INTRODUCTION

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ALTHOUGH AORTIC PRESSURE (P_Ao) is the main determinant of coronary arterial pressure and flow, it is clear that coronary arterial pressure and flow are not simple functions of P_Ao (15). The coronary circulation is particularly complicated, in that blood flows through the myocardium, which, as it contracts, increasingly impedes flow. In the arteries perfusing the left ventricle (LV), systolic coronary flow is small compared with diastolic flow (5-7, 27, 30), in contradistinction to those arteries perfusing the right ventricle, in which maximal flow occurs during systole (3). [That systolic flow is small in large coronary arteries is related to the fact that flow reverses in the penetrating arteries (4), that subendocardial flow is retrograde (8), and that the capacitance of large epicardial coronary arteries is substantial (4).] The mechanisms by which LV contraction impedes left coronary blood flow have been studied for many years. The "vascular waterfall" (7) and the "intramyocardial pump" models (30) have been used to explain how increasing intramyocardial pressure impedes coronary blood flow during systole. Using a "time-varying elastance" model, Krams and colleagues (16) explained how systolic flow is impeded by changes in extravascular stiffness that result from contraction of the fibers surrounding intramyocardial blood vessels.

These models explain the early-systolic decrease in coronary blood flow, but they do have limitations. First, they cannot explain the increase in coronary blood flow (4) that occurs after the initial minimum, despite the continuing increase in intramyocardial pressure and myocardial elastance. Second, because perfusion pressure was held constant in many previous studies, the results of those studies might not apply to physiological conditions when coronary pressure and flow vary throughout a cardiac cycle. Furthermore, coronary pressure and flow are determined by 1) upstream aortic effects, which are related to LV function and the properties of the systemic circulation, and 2) downstream microcirculatory effects, which are also related. Changes in LV function (e.g., changes in contractility) will affect coronary perfusion pressure and myocardial compressive force, and results from studies using constant perfusion pressure and maximal coronary vasodilation may over- or underestimate the effects of contractility on coronary blood flow.

Therefore, because of the need to identify and quantitate upstream and downstream effects, we employed wave-intensity analysis (WIA), a time-domain analysis introduced by Parker and colleagues (13, 22, 23). [Recently, WIA was employed to elucidate the dynamics of pulmonary venous flow (29) and, in the neonate, pulmonary arterial pressure (10).] On the basis of measurements of left coronary arterial pressure and velocity, WIA can discriminate downstream from upstream events and represent their interaction.

The purposes of the present study were 1) to clarify the dynamic pressure and velocity characteristics of the distal LV coronary circulation and 2) to provide a mechanistic explanation for acceleration and deceleration of coronary flow with use of WIA.

Glossary

c	Wave speed
dIW	Net intensity (formerly called dPdU)
dIW+	Intensity of a forward-going wave
dIW	Intensity of a backward-going wave
dP	Incremental change in pressure during the sampling interval at any time and location
dP+	Difference in pressure across a forward-going wave
dP	Difference in pressure across a backward-going wave
dU	Incremental change in velocity during the sampling interval at any time and location
IW+	Energy of a forward-going wave
IW	Energy of a backward-going wave
LCx	Left circumflex coronary artery
LV	Left ventricle (ventricular)
P	Pressure
	Density
U	Velocity
WIA	Wave-intensity analysis

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Instrumentation. The studies were performed on 10 18- to 20-kg mongrel dogs of either gender. Dogs were anesthetized with thiopental sodium and then with fentanyl citrate and ventilated with a constant-volume respirator to maintain normal blood gas tensions and pH. The pericardium was opened along the atrioventricular groove. P_Ao and LV pressure (P_LV) were measured using catheter-tipped manometers (Millar Instruments, Houston, TX) inserted via the right femoral and left carotid arteries, respectively. The catheter-tipped manometers in the aorta (just beyond the aortic valve) and LV were referenced via their fluid-filled lumens so that absolute values of pressure could be ascertained. All pressures were referenced to the midplane of the LV. A pneumatic constrictor (In Vivo Metrics, Healdsburg, CA) was placed around the inferior vena cava. After cardiac instrumentation, the pericardium was reapproximated by single interrupted sutures.

