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Am J Physiol Heart Circ Physiol 292: H1533-H1540, 2007. First published November 17, 2006; doi:10.1152/ajpheart.00837.2006 Free Article
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Wave intensity analysis of left atrial mechanics and energetics in anesthetized dogs

Tracy N. Hobson, Jacqueline A. Flewitt, Israel Belenkie, and John V. Tyberg

Departments of Cardiac Sciences and Physiology/Biophysics, Libin Cardiovascular Institute of Alberta, University of Calgary, Calgary, Alberta, Canada

Submitted 3 August 2006 ; accepted in final form 9 November 2006


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The left atrium (LA) acts as a booster pump during late diastole, generating the Doppler transmitral A wave and contributing incrementally to left ventricular (LV) filling. However, after volume loading and in certain disease states, LA contraction fills the LV less effectively, and retrograde flow (i.e., the Doppler Ar wave) into the pulmonary veins increases. The purpose of this study was to provide an energetic analysis of LA contraction to clarify the mechanisms responsible for changes in forward and backward flow. Wave intensity analysis was performed at the mitral valve and a pulmonary vein orifice. As operative LV stiffness increased with progressive volume loading, the reflection coefficient (i.e., energy of reflected wave/energy of incident wave) also increased. This reflected wave decelerated the forward movement of blood through the mitral valve and was transmitted through the LA, accelerating retrograde blood flow in the pulmonary veins. Although total LA work increased with volume loading, the forward hydraulic work decreased and backward hydraulic work increased. Thus wave reflection due to increased LV stiffness accounts for the decrease in the A wave and the increase in the Ar wave measured by Doppler.

hemodynamics; left atrium; A wave; Ar wave; Doppler echocardiography

THE LEFT ATRIUM (LA) functions as a booster pump during late diastole, contributing ~20% to left ventricular (LV) filling (32). Doppler echocardiography has shown that there can be retrograde flow (i.e., the atrial reversal or Ar wave) into the pulmonary veins (PV) as blood is propelled forward into the LV during atrial systole (i.e., the transmitral A wave) (30). Analysis of the A and Ar waves may be useful in the assessment of various cardiac conditions (11, 12, 30, 33).

Previous studies have demonstrated an inverse relationship between LV end-diastolic pressure (PLVED) and forward flow during atrial systole (16, 25, 31). Increased LV operative stiffness, which is related to the increase in PLVED, is recognized as one mechanism responsible for diminished atrial contribution to LV filling (32, 45) and augmented reversed flow into the PV (2, 22, 24, 32, 41). Although it is intuitive that such a relationship would exist, the fundamental mechanisms have not been studied.

Wave intensity analysis (WIA) (34, 35, 43) can be used to discriminate between the effects of upstream and downstream events at a specific location and provides a means of quantifying the energy carried by waves traveling through the heart and vasculature. A wave [i.e., a "propagated disturbance" (26)] changes both pressure (P) and blood velocity (U); wave "intensity" is an instantaneous function of the incremental changes in P and U and is expressed as power normalized by cross-sectional area (W/m2). Waves are considered to be forward-going when they travel in the direction of the net blood flow. "Compression" waves always increase P and "expansion" waves always decrease P. In the forward direction, compression waves increase U and expansion waves decrease U; in the backward direction, compression waves decrease U and expansion waves increase U.

Therefore, to assess the mechanisms responsible for diminished forward and increased backward flow with increased LV stiffness, we performed an energetic analysis of LA systole: we measured LA pressure-volume work, directional hydraulic work, and wave energy. Our results show that the increased wave reflection associated with increased LV operative stiffness is responsible for the decreased forward flow into the LV and the increased retrograde flow into the pulmonary veins.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Animal preparation. Following a protocol approved by the Institutional Animal Care Committee, six healthy mongrel dogs (20–26 kg) were anesthetized initially with thiopental sodium (20 mg/kg) and subsequently with fentanyl citrate (30 µg·kg–1·h–1) and were ventilated with a 1:1 nitrous oxide-oxygen mixture. The rate of a constant-volume respirator (tidal volume, 15 ml/kg; model 607, Harvard Apparatus, Natick, MA) was adjusted to maintain normal blood gas tensions and pH. Body temperature was maintained at 37°C with a circulating water warming blanket and a heat lamp. A large-bore catheter was inserted into a jugular vein for infusion of volume (saline-Pentastarch mixture).

Pressures were measured in the LV (PLV), aorta (PAO), LA (PLA), and a PV (PPV)with the use of high-fidelity catheter-tip manometers and a 2-F micromanometer (Millar Instruments; Houston, TX), all referenced to the mid-LV plane via fluid-filled lumens and external transducers. The LV catheter was introduced through a carotid artery, the LA catheter through the appendage, and the PV catheter through a small right PV branch (the PV catheter was then threaded across the LA into an opposite PV with the aid of a stiff introducer). Ultrasonic flow probes were positioned on the proximal ascending aorta and on the downstream end of a PV (beside the one that contained the pressure transducer) and were connected to a flowmeter (Transonic Systems, Ithaca, NY). Pericardial pressure (PPeri) was measured over the LA with a 2.5 x 2.5-cm flat, liquid-containing balloon transducer (17). The pericardium was reapproximated and sutured following instrumentation (40). Before data collection, all pressures were matched to a reference pressure to correct for any baseline drift. A 5-MHz transesophageal echocardiographic probe (model 77020AC; Hewlett-Packard, Palo Alto, CA) was used to obtain apical two- or four-chamber views of the heart. Mitral inflow velocity (Doppler) was measured at the tips of the mitral leaflets. Echocardiographic and hemodynamic data were synchronized using a video frame counter (MicroEmbedded Consulting, Calgary, Alberta, Canada). Data analysis was performed using specially designed software (CV Works; Advanced Measurements, Calgary, Alberta, Canada).

