Am J Physiol Heart Circ Physiol 295: H482-H490, 2008.
First published May 30, 2008; doi:10.1152/ajpheart.00223.2008
0363-6135/08 $8.00
TRANSLATIONAL PHYSIOLOGY
Windkesselness of coronary arteries hampers assessment of human coronary wave speed by single-point technique
Christina Kolyva,1
Jos A. E. Spaan,1
Jan J. Piek,2 and
Maria Siebes1,2
Departments of 1Medical Physics and 2Cardiology, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands
Submitted 3 March 2008
; accepted in final form 27 May 2008
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ABSTRACT
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A novel single-point technique to calculate local arterial wave speed (SPc) has recently been presented and applied in healthy human coronary arteries at baseline flow. We investigated its applicability for conditions commonly encountered in the catheterization laboratory. Intracoronary pressure (Pd) and Doppler velocity (U) were recorded in 29 patients at rest and during adenosine-induced hyperemia in a distal segment of a normal reference vessel and downstream of a single stenosis before and after revascularization. Conduit vessel tone was minimized with nitroglycerin. Microvascular resistance (MR) and SPc were calculated from Pd and U. In the reference vessel, SPc decreased from 21.5 m/s (SD 8.0) to 10.5 m/s (SD 4.1) after microvascular dilation (P < 0.0001). SPc was substantially higher in the presence of a proximal stenosis and decreased from 34.4 m/s (SD 18.2) at rest to 27.5 m/s (SD 13.4) during hyperemia (P < 0.0001), with a concomitant reduction in Pd by 20 mmHg and MR by 55.4%. The stent placement further reduced hyperemic MR by 26% and increased Pd by 26 mmHg but paradoxically decreased SPc to 13.1 m/s (SD 7.7) (P < 0.0001). Changes in SPc correlated strongly with changes in MR (P < 0.001) but were inversely related to changes in Pd (P < 0.01). In conclusion, the single-point method yielded erroneous predictions of changes in coronary wave speed induced by a proximal stenosis and distal vasodilation and is therefore not appropriate for estimating local wave speed in coronary vessels. Our findings are well described by a lumped reservoir model reflecting the "windkesselness" of the coronary arteries.
coronary hemodynamics; pulse wave velocity; microvascular resistance; intramyocardial pump; stenosis
ARTERIAL PULSE WAVE VELOCITY is directly related to the elastic properties of the vessel wall by the well-known Moens-Korteweg equation (14) and represents an important marker of vascular pathology associated with the risk of cardiovascular events (2, 17, 27). Consequently, wave speed is influenced by factors that affect wall stiffness, such as age, vascular disease, distending pressure, and vascular tone (2, 11, 13, 15, 23). It is also a fundamental parameter required in wave intensity analysis for the separation of traveling waves into their forward and backward components (4, 8, 16).
The average wave speed along a vessel segment with fairly uniform wall properties can be determined with the standard foot-to-foot method from the pulse delay between two measurement locations (1, 14). Local wave speed based on simultaneous pressure and velocity measurements at a single location can be obtained by the pressure-velocity loop method (7, 8), but it requires unidirectional waves during at least part of the cycle. Neither method is suitable for the coronary circulation, where the short length and motion of the tortuous vessels prevent reliable application of the first method, whereas the generation of concurrent coronary waves by proximal and distal sources conflicts with the requirements of the second method.
Recently, Davies et al. (3) proposed a new technique for local wave speed determination that was derived from wave intensity analysis and uses complete heart cycles without restrictions about wave travel direction. This single-point technique yielded good agreement in the aorta compared with wave speed obtained with the foot-to-foot method. The lack of alternative methods to measure wave speed in human coronary arteries precluded direct experimental validation. However, a close correlation was demonstrated between aortic wave speed and that obtained in healthy coronary vessels at resting flow conditions. Furthermore, the single-point estimate of coronary wave speed was shown to increase with age and to decrease after relaxing conduit vessel smooth muscle tone by the administration of a nitric oxide donor. Based on these indirect pieces of evidence, the authors (3) concluded that the derived single-point equation correctly predicted local wave speed in human coronary arteries.