View larger version (20K): [in this window] [in a new window]   Fig. 1.   Schematic diagram of the placement of the catheter-tipped pressure transducer and the Doppler Flowire within the distal left circumflex coronary artery (LCx). Pressure and velocity were measured at the same location.

Doppler delay. Using a linear potentiometer to measure the position of the plunger of a 5-ml syringe (11), we compared the differentiated position signal with fluid velocity as measured using a Doppler Flowire (Cardiometrics, Mountainview, CA). We measured the delay by a foot-to-foot method (method 1) and a 50% maximum method (method 2; Fig. 2). Forty-nine observations were analyzed.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Determination of delay time of Doppler Flowire. A foot-to-foot method (method 1) or a 50% maximum method (method 2) was used to compare velocity of the syringe plunger (Uplunger) with velocity of the water (UFlowire).

Protocols. After instrumentation and a 15- to 20-min stabilization interval, all hemodynamic data (P_LV, P_LCx, P_Ao, U_LCx, and L_LV) were recorded while the heart was paced from the right atrium (control 1). A second set of control data (control 2) was recorded while the heart was paced from the right ventricle with single stimuli. Finally, paired pacing data were recorded while the heart was paced from the right ventricle with paired stimuli to increase contractility (25). Using P_LV-L_LV loops described during caval constriction under control 2 and paired-pacing conditions, we defined a linear end-systolic P_LV-L_LV relation, the slope of which [maximal elastance (E_max)] was taken as a measure of contractility. Individual hearts were paced at the same rate in control 1, control 2, and paired-pacing conditions. Among the different dogs, heart rate ranged from 85 to 100 min¹. All the hemodynamic data were sampled at ~200 Hz and recorded using a computer system (Sonometrics, London, ON, Canada).

WIA. WIA was used to identify and quantitate upstream (aortic) and downstream (coronary microcirculatory) events and their interaction. WIA provides information regarding the direction, intensity, and type of waves present at any given moment and location in a blood vessel (12, 22, 23). Because WIA is a time-domain analysis, wave intensity can be related temporally to hemodynamic parameters and beat-to-beat analyses can be performed (13, 22). WIA was developed by solving nonlinear one-dimensional equations of motion and is based on the concept that "waves" (i.e., propagated disturbances) that travel through the vasculature are manifested by changes in pressure and velocity (23). The energy that is transported by a wave can be quantified by measuring the changes in pressure and velocity across the wave front (19). Waves can be forward going (i.e., in the direction of net blood flow) or backward going in direction and compression or expansion in type. Thus there are four possible combinations: forward-compression, backward-compression, forward-expansion, and backward-expansion (Table 1). Compression waves have a "pushing" effect and increase pressure. Forward-going compression waves increase pressure and increase velocity, whereas backward-going compression waves increase pressure and decrease velocity (in the forward direction). Expansion waves have a "pulling" effect and decrease pressure. Forward-going expansion waves decrease pressure and decrease velocity, whereas backward-going expansion waves decrease pressure and increase velocity (in the forward direction).

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Data analysis. Using specialized software (CVSOFT, Odessa Computer Systems, Calgary, AB, Canada), we calculated dP and dU, the incremental difference in P_LCx and U_LCx during a sampling interval from measured P_LCx and U_LCx. dI_W⁺, dI_W, dI_W, I_W⁺, and I_W were calculated as described above. On the basis of Doppler delay measurements (see below) and as confirmed by the manufacturer, we advanced all the Doppler Flowire data 20 ms in time.

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View larger version (23K): [in this window] [in a new window]   Fig. 3.   A: left ventricular pressure (PLV), aortic pressure (PAo, dashed line), LCx pressure (PLCx), and LCx velocity (ULCx) waveforms during an early-systolic interval of a representative cardiac cycle. B: backward intensity (dIW, light solid line), forward intensity (dIW+, dashed line), and net wave intensity (dIW, heavy solid line) waveforms. C, compression wave. Solid vertical lines indicate end diastole (ED), the instant at which PLV exceeds PAo (i.e., the PLV-PAo crossover), and the time at which PLV achieves its peak value. Dashed vertical line, ULCx minimum.