Two quasi-diametric LA dimensions, DL (length) and DT (thickness), were measured by sonomicrometry (Sonometrics, London, Ontario, Canada). DL was defined by a pair of crystals placed across the length of the LA, one deep to the appendage at the base of the aorta and the other on the posterior (dorsal) surface of the LA, superior (cephalad) to the coronary sinus; DT was defined by a pair of crystals placed across the thickness of the LA, one on the anterior (ventral) surface of the LA at the LA-LV border and the other on the most superior (cephalad) aspect of the LA, lateral to the aorta. Three orthogonal LV dimensions also were measured: anteroposterior (DA-P), base to apex (DB-A), and septum to free wall (DS-F). The ultrasonic signals were filtered (low pass; 20–30 Hz) and edited to eliminate artifacts due to imperfect signal reception (Cardiosoft; Sonometrics).

Experimental protocol. The animals were volume-loaded to relate LA pressure-volume work, forward and backward hydraulic work, and wave energy to LV operative stiffness throughout a range of loading conditions. After control recordings were taken at PLVED {approx} 7 mmHg, PLVED was increased in ~5-mmHg increments to ~27 mmHg with measurements taken while the ventilator was turned off at end expiration for 30 s. These measurements included PLA, PLV, PAO, PPV, PPeri, aortic flow (QAo), PV flow (QPV), LA and LV dimensions, and Doppler flow velocity at the mitral valve. The animals were given enough time to recover hemodynamically between each incremental volume load. At the end of the experiment, while deeply anesthetized, the dogs were euthanized by an intracardiac injection of KCl.

Data analysis. The beginning of LA systole (i.e., the A wave) was defined by the rapid increase in PLA [if equivocal, the time of the initial decrease in LA volume (VLA) was used], and the end was defined by the subsequent minimum in PLA (or VLA) values before the abrupt rise in PLV. VLA was assumed to be a function of the product of the dimensions: VLA = kLA·DL·DT, analogous to VLV = kLV·DA-P·DB-A·DS-F (kLA and kLV were determined as described below). Pressure-volume work (WP-V), defined as total work produced by the LA during atrial systole, was calculated by integrating the area described by the LA transmural P-V loop during atrial systole, where PLA-Tm = PLA – PPeri. LV stiffness was calculated as {Delta}PLV/{Delta}VLV, where {Delta}PLV was the difference in PLV from minimum LV diastolic pressure to the pre-A-wave pressure and {Delta}VLV was the corresponding change in VLV.

We accepted the accuracy of stroke volume (SV) measured by the aortic flow probe and scaled mitral and PV flows and VLA and VLV accordingly, assuming a momentary steady state and that the measured PV flow was representative of total inflow to the LA. Over one cardiac cycle, aortic stroke volume was calculated by integrating aortic flow (QAo) with respect to time: SV = {int}QAo·dt. During ejection, the DA-P·DB-A·DS-F product was plotted vs. {int}QAo·dt; the slope of this relation was found by linear regression and set equal to kLV. Thus SV = {Delta}Vmitral = Amitral·{int}Umitral·dt, where Amitral is the average area of the mitral orifice and Umitral is the mitral velocity determined from Doppler echocardiography. Total PV flow (QPV) during a cardiac cycle was also set equal to aortic stroke volume: SV = {Delta}VPV = kPV·{int}QPV·dt, where QPV was determined by flowmeter. Finally, the change in LA volume ({Delta}VLA) was set equal to the instantaneous difference between the integrals of LA inflow and outflow: thus {Delta}VLA = kLA·{int}(kPV·QPV – Amitral·Umitral)·dt.

Hydraulic work (WH) was defined as the LA pump work, the time-integral of pressure and flow. Therefore, forward hydraulic work is the work done to move blood forward through the mitral valve during atrial systole: WH-mitral = Amitral·{int}PLA·Umitral·dt. Backward hydraulic work is the work done to move blood retrogradely into the PVs during atrial systole: WH-PV = kPV·{int}PLA·QPV·dt. The total hydraulic work produced by LA contraction is the sum of the forward and backward hydraulic work: WH = WH-mitral + WH-PV.

