Background
Peak systolic mitral annular velocity (S m ) measured by tissue Doppler echocardiography has been recognized as an independent predictor of mortality in patients with heart failure and in the general population. However, the mechanical determinants of S m remain poorly defined.
Methods
A theoretical model of S m was derived, which indicates that S m is affected positively by left ventricular (LV) contractility and preload and inversely by LV afterload and ejection time (EJT). In 16 anesthetized dogs, S m , LV volume, and LV pressure were measured using sonomicrometry and catheter-tip micromanometry. LV contractility, preload, and afterload were indexed by the end-systolic pressure/volume ratio (E es ′), end-diastolic volume (V ed ), and effective arterial elastance (E a ), respectively. LV contractility, loading conditions, and heart rate were varied over wide ranges, and a total of 76 data sets were obtained for S m (1.2–9.1 cm/sec), E es ′ (1.5–17.6 mm Hg/mL), V ed (11–99 mL), E a (3.6–58.4 mm Hg/mL), EJT (100–246 msec), heart rate (66–192 beats/min), and the ventricular-arterial coupling ratio (E es ′/E a ; 0.2–3.0).
Results
The theoretical model accurately predicted S m ( R 2 = 0.79, P < .0001). By univariate analysis, S m was correlated significantly with E es ′ ( R 2 = 0.64, P < .0001) and with the reciprocal of E a ( R 2 = 0.49, P < .01). V ed and EJT did not affect S m . E es ′/E a was correlated strongly with S m ( R 2 = 0.73, P < .0001). E es ′ and the reciprocal of E a were not correlated with each other.
Conclusions
LV contractility and afterload independently determine S m . The effects of LV preload and EJT on S m might be small, even though they are theoretically associated with S m . S m strongly reflects the status of ventricular-arterial coupling.
Left ventricular (LV) longitudinal shortening during ejection is reflected by systolic mitral annular velocity, which can be measured by tissue Doppler (TD) echocardiography in clinical practice. Peak systolic mitral annular velocity (S m ) has been reported to be an index of global LV systolic function. Measurement of S m allows the detection of cardiac dysfunction more sensitively than the evaluation of other conventional LV function indexes, such as LV ejection fraction (LVEF). S m is a powerful prognosticator of mortality in patients with heart failure and in the general population. Although these previous studies have highlighted the clinical utility of S m measurement, the mechanical determinants of S m remain poorly defined.
S m is correlated positively with LVEF in patients with cardiac diseases. A recent animal study demonstrated that S m is correlated with the maximum value of the time derivative of LV pressure (LVP) (LV dP/dt max ), an indicator of LV systolic function. These findings suggest that LV contractility contributes significantly to S m . However, the magnitudes of LVEF and dP/dt max change in response to alteration in loading conditions, even if the intrinsic LV contractility is preserved. Intriguingly, S m and LV end-systolic elastance (E es ; a relatively load independent index of LV contractility) were found not to be correlated in patients with hypertension. Henein et al. assessed the effects of acute alterations in afterload on S m during peripheral vascular surgery and reported that an increase in afterload by aortoiliac clamping decreased S m . In contrast, in patients undergoing cardiac surgery, S m was insensitive to changes in afterload after infusions of vasoactive agents.
Whether and to what degree LV contractility and loading conditions independently affect S m remain controversial. A more comprehensive approach is required to address this issue. The purpose of this study was to clarify the mechanisms that regulate the magnitude of S m . To that end, we first derived the theoretical relationship between S m and cardiovascular parameters describing LV contractility, afterload, and preload. Second, in canine experiments, we simultaneously acquired LVP, LV volume (LVV), and S m using a catheter-tipped micromanometer and sonomicrometer, while varying LV contractility and loading conditions over wide ranges. We compared these experimental data with the theoretical predictions and evaluated the independent effects of the parameters on S m .
