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Libin Cardiovascular Institute of Alberta and Departments of Cardiac Sciences, Physiology and Biophysics, Civil Engineering, and Mechanical Engineering, University of Calgary, Calgary, Alberta, Canada
Submitted 29 August 2006 ; accepted in final form 30 January 2007
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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transmitral flow; mitral velocity; E wave; diastolic suction
Wave intensity analysis (WIA) uses changes in pressure and velocity to quantify wave energy. However, the measured change in pressure may not be due entirely to waves; if we consider the reservoir function of the left heart, it becomes apparent that there needs to be a correction for the effects of compliance. As a first approximation of left heart compliance, we have used a linear estimation of the compliance of the passive LV to separate out the change in pressure caused by waves from that due to LV compliance (CLV). Only the change in pressure caused by waves should be incorporated into transmitral WIA.
Glossary
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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WIA applied to LV filling dynamics. The fundamental principles of WIA are outlined in the APPENDIX. WIA was applied at the mitral valve to quantify the energy of waves traveling to/from the LV throughout diastole. Pressure and velocity were measured at the mitral valve.
LV wave speed (c), which varies considerably throughout the cardiac cycle with changes in LV elastance, can be calculated continuously as
 | (1) |
is the density of the blood and D is the distensibility of the LV
 | (2) |
Windkessel. Any compliant structure in the cardiovascular system will behave as a reservoir. Wang et al. developed the windkessel theory in which the arterial (21) and venous (20) systems have been modeled as a blood-conducting system and a reservoir. The reservoir, or windkessel, is a hydraulic integrator where the change in pressure is related to the change in volume via the compliance of the chamber. In the case where we assume compliance to be constant, reservoir pressure is referred to as windkessel pressure (PWk) to be consistent with previous work (20, 21). Pmeas has been shown to be the instantaneous summation of a time-varying reservoir (i.e., windkessel) pressure and Pex, which represents the effects of traveling waves (21).
As described above, wave intensity is calculated from incremental changes in pressure. Conventionally, this has been calculated as the change in Pmeas. On the basis of windkessel theory, Pmeas should be divided into its reservoir (PWk) and wave components (Pex)
 | (3) |
With the use of linear regression, CLV was estimated as the slope of the LV pressure-volume (P-V) relation (calculated by sonomicrometry) during the interval between the nadir in LV pressure (PLV, when wave action related to early diastolic filling has ceased) and the onset of LA contraction (Fig. 1) (11)
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 | (5) |
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 | (6) |
 | (7) |
 | (8) |
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Experimental Preparation and Protocol
The protocol for the animal experiments conformed to the "Guiding Principles of Research Involving Animals and Human Beings" of the American Physiological Society and was approved by the University of Calgary Animal Care Committee.
Studies were performed in six healthy mongrel dogs (21–27 kg body wt), which were anesthetized initially with thiopental sodium (25 mg/kg); a surgical plane of anesthesia was maintained with fentanyl citrate (4 mg/h iv), adjusted as necessary. The dogs were ventilated with 1:1 nitrous oxide-oxygen via a constant-volume respirator set to deliver a tidal volume of 19 ml/kg at a rate of 18 breaths/min. Blood gases were monitored and ventilatory rates were adjusted to maintain normal levels and pH. Normal body temperature was maintained with a heating pad.
Instrumentation was performed through a midline thoracotomy. Ultrasonic flow probes (Transonic Systems, Ithaca, NY) were placed around the aorta (as close to the aortic valve as possible) and a branch of a pulmonary vein (PV). Micromanometer-tipped catheters (8-Fr, model PC-480, Millar Instruments, Houston, TX) with fluid-filled reference lumens were introduced retrogradely through the femoral artery and the left carotid artery and used to measure pressure in the aorta and the LV, respectively. The tip of the LV catheter was placed close to the mitral valve. Micromanometer-tipped catheters (3.5-Fr, model SPR-524, Millar Instruments) were introduced directly through the appendage and a PV and used to measure pressure in the PV and LA, respectively. A stiff plastic introducer was used to insert the PV catheter into a right PV. The PV catheter was then advanced to a left PV, different from the PV with the flow transducer. Orthogonal LV dimensions were measured with pairs of sonomicrometry crystals positioned near the endocardium: base-apex (Dba), septum-free wall (Dsfw), and anterior-posterior (Dap) dimensions. A large-bore catheter was inserted into the left jugular vein for volume loading. A single-lead ECG was recorded.
After instrumentation, the pericardium was reapproximated with single interrupted sutures (17). The dog was turned slightly toward its right, and a 5-MHz transesophageal probe (model 77020AC, Hewlett-Packard, Palo Alto, CA) was advanced to the level of the heart. The echocardiographic two-chamber, long-axis view(s) was used to place the sample volume at the level of the tips of mitral valve leaflets, and the transducer position was adjusted to record maximum mitral flow velocity (model 5500, Philips Medical Systems, Markham, ON, Canada). The traces were recorded on VHS videotape for subsequent analysis. Heart rate was maintained at 60–90 beats/min with ULFS-49 (7) as needed. The ventilator was turned off at end expiration during each 30-s period of data collection.