The intensity of a forward-going wave (dIW+) is equal to ({rho}c/4)·(dP + {rho}cdU)2, and the intensity of a backward-going wave (dIW–) is equal to –({rho}c/4)·(dP – {rho}cdU)2, where {rho} is the density of the blood, c is the wave speed, and dU is the incremental change in velocity during a sampling interval (~5 ms), measured by Doppler echocardiography for the mitral orifice and by flowmeter for the PV (QPV = UPV·APV, where APV was estimated from the size of the flow probe). Wave speed was calculated using the equation c = dP/{rho}dU at the beginning of atrial systole, when a compression wave is present and reflections from previous wave activity were assumed to be minimal. The net intensity (dIW or dPdU) is the (instantaneous) sum of the intensities of the forward (dIW+)- and backward-going (dIW–) wave and therefore is equal to (dIW+ + dIW–) (43). It measures the combined wave effects at that instant and location and thus indicates whether the forward or backward wave is dominant at a given instant. The time integral of intensity is the energy (IW±) carried by a wave. Because WIA is a time-domain analysis, waves can be temporally related to changes in hemodynamic parameters (34).

The reflection coefficient at the mitral valve was calculated by dividing the energy of the (reflected) backward compression wave by the energy of the (incident) forward compression wave generated by LA contraction (IW–/IW+). Linear regressions were performed, and pooled data are expressed as means (SD).


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Hemodynamic data recorded under control conditions are shown in Table 1. Figure 1A shows the relations between intracavitary and transmural LA pre-A-wave pressure (PLA and PLA-Tm, respectively) and normalized LA volume (VLA; percent control) for each dog. Figure 1B shows the relations between PLA and PLA-Tm and VLA for the pooled data. The regressions of the pooled data indicate that increasing VLA by 50% was associated with an increase in PLA from 8.9 to 19.1 mmHg; however, PLA-Tm only increased from 3.1 to 5.6 mmHg. The difference between intracavitary and transmural pressure is due to pericardial constraint.


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  		Table 1. Hemodynamic data at PLVED = 8, 16, and 24 mmHg

 

Figure 1
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  		Fig. 1. A: pre-A-wave left atrial (LA) intracavitary pressure (PLA; bullet) and transmural pressure (PLA-Tm; {circ}) vs. normalized pre-A-wave LA volume (VLA; %control). At each value of VLA, the difference between PLA and PLA-Tm is equal to LA pericardial pressure (PPeri). Number at top left of each plot indicates the dog number. B: pooled data from 6 dogs showing PLA (bullet; PLA = 0.20VLA – 11.5) and PLA-Tm ({circ}; PLA-Tm = 0.05VLA – 1.9) vs. normalized VLA.

 
Normalized PLA-Tm-V work (WP-V; percent control) and normalized pre-A-wave VLA were found to be directly, quasi-linearly correlated (data not shown), demonstrating the Frank-Starling relation. Figure 2 shows the relations between normalized WP-V and, as alternative measures of LA preload, pre-A-wave PLA and PLA-Tm (pooled data).


Figure 2
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  		Fig. 2. A: Pooled data from 6 dogs showing normalized LA pressure-volume work (WP-V; %control) vs. PLA-Tm ({circ}) and PLA (bullet). WP-V = 145 PLA-Tm – 124.

 
Figure 3, A and B, shows transmitral forward volume (A-wave volume) and retrograde volume into the PVs (Ar-wave volume), respectively derived from integrated A-wave velocities and PV flows, plotted vs. PLVED. At higher values of PLVED, A-wave volume decreased and Ar-wave volume increased. The ratio of retrograde-to-forward volume (Ar/A-wave volume) vs. PLVED is shown in Fig. 4. Since the time courses of the two waves are similar, this plot implies that retrograde flow (Ar wave) increases at a greater rate than forward flow (A wave) as PLVED increases. The difference in the duration of the Ar wave and the A wave (Ard – Ad) also increased with increasing PLVED, as shown in Fig. 5A. Consistent with previous investigations, if PLVED exceeded 13.7 mmHg, the duration of the Ar wave exceeded that of the A wave (30).


Figure 3
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  		Fig. 3. A: A-wave volume vs. left ventricular end-diastolic volume (PLVED). B: Ar-wave volume vs. PLVED. Smooth lines were drawn [SigmaPlot, Richmond, CA; Graphic Properties; Smoothed (spline)] connecting the changes in A-wave volume and Ar-wave volume as PLVED increased for each dog. At higher values of PLVED, compare decreases in A-wave volume with the increases in Ar-wave volume. Note that volume scales are different. Color code: dog 1, yellow-green; dog 2, red; dog 3, cyan blue; dog 4, green; dog 5, purple; dog 6, black.

 

Figure 4
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  		Fig. 4. Ratio of Ar-wave volume to A-wave volume vs. PLVED. These data imply that retrograde flow increases faster than forward flow as PLVED increases.

 

Figure 5
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  		Fig. 5. A: difference between the duration of the Ar wave and the duration of the A wave (Ard – Ad) vs. PLVED [(Ard – Ad) = 0.004PLVED – 0.06 (r2 = 0.55)]. When PLVED exceeded 13.7 mmHg, the duration of the Ar wave exceeded that of the A wave. B: ratio of Ar-wave volume to A-wave volume vs. PLVED; the data shown in Fig. 4 were pooled and correlated. (Two outliers, the ratios of 0.4 in dogs 3 and 5, were arbitrarily excluded.) [(Ar-wave volume/A-wave volume) = 0.006PLVED – 0.02 (r2 = 0.25)]. Note that the volume ratio is 0.1 when PLVED = 15 mmHg.