Methods
Theoretical Relationship Between S m and Cardiovascular Parameters
We based our theoretical modeling on the LVP-LVV framework, as shown in Figure 1 . E es , the slope of the relationship between end-systolic pressure (P es ) and end-systolic volume (V es ), is an index of LV contractility ( Figure 1 A). Effective arterial elastance, E a , the slope of the relationship between P es and stroke volume (SV), is an index of LV afterload. The time-elastance curve of the left ventricle has a distinct waveform ( Figure 1 B). The time-elastance curve during systole can be approximated to two straight lines, one for the isovolumic contraction phase and the other for the ejection phase ( Figure 1 B). S m is related to E es , E a , LV end-diastolic volume (V ed ) and ejection time (EJT) by the following formula:
S m = α 3 ⋅ E es E a ⋅ V ed 1 / 3 EJT ,
Animal Experiments
We used 22 adult mongrel dogs (both sexes; weight, 20–30 kg). The investigation conformed with the Guide for the Care and Use of Laboratory Animals . All protocols were approved by the Animal Subjects Committee of the National Cerebral and Cardiovascular Center.
Experiment 1: Comparison of Mitral Annular Velocities Measured by Sonomicrometry and TD Echocardiography
Preparation
Six animals were used. After anesthesia was induced with sodium pentobarbital (25 mg/kg), the animals were intubated endotracheally and ventilated artificially. An appropriate level of anesthesia was maintained by continuous inhalation of 1.5% isoflurane. A sterile left lateral thoracotomy was performed, and the pericardium was opened. Three spheric sonomicrometer crystals (2 mm in diameter) were implanted in the subepicardium at the base ( Figure 2 A, points 1 and 2) and apex ( Figure 2 A, point 3) of the left ventricle. All wires were exteriorized through the back of the neck. The pericardium and chest wall were closed, and the animal was allowed to recover.
After the animals had fully recovered from the procedure (10–14 days after surgery), mitral annular velocities were measured by sonomicrometry and TD echocardiography. During measurements, the dogs were anesthetized and artificially ventilated and were laid in a sling. Surface electrocardiograms were recorded.
Mitral Annular Velocity Measurement by Sonomicrometry
To obtain LV dimensions, sonomicrometric signals were processed with a digital system (Sonolab, Sonometrics Corporation, London, Canada) while each crystal sent a signal to and received a signal from each of the other crystals. Analog signals of sonomicrometric LV dimensions and electrocardiography were digitized at 200 Hz and stored for offline analysis (Sonolab). The dimensions of the three sonomicrometer crystals were used to calculate the LV longitudinal length (L), which is the distance between the LV apex and the center of the base ( Figure 2 A). The time derivative of L (dL/dt) was used as instantaneous mitral annular velocity, and a positive velocity was reported to indicate shortening of L. Peak dL/dt during LV systole was used as S m .
Mitral Annular Velocity Measurement by TD Echocardiography
Transthoracic echocardiography was performed using an echocardiographic system equipped with a 6-MHz transducer (Artida; Toshiba Corporation, Tokyo, Japan). Mitral annular velocity was obtained with pulsed TD from the apical four-chamber view by placing a 2-mm-wide sample volume at the septal side of the mitral annulus ( Figure 2 B). Peak systolic myocardial velocity (S mTD ) was obtained.
Data Acquisition
All data were acquired at end-expiration. To avoid interference between sonomicrometry and TD echocardiography, we first recorded echocardiographic data for 10 sec and then sonomicrometric dimensions during the subsequent 10 sec. Doses of dobutamine (2, 4, 8, and 16 μg/kg/min) and propranolol (0.2 mg/kg) were administered intravenously to each dog to modulate LV inotropy. S m and S mTD were determined after administration of each dose.