View larger version (12K): [in this window] [in a new window]   Fig. 4.   An idealized magnification of coronary pressure and PAo during isovolumic contraction (cf. Fig. 3) illustrates how we measured the effects of LV systolic contraction on coronary pressure. The 2 vertical lines indicate end-diastole (ED) and the moment at which the PLV-PAo crossover occurred; PX indicates the PLCx-PAo pressure difference at that moment. dPLCx/dt and dPAo/dt, average slopes of PLCx and PAo during the isovolumic interval.

Statistics. Under each condition (control 1, control 2, and paired pacing), 10 cardiac cycles were randomly selected and the average values were obtained. Results from the 10 dogs are expressed as means ± SD. Student's paired t-test was used to identify statistically significant differences; P < 0.05 was considered significant.

	RESULTS

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Measurement of Doppler delay. According to method 1 (Fig. 2), the mean delay was 22.7 ± 0.6 ms and the median was 22.9 ms. According to method 2, the mean delay was 22.0 ± 0.8 ms and the median was 21.7 ms.

Net wave intensity. Figure 5 indicates the changes in coronary net wave intensity during a typical cardiac cycle. Between end diastole and the moment that U_LCx reached a minimum, a backward-going compression wave was dominant, which was associated with increasing P_LCx and decreasing U_LCx. Between the U_LCx minimum and the moment that P_LCx reaches a maximum, a forward-going compression wave was dominant, which was associated with a further increase in P_LCx and increasing U_LCx. Later, during LV relaxation, a forward-going expansion wave developed and became dominant until the aortic valve closed at the incisura. This expansion wave was associated with decreases in P_LCx and U_LCx. At the incisura, there was a brief, dominant, forward-going compression wave that was associated with increases in P_LCx and U_LCx. As LV relaxation continued, however, a backward-going expansion wave that was associated with decreased P_LCx and increased U_LCx became dominant.

View larger version (22K): [in this window] [in a new window]   Fig. 5.   A: PLV, PAo (dashed line), PLCx, and ULCx waveforms during a representative cardiac cycle. B: net wave intensity (dIW) waveform. C, compression wave; E, expansion wave. Solid vertical line, end diastole (ED); dashed vertical lines, ULCx minima.

Intensity of forward- and backward-going waves during LV contraction. Figure 3 illustrates early systolic events in detail. Figure 3A shows how P_LCx differs from P_Ao. Diastolic P_Ao fell monotonically until it was exceeded by P_LV (i.e., at the P_Ao-P_LV crossover). From middiastole, distal P_LCx was identical to P_Ao but, at the beginning of LV isovolumic contraction (i.e., at end diastole), P_LCx stopped falling. Thereafter, it remained constant or began to increase somewhat, but in either case it exceeded P_Ao until near the end of LV ejection.

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Effects of paired pacing. During control 1, P_X was 4.3 ± 2.5 mmHg, which doubled during paired pacing (P < 0.0001), an intervention that increased E_max (i.e., contractility) almost threefold (Table 2). During the isovolumic contraction interval, dP_Ao/dt was 53.9 ± 19.5 mmHg/s during control 1 and did not change with paired pacing. dP_LCx/dt was 3.4 ± 4.4 during control 1 (P < 0.0001 vs. dP_Ao/dt) and increased to 142 ± 25 mmHg/s during paired pacing (P < 0.0001). As shown in Table 2, paired pacing increased the peak value of dI_W by a factor of ~3 and I_W by a factor of ~4. (There were no significant differences between data obtained during control 1 and control 2.)

Intensity of forward- and backward-going waves during LV relaxation. As illustrated in Fig. 6, after the beginning of LV relaxation and the beginning of the decrease in P_LCx, forward and backward expansion waves began to be generated. Typically, relaxation was characterized by triplets of forward and backward waves. The forward and backward expansion waves in late systole were followed by forward and backward compression waves temporally related to aortic valve closure, after which there were paired forward and backward expansion waves.

View larger version (23K): [in this window] [in a new window]   Fig. 6.   A: PLV, PAo (dashed line), PLCx, and ULCx waveforms during early relaxation of a representative LV cycle. B: backward intensity (dIW, light solid line), forward intensity (dIW+, dashed line), and net wave intensity (dIW, heavy solid line). E, expansion wave; C, compression wave.