 
The data shown in Fig. 4 suggest that the relation between the durations of the A and Ar waves and PLVED (Fig. 5A) might be paralleled by a relation between the ratio of A- and Ar-wave volumes and PLVED. Accordingly, the data shown in Fig. 4 were pooled and correlated (see Fig. 5B). (Two outliers, the ratios of ~0.4 in dogs 3 and 5, were arbitrarily excluded.) Note that the volume ratio is ~0.1 when PLVED = 15 mmHg.

Figure 6 shows representative hemodynamic measurements during LA contraction and WIA of transmitral flow velocity and PV flow. As the LA begins to contract (indicated by the increase in Umitral and PLA in Fig. 6A; note vertical line), it generates a compression wave that travels both forward, into the LV (Fig. 6C), and backward, into the PVs (Fig. 6D). The backward-going compression wave decelerates the antegrade PV flow (indicated by diminishing QPV, Fig. 6B) and increases PPV, whereas the forward-going compression wave accelerates blood into the LV and is partially reflected, generating a backward compression wave at the mitral orifice (Fig. 6C). The reflected backward compression wave is transmitted from the LV across the LA to the PVs and appears to augment the backward compression wave seen in the PVs (Fig. 6D, second peak; note dashed slanting line). Net intensity (dIW), the (instantaneous) sum of the intensities of the forward (dIW+)- and backward-going waves (dIW–), is a measure of the combined wave effects at that instant and location.


Figure 6
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  		Fig. 6. Wave intensity analysis of LA contraction. A: LV (PLV) and LA (PLA) pressures and mitral velocity (Umitral). B: pulmonary venous pressure (PPV) and flow (QPV). C: intensity of forward (dIW+, light solid line above zero)- and backward-going waves (dIW–; dashed line below zero) and net intensity (dIW; thick solid line) at the mitral valve. D: intensity of forward (dIW+, light solid line above zero)- and backward-going waves (dIW–; dashed line below zero) and net intensity (dIW; thick solid line) in a pulmonary vein (PV). At the beginning of its contraction, the LA generates a forward-going compression wave (FCW) through the mitral valve that is partially reflected (BCW; C). It also generates a backward-going compression wave (BCW) into the orifice of the pulmonary vein (D). Note that the BCW in C appears to account for the second peak in the BCW in D, which occurs after a delay consistent with propagation across the LA.

 
If wave energy (i.e., the time-integral of intensity) is a measure of the work applied to accelerate or decelerate the blood, hydraulic work (WH) should depend on net wave energy (IW). Accordingly, we plotted the A-wave WH vs. mitral IW (Fig. 7A) and the Ar-wave WH vs. PV IW (Fig. 7B). For each dog, WH was linearly related to IW (r2 ranged from 0.79 to 0.98 in Fig. 7A and from 0.94 to 0.99 in Fig. 7B). Slopes were on the order of 100, implying that IW is ~1% of total WH.


Figure 7
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  		Fig. 7. A: A-wave hydraulic work vs. the net energy of the forward wave (IW) at the mitral valve. B: Ar-wave hydraulic work vs. the net energy of the backward wave (IW) at the orifice of the PV. For both the mitral valve and the PV, net wave energy predicts hydraulic work. For color code, see Fig. 4.

 
Figure 8 shows that LV stiffness was proportional to pre-A-wave PLV. Acute volume loading results in an increase in the operative stiffness of the chamber, consistent with a curvilinear diastolic P-V relation. We do not suggest that the diastolic P-V relationship is shifted upward, which would indicate a change in the intrinsic structure of the muscle or increase in external constraint. Figure 9 demonstrates that the reflection coefficient (i.e., the energy of the reflected wave divided by the energy of the incident wave, IW–/IW+) was proportional to LV stiffness. The relations were linear for each dog (r2 ranged from 0.64 to 0.94).


Figure 8
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  		Fig. 8. LV stiffness ({Delta}P/{Delta}V) vs. pre-A-wave PLV. Stiffness was proportional to PLV in each case. For color code, see Fig. 4.

 

Figure 9
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  		Fig. 9. Reflection coefficient (i.e., the energy of the reflected wave divided by the energy of the incident wave, IW–/IW+) vs. LV stiffness. The reflection coefficient was proportional to stiffness in each case. For color code, see Fig. 4.

 
Figure 10 shows Ar-wave volume plotted vs. the energy of the reflected mitral wave (IW–), indicating that backward flow into the PVs is directly related to the net energy of the reflected wave (r2 ranged from 0.63 to 0.98).


Figure 10
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  		Fig. 10. Ar-wave volume vs. the energy of the reflected mitral wave (IW–) for each dog. The volume that proceeds backward into the PVs is proportional to the energy of the reflected wave.

 

   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
In the present study of the dynamics of LA systole in normal anesthetized dogs, we used WIA to assess forward flow through the mitral valve and backward flow into the pulmonary veins. This technique allowed us to quantitatively assess the mechanisms responsible for changes in forward and backward flow at different LV filling pressures. Our results are consistent with what has been observed by others in that, at elevated PLVED during volume loading, forward flow was reduced and retrograde flow into the pulmonary veins increased. However, WIA also showed that increased operative LV stiffness increases the reflection coefficient so that a greater proportion of the incident forward compression wave generated by LA contraction is reflected back toward the LA. This backward compression wave diminishes forward flow into the LV and increases retrograde flow through the PVs. Thus WIA helped to clarify the mechanisms underlying the previously described clinical observations.