Experiment 2: Effects of Cardiovascular Parameters on S m
Preparation
Sixteen animals were used. Anesthesia and artificial ventilation were conducted as described above. A fluid-filled catheter (8Fr) was placed in the right femoral artery to measure systemic arterial pressure. The fluid-filled catheter was connected to a pressure transducer (DX-200; Nihon Kohden, Tokyo, Japan). After a median sternotomy, the heart was suspended in a pericardial cradle. A pair of pacing electrodes was fixed at the right atrial appendage for atrial pacing. A catheter-tipped micromanometer (PC-751; Millar Instruments, Houston, TX) was inserted via the LV apex to measure LVP. As depicted in Figure 3 A, 10 sonomicrometer crystals were implanted in the subepicardium of the left ventricle and the right side of the interventricular septum to obtain LV dimensions. Surface electrocardiograms were recorded. After the instrumentation was completed, the pericardium was closed. All data acquisitions were done at end-expiration. Analog signals of arterial pressure, LVP, sonomicrometric LV dimensions, and electrocardiography were digitized at 200 Hz and stored for offline analysis.
Experimental Protocols
After the initial preparation and surgical procedures were complete, the animals were allowed to stabilize for 30 min. Under steady-state baseline condition, we recorded the analog signals for about 10 sec in each animal. After obtaining the hemodynamic data at baseline conditions, we created various hemodynamic conditions, as described in the following protocols. In each protocol, we waited 20 min to confirm that hemodynamic conditions reached steady state.
Contractility Run ( n = 9)
Hemodynamic data were recorded while LV contractility was increased by dobutamine infusion (5 μg/kg/min). After the data were recorded, dobutamine infusion was temporarily suspended. We created acute heart failure by embolizing the left coronary artery with glass microspheres (90 μm in diameter). Data recording was repeated under depressed LV contractility. Hemodynamic data were also recorded after LV contractility was restored by reinfusion of dobutamine.
Loading Run ( n = 7)
Hemodynamic data were recorded after pharmacologically altering vascular resistance (afterload) and LV filling (preload) by infusing norepinephrine (0.2 μg/kg/min), sodium nitroprusside (3 μg/kg/min), or 250 mL of 10% dextran 40.
Heart Rate (HR) Run ( n = 6)
The possible dependence of S m on HR was tested by suppressing the intrinsic atrial beat using zatebradine (UL-FS49; 0.5 mg/kg) and instituting atrial pacing to obtain hemodynamic data at different HRs (±25% of baseline HR).
Six animals underwent both loading and HR runs. At the conclusion of the experiments, the dogs were sacrificed with an intravenous injection of pentobarbital and potassium chloride. Autopsies were performed to verify the position of the sonomicrometer crystals and catheters. After excision of the adjacent right ventricular muscle, valvular tissue and fat, LV myocardial volume was measured by water displacement in a volumetric cylinder.
Data Analysis and Definitions
Calculation of S m
Dimensions between the sonomicrometer crystals placed at the LV base ( Figure 3 A, points 1 and 2) and the LV apex ( Figure 3 A, point 3) were used to calculate S m , as described above.
LVV Calculation Using Sonomicrometric LV Dimensions
The three-dimensional position of each crystal was defined as a function of time on the basis of the distances between the crystals. The LV epicardial volume (including LVV and LV myocardial volume) was estimated using software that applied an ellipsoidal shell model to the coordinates of all 10 crystals ( Figure 3 A). LVV was obtained by subtracting LV myocardial volume from the estimated LV epicardial volume. Our preliminary study demonstrated that ex vivo LVV thus estimated agreed reasonably well with the volume measured by intraventricular balloon method (LVV ba ) in four canine hearts (LVV = 1.0 × LVV ba − 7.0; r = 0.98; SEE = 14 mL; 20 ≤ LVV ba ≤ 70 mL).
Cardiovascular Parameters
End-systole was defined as the time when LV dP/dt decreased to 20% of its minimum. LV contractility was indexed by the P es /V es ratio (E es ′ = P es /V es ), which is an approximation of E es . V ed (an index of LV preload) was defined as LVV at the peak of the R wave on the electrocardiogram. E a (an index of LV afterload) was defined as the ratio of P es to SV (SV = V ed − V es ). The end of the isovolumic contraction phase was defined as the moment when LV dP/dt decreased to 80% of its maximum, according to a previous study with minor modification. EJT was obtained by subtracting the end of the isovolumic contraction phase from end-systole. Systemic vascular resistance (SVR) was defined as time-averaged arterial pressure divided by the product of SV and HR. A previous study demonstrated that E a is related to SVR and HR as follows: E a ≈ k × SVR × HR, where k is a constant. The E es ′/E a ratio was used as an index of ventricular-arterial coupling.