Data were first recorded under control conditions at an LV end-diastolic pressure (LVEDP) of 
7 mmHg. By volume loading (10% pentastarch in 0.9% NaCl; Pentaspan, Bristol-Myers Squibb Canada), LVEDP was increased in 3-mmHg increments to 25 mmHg; data were recorded at each level.
Data Handling
Signals were recorded at a sampling rate of 200 Hz using data acquisition software (CARDIOSOFT, Sonometrics, London, ON, Canada). A frame counter was used to synchronize the hemodynamic data and Doppler flow velocities. Static images of Doppler flow velocity at the mitral valve and the ECG were captured from videotape (Video Studio 6, Ulead Systems, Taipei, Taiwan) and digitized using a custom-made program (Matlab, Mathworks, Natick, MA); the ECG and mitral flow velocity waveforms were exported to a spreadsheet (Excel, Microsoft Office, Microsoft, Redmond, WA). Sonomicrometry dimension recordings were "cleansed" (CARDIOSOFT) of extraneous noise. All hemodynamic data were exported to a data-analysis program (CVWorks, Advanced Measurements, Calgary, AB, Canada), and the data from the beat selected for analysis were isolated. The frame count and end-systolic and end-diastolic points were identified. Data were exported to a spreadsheet (Excel) and aligned in time with respect to mitral flow velocity. All data were filtered at 30 Hz (low-pass Butterworth filter; Matlab).
LV volume (VLV) was calculated as
 | (10) |
 | (11) |
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Data from a representative cardiac cycle and the results of WIA are shown in Fig. 2. From end systole to the start of LA contraction, the change in pressure associated with the increasing volume (dPWk) was calculated and subtracted from the change in Pmeas (dPmeas); the result is the change in pressure due only to wave action (dPex; Fig. 2B). During early diastole, dPWk > 0, increasing the absolute magnitude of dPex. As the LV relaxes, a backward expansion wave (BEW) slows thecolumn of ejected blood, contributing to aortic valve closure (Fig. 2, C and D). After valve closure, net intensity becomes zero, because the incremental change in velocity (dU) is zero. During isovolumic relaxation, pressure decreases rapidly, due to decreasing elastance. Because of the dP dependence of Eqs. 6 and 7, WIA yields equal and opposite intensities. Because LV relaxation is not complete when the mitral valve opens, a net BEW in the LV tends to pull blood from the LA [diastolic suction (DS)]. The effect of the windkessel correction (i.e., using dPex, rather than dPmeas) is greatest during the acceleration phase of the E wave; quantitative results are presented in Table 3. The average energy of diastolic suction (IW-DS) was 0.26 J/m2 originally and increased by a factor of 2.6 (to 0.68 J/m2) after the correction was applied. A t-test showed these values to be significantly different from zero, with P = 0.0014 and 0.0070, respectively. The paired t-test showed a significant effect of the correction (P = 0.017). IW-DS increased with LVEDP before and after the correction (Fig. 4). The relative increase was independent of LVEDP.
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Having scaled the rate of change of LV emptying (i.e., dVLV/dt) to the integral of Qao, we can compare dVLV/dt (equivalent to transmitral flow) with Umitral. Averaged E wave patterns of dVLV/dt and Umitral from all experiments are shown in Fig. 5. The peak occurs substantially earlier for dVLV/dt than for Umitral. Peak dVLV/dt occurs at approximately the time of the maximum left atrial pressure (PLA)-PLV gradient; peak Umitral occurs at approximately the time of the PLA-PLV crossover, i.e., when PLA = PLV.
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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The parameters of WIA are calculated from incremental changes in pressure and velocity at a specific cross section of a vessel or chamber. Although the passage of waves clearly induces incremental changes in pressure, not all incremental changes in pressure are due to the passage of waves: changes in pressure may also be due to the elastance of a structure. For example, during isovolumic contraction and relaxation, ventricular pressure changes, because the elastance of the ventricle increases or decreases, respectively, while volume nominally remains constant. During these intervals, waves are absent. In contrast, when the LV ejects blood into the elastic (compliant) aorta, arterial pressure increases, because aortic inflow is temporarily greater than aortic outflow, and, thus, aortic volume increases (21). Therefore, to quantify properly the effects of waves on arterial pressure and velocity (flow), measured arterial pressure first must be "corrected" to exclude the component of the incremental change in pressure that is due only to this increase in arterial volume and not, fundamentally, due to the passage of waves. This is the rationale for separation of arterial pressure into the sum of a PWk and a wave-related pressure.
Windkessel Correction Applied to LV Filling
In this study, we have applied that same rationale to transmitral flow and found that the energy associated with DS was more than doubled (by a factor of 2.6) by the correction. This was because the corrected change in wave-related pressure (i.e., 
Pex) was greater than the change in Pmeas (Pmeas) during early filling. Increasing volume is associated with increasing PWk because of the elastance of the passive LV. As illustrated in Fig. 1, Pmeas decreased, despite the increasing volume, thus intimating that had it not been for the windkessel effect, the decrease in pressure would have been even greater than that actually measured.
