcomputer with custom software. Total arterial compliance was calculated from the diastolic central aortic pressure decay (15). The delays between proximal and distal pressure waveforms were evaluated by hand and were calculated by four automated techniques, two of which were foottofoot techniques. The first automated technique was an adaptive thresholdbased approach (“threshold” method) that defined the foot of the pressure waveform by evaluating the first derivative of pressure (dP/dt). Each waveform was scanned to find the maximum value of dP/dt, which was calculated by using a fivepoint linear least squares fit. To avoid noise in late diastole, a preliminary threshold was initially set at 50% of this maximum value. Starting in late diastole, dP/dt was then searched for the first value that exceeded this threshold. Starting from this point, the first derivative was then searched backward for the earliest point at which dP/dt exceeded 20% of the maximum derivative. This point was taken as the foot of the waveform.
The second approach defined the foot of the waveform as the point of intersection of tangent lines drawn through late diastole and early systole (“intersection” method) (1, 13). The tangent through the upstroke was determined by linear regression of five points, starting with the point defining the foot of the waveform by the threshold approach described above. Next, the waveform was searched backward through its nadir to the diastolic point that was isobaric with the threshold foot, again to avoid any presystolic noise. Linear regression through that and the preceding 16 points (17 ms total) determined the diastolic line. The intersection of the diastolic and systolic tangent lines was taken as the foot of the waveform.
The next two techniques used the transfer function between proximal and distal pressures to determine the time delay as previously described (14). Proximal and distal pressure waveforms were transformed to the first 10 harmonics of their respective Fourier series. The real and imaginary components of the transfer function at each harmonic were then calculated by dividing the respective distal pressure component by the proximal aortic pressure component. The regression line of phase vs. frequency for the 10 harmonics of the transfer function phase was then calculated, and the slope of that line was converted to a time delay: t = slope/2π (“phaseslope” method).
The final technique (“impulse response” method) used the impulse response of the pressure transfer function, which was filtered and inverse transformed by a modification of a previously described technique for calculating the flow/pressure impulse train response of the arterial system (18). The resulting pressurepressure impulse response represents the pressure that would be recorded at the distal pressure site if an impulse of pressure were introduced at the proximal site at time 0 (14). The timing of the peak of this waveform was therefore taken as the time delay between proximal and distal pressures.
The femoral pullback data were used to calculate pulsewave velocity and the distance between transducers. Time delays were calculated on five consecutive cardiac cycles at each catheter location, and the results were averaged. If the SD of the delay for the five cardiac cycles at a given location was >1 ms, that location was excluded from the pullback analysis for that method. Linear regression analysis of catheter insertion distance vs. time delay for each catheter position was performed. The (negative) slope of this line was proportional to the spatially and temporally averaged pulsewave velocity during the pullback procedure. The yintercept was the distance between the insertion point in the femoral artery and the proximal pressure transducer, i.e., the insertion distance at which the time delay would have become zero. The distance between transducers at any insertion point could then be determined by subtracting the insertion distance from theyintercept of this regression line. For example, if the catheter was placed at the 5cm point, and the intercept of the regression line was 13 cm, the transducers would be 8 cm apart. This approach assumed that pulsewave velocity was relatively constant along the length of the aorta under study. Deviations from this assumption should be evident from a poor fit of the regression line between location and delay and a reduction in the correlation coefficient for the regression line.
Pulsewave velocity (slope) and distance between transducers (intercept) obtained by using each of the four automatic techniques were compared with a “measured” pulsewave velocity and the actual distance between transducers (length of polyethylene tubing) at the completion of the study. This distance, measured when the femoral catheter was at the 5cm location, was converted to an equivalent intercept by adding 5 cm. The delay used in calculating the measured pulsewave velocity was determined manually by positioning a pair of cursors on the foot of the proximal and distal waveforms, which were displayed on a highresolution computer monitor.