S m and cardiovascular parameters were the averages of approximately 10 beats.
Statistical Analysis
All data are presented as mean ± SD. Statistical analyses were performed using commercially available software (Statistica; Statsoft, Inc., Tulsa, OK). In experiments 1 and 2, the associations among variables were analyzed using a mixed-model procedure to handle the dependencies in repeated measurements within the same animal. The coefficient of determination ( R 2 ) was used to evaluate the strength of association, because it measures how much variability of the dependent variable is the result of the independent variable. In experiment 2, the coefficient of variation (CV) was calculated as the ratio of the SD to the mean (reported as a percentage) and used to quantify the variability of measurements. One-way repeated-measures analyses of variance with Dunnett’s test were used in multiple comparisons relative to baseline for each intervention. P values < .05 were considered statistically significant.
Results
Experiment 1: Mitral Annular Velocity Measured by Sonomicrometry and TD Echocardiography
Figure 2 C displays representative recordings of mitral annular velocity measured by TD echocardiography and dL/dt measured by sonomicrometry when LV contractility was pharmacologically modulated. Waveforms derived from TD echocardiography were slightly different from those derived from sonomicrometry. As shown in Figure 2 D, the values of S mTD were consistently larger than those of S m , but the two were correlated strongly on the basis of the data obtained from six canine hearts over a wide range of LV inotropy ( R 2 = 0.92). Percentage change in S mTD was also correlated highly with percentage change in S m ( R 2 = 0.92; Figure 2 E). On the basis of these findings, instead of S mTD , we used S m by sonomicrometry to investigate the mechanical determinants of systolic mitral annular velocity, because this allowed analyses of all variables, including LVP and LVV, from the same heartbeat.
Experiment 2: Effects of Cardiovascular Parameters on S m
Figure 3 B shows traces of hemodynamic variables in one animal under baseline conditions. As predicted in our theoretical analysis ( Appendix ), S m was detected early in the ejection phase.
Effects of Various Interventions on S m and Cardiovascular Parameters
Table 1 summarizes the effects of various interventions on S m and cardiovascular parameters (a total of 76 data sets). The CVs for S m , E es ′, V ed , E a , EJT, SVR, HR, and E es ′/E a were 44%, 49%, 41%, 77%, 24%, 77%, 21%, and 64%, respectively. S m and all the cardiovascular parameters changed over reasonably wide ranges by the interventions.
| Variable | S m (cm/sec) 3.3 ± 1.5 (1.2–9.1) | E es ′ (mm Hg/mL) 7.5 ± 3.7 (1.5–17.6) | V ed (mL) 37 ± 16 (11–99) | E a (mm Hg/mL) 9.2 ± 7.1 (3.6–58.4) | EJT (msec) 150 ± 36 (100–246) | SVR (mm Hg/sec/mL) 4.4 ± 3.3 (1.3–21.4) | HR (beats/min) 130 ± 28 (66–192) | E es ′/E a 1.0 ± 0.7 (0.2–3.0) | n 76 |