Because of the clinical relevance of coronary pulse wave velocity, the aim of the present study was to further investigate the applicability of the single-point technique in both diseased and normal coronary vessels and for interventions commonly applied in the catheterization laboratory. The first intervention was the administration of adenosine, which dilates coronary resistance vessels in the microcirculation and not the larger coronary arteries (10, 22). This intervention should therefore have no direct effect on local wave speed measured in an epicardial conductance vessel. The second intervention was revascularization of a proximal atherosclerotic lesion. With the measurement site several centimeters downstream of the stenosis location, one would expect that the increase in distal pressure resulting from stent placement would expand the downstream vessel segment, thereby stiffening the wall and increasing local wave speed. The results of this study do not support these expected outcomes with respect to wave speed but instead are consistent with predictions of a lumped reservoir model of the coronary circulation. We presume that the length of epicardial coronary arteries may not be sufficient to sustain conditions necessary for techniques based exclusively on wave transmission models, thereby limiting the applicability of the single-point wave speed equation.
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METHODS
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Study population.
The study group consisted of 29 subjects [mean age, 59 yr (SD 9); 23 males] with stable angina pectoris who were scheduled for elective balloon angioplasty and stent placement. All patients had at least one angiographically normal vessel (<30% diameter stenosis) and one vessel with a single de novo lesion. Exclusion criteria included prior coronary intervention, subtotal or serial lesions, diffuse disease, recent myocardial infarction, cardiomyopathies, valvular disease, and the presence of visible collaterals. The protocol was approved by the Medical Ethics Committee of our institution, and all patients gave written informed consent.
Medication and protocol.
All patients continued their prescribed antianginal and antiplatelet medication. Cardiac catheterization was performed by the femoral approach using a 5-Fr or 6-Fr guiding catheter. An intracoronary bolus of 0.1 mg nitroglycerin was given at the beginning of the procedure and repeated every 20–30 min thereafter to minimize large vessel tone throughout the protocol. Hemodynamic measurements were obtained in a distal segment of an angiographically normal reference vessel and downstream of the stenosis in a diseased vessel before and after revascularization by stent placement. Data were collected continuously at rest and throughout the hyperemic response to a 20–40-µg bolus of adenosine.
Hemodynamic measurements.
Aortic pressure was measured via the guiding catheter at the coronary ostium. A 0.014-in. dual-sensor guide wire (Volcano, Rancho Cordova, CA) with a Doppler sensor at the tip and a pressure sensor 3 cm proximal to the tip was advanced to a distal location in the interrogated coronary vessel to record intracoronary perfusion pressure (Pd) and flow velocity (U) signals (20, 25). Care was taken to place both sensors in a smooth vessel segment and to obtain an optimal and stable velocity signal according to recommended techniques for sensor-wire measurements (6). The sensor position was maintained before and after the stent placement. After the processing by the respective instrument consoles (WaveMap and FloMap, Volcano), the hemodynamic signals and ECG were digitized at 120 Hz for off-line analysis.
Data analysis.
Data processing was performed using custom software written in Delphi (version 6.0, Borland Software, Cupertino, CA). Average aortic and distal pressure and velocity were calculated during resting and peak hyperemic flow conditions over 8 to 9 and 2 to 3 cycles, respectively. A corresponding velocity-based index of microvascular resistance was derived as MR = Pd/U (20, 25). Filtered derivatives of the Pd and U signals were obtained by the Savitzky-Golay convolution method, which reduces signal noise with minimal influence on peak magnitudes (19). An estimate of local coronary wave speed by the single-point technique (SPc) was obtained as previously reported (3):
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where dPd and dU are the distal pressure and velocity differentials between successive sampling points and the summations were taken over complete consecutive heart cycles during resting and hyperemic flow periods. A value of 
= 1,050 kg/m3 was used for blood density.
Statistical analysis.
Data are expressed as means (SD). Results for different steps of the protocol were compared using analysis of variance with repeated measures, followed by contrast analysis (SPSS, version 12.0). Data obtained for resting and hyperemic conditions at each step of the protocol were compared using Student's paired t-test. Linear regression analysis was used to investigate relations between continuous parameters. Statistical significance was assumed at P < 0.05.
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RESULTS
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Distal coronary artery measurements were obtained in all 29 patients before and after stent placement. Mean diameter stenosis was 55.7% (SD 11.4). Suitable measurements in the reference vessel were not available in six patients. Stenotic lesions were predominantly located in the left anterior descending artery (n = 19), whereas most reference vessels were the circumflex coronary artery (n = 19).
A typical measurement sequence obtained in a reference vessel is depicted in Fig. 1. The aortic pressure signal shows two short periods where adenosine was injected into the coronaries and the catheter was flushed. The resulting dilation of the microvascular resistance vessels is apparent from the flow velocity increase (Fig. 1, top). Distal coronary pressure (second trace from the top) is hardly affected by the adenosine administration. The beat-averaged microvascular resistance decreased by a factor of three, and the corresponding calculated single-point wave speed fell concomitantly by a factor of two due to the increased time derivative of the velocity signal.