	DISCUSSION

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Among the systemic circulations, the LV coronary circulation is particularly complicated, because its driving force and impedance to flow are dynamic functions of contraction. LV contraction not only increases coronary perfusion pressure but, several milliseconds earlier at end diastole, begins to increase the compression of the microcirculation. LV relaxation not only decreases coronary perfusion pressure but decreases the compression of the microcirculation. Therefore, coronary blood velocity is determined by upstream (aortic) and downstream (microcirculatory) events. Compared with previous approaches, the salient advantage of WIA is that it provides information about upstream and downstream events in the time domain and, therefore, on a beat-to-beat basis, provides direct information about the interaction of the upstream and downstream effects.

From the outset, it should be made clear that our WIA approach to waves in the arteries is fundamentally different from those approaches that are based on Fourier analysis. Fourier analysis is based on the observation that any periodic waveform can be expressed as the summation of sinusoidal waves of different frequencies (harmonics), each with the appropriate amplitude and phase. These sinusoidal wave trains are the fundamental basis of any Fourier technique, an archetypal example being the synthesis of speech from different sinusoidal tones.

An alternative approach to waves, WIA, is to consider the propagation of individual wave fronts characterized by a change in pressure, dP, and velocity, dU. An example of this type of wave is the "bore" seen in some river estuaries, notably the Severn, where a single wave front generated by the tide propagates up the river. It is convenient to consider small, infinitesimal wave fronts as the fundamental elements of our analysis, since any finite waveform can be constructed from a sequence of individual wave fronts of the appropriate magnitude. For example, any waveform sampled at uniform intervals can be thought of as the summation of the changes between successive samples. This approach to the synthesis of a finite waveform has the advantage that it does not make any assumptions about periodicity and can therefore be applied to transient and periodic waveforms. Beat-to-beat analysis is amenable to WIA, whereas it is not if Fourier techniques are employed.

The pressure change across a wave front can be positive, dP > 0 (which defines the wave as a compression wave), or negative, dP < 0 (which defines it as an expansion wave). Compression waves arise from pushing or blowing, and they cause an increase of velocity in the direction of the wave. Expansion waves arise from pulling or sucking, and they cause a decrease of velocity in the direction of the wave. If we define velocity to be positive in the direction of mean blood flow, a forward-going compression wave will accelerate the blood (dU > 0), whereas a backward-going compression wave will decelerate the blood (dU < 0). Similarly, a forward-going expansion wave will decelerate the blood (dU < 0), whereas a backward-going expansion wave will accelerate the blood (dU > 0). It may be helpful to think of blood flow in a coronary artery being manipulated by two "Maxwell demons," one at the arterial end of the artery and the other at the microcirculation end. The arterial demon could accelerate coronary blood flow by blowing into his end of the artery, which would increase the pressure, which would result in a forward-going compression wave. If, however, the microcirculation demon blew into his end of the artery, the pressure would be similarly increased, creating a backward-going compression, which would decelerate the flow. If the microcirculation demon wanted to accelerate the flow, he would have to suck on the artery, thereby decreasing the pressure. Simply measuring the change in pressure at some point in the artery cannot reveal the direction of travel of the wave front causing the change in pressure. To do this, it is necessary to simultaneously measure the change in velocity. If, however, there are simultaneous forward and backward waves, as is generally the case in the coronary arteries, then further analysis of the measured dP and dU is necessary to distinguish the properties of the two waves. WIA allows us to do this.

Between end diastole and the moment that U_LCx reached a minimum, LV contraction generated a dominant, backward-going compression wave, which had the effect of increasing P_LCx and decreasing U_LCx (Fig. 5). (The compression of the vasculature resulted in a "pushing" effect that traveled backward, against the direction of blood flow.) Between the U_LCx minimum and the moment that P_LCx reaches a maximum, a forward-going compression wave generated by the increasing P_Ao became dominant, which continued to increase P_LCx further and to increase U_LCx. (The increase in P_Ao resulted in a pushing effect that traveled forward, in the same direction as blood flow.) Later, as the LV began to relax and P_Ao began to fall, a forward-going expansion wave developed and became dominant until the aortic valve closed at the incisura. (The decrease in P_Ao resulted in a "pulling" effect that traveled forward, in the same direction as blood flow.) This expansion wave decreased P_LCx and U_LCx. Aortic closure generated a brief, dominant, forward-going compression wave that increased P_LCx and U_LCx. As LV relaxation continued, however, a backward-going expansion wave became dominant, which decreased P_LCx and increased U_LCx. (Decreasing LV compression resulted in a pulling effect that traveled backward, against the direction of blood flow.)