|---|---|---|---|---|---|---|---|---|---|
| Contractility run | |||||||||
| Baseline | 3.4 ± 1.2 | 6.2 ± 1.7 | 38 ± 9 | 6.7 ± 1.4 | 134 ± 12 | 2.9 ± 0.7 | 130 ± 11 | 1.0 ± 0.4 | 9 |
| DOB | 6.0 ± 1.8 † | 10.5 ± 3.7 † | 45 ± 5 | 6.1 ± 1.6 | 127 ± 8 | 2.7 ± 1.1 | 136 ± 24 | 1.9 ± 0.9 † | 9 |
| AHF | 2.2 ± 1.0 ∗ | 2.7 ± 0.8 † | 50 ± 17 † | 8.4 ± 2.4 ∗ | 121 ± 13 † | 3.2 ± 1.0 | 145 ± 12 | 0.3 ± 0.1 ∗ | 9 |
| AHF with DOB | 3.5 ± 0.9 | 4.3 ± 1.4 | 56 ± 17 † | 7.4 ± 1.3 | 117 ± 6 † | 2.8 ± 0.8 | 156 ± 26 † | 0.6 ± 0.1 | 9 |
| Loading run | |||||||||
| Baseline | 2.9 ± 0.7 | 9.3 ± 3.2 | 24 ± 7 | 10.6 ± 4.5 | 161 ± 21 | 5.2 ± 2.4 | 127 ± 19 | 1.1 ± 0.7 | 7 |
| NE | 2.8 ± 0.6 | 10.9 ± 3.9 | 29 ± 9 | 14.8 ± 7.9 † | 165 ± 25 | 9.0 ± 5.4 † | 103 ± 24 † | 0.9 ± 0.4 | 7 |
| SNP | 3.1 ± 0.6 | 9.5 ± 3.6 | 19 ± 6 ∗ | 9.1 ± 4.3 | 158 ± 31 | 4.6 ± 2.0 | 127 ± 17 | 1.3 ± 0.8 | 7 |
| DEX | 3.1 ± 0.9 | 7.2 ± 1.6 | 39 ± 10 † | 7.1 ± 3.5 ∗ | 209 ± 26 † | 3.9 ± 1.9 | 107 ± 14 ∗ | 1.2 ± 0.5 | 7 |
| Heart rate run | |||||||||
| Baseline | 2.8 ± 0.7 | 9.9 ± 3.0 | 24 ± 7 | 10.5 ± 5.0 | 155 ± 16 | 4.8 ± 2.3 | 134 ± 8 | 1.1 ± 0.7 | 6 |
| ZAT | 2.9 ± 1.1 | 6.9 ± 1.0 ∗ | 39 ± 9 † | 6.6 ± 3.0 | 204 ± 33 † | 4.5 ± 2.2 | 86 ± 4 † | 1.2 ± 0.4 | 6 |
| PACE | 3.0 ± 1.4 | 10.0 ± 2.7 | 22 ± 9 | 18.4 ± 19.9 | 143 ± 22 | 6.9 ± 7.3 | 165 ± 12 † | 0.9 ± 0.4 | 6 |
Contractility Run
S m , E es ′, and E es ′/E a changed in a similar pattern from their respective baseline values. They increased significantly with dobutamine infusion, decreased significantly after acute heart failure induction, and recovered to baseline levels with reinfusion of dobutamine. V ed and E a significantly increased and EJT significantly decreased from their respective baseline values after acute heart failure induction.
Loading Run
S m , E es ′, and E es ′/E a did not change significantly in response to changes in loading conditions. Norepinephrine infusion significantly increased E a and SVR and significantly decreased HR. Sodium nitroprusside infusion significantly decreased V ed but did not significantly reduce E a and SVR. Dextran infusion significantly increased V ed and EJT and significantly decreased E a and HR.
HR Run
Zatebradine infusion significantly decreased HR and E es ′ and significantly increased V ed and EJT. Atrial tachypacing significantly increased HR. E a was apparently decreased by zatebradine and increased by atrial tachypacing, although the differences were not significant.
Relationships Between S m and Cardiovascular Parameters
Using the 76 data sets from all interventions, we examined whether S m was related to the cardiovascular parameters as predicted by equation 1 . As shown in Figure 4 A, S m was correlated significantly with the product of E es ′ and the cubic root of V ed divided by E a and EJT. The R 2 value was 0.79, indicating that the theoretical model accurately predicts S m .