LA mechanics and the pericardium. As our group has shown previously for the LV (3, 28), LA transmural pressure increases during volume loading, but much less than LA intracavitary pressure (Fig. 1). Also, LA transmural pressure is a better measure of LA preload, in that the relationship between LA work and transmural pressure is more coherent than that with intracavitary pressure (Fig. 2).

Duration of A and Ar waves. The inverse relationship among elevated PLVED, decreased transmitral A wave flow, and augmented PV retrograde flow has been well established (2, 15, 30) such that LV diastolic function can be assessed clinically by measuring the Ar wave velocity and Ard-Ad wave duration difference as an indicator of increased PLVED (1, 8, 14, 25, 37, 38, 45). In 1993, Rossvoll and Hatle (38) showed that a positive Ard-Ad difference predicts a PLVED in excess of 15 mmHg. Greenberg et al. (16) explained the diminished atrial contribution to LV filling with elevated PLVED by the curvilinear nature of the LV diastolic P-V relation. As PLVED increases, the slope of the LV P-V curve (i.e., LV stiffness) increases such that a given LA contraction will increase LV pressure more and increase LV volume less (27). Rossvoll and Hatle (38) further suggested that increased LV stiffness contributes to augmenting PV retrograde flow by rapidly elevating PLA during atrial contraction. Our results are in accordance with accepted theories such that elevated LV stiffness due to volume loading (Fig. 8) results in diminished A volume and augmented Ar volume (Fig. 3, A and B). As well, Fig. 5 shows that a positive Ard-Ad difference occurs at PLVED above ~14 mmHg. However, our results clarify the mechanisms involved by demonstrating the effects of reflected waves from the LV on forward transmitral flow and retrograde flow into the PVs. In particular, they suggest that the A- to Ar-wave volume ratio is approximately proportional to PLVED; approximately one-tenth the forward volume goes backward when PLVED = 15 mmHg and two-tenths, when PLVED = 30 mmHg (see Fig. 5B).

Wave reflection. The potential for wave reflection to have a negative effect on forward flow through the mitral valve and positive effect on backward flow into the pulmonary veins has not been studied previously. We demonstrate presently that as the LV becomes stiffer by moving along its P-V curve, the reflection coefficient (i.e., the fraction of the energy of the forward incident wave generated by the contracting LA that is reflected backward from the LV) is increased from negligible values at low diastolic pressures to ~0.4. The nature of a reflected wave (i.e., compression or expansion) and the ratio of the reflected to the incident wave depend on the reflection site (34). Therefore, although both IW+ and IW– increase with PLVED, as the LV (reflection site) became stiffer, the increase in IW– was greater than the increase in IW+ (Fig. 9). Since wave energy is additive (i.e., IW = IW+ + IW–), the energy of the (reflected) backward compression wave partially negates the energy of the forward compression wave. WIA quantifies the energy needed to overcome inertance and accelerate blood (16). When LV stiffness increases, the (reflected) backward compression wave increasingly negates the effect of the (incident) forward compression wave, limiting the acceleration of blood through the mitral valve (i.e., decelerating the forward flow of blood).

We further suggest that the (reflected) backward compression wave is transmitted across the LA to the PV and acts to augment PV retrograde flow (i.e., the Ar wave). This is consistent with the conclusions of Dernellis and Panaretou (9), who demonstrated that LA input impedance (frequency-dependent pressure-flow ratios, a measure of the opposition to blood flow from the PV to the LA) and peak PV Ar flow were increased in hypertensive patients compared with controls. They commented that LA input impedance is dependent on the downstream circulation (e.g., the LV), in accordance with our finding that increased LV stiffness augments the (reflected) backward compression wave and PV Ar flow. Our findings also are consistent with those of Hellevik et al. (18), who demonstrated with a mathematical model that all propagated or reflected waves in the PVs originate in the left heart.

LA work directed forward through the mitral valve (i.e., forward hydraulic work) and work directed backward through the PV (i.e., backward hydraulic work; the respective integrals of the products of PLA and QA and of PPV and QAr) include the energy spent to overcome inertance, the energy used to overcome viscous losses, and the energy expended against elastance. Similar to LV systole, which was described by Rushmer (39) as causing an "initial ventricular impulse," the impulse generated by the LA during systole produces a forward compression wave through the mitral valve and a backward compression wave through the PV. The impulse that accelerates QA was quantified as the energy under the forward compression wave at the mitral valve (Fig. 6C) and the impulse that accelerates QAr was quantified as the energy under (or above, because the wave is plotted negatively) the backward compression wave at the PV (Fig. 6D).

As shown in Fig. 7, the hydraulic work propelling blood through a specific site is proportional to the net wave energy at that site. Therefore, as LV stiffness increases, the backward compression wave increasingly negates the effect of the forward compression wave and contributes, at least in part, to the decline in transmitral hydraulic work (forward flow). It is also noteworthy that the Ar volume propelled backward into the PVs is proportional to the energy of the reflected wave (Fig. 10). We suggest that the reflected backward compression wave augments the effect of the primary PV backward compression wave (generated directly by LA contraction), accelerating blood in the retrograde direction and increasing backward hydraulic work. Thus increased LV stiffness limits forward flow during atrial systole by generating a backward-going compression wave that also augments retrograde flow into the pulmonary veins.