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Fig. 1. Response to adenosine-induced vasodilation recorded in a reference vessel. Tracings show continuous recordings of distal velocity (U) and pressure (Pd), aortic pressure (Pa), and ECG. Per-beat values of microvascular resistance (MR) and single-point wave speed (SPc) are displayed in the two lower tracings. Adenosine injection takes place at around t = 10 s. The resulting vasodilation of the microcirculation has an immediate and prominent effect on MR and SPc.
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Effect of microvascular vasodilation and revascularization.
Hemodynamic data and local wave speed estimated from the single-point equation are summarized in Table 1 for all steps of the protocol. Heart rate did not change throughout the procedure. Mean aortic pressure was 103 mmHg (SD 15) at rest and decreased slightly during hyperemia, whereas coronary flow velocity increased substantially (P < 0.0001).
The effect of age on SPc is depicted in Fig. 2 for the reference vessel as well as the target vessel before and after stent placement. There was a significant positive relation between SPc and age for all vessel conditions at rest (Fig. 2A). The two highest values above 80 m/s were obtained before and after stenting in the moderately diseased vessel of a 76-yr-old patient who had a low heart rate and a pulse pressure exceeding 130 mmHg. Between the youngest and oldest patient, the SPc in the reference vessel ranged from 11.3 to 25.1 m/s. After vasodilation, significant age dependency was only maintained for the undiseased reference vessel (Fig. 2B). The slopes of the regression lines were not significantly different between vessel conditions or between rest and vasodilation for corresponding conditions.
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Fig. 2. Relationship between SPc and age at rest (A) and during hyperemia (B). There was no significant difference in the slopes of the regression lines between healthy, stented, and diseased vessels or between resting and hyperemic conditions.
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Figure 3 illustrates changes in distal coronary pressure and SPc induced by hyperemia and stent placement. Coronary SPc decreased after microvascular vasodilation in all conditions (P < 0.001). Both at rest and during hyperemia, SPc was substantially higher in the presence of a proximal stenosis than after revascularization or in the reference vessel (P < 0.005). SPc distal to the stenosis decreased from 34.4 m/s (SD 18.2) at rest to 27.5 m/s (SD 13.4) during hyperemia. After revascularization by stent placement, local SPc downstream of the treated segment was 25.0 m/s (SD 14.6) at rest and decreased to 13.1 m/s (SD 7.7) during microvascular vasodilation.
Corresponding relative changes are shown in Fig. 4. Hyperemia induced by microvascular vasodilation (Fig. 4A) reduced MR by 64% (SD 13) averaged over all vessel conditions (P < 0.0001). This was associated with a reduction in distal pressure by 20 mmHg (SD 9) with stenosis present and by 14 mmHg (SD 11) and 7 mmHg (SD 5) after revascularization and in the reference vessel, respectively (all P < 0.0001). Despite the larger drop in distal distending pressure in the presence of a stenosis, the single-point wave speed decreased by the smallest amount in this condition. SPc declined by 6.9 m/s (SD 9.6) (17%) in the presence of the stenosis (P < 0.001) compared with 11.8 m/s (SD 10.9) (42%) in the treated and 10.9 m/s (SD 5.9) (49%) in the reference vessel (both P < 0.0001). Revascularization (Fig. 4B) lowered hyperemic MR by 26% (SD 28) (P < 0.005), whereas basal MR remained unchanged. Although stent placement restored distal coronary pressure (P < 0.0001) close to reference levels, this increase in distending pressure was associated with a paradoxical decrease in the single-point wave speed. SPc fell by 9.4 m/s (SD 14.3) (18%) at resting conditions (P < 0.005) and by 14.3 m/s (SD 12.9) (43%) during hyperemia (P < 0.0001).
Figure 5 depicts the relationships between changes in SPc and changes in MR and Pd. The decrease in SPc after distal vasodilation (Fig. 5A) was positively correlated with the corresponding adenosine-induced reduction in MR (Fig. 5A, left) both in the reference and the stented vessel (r = 0.46, P < 0.03; and r = 0.69, P < 0.0001, respectively) but not in the stenotic vessel (r = 0.29, P = 0.13). Although the hyperemia-induced decrease in distending pressure was on average associated with a decrease in wave speed, no significant linear relation existed between 
SPc and Pd for either of the vessel conditions (Fig. 5A, right). Similar to the findings after vasodilation, stent placement (Fig. 5B) resulted in significant positive correlations between SPc and MR (Fig. 5B, left) for both resting (r = 0.58, P < 0.001) and hyperemic (r = 0.61, P < 0.001) conditions. In contrast, the increase in distal distending pressure after revascularization of the proximal stenosis was associated with a paradoxical decrease in single-point wave speed (Fig. 5B, right) with a significant negative correlation between SPc and Pd at hyperemia (r = 0.48, P < 0.01).