Regional variability in pulsewave velocity along the full length of the descending aorta was assessed by a variety of techniques. First, average pulsewave velocity for each segment of the aorta was obtained by taking the negative slope of a linear least squares regression line through the delays for each group of three adjacent locations from the pullback data. For example, the local velocity atlocation 11 was obtained by fitting a line through delays obtained with the distal catheter at the 10, 11, and 12cm points. This procedure was performed for the thresholdbased foottofoot delays and for the phaseslope delays to comparec
_{ff} andc
_{
a̅
p̅
p̅
}for each region of the aorta. Next, individual apparent phase velocities were calculated for each location and harmonic by evaluating the progressive phase delay at each harmonic as the distal catheter was withdrawn along the aorta. To minimize noise (due to slight variations in positioning of the distal catheter and asynchronous acquisition of the pressures), the change in phase of the transfer function was averaged over three locations by fitting a regression line to phase delay vs. position at each harmonic. For example, the phase of the first harmonic of the transfer function at locations 10–12 was fitted with a regression line and the slope (dφ/dx) of phase delay (φ) vs. axial location in the aorta (x) was converted toc
_{app} by usingc
_{app} = 2πnf_{1}/(dφ/dx), where n is the harmonic and f_{1} is the fundamental frequency of the cardiac cycle. This example yieldsc
_{app} for the first harmonic at location 11. This procedure was repeated for each harmonic and each location in every animal and averaged, producing a threedimensional contour map ofc
_{app} vs. location and harmonic. For each location (4–11) on this map,
Statistical analysis. The slopes and intercepts of the pullback data, obtained in a total of seven animals by each of the four automated methods, were compared with the “measured” value by using repeated measures analysis of variance with Sheffé’s subtesting of individual means. The repeatability of each of the automated techniques was assessed by computing the mean and coefficient of variation of pulsewave velocity determined during the four steadystate recordings in a total of 13 animals. The pulsewave velocity for each of the four recordings represented the mean value from five consecutive beats. The coefficient of variation was defined as the SD of these four values divided by their mean. The relationship between pulsewave velocity, technique, and mean arterial pressure was assessed by repeated measures analysis of variance with Scheffé’s subtesting. Regional pulsewave velocities were similarly compared. All values are presented as means ± SD, except as noted in the figures.
RESULTS
Slopes and intercepts of the pullback analyses are presented in Table1, and the averaged delays by location are presented in Fig. 1. From Table 1, it can be seen that when either of the automated footdetection algorithms was used, the pullback technique proved to be a reliable method of assessing both pulsewave velocity, as indicated by the slope of the pullback regression line, and the distance between pressure transducers, as indicated by the values for intercept. In contrast, both of the transfer functionbased techniques (“phase slope” and “impulse response”) underestimated pulsewave velocity (slope) and the distance between the pressure transducers (intercept). Figure 1 illustrates the discrepancies between the techniques. The average delays are plotted by location for each technique. The solid line in each of the panels has a slope and intercept equal to the population means for the given technique. The dashed line, which represents the “gold standard,” is the same in each panel. This line was drawn by setting the slope equal to the negative of the manually measured pulsewave velocity and the intercept equal to the measured distance between transducers at the completion of the experiment plus 5 cm (the final location of the femoral catheter). The close fit between the foottofoot delays and both the actual and theoretical regression lines suggests that the assumption of a relatively constant pulsewave velocity along the length of the aorta was reasonable. In contrast, significant deviations from the theoretical regression line were seen for the transfer functionbased techniques and the basis for these deviations was explored.
The impulse response technique progressively overestimated the transmission delay as the distal catheter was pulled back into the abdominal aorta and beyond (locations 3–7) (Fig.1 D). This region is expected to be influenced by wave reflections; evidence for this is seen in Fig.2, which presents a series of impulse response functions for a single representative animal. The initial peak was used to evaluate the time delay between proximal and distal transducers. The smaller secondary peak represents the reflected wave. As the distal catheter was pulled down the aorta, the initial peak occurred later, due to the increased separation between transducers, and the secondary peak occurred earlier, as the distal transducer approached the reflecting site. The progressive overlap between the relatively broad primary and reflected peaks added an additional rightward shift to the primary peak. This becomes apparent when the timing of the peak of the impulse response is compared with the corresponding thresholdbased foottofoot delays (vertical arrows in Fig. 2) at each position.
The analysis of regional pulsewave velocity provided an explanation for the decreased slope and intercept of the pullback regression line obtained from the phaseslope delays. Regional pulsewave velocities obtained by this and the thresholdbased foottofoot technique were evaluated (Fig.3 A). As suggested in Fig. 1, regionalc _{ff} was relatively constant along the aorta. In contrast, there was a region of lowc _{ a̅ p̅ p̅ }in the midaorta (locations 7–8; Fig. 3 A) detected by the phaseslope method. This region of lowc _{ a̅ p̅ p̅ }(longer delays) produced a small offset along the time axis in the midaorta and resulted in a counterclockwise rotation of the pullback regression line, accounting for the diminished slope andyintercept obtained in the pullback analysis (Fig. 1, Table 1).