With respect to both mitral and PV flow, hydraulic work is proportional to wave energy, the magnitude of this proportionality being on the order of 100 to 1 (Fig. 7). This value is consistent with unpublished data from this laboratory and the comment by Jones and Sugawara (21) that wave intensity represents only a small proportion of the total power generated.

LA work. Since the atrial contribution to LV filling is reduced during volume loading (22, 25) and in advanced forms of heart failure (23), the LA may perform poorly when PLVED is elevated. Although this is true in end-stage heart failure when the progressive decrease in LA work may be related directly to failure of atrial muscle (4), we have shown that total LA work and the sum of the forward and backward hydraulic work actually increase with increasing levels of PLVED (Fig. 2). We have found that the Frank-Starling mechanism governs LA performance: P-V work increased in proportion to pre-A-wave VLA, which in turn was proportional to transmural pressure (16, 19–22, 36, 39). The decrease in forward flow was associated with increased retrograde flow (Fig. 3) such that the total volume and work associated with LA contraction continued to increase with increased PLVED. This is consistent with previous work that showed an initial increase in LA pump function associated with elevated LV stiffness in mild heart failure (10). As demonstrated by Hoit et al. (20) in an open-pericardium model, both LA work and stroke volume increase in volume-loaded conditions; however, the efficiency of the LA appears to decrease as the fraction of forward or effective output decreases (10, 20, 23). These results might seem to contradict clinical experience, given that patients with stiff ventricles (e.g., hypertension, and hypertrophic cardiomyopathy) might not tolerate well the loss of the atrial contribution to LV filling. However, these observations in acute experiments merely indicate that the normal LA is less efficient when LV stiffness is increased. With compensatory LA hypertrophy and dilatation, even if some of the LA output is directed backward, forward output clearly is still beneficial and may be critical to LV performance.

Limitations. These acute experiments were performed in anesthetized, open-chest dogs that had been extensively instrumented. As well, short-term volume loading may not be representative of the changes that occur in chronic pathological conditions such as structural remodeling of the heart wall. Thus it would be desirable for more physiological experiments and clinical studies to be designed to confirm our results and conclusions.

As discussed in previous studies (29, 42, 44), there are limitations in applying one-dimensional WIA to the complex three-dimensional geometry of the LV. However, we assume that the quasi-cylindrical mitral orifice can be considered to be a one-dimensional system, regardless of the possible complexity of wave motion in the LV cavity.

Although the mitral valve area decreases during the course of the Doppler E wave (5), it was not possible to take this into account, and instead, we calculated an average value based on the relation of the integrals of the E and A waves to the LV stroke volume. As well, we were not able to account for possible changes in cross-sectional area. Bowman and Kovacs (6) suggested that effective PV area varies throughout the cardiac cycle and becomes smaller during late diastole, which would tend to minimize retrograde flow and help preserve antegrade flow. Comparing the flow patterns in different PVs, they also concluded that peak flows were not reached simultaneously (6, 7, 13). Thus our assumption that the flow in a single PV was representative of total LA inflow may not be entirely accurate.

Finally, there is no gold standard for calculating LA volume due to the complex shape of the chamber. In the present study, LA volume was calculated with sonomicrometry using a modified ellipsoid shape, {Delta}VLA = kLA·DL·DT, and was then scaled according to {Delta}VLA calculated from LA outflow minus inflow. This method does not consider the volume of the atrial appendage; however, we found that appendage dimension and shortening depended on transmural pressure in the same way that was true of the LA (data not shown).

In conclusion, using WIA analysis, we were able to show that as LV stiffness was increased acutely, the reflected backward compression wave also increased. This larger reflected wave partially negated the effect of the forward compression wave in propelling blood forward through the mitral valve and augmented the backward compression wave propelling blood back through the pulmonary veins. Thus, despite increased LA work, forward hydraulic work and flow were reduced and backward hydraulic work and flow were increased. These results explain, at least in part, the changes that occur to the transmitral A wave and pulmonary venous Ar wave with increased LV stiffness.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
The study was supported by an operating grant (#67223) from the Canadian Institutes for Health Research (Ottawa) to J. V. Tyberg and I. Belenkie.


   ACKNOWLEDGMENTS
 
We thank Professor K. H. Parker and Dr. Jiun-Jr Wang for helpful comments, Cheryl Meek for outstanding surgical assistance, and Rozsa Sas for help in preparing the figures.