Figures 4 B to 4 H shows univariate relationships between S m and each of the cardiovascular parameters. S m was correlated significantly with E es ′ ( Figure 4 B). In accordance with equation 1 , we related S m with the cubic root of V ed (V ed 1/3 ; Figure 4 C), with the reciprocal of E a (E a −1 ; Figure 4 D), and with the reciprocal of EJT (EJT −1 ; Figure 4 E). The CVs for E a −1 , V ed 1/3 , and EJT −1 were 41%, 14%, and 21%, respectively. S m was correlated significantly with E a −1 but not with V ed 1/3 and EJT −1 . Because E a was correlated linearly with the product of SVR and HR, as described above, we related S m with the reciprocal of SVR (SVR −1 ; Figure 4 F) and with the reciprocal of HR (HR −1 ; Figure 4 G). S m was correlated significantly with SVR −1 but not with HR −1 . Figure 4 H indicates that E es ′/E a was tightly correlated with S m .
We analyzed the correlations between the cardiovascular parameters. E es ′ was not correlated with E a −1 ( P = .96), indicating that the two affect S m independently. E es ′ was correlated inversely with V ed 1/3 (E es ′ = −4.3 × V ed 1/3 + 21.7; R 2 = 0.56, P < .001). E a −1 was correlated inversely with EJT −1 (E a −1 = −0.03 × EJT −1 + 0.34; R 2 = 0.76, P < .0001). E a −1 was correlated positively with V ed 1/3 (E a −1 = 0.05 × V ed 1/3 + 0.03; R 2 = 0.68, P < .01). V ed 1/3 was correlated inversely with EJT −1 (V ed 1/3 = −0.16 × EJT −1 + 4.45; R 2 = 0.76, P < .001).
Results
Experiment 1: Mitral Annular Velocity Measured by Sonomicrometry and TD Echocardiography
Figure 2 C displays representative recordings of mitral annular velocity measured by TD echocardiography and dL/dt measured by sonomicrometry when LV contractility was pharmacologically modulated. Waveforms derived from TD echocardiography were slightly different from those derived from sonomicrometry. As shown in Figure 2 D, the values of S mTD were consistently larger than those of S m , but the two were correlated strongly on the basis of the data obtained from six canine hearts over a wide range of LV inotropy ( R 2 = 0.92). Percentage change in S mTD was also correlated highly with percentage change in S m ( R 2 = 0.92; Figure 2 E). On the basis of these findings, instead of S mTD , we used S m by sonomicrometry to investigate the mechanical determinants of systolic mitral annular velocity, because this allowed analyses of all variables, including LVP and LVV, from the same heartbeat.
Experiment 2: Effects of Cardiovascular Parameters on S m
Figure 3 B shows traces of hemodynamic variables in one animal under baseline conditions. As predicted in our theoretical analysis ( Appendix ), S m was detected early in the ejection phase.
Effects of Various Interventions on S m and Cardiovascular Parameters
Table 1 summarizes the effects of various interventions on S m and cardiovascular parameters (a total of 76 data sets). The CVs for S m , E es ′, V ed , E a , EJT, SVR, HR, and E es ′/E a were 44%, 49%, 41%, 77%, 24%, 77%, 21%, and 64%, respectively. S m and all the cardiovascular parameters changed over reasonably wide ranges by the interventions.