Figure 6 illustrates that microvascular dilation by adenosine hardly affected the magnitude of the pressure-related numerator of Eq. 1 (Fig. 6A), whereas it had a major effect on the magnitude of the velocity-related denominator of the SPc equation (Fig. 6B). It is also apparent that presence of a stenosis increased the pressure derivatives but decreased the velocity derivatives.
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Fig. 6. Variation of pressure (A) and velocity pulsations (B) with reduction in MR due to vasodilation. Although the summed squares of pressure derivatives (numerator of Eq. 1) are relatively unaffected, a large change occurs for summed squares of velocity derivatives (denominator of Eq. 1) in the vessels without a stenosis. White symbols, resting conditions; black symbols, hyperemia.
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DISCUSSION
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Pulse wave velocity relates to arterial stiffness, which in turn is an inverse function of distending pressure (5, 14). In contrast, we found that the local wave speed estimate, SPc, based on the single-point technique (3) in normal and diseased coronary vessels, did not follow this well-established relationship. The results of this study show that SPc in a distal vessel segment was influenced by the presence and treatment of a proximal stenosis and by a reduction in downstream microvascular resistance induced by adenosine in a way that is inconsistent with wave speed behavior. First, despite lower distending pressure distal to the stenosis, SPc was higher than in an undiseased reference vessel. When intraluminal pressure was restored by revascularization of the proximal stenosis, SPc in the poststenotic segment decreased instead of increased. Second, a change in microvascular resistance should have no influence on wave speed in a coronary conduit vessel, but SPc was lowered by microvascular dilation. This suggests that the parameter calculated by the single-point technique does not represent coronary wave speed.
Comparison with earlier measurements of coronary wave speed in undiseased vessels.
The observed effect of age on coronary SPc in the present study (SPc = 0.39 x age – 1.1) agrees with that derived from data reported by Davies et al. (3) (SPc = 0.33 x age + 1.9) and is consistent with the generally accepted concept of an age-dependent increase in wall stiffness (5, 9). Our result of SPc = 21.5 m/s for the reference vessels at rest compares favorably with the value of 20.4 m/s reported for healthy human coronary arteries in the earlier study proposing the single-point measurement of wave speed (3), which attests to the correct application of this technique in our study. Within 1 min after the administration of 1 mg intracoronary isosorbide dinitrate, the single-point wave speed in the study of Davies et al. (3) dropped to 9.3 m/s, close to the value of 10.5 m/s that we obtained at full arteriolar vasodilation with adenosine. The authors suggested that the reduced conduit vessel tone after isosorbide dinitrate was responsible for the observed reduction of SPc. Their observed response to nitrate administration is also consistent with the effects of flow-mediated dilation on pulse wave velocity in vasoactive vessels (13). However, nitrates also affect resistance vessels >100 µm in the microcirculation (10), especially in the early transition period before compensatory action by autoregulatory control. A 50% increase in coronary flow has been reported 2 min after a 0.2 mg bolus of nitroglycerin (22). It is therefore not unlikely that the 1 mg dose of isosorbide dinitrate induced a transient decline in microvascular resistance during the 1-min measurement period. In addition, perfusion pressure could have decreased, thereby reducing wave speed directly, and induced compensatory microvascular dilation, which would also act to decrease SPc according to our findings. Unfortunately, no data on coronary pressure or flow velocity were reported by the authors that would allow for the assessment of changes in perfusion pressure or microvascular resistance after nitrate administration.
The above quantitative agreements between SPc results obtained in the reference vessel in this study and in undiseased vessels in the earlier study by Davies et al. (3) are consistent with the early microvascular response to nitrates over the period of measurement. In this context it is important to note that our patients received a 0.1 mg intracoronary bolus of nitroglycerin at the beginning of the procedure and at regular intervals of about 20–30 min to prevent coronary spasm as well as flow-mediated dilation of the conductance vessels. However, our hemodynamic measurements were not obtained in the immediate period after nitroglycerin administration, when transient microvascular effects take place.
Other data on coronary wave speed in humans are lacking. Studies on coronary wave speed in animals determined with the foot-to-foot method (1, 18) report values in the order of 10 m/s for healthy vessels at resting conditions. These wave speeds are lower than our SPc values for the reference vessels at rest but are close to the value we found during microvascular vasodilation. Three possible explanations deserve consideration in this context. First, our patients had a mean age of 59 yr, whereas the animals were likely young and healthy. Second, anesthesia-related reduced systemic pressure and microvascular dilation may have been present during those animal studies. Finally, SPc may not represent true pulse wave velocity in coronary arteries.