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. V. Tyberg, Health Sciences Centre, Univ. of Calgary, 3330 Hospital Drive N.W., Calgary, Alberta, Canada T2N 4N1 (e-mail: jtyberg{at}ucalgary.ca)

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.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

  1. Appleton CP. Doppler assessment of left ventricular diastolic function: the refinements continue. J Am Coll Cardiol 21: 1697–1700, 1993.[Web of Science][Medline]
  2. Appleton CP. Hemodynamic determinants of Doppler pulmonary venous velocity components: new insights from studies in lightly sedated normal dogs. J Am Coll Cardiol 30: 1562–1574, 1997.[Abstract]
  3. Belenkie I, Dani R, Smith ER, Tyberg JV. Ventricular interaction during experimental acute pulmonary embolism. Circulation 78: 761–768, 1988.
  4. Bove AA, Santamore WP. Ventricular interdependence. Prog Cardiovasc Dis 23: 365–387, 1981.[CrossRef][Web of Science][Medline]
  5. Bowman AW, Frihauf PA, Kovacs SJ. Time-varying effective mitral valve area: prediction and validation using cardiac MRI and Doppler echocardiography in normal subjects. Am J Physiol Heart Circ Physiol 287: H1650–H1657, 2004.[Abstract/Free Full Text]
  6. Bowman AW, Kovacs SJ. Left atrial conduit volume is generated by deviation from the constant-volume state of the left heart: a combined MRI-echocardiographic study. Am J Physiol Heart Circ Physiol 286: H2416–H2424, 2004.[Abstract/Free Full Text]
  7. Bowman AW, Kovacs SJ. Prediction and assessment of the time-varying effective pulmonary vein area via cardiac MRI and Doppler echocardiography. Am J Physiol Heart Circ Physiol 288: H280–H286, 2005.[Abstract/Free Full Text]
  8. Brunner-LaRocca HP, Rickli H, Jost CHA, Jenni R. Left ventricular end-diastolic pressure can be estimated by either changes in transmitral inflow pattern during Valsalva maneuver or analysis of pulmonary venous flow. J Am Soc Echocardiogr 13: 599–607, 2005.
  9. Dernellis J, Panaretou M. Assessment of left atrial input impedance in normal subjects and in hypertensive patients. Eur J Heart Fail 7: 63–68, 2005.[CrossRef][Web of Science][Medline]
  10. Dernellis JM, Stefanadis CI, Zacharoulis AA, Toutouzas PK. Left atrial mechanical adaptation to long-standing hemodynamic loads based on pressure-volume relations. Am J Cardiol 81: 1138–1143, 1998.[CrossRef][Web of Science][Medline]
  11. Diwan A, McCulloch M, Lawrie GM, Reardon MJ, Nagueh SF. Doppler estimation of left ventricular filling pressures in patients with mitral valve disease. Circulation 111: 3281–3289, 2005.
  12. Firstenberg MS, Greenberg NL, Smedira NG, Prior DL, Scalia GM, Thomas JD, Garcia MJ. Doppler echo evaluation of pulmonary venous-left atrial pressure gradients: human and numerical model studies. Am J Physiol Heart Circ Physiol 279: H594–H600, 2000.[Abstract/Free Full Text]
  13. Fyrenius A, Wigstrom L, Ebbers T, Karlsson M, Engvall J, Bolger AF. Three dimensional flow in the human left atrium. Heart 86: 448–455, 2001.[Abstract/Free Full Text]
  14. Garcia MJ, Thomas JD, Klein AL. New Doppler echocardiographic applications for the study of diastolic function. J Am Coll Cardiol 32: 865–875, 1998.[Abstract/Free Full Text]
  15. Gesell RA. The effects of change in auricular tone and amplitude of auricular systole on ventricular output. Am J Physiol 38: 404–413, 1915.[Free Full Text]
  16. Greenberg B, Chatterjee K, Parmley WW, Werner JA, Holly AN. The influence of left ventricular filling pressure on atrial contribution to cardiac output. Am Heart J 98: 742–751, 1979.[CrossRef][Web of Science][Medline]
  17. Hamilton DR, deVries G, Tyberg JV. Static and dynamic operating characteristics of a pericardial balloon. J Appl Physiol 90: 1481–1488, 2001.[Abstract/Free Full Text]
  18. Hellevik LR, Segers P, Stergiopulos N, Irgens F, Verdonck P, Thompson CR, Lo K, Miyagishima RT, Smiseth OA. Mechanism of pulmonary venous pressure and flow waves. Heart Vessels 14: 67–71, 1999.[CrossRef][Web of Science][Medline]
  19. Hoit BD, LeWinter M, Lew WYW. Independent influence of left atrial pressure on regional peak lengthening rates. Am J Physiol Heart Circ Physiol 259: H480–H487, 1990.[Abstract/Free Full Text]
  20. Hoit BD, Shao Y, Gabel M, Walsh RA. In vivo assessment of left atrial contractile performance in normal and pathological conditions using a time-varying elastance model. Circulation 89: 1829–1838, 1994.
  21. Jones CJH, Sugawara M. "Wavefronts" in the aorta—implications for the mechanisms of left ventricular ejection and aortic valve closure. Cardiovasc Res 27: 1902–1905, 1993.[Free Full Text]
  22. Keren G, Sherez J, Megidish R, Levitt B, Laniado S. Pulmonary venous flow pattern—its relationship to cardiac dynamics. Circulation 71: 1105–1112, 1985.