Effects of LV contraction on coronary blood pressure and velocity. From high-fidelity measurements of aortic and distal coronary pressure, we have demonstrated that P_LCx is greater than P_Ao during LV isovolumic contraction, an observation that, to our knowledge, has not been reported previously. WIA identified an early-systolic backward-going compression wave [presumably generated by the contracting myocardium, which causes retrograde subendocardial flow (4) and reverses flow in small penetrating branches (8)] that increased P_LCx and decreased U_LCx. When LV contractility was augmented by paired pacing, the changes in coronary pressure and the changes in the backward-going compression wave were consistent: P_X, dP_LCx/dt, dI_W, and I_W increased (Table 2). Westerhof and Sipkema and their colleagues (16-18, 33) related LV elastance to coronary flow impediment, we have preliminary data that demonstrate that the peak intensity of the backward compression wave is directly related to systolic coronary flow reduction (32), and Suga and Sagawa and co-workers (28, 31) equated increased myocardial elastance with increased contractility. Thus we conclude that paired pacing increased I_W, which caused the changes in P_LCx.

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Effects of LV relaxation on coronary blood pressure and velocity. Consistent with the concept that changes in LV elastance are similarly reflected in all of its cavities, luminal and vascular (16), LV relaxation would appear to generate "aspirating forces" (34), which are manifest as forward- and backward-going expansion waves. With respect to the LV lumen, relaxation decelerates the column of aortic blood and decreases P_Ao; this effect is observed in the coronary artery as a forward expansion wave. With respect to the intramural LV vasculature, relaxation decreases microvascular compression; this effect is observed in the coronary artery as a backward expansion wave. Thus, in the coronary artery, the effects of LV relaxation are seen as forward (via the aorta) and backward (via the vasculature) expansion waves. Closure of the aortic valve generated forward and backward compression waves that interrupted the expansion waves that preceded and followed them. (Presumably the forward compression wave generated by aortic closure was primary, and the backward compression wave generated by positive reflection from "closed-end" microcirculatory reflection sites was secondary.) Consistent with the fact that dI_W was positive during this interval (i.e., the forward compression wave was larger than the backward wave), velocity increased. After these paired forward and backward compression waves, relaxation again dominated as manifest by paired (i.e., forward and backward) expansion waves. Thus LV relaxation seems to become manifest as triplets of forward and backward waves.

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Limitation of the study. As described in METHODS, because the caliber of the circumflex branch did not admit a catheter with a lumen, the absolute value of the high-fidelity P_LCx could not be ascertained by comparison to the output of an external transducer. Because dI_W⁺ and dI_W were negligible in the coronary artery during the interval preceding end diastole, we assumed that P_LCx was equal to P_Ao, and we therefore matched P_LCx to P_Ao at end diastole. (This assumption was supported by measurements using an open catheter.) To the degree that this procedure was not accurate or appropriate, the values of P_X might have been over- or underestimated. However, the slopes of P_Ao and P_LCx do not depend on the absolute values of P_Ao and P_LCx, and the facts that the two pressures diverged and diverged more rapidly after paired pacing are unequivocal.

Conclusions. WIA elucidates the dynamics of coronary blood flow and identifies and quantitates the upstream (i.e., aortic) and downstream (i.e., coronary vascular) effects. During isovolumic contraction, distal coronary pressure exceeds P_Ao and coronary velocity decreases, caused by a backward-going compression wave that is generated by increasing myocardial elastance, effects that are magnified when LV contractility is augmented by paired pacing. During LV relaxation, decreasing elastance appears to generate forward-going (via the aorta) and backward-going (via the coronary vasculature) expansion waves. Thus, during contraction, upstream and downstream effects produce compression waves, and, during relaxation, upstream and downstream effects produce expansion waves. Coronary pressure and velocity depend on the balance of these effects.