The basis for the region of lowc
_{
a̅
p̅
p̅
}in the midaorta was established by evaluating thec
_{app} contour map (Fig. 4). Considerable regional and frequencydependent variation inc
_{app} was found. There were markedly elevated values at low frequencies due to the effects of reflected waves, which rapidly reached a minimum then oscillated about a value that was approximately the same asc
_{ff}. Additionally, for each harmonic, acceleration ofc
_{app} was seen inregions 5–6 in the distal aorta, suggesting a region of wave reflection. A second region of acceleratedc
_{app} was seen in the proximal aorta (regions 10–11) in the higher frequency range (6th7th harmonics), suggesting a proximal reflecting site, since this peak was higher than the distal peak (regions 5–6) in the same harmonics. Between these peaks was a deep trough of low pulsewave velocity that started at the 3rd harmonic at position 11 and hooked around between the proximal and distal peaks ending at the 10th harmonic at position 7–8. As a result of this trough,
The repeatability of each of the techniques during a series of four consecutive steadystate measurements was assessed in 13 animals with the catheter at the final 5cm location. To focus on variability in the delay measurement, the actual measured distance between transducers was used for all techniques. Under basal conditions, mean pulsewave velocity was comparable for all but the impulse response method, which overestimated the transmission delay and thus underestimated pulsewave velocity, for the reasons described above (threshold of 598 ± 65; intersecting lines of 604 ± 61; phase slope of 600 ± 50; impulse response of 565 ± 54 cm/s;P < 0.001). Repeatability, as assessed by the coefficient of variability, was not different for threshold (2.3 ± 1.3%), intersecting lines (2.3 ± 1.1%), and impulse response (2.5 ± 1.2%) methods. The phaseslope method did, however, have a higher variability (3.6 ± 1.3%) than either of the footdetection techniques (P < 0.05).
The performance of each of the techniques was evaluated over the wide range of vasodilation and vasoconstriction produced by nitroprusside and methoxamine, respectively (Fig. 5). As expected, vasodilation, with its associated reduction in the magnitude of reflected waves, produced a striking concordance between the four techniques. Conversely, vasoconstriction augmented the differences between the techniques, with the transfer functionbased techniques progressively underestimating pulsewave velocity compared with the footdetection algorithms. In addition, during the two levels of methoxamine infusion, the impulseresponse technique returned markedly erroneous results in 5 of 26 analyses involving 4 of the 13 animals, accounting for the relatively wide SE values for that technique (Fig.5). These sporadic results were produced by the marked difference in harmonic content between proximal and distal waveforms. With vasoconstriction, the harmonic content of the distal waveform was augmented in the higher frequencies (4th8th harmonics) due to the brisk monophasic upstroke produced by superimposition of the forward and reflected waves. As a result, there were sporadic harmonics with considerable power in the distal waveform, which fell below the resolution of the measuring system in the proximal waveform. The resulting spike in the transfer function produced an augmented harmonic in the impulse response that obscured all useful data.
Finally, the correlation between pulsewave velocity and total arterial compliance was assessed during vasodilation and vasoconstriction as an independent indicator of the accuracy of the four techniques. Although the correlation between single measurements of pulsewave velocity and total arterial compliance is poor, because of the stronger effects of volume of the arterial system on compliance than on pulsewave velocity, the directional changes in the two parameters should be opposite and highly correlated when mean arterial pressure is varied. We found a strong correlation between pulsewave velocity and compliance when either of the footdetection algorithms was used (R = −0.79;P < 0.05 for each technique). The phase slope and impulseresponse techniques produced lower correlation coefficients that were, however, still statistically significant (R = −0.50 and −0.39, respectively).
DISCUSSION
This study is the first to compare various methods for measuring pulsewave velocity in the rat. We have described a new technique for determining the curvilinear distance between the proximal and distal pressure transducers and have presented a simple yet robust technique for determining the time delay between proximal and distal pressure waveforms. We compared this new footdetection algorithm to three previously described methods and found that its accuracy and reproducibility met or exceeded that of the more complex methods. We have further described the regional variability in pulsewave velocity (c _{ff} andc _{app}) along the length of the aorta and evaluated the effects of averaging criteria on regionalc _{ a̅ p̅ p̅ }.
Although the concept of pulsewave velocity measurement is quite simple, implementation of a robust method for making the measurement can be complex due to limitations in determining both the transmission delay and the distance between pressure sensors. We have presented a simple pullback method for accurately determining the curvilinear distance between the transducers. The method assumes that pulsewave velocity is reasonably constant along the segment of the aorta under study. The accuracy of the method was likely dependent on having at least one pair of recordings taken with the transducers as closely spaced as possible to minimize errors that could result from extrapolating the regression line to the location intercept. By keeping the distal catheter just beyond the highly curved proximal aorta when the transducers were at their closest point, however, we eliminated the ambiguity of establishing the actual curvilinear distance between transducers in that region, which presents a problem even when the transducers are mounted a fixed distance apart on a single catheter (13, 29).