Relationship between SPc, intraluminal pressure, and coronary MR.
In the presence of a proximal stenosis, we found a value of 34.4 m/s for SPc at rest, which was substantially higher than in the reference vessel despite a lower distending pressure at the measurement location several vessel diameters downstream of the stenotic lesion. This higher SPc could be indicative of an overall stiffer vessel wall in the diseased vessels. However, after revascularization of the proximal stenosis, SPc at the same distal measurement site dropped by 30% to a value similar to that in the reference vessel, although distal pressure increased by 23%. Stent placement had an even larger effect during hyperemic conditions, with a 52% decrease in SPc despite a 30 mmHg pressure rise in the downstream vessel segment. In contrast, Arts et al. (1) reported a 40% increase in coronary wave speed for a pressure increase from 50 to 100 mmHg. It is therefore unlikely that SPc represents true wave speed when measured distal of a stenosis or that it reflects an actual change in wave speed when distal pressure is altered by revascularization of a proximal stenosis.
The administration of adenosine substantially lowered coronary microvascular resistance but also resulted in a decline in local SPc. Obviously, it is highly unlikely that a change in microvascular resistance has a direct effect on wave speed in the epicardial conduit arteries. Arts et al. (1) did not report a change in coronary wave speed measured by the foot-to-foot method in dogs after coronary resistance was reduced by administration of dipyridamole. The question then is how the changes observed in the present study are causally related. One option is that adenosine decreased the wall stiffness of the epicardial arteries by lowering local tone, thereby reducing wave speed directly. However, adenosine is known to exclusively dilate small resistance vessels <150 µm (10). Sudhir et al. (22) specifically studied the dilatory effects of adenosine and nitroglycerin with an ultrasound imaging catheter and Doppler velocimetry in dogs and reported that even a 6-mg adenosine bolus did not alter the diameter or compliance of epicardial vessels. Moreover, the epicardial vessels in our patients were already dilated with nitroglycerin before adenosine administration. Hence, a direct adenosine effect on true wave speed in epicardial arteries is highly unlikely.
Another possibility is an indirect effect via a reduction in coronary pressure due to elevated flow after microvascular dilation. However, there was no correlation between SPc change and change in coronary pressure, although distal pressure in the presence of a stenosis decreased significantly during hyperemia (Fig. 5A). Instead, we found a correlation between the change in SPc and the decrease in microvascular resistance after adenosine administration. Similarly, the decrease in SPc after stenosis revascularization also correlated with the change in microvascular resistance (Fig. 5B). In that case hyperemic microvascular resistance is reduced by increased coronary pressure distending the microcirculation (25). The equation to calculate SPc (Eq. 1) should therefore be examined in light of alternative explanations.
Consistency of SPc with pressure and velocity variations predicted by a lumped model of the coronary circulation.
Distal vasodilation hardly affected the magnitude of the pressure-related numerator of Eq. 1, whereas the summed velocity derivatives in the denominator increased (Fig. 6). This behavior of the two signal components corresponds very well with that predicted by a traditional lumped model of the coronary circulation derived from Spaan et al. (21) as depicted in Fig. 7. This model does not describe wave behavior in epicardial arteries but systolic-diastolic variations of coronary arterial pressure and flow and the effects of microvascular vasodilation and stenosis resistance on these epicardial signals.
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Fig. 7. Lumped model of the coronary circulation. Lumped epicardial vessel compliance (Ce) is separated from the much larger intramyocardial compliance (Cim) by a resistance (Rc) that represents the coronary resistance vessels. Intramyocardial tissue compliance (Cim) is connected to the large veins by an outflow resistance (Ro). Variations in arterial flow are caused by variation in Pa and by variations in intramyocardial tissue pressure (Pim) compressing the intramural vessels. Pim is assumed to have a fixed pattern, synchronized in time to left ventricular pressure and being higher in systole than in diastole. Rs, stenosis resistance; Pv, venous pressure.