| Variable | S m (cm/sec) 3.3 ± 1.5 (1.2–9.1) | E es ′ (mm Hg/mL) 7.5 ± 3.7 (1.5–17.6) | V ed (mL) 37 ± 16 (11–99) | E a (mm Hg/mL) 9.2 ± 7.1 (3.6–58.4) | EJT (msec) 150 ± 36 (100–246) | SVR (mm Hg/sec/mL) 4.4 ± 3.3 (1.3–21.4) | HR (beats/min) 130 ± 28 (66–192) | E es ′/E a 1.0 ± 0.7 (0.2–3.0) | n 76 |
|---|---|---|---|---|---|---|---|---|---|
| Contractility run | |||||||||
| Baseline | 3.4 ± 1.2 | 6.2 ± 1.7 | 38 ± 9 | 6.7 ± 1.4 | 134 ± 12 | 2.9 ± 0.7 | 130 ± 11 | 1.0 ± 0.4 | 9 |
| DOB | 6.0 ± 1.8 † | 10.5 ± 3.7 † | 45 ± 5 | 6.1 ± 1.6 | 127 ± 8 | 2.7 ± 1.1 | 136 ± 24 | 1.9 ± 0.9 † | 9 |
| AHF | 2.2 ± 1.0 ∗ | 2.7 ± 0.8 † | 50 ± 17 † | 8.4 ± 2.4 ∗ | 121 ± 13 † | 3.2 ± 1.0 | 145 ± 12 | 0.3 ± 0.1 ∗ | 9 |
| AHF with DOB | 3.5 ± 0.9 | 4.3 ± 1.4 | 56 ± 17 † | 7.4 ± 1.3 | 117 ± 6 † | 2.8 ± 0.8 | 156 ± 26 † | 0.6 ± 0.1 | 9 |
| Loading run | |||||||||
| Baseline | 2.9 ± 0.7 | 9.3 ± 3.2 | 24 ± 7 | 10.6 ± 4.5 | 161 ± 21 | 5.2 ± 2.4 | 127 ± 19 | 1.1 ± 0.7 | 7 |
| NE | 2.8 ± 0.6 | 10.9 ± 3.9 | 29 ± 9 | 14.8 ± 7.9 † | 165 ± 25 | 9.0 ± 5.4 † | 103 ± 24 † | 0.9 ± 0.4 | 7 |
| SNP | 3.1 ± 0.6 | 9.5 ± 3.6 | 19 ± 6 ∗ | 9.1 ± 4.3 | 158 ± 31 | 4.6 ± 2.0 | 127 ± 17 | 1.3 ± 0.8 | 7 |
| DEX | 3.1 ± 0.9 | 7.2 ± 1.6 | 39 ± 10 † | 7.1 ± 3.5 ∗ | 209 ± 26 † | 3.9 ± 1.9 | 107 ± 14 ∗ | 1.2 ± 0.5 | 7 |
| Heart rate run | |||||||||
| Baseline | 2.8 ± 0.7 | 9.9 ± 3.0 | 24 ± 7 | 10.5 ± 5.0 | 155 ± 16 | 4.8 ± 2.3 | 134 ± 8 | 1.1 ± 0.7 | 6 |
| ZAT | 2.9 ± 1.1 | 6.9 ± 1.0 ∗ | 39 ± 9 † | 6.6 ± 3.0 | 204 ± 33 † | 4.5 ± 2.2 | 86 ± 4 † | 1.2 ± 0.4 | 6 |
| PACE | 3.0 ± 1.4 | 10.0 ± 2.7 | 22 ± 9 | 18.4 ± 19.9 | 143 ± 22 | 6.9 ± 7.3 | 165 ± 12 † | 0.9 ± 0.4 | 6 |
Contractility Run
S m , E es ′, and E es ′/E a changed in a similar pattern from their respective baseline values. They increased significantly with dobutamine infusion, decreased significantly after acute heart failure induction, and recovered to baseline levels with reinfusion of dobutamine. V ed and E a significantly increased and EJT significantly decreased from their respective baseline values after acute heart failure induction.
Loading Run
S m , E es ′, and E es ′/E a did not change significantly in response to changes in loading conditions. Norepinephrine infusion significantly increased E a and SVR and significantly decreased HR. Sodium nitroprusside infusion significantly decreased V ed but did not significantly reduce E a and SVR. Dextran infusion significantly increased V ed and EJT and significantly decreased E a and HR.
HR Run
Zatebradine infusion significantly decreased HR and E es ′ and significantly increased V ed and EJT. Atrial tachypacing significantly increased HR. E a was apparently decreased by zatebradine and increased by atrial tachypacing, although the differences were not significant.
Relationships Between S m and Cardiovascular Parameters
Using the 76 data sets from all interventions, we examined whether S m was related to the cardiovascular parameters as predicted by equation 1 . As shown in Figure 4 A, S m was correlated significantly with the product of E es ′ and the cubic root of V ed divided by E a and EJT. The R 2 value was 0.79, indicating that the theoretical model accurately predicts S m .