Measurement of the transmission delay is complicated by the small magnitude of the delay and by the dissimilar nature of the proximal and distal waveforms due to the presence of reflected waves in the arterial system. Attempts to lengthen the transmission delay by increasing the separation between transducers increases the effects of reflected waves on the waveforms. The foot of the pressure waveform, which is too early to be significantly affected by reflections, is often used as a landmark for determining the delay. The resultingc _{ff} has been shown to correlate well withc _{ph} calculated from the MoensKorteweg equation (10) and eliminates the need to average apparent phase velocities over an empirically determined range of harmonics. However, there is no precise definition for what constitutes the “foot” of the waveform. Many investigators have drawn (or computed) tangent lines through the last part of diastole and the first part of systole and used the intersection between these lines as the foot. To avoid contamination by the reflected wave, the line through the upstroke of pressure must be limited to the earliest portion of systole. If not, the reflected wave may influence the slope of the line enough to modify the intersection point. The initial point to be used in defining the upstroke must also be qualified. The points immediately after the absolute pressure minimum cannot be used because of the possibility of false triggering due to noise in late diastole, where the pressure tracing can be relatively flat. If such an absolute minimum pressure occurred even 2–3 ms before the actual upstroke, the slope of the line would be considerably blunted, since the entire line is based on only 5 ms.
We tested a related, though less complex (threshold) algorithm that used dP/dt alone to define the foot of the waveform. To avoid the possibility of false triggering due to late diastolic noise, we found this point by searching backward from the point at which dP/dt reached 50% of its maximal value. We searched forward to find the initial 50% threshold to avoid the possibility of triggering on the inflection point between primary and secondary pressure peaks in pressure waveforms with late systolic augmentation due to a reflected wave. This approach was computationally related to the intersecting lines technique. However, it avoided the need to fit a line to the intrinsically curvilinear diastolic portion of the pressure waveform, which can also be affected by reflected pressure waves. We based the threshold for each waveform (proximal or distal) on a percentage of peak dP/dt for that waveform, avoiding the possibility that a distal pressure waveform, adjacent to a reflecting site, would reach the threshold prematurely due to its steeper upstroke. The threshold and intersecting lines techniques gave results that were no different from manually determined values during the pullback procedure. Their repeatability was comparable during multiple steadystate recordings, and they both gave reliable results over a wide range of vasoconstriction and vasodilation.
We compared these foottofoot techniques to two additional techniques that were based on the pressurepressure transfer function. Because the latter techniques use the entire waveform to assess the delay between proximal and distal pressure recordings, they are more susceptible to the effects of wave reflection (20). The phaseslope technique used linear regression to effectively average out the oscillations of phase between the 1st and 10th harmonics (14). This proved comparable to averaging c _{app}over approximately the 5th through 10th harmonics, as has been done by others (29). The difference in frequency band required to produce a comparablec _{ a̅ p̅ p̅ }resulted from the differential weight that low and highfrequency bands had when phase shift rather than phase velocity was averaged. The phaseslope technique was relatively insensitive to the marked increases in c _{app}in the lowfrequency range because these large velocities corresponded to relatively small deviations in phase. Thus marked differences inc _{app} in the lowfrequency range minimally affected the slope of the phasefrequency regression line. In contrast, when averaging was done across harmonics of c _{app}, the lowfrequency values, which may be severalfold greater thanc _{ph} orc _{ff}, had a greater effect on the mean.
Several studies have documented regional variation in and discordance between c
_{ff} andc
The impulse response method was also less reliable than the footbased methods. If a greater number of harmonics could be calculated and the filtering effect reduced, resulting in primary and secondary peaks that more closely resemble true impulses, then this technique might prove more reliable. Unfortunately, as noted above, the modulus of pressure rapidly approaches the resolution of the measurement system by the 10th harmonic. Therefore, it would be necessary to introduce a waveform with a higher content of power in the highfrequency band to further refine this method (19).
In conclusion, pulsewave velocity can be reliably measured in smallanimal models such as the rat. Unless the goal of the analysis is to study reflected waves, foottofoot techniques are more reliable than methods that assess the entire pressure waveform. Careful analyses of pulsewave velocity should further our understanding of the complex interaction between heart and conduit vessels.
Footnotes

Address for reprint requests: G. F. Mitchell, Cardiovascular Division, Brigham and Women’s Hospital, 75 Francis St., Boston, MA 02115.
 Copyright © 1997 the American Physiological Society