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In the absence of a stenosis resistance (Rs = 0), the findings for SPc are readily explained by this model. A decrease in coronary resistance by vasodilation has no effect on the pulsatile pressure in the undiseased coronary artery, but both mean flow and the magnitude of flow variations increase, thereby increasing the summed velocity differentials, 
dU2. Hence, the ratio of summed pressure and velocity differentials, and thus SPc, are predicted to decrease with vasodilation. We observed an average reduction of about 70% in microvascular resistance with adenosine but only a 46% fall in SPc. This agrees with earlier findings in animals that variations in coronary flow increase proportionately less than the time-averaged flow with vasodilation (21). The effect of age on SPc is also fully consistent with the lumped model in Fig. 7, which predicts a decrease in flow velocity variations at higher vessel wall stiffness, i.e., lower epicardial compliance (Ce) and therefore an increased value of SPc.
The higher pressure pulsation-dependent numerator of the SPc equation in the presence of a stenosis (Fig. 6A) is also consistent with the lumped model, since the addition of Rs will make Pd more dependent on the large variations in intramyocardial tissue pressure. At the same time, the combination of Rs and Ce forms a low-pass filter, reducing the high-frequency content of the flow signal. Hence, the combination of an increased pulse pressure in Pd and decreased magnitude of flow variations results in a higher SPc in the presence of a stenosis on purely mathematical grounds.
"Windkesselness" of the coronary arteries.
An important point of consideration for the applicability of a lumped model is the relationship between the pulse wavelength and the length of the vessel under study. It has recently been shown that the difference between a transmission line model and a windkessel model of the systemic arterial circulation disappears when the wavelength exceeds twice the characteristic length of the vascular bed under study (12). The typical length of the epicardial arteries from base to apex is in the order of 10–15 cm. The distance from the site of measurement to entry points of transmural vessels is even less, and distal from this point of entry the vessels are compressed by cardiac muscle, generating waves. The wavelength that is relevant for our comparison depends on the frequency content of the physiological signals. In practice, this is bound by the sampling frequency of the measuring instrument, which was 100 Hz for flow velocity in our study. Hence, only signal frequencies of 50 Hz or lower carried sensible information. For a wave speed of 20 m/s, this corresponds to a minimal wavelength of 40 cm (wavelength = wave speed/frequency), which is substantially more than twice the typical coronary vessel length. Additional support for the above reasoning is gained from an earlier study by van Huis et al. (24) who demonstrated by using impedance analysis that the coronary system consists of a proximal part that can be described by a windkessel and a distal part that is not seen by high-frequency perturbations.
In light of these considerations, we have to conclude that our experimental observations are better described by a lumped reservoir model reflecting the windkesselness of the coronary circulation than by a wave transmission model from which the SPc equation (3) was originally derived. Based on similar reasoning, Wang et al. (26) recently proposed a hybrid model to describe aortic waveforms, where low-frequency variations in aortic pressure and flow are explained by a windkessel model and higher frequencies by wave equations. Khir et al. (8) also alluded to the dual windkessel/wave nature in the aorta that incorporates mechanics due to the windkessel effect with those of local wall mechanics giving rise to the wave nature of flow. It may be possible that an improved wave speed equation can be derived for the coronary arteries after higher frequency phenomena affected by epicardial compliance are separated from low-frequency effects of intramyocardial volume changes.
Methodological considerations.
Nitroglycerin was routinely given at the start of each procedure before inserting the dual-sensor guide wire. All hemodynamic measurements were obtained several minutes after nitrate administration, and we therefore could not assess a possible direct effect of nitroglycerin on SPc.
The hemodynamic signals in this study were digitized at a sampling frequency of 120 Hz. Since the velocity signal is only computed every 10 ms by the equipment console, the meaningful frequency content of the sampled analog output signal is limited to 50 Hz according to the Nyquist theorem, and digitizing at a frequency above 100 Hz is not very useful.
The pressure and velocity sensors at the tip of the guide wire used in our study were 3 cm apart, and one may argue that this violates a single-point measurement. Care was taken to place both sensors in a normal vessel segment without focal obstructions. As discussed above, the shortest wavelength of interest is about 40 cm, which is an order of magnitude longer than the distance between the sensors. Moreover, the rate of change is separately assessed for pressure and velocity signals in the SPc equation and integrated over a complete cardiac cycle. SPc has therefore lost connection with the well-defined periods in time. It is therefore unlikely that this sensor distance was of any consequence in the determination of SPc. This conclusion is supported by the similarity of findings for undiseased vessels at rest between this study and that of Davies at al. (3), where much care was taken to measure at the same location with two separate wires.
Acquisition of a high-quality ultrasound Doppler spectrum at low-flow conditions can be challenging. It could therefore be argued that velocity variations at baseline were underestimated due to a low-quality signal, thereby contributing to an apparent overestimation of SPc. Our group has ample experience with wire-based intracoronary velocity measurements (6, 20, 25), and only the recordings with high-quality velocity tracings both at rest and during vasodilation were included in this study. The close agreement between the baseline values found for undiseased vessels in the present study and in the also carefully executed study by Davies et al. (3) does not lend support to the existence of a systematic error due to low signal quality. Moreover, poor Doppler signals would introduce high-frequency noise, which would tend to increase dU2 in the denominator of Eq. 1.
In summary, we tested the applicability of the wave speed parameter SPc, derived from the single-point technique (3) to estimate local coronary pulse wave velocity in humans, for conditions commonly encountered in the catheterization laboratory. SPc was found to change with microvascular resistance and coronary pressure in a way that is inconsistent with wave speed behavior. Instead, the single-point estimate of wave speed was dominated by the systolic-diastolic variations of the pressure and velocity signals. These low-frequency characteristics of the intracoronary hemodynamic waveforms are not related to wave travel but to intramyocardial pump action and the presence of a stenosis, as described by a lumped reservoir model of the coronary circulation (21). The single-point method was derived from one-dimensional wave theory, which is appropriate for long systemic arteries, but the underlying concept may not be applicable to the coronary circulation that is characterized by short vessels, multiple sources of waves, and changing peripheral resistance during each cardiac cycle. Based on the findings reported in this study, we have to conclude that the single-point equation for SPc is inappropriate for estimating wave speed in coronary arteries.
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GRANTS
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This study was supported in part by the Netherlands Heart Foundation Grants 2000.090 and 2006B186.
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ACKNOWLEDGMENTS
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We gratefully acknowledge the skilled support of the clinical and nursing staff at our cardiac catheterization laboratory. Present address for C. Kolyva: Brunel Inst. for Bioengineering, Brunel Univ. West London, Uxbridge, UK.
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FOOTNOTES
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Address for reprint requests and other correspondence: M. Siebes, Dept. of Medical Physics, Academic Medical Ctr., Meibergdreef 9, 1105 AZ Amsterdam, The Netherlands (e-mail: m.siebes{at}amc.uva.nl)
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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REFERENCES
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|---|
- Arts T, Kruger TI, Van Gerven W, Lambregts JA, Reneman RS. Propagation velocity and reflection of pressure waves in the canine coronary artery. Am J Physiol Heart Circ Physiol 237: H469–H474, 1979.[Abstract/Free Full Text]
- Asmar R, Rudnichi A, Blacher J, London GM, Safar ME. Pulse pressure and aortic pulse wave are markers of cardiovascular risk in hypertensive populations. Am J Hypertens 14: 91–97, 2001.[CrossRef][Web of Science][Medline]
- Davies JE, Whinnett ZI, Francis DP, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans. Am J Physiol Heart Circ Physiol 290: H878–H885, 2006.[Abstract/Free Full Text]
- Davies JE, Whinnett ZI, Francis DP, Manisty CH, Aguado-Sierra J, Willson K, Foale RA, Malik IS, Hughes AD, Parker KH, Mayet J. Evidence of a dominant backward-propagating "suction" wave responsible for diastolic coronary filling in humans, attenuated in left ventricular hypertrophy. Circulation 113: 1768–1778, 2006.[Abstract/Free Full Text]
- Hirata K, Kawakami M, O'Rourke MF. Pulse wave analysis and pulse wave velocity. A review of blood pressure interpretation 100 years after Korotkov. Circ J 70: 1231–1239, 2006.[CrossRef][Web of Science][Medline]
- Kern MJ, Lerman A, Bech JW, De Bruyne B, Eeckhout E, Fearon WF, Higano ST, Lim MJ, Meuwissen M, Piek JJ, Pijls NH, Siebes M, Spaan JA. Physiological assessment of coronary artery disease in the cardiac catheterization laboratory: a scientific statement from the American Heart Association Committee on Diagnostic and Interventional Cardiac Catheterization, Council on Clinical Cardiology. Circulation 114: 1321–1341, 2006.[Abstract/Free Full Text]
- Khir AW, Swalen MJ, Feng J, Parker KH. Simultaneous determination of wave speed and arrival time of reflected waves using the pressure-velocity loop. Med Biol Eng Comput 45: 1201–1210, 2007.[CrossRef][Web of Science][Medline]
- Khir AW, O'Brien A, Gibbs JS, Parker KH. Determination of wave speed and wave separation in the arteries. J Biomech 34: 1145–1155, 2001.[CrossRef][Web of Science][Medline]
- Khoshdel AR, Thakkinstian A, Carney SL, Attia J. Estimation of an age-specific reference interval for pulse wave velocity: a meta-analysis. J Hypertens 24: 1231–1237, 2006.[Web of Science][Medline]
- Komaru T, Kanatsuka H, Shirato K. Coronary microcirculation: physiology and pharmacology. Pharmacol Ther 86: 217–261, 2000.[CrossRef][Web of Science][Medline]
- Megnien JL, Simon A, Valensi P, Flaud P, Merli I, Levenson J. Comparative effects of diabetes mellitus and hypertension on physical properties of human large arteries. J Am Coll Cardiol 20: 1562–1568, 1992.[Abstract]
- Mohiuddin MW, Laine GA, Quick CM. Increase in pulse wavelength causes the systemic arterial tree to degenerate into a classical windkessel. Am J Physiol Heart Circ Physiol 293: H1164–H1171, 2007.[Abstract/Free Full Text]
- Naka KK, Tweddel AC, Doshi SN, Goodfellow J, Henderson AH. Flow-mediated changes in pulse wave velocity: a new clinical measure of endothelial function. Eur Heart J 27: 302–309, 2006.[Abstract/Free Full Text]
- Nichols W, O'Rourke M. McDonald's Blood Flow in Arteries: Theoretic, Experimental and Clinical Principles (3rd ed.). Philadelphia, PA: Lea & Febiger, 1990, pp. 85–86, 102–110.