Mitral Flow, Velocity, and Effective Area
This study extends and enhances our recent description of DS in the LV (23), in that we have shown that the magnitude of the energy we associate with DS is even greater after we account for the windkessel effect. However, the results of this study also raise new questions about our previous interpretations. We suggested previously that the energy of the BEW accelerated the motion of blood from the LA to the LV at the beginning of filling. This interpretation was consistent with the facts that the maximum PLA-PLV gradient coincided with the maximum rate of change of E wave velocity and that the peak E wave velocity was achieved when the PLA-PLV gradient returned to zero. [This timing is also supported by the work of Courtois et al. (3).] This relation of pressure gradient to velocity suggests that the inertia of the blood is important and dominant. As others had done before us (13), we implicitly assumed that the Doppler-measured flow velocity was representative of transmitral flow.
We found that the time course of LV filling during the E wave was markedly and fundamentally different, depending on whether it was assessed by velocity or volumetric flow (using the derivative of VLV measured by sonomicrometry). As illustrated in Fig. 5, peak flow occurred relatively early, at the time of the peak PLA-PLV gradient. If both observations are to be accepted, it could be due to a decrease in effective mitral valve area, which would account for a high velocity, despite decreasing flow (9, 11). A similar conclusion was reached recently by Bowman et al. (2), who measured velocity by Doppler echocardiography and flow as the derivative of MRI-calculated VLV in patients. However, our observation and that of Bowman et al. could be due to the vagaries of so-called shape changes. We found that VLV, as estimated from orthogonal crystals, increased during "isovolumic" relaxation, producing nonrectangular P-V loops and dVLV/dt > 0 (Fig. 6). These shape changes equate to a filling volume flow rate on the order of 50 ml/s, which is not insignificant on the scale of transmitral flow. An increase in VLV during the isovolumic period has also been noted by others (1, 11, 16) and documented as an outward motion of the LV wall. Ruttley et al. (16) found that VLV can increase up to 10% during this interval. If isovolumic relaxation is truly isovolumic, an outward motion must occur concurrently with an inward motion. Ruttley et al. and Altieri (1) pointed out that this change in LV shape may be fundamentally related to the descent of the mitral valve late in the isovolumic period. More recently, the work of Karlsson et al. (8) supported this view by demonstrating downward mitral leaflet motion before leaflet separation. The P-V loops published by Little et al. (11) appear to have the same nonrectangular shape as our P-V loop, indicating a volume change during isovolumic relaxation, but this does not appear to be consistent with their dV/dt plots. They suggest that the time course of LV dV/dt is similar to that of Doppler-measured Umitral.
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Limitations
These studies were conducted in open-chest anesthetized dogs, because it was not feasible to measure all these parameters in a more intact experimental preparation. Accordingly, artifacts may have been introduced, and the salient conclusions from this study require validation from more physiological experimental models or clinical observations.
Doppler echocardiography may underestimate true peak flow velocity for two reasons: 1) placement of the sample volume is static, whereas the mitral annulus moves throughout diastole, displacing the leaflets and, therefore, the maximum-velocity location, and 2) for measurement of the maximum velocity, the scan line must be exactly aligned with the flow, and any misalignment will underestimate the true velocity, in proportion to the cosine of the angle. Thus it is likely that the maximum-velocity point might be missed and/or it might be interrogated from a nonoptimal angle, especially if we consider that the view is only two-dimensional during recording.
As a first approximation and because of the limitations of the data, we used a linear estimate of CLV as the basis for our windkessel correction. This approach neglects the effects of any possible changes in LA volume (VLA) and the complexities of the LV P-V relation, which has been shown to be sigmoidal (12, 19). Thus, depending on the volume and the position along this sigmoidal relation, the correction for compliance could be even greater than we have shown. However, our intent was merely to illustrate the compliance dependence qualitatively. In principle, this study could be repeated with alternative techniques (e.g., MRI) that could account for VLA and VLV changes accurately.
In conclusion, the left heart reservoir function implies that changes in VLA and VLV will change pressure, and when these changes in pressure are discounted, we find that the energy associated with DS is more than twice as great as that calculated previously. In principle, within the heart as well as in the vasculature, volume-related changes in pressure (i.e., the windkessel or reservoir effect) should be discounted when the effects of wave motion are assessed.
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APPENDIX |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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) of the blood and the wave speed (c), intensities of simultaneous forward- and backward-going waves (dIW+ and dIW–, respectively) can be calculated separately (14, 18)
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The characteristics of a wave (i.e., expansion or compression) are distinguished by the sign of dP
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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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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TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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, IW-DS from original WIA; 
, IW-DS from corrected WIA. IW-DS increases with volume loading. Original and corrected IW-DS are linearly correlated with increasing LVEDP (r2 = 0.20 and 0.37, respectively).