Figures 4 B to 4 H shows univariate relationships between S m and each of the cardiovascular parameters. S m was correlated significantly with E es ′ ( Figure 4 B). In accordance with equation 1 , we related S m with the cubic root of V ed (V ed 1/3 ; Figure 4 C), with the reciprocal of E a (E a −1 ; Figure 4 D), and with the reciprocal of EJT (EJT −1 ; Figure 4 E). The CVs for E a −1 , V ed 1/3 , and EJT −1 were 41%, 14%, and 21%, respectively. S m was correlated significantly with E a −1 but not with V ed 1/3 and EJT −1 . Because E a was correlated linearly with the product of SVR and HR, as described above, we related S m with the reciprocal of SVR (SVR −1 ; Figure 4 F) and with the reciprocal of HR (HR −1 ; Figure 4 G). S m was correlated significantly with SVR −1 but not with HR −1 . Figure 4 H indicates that E es ′/E a was tightly correlated with S m .
We analyzed the correlations between the cardiovascular parameters. E es ′ was not correlated with E a −1 ( P = .96), indicating that the two affect S m independently. E es ′ was correlated inversely with V ed 1/3 (E es ′ = −4.3 × V ed 1/3 + 21.7; R 2 = 0.56, P < .001). E a −1 was correlated inversely with EJT −1 (E a −1 = −0.03 × EJT −1 + 0.34; R 2 = 0.76, P < .0001). E a −1 was correlated positively with V ed 1/3 (E a −1 = 0.05 × V ed 1/3 + 0.03; R 2 = 0.68, P < .01). V ed 1/3 was correlated inversely with EJT −1 (V ed 1/3 = −0.16 × EJT −1 + 4.45; R 2 = 0.76, P < .001).
Discussion
To the best of our knowledge, this is the first study to comprehensively evaluate the relations between S m and cardiovascular parameters using theoretical modeling and also well-controlled animal experiments. The theoretical model of S m indicates that S m is affected by LV contractility, preload, afterload, and EJT. Experimental data confirmed that the theoretical model accurately predicts S m . Further analysis of the experimental data showed that LV contractility and afterload have independent effects on S m , but LV preload and EJT do not. S m strongly reflects the status of ventricular-arterial coupling.
Mechanical Determinants of S m
The theoretical model of S m is rational mechanically because the right side of equation 1 corresponds to the mean velocity of LV shortening. The product of E es /E a and V ed positively correlates with SV. Therefore, the product of E es /E a and the cubic root of V ed , which corresponds to LV end-diastolic dimension, positively correlates with the stroke dimension of the left ventricle. The stroke dimension of the left ventricle divided by EJT equals the mean velocity of LV shortening.
In our theoretical analysis, we assumed that changes in LV length couple with changes in LVV ( Appendix ). Actually, this is not the case throughout the cardiac cycle. In the isovolumic contraction phase, LV longitudinal and short-axis lengths change without change in LVV. However, during the ejection phase, which was the phase of interest in our analysis, both LV longitudinal and short-axis lengths decreased in parallel with LVV. We also assumed that the ratio of LV longitudinal length to short-axis length is constant during the ejection phase ( Appendix ). The ratio is actually not constant. The ratio averaged for eight dogs in a previous study was 1.65 at the beginning of the ejection phase. At the end of the ejection phase, the ratio increased to 1.88. If these values are translated into α in equation 1 , α increases from 1.73 to 1.89 (a net increase of 10%) during the ejection phase. Hence, α is actually not constant within one animal. Although this can be a confounder in this theoretical analysis ( Appendix ), its effect would be quantitatively small. Apart from α, the time-varying LV elastance, E( t ), also determines S m (equation A 9 in Appendix ). If E( t ) is constant, S m is achieved when α is maximum, that is, at the end of the ejection phase. Meanwhile, if α is constant, S m is achieved when E( t ) is minimum, that is, at the beginning of the ejection phase. During the ejection phase, E( t ) increases from 5 to 10 mm Hg/mL in dogs (a net increase of 100%). A numerical simulation using these published data indicates that the contribution of E