- Nichols WW, Singh BM. Augmentation index as a measure of peripheral vascular disease state. Curr Opin Cardiol 17: 543–551, 2002.[CrossRef][Web of Science][Medline]
- Parker KH, Jones CJ. Forward and backward running waves in the arteries: analysis using the method of characteristics. J Biomech Eng 112: 322–326, 1990.[Web of Science][Medline]
- Reneman RS, Meinders JM, Hoeks AP. Non-invasive ultrasound in arterial wall dynamics in humans: what have we learned and what remains to be solved. Eur Heart J 26: 960–966, 2005.[Abstract/Free Full Text]
- Rumberger JA Jr, Nerem RM, Muir WW 3rd. Coronary artery pressure development and wave transmission characteristics in the horse. Cardiovasc Res 13: 413–419, 1979.[Abstract/Free Full Text]
- Savitzky A, Golay MJ. Smoothing and differentiation of data by simplified least squares procedures. Anal Chem 36: 1627–1639, 1964.
- Siebes M, Verhoeff BJ, Meuwissen M, de Winter RJ, Spaan JA, Piek JJ. Single-wire pressure and flow velocity measurement to quantify coronary stenosis hemodynamics and effects of percutaneous interventions. Circulation 109: 756–762, 2004.[Abstract/Free Full Text]
- Spaan JA, Breuls NP, Laird JD. Diastolic-systolic flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res 49: 584–593, 1981.[Free Full Text]
- Sudhir K, MacGregor JS, Barbant SD, Foster E, Fitzgerald PJ, Chatterjee K, Yock PG. Assessment of coronary conductance and resistance vessel reactivity in response to nitroglycerin, ergonovine and adenosine: in vivo studies with simultaneous intravascular two-dimensional and Doppler ultrasound. J Am Coll Cardiol 21: 1261–1268, 1993.[Abstract]
- Ting CT, Chang MS, Wang SP, Chiang BN, Yin FC. Regional pulse wave velocities in hypertensive and normotensive humans. Cardiovasc Res 24: 865–872, 1990.[Abstract/Free Full Text]
- Van Huis GA, Sipkema P, Westerhof N. Coronary input impedance during cardiac cycle as determined by impulse response method. Am J Physiol Heart Circ Physiol 253: H317–H324, 1987.[Abstract/Free Full Text]
- Verhoeff BJ, Siebes M, Meuwissen M, Atasever B, Voskuil M, de Winter RJ, Koch KT, Tijssen JG, Spaan JA, Piek JJ. Influence of percutaneous coronary intervention on coronary microvascular resistance index. Circulation 111: 76–82, 2005.[Abstract/Free Full Text]
- Wang J Jr, O'Brien AB, Shrive NG, Parker KH, Tyberg JV. Time-domain representation of ventricular-arterial coupling as a windkessel and wave system. Am J Physiol Heart Circ Physiol 284: H1358–H1368, 2003.[Abstract/Free Full Text]
- Weber T, Auer J, O'Rourke MF, Kvas E, Lassnig E, Berent R, Eber B. Arterial stiffness, wave reflections, and the risk of coronary artery disease. Circulation 109: 184–189, 2004.[Abstract/Free Full Text]
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ABSTRACT
METHODS
P < 0.005 compared with previous step; 
P < 0.005 reference vessel compared with stenotic vessel.