  23. Kono T, Sabbah HN, Rosman H, Alam M, Stein PD, Goldstein S. Left atrial contribution to ventricular filling during the course of evolving heart failure. Circulation 86: 1317–1322, 1992.
  24. Kuecherer HF, Kusumoto F, Muhiudeen IA, Cahalan MK, Schiller NB. Pulmonary venous flow patterns by transesophageal pulsed Doppler echocardiography: relation to parameters of left ventricular systolic and diastolic function. Am Heart J 122: 1683–1693, 1991.[CrossRef][Web of Science][Medline]
  25. Kuecherer HF, Ruffmann K, Schaefer E, Kuebler W. Doppler echocardiographic assessment of left ventricular filling dynamics in patients with coronary heart disease and normal systolic function. Eur Heart J 9: 649–656, 1988.[Abstract/Free Full Text]
  26. Lighthill MJ. Waves in Fluids. Cambridge, UK: Cambridge University Press, 1978.
  27. Linden RJ, Mitchell JH. Relationship between left ventricular diastolic pressure and myocardial segment length and observations on the contribution of atrial systole. Circ Res 8: 1092–1099, 1960.[Abstract/Free Full Text]
  28. Linderer T, Chatterjee K, Parmley WW, Sievers RE, Glantz SA, Tyberg JV. Influence of atrial systole on the Frank-Starling relation and the end- diastolic pressure-diameter relation of the left ventricle. Circulation 67: 1045–1053, 1983.
  29. MacRae JM, Sun YH, Isaac DL, Dobson GM, Cheng CP, Little WC, Parker KH, Tyberg JV. Wave-intensity analysis: a new approach to left ventricular filling dynamics. Heart Vessels 12: 53–59, 1997.[Web of Science][Medline]
  30. Matsumoto AY, Arteaga E, Ianni BM, Braga AM, Buck PC, Mady C. Relationships among exercise capacity, hypertrophy, and left ventricular diastolic function in nonobstructive hypertrophic cardiomyopathy. Am Heart J 150: 144–149, 2005.[CrossRef][Web of Science][Medline]
  31. Myreng Y, Smiseth OA. Assessment of left ventricular relaxation by Doppler echocardiography. Circulation 81: 260–266, 1990.
  32. Nishimura RA, Abel MD, Hatle LK, Tajik AJ. Relation of pulmonary vein to mitral flow velocities by transesophageal Doppler echocardiography. Effect of different loading conditions. Circulation 81: 1488–1497, 1990.
  33. Oh JK, Appleton CP, Hatle LK, Nishimura RA, Seward JB, Tajik AJ. The noninvasive assessment of left ventricular diastolic function with two-dimensional and Doppler echocardiography. J Am Soc Echocardiogr 10: 246–270, 1997.[CrossRef][Web of Science][Medline]
  34. Parker KH, Jones CJH. 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]
  35. Parker KH, Jones CJH, Dawson JR, Gibson DG. What stops the flow of blood from the heart? Heart Vessels 4: 241–245, 1988.[CrossRef][Medline]
  36. Prinzmetal M. The Auricular Arrhythmias. Springfield, IL: Charles C. Thomas, 1952.
  37. Rossi A, Loredana L, Cicoira M, Bonapace S, Zanolla L, Zardini P, Golia G. Additional value of pulmonary vein parameters in defining pseudonormalization of mitral inflow pattern. Echocardiography 18: 673–679, 2001.[CrossRef][Web of Science][Medline]
  38. Rossvoll O, Hatle LK. Pulmonary venous flow velocities recorded by transthoracic Doppler ultrasound: Relation to left ventricular diastolic pressures. J Am Coll Cardiol 21: 1687–1696, 1993.[Abstract]
  39. Rushmer RF. Initial ventricular impulse. A potential key for cardiac evaluation. Circulation 29: 268–283, 1964.
  40. Scott-Douglas NW, Traboulsi M, Smith ER, Tyberg JV. Experimental instrumentation and left ventricular pressure- strain relationship. Am J Physiol Heart Circ Physiol 261: H1693–H1697, 1991.[Abstract/Free Full Text]
  41. Smiseth OA. Assessment of ventricular diastolic function. Can J Cardiol 17: 1167–1176, 2001.[Web of Science][Medline]
  42. Sun Y, Belenkie I, Wang JJ, Tyberg JV. Assessment of right ventricular diastolic suction in dogs with the use of wave intensity analysis. Am J Physiol Heart Circ Physiol 291: H3114–H3121, 2006.[Abstract/Free Full Text]
  43. Sun YH, Anderson TJ, Parker KH, Tyberg JV. Wave-intensity analysis: a new approach to coronary dynamics. J Appl Physiol 89: 1636–1644, 2000.[Abstract/Free Full Text]
  44. Wang Z, Jalali F, Sun YH, Wang JJ, Parker KH, Tyberg JV. Assessment of left ventricular diastolic suction in dogs using wave-intensity analysis. Am J Physiol Heart Circ Physiol 288: H1641–H1651, 2005.[Abstract/Free Full Text]
  45. Yamamoto K, Nishimura RA, Burnett JC Jr, Redfield MM. Assessment of left ventricular end-diastolic pressure by Doppler echocardiography: contribution of duration of pulmonary venous versus mitral flow velocity curves at atrial contraction. J Am Soc Echocardiogr 10: 52–59, 1997.[CrossRef][Web of Science][Medline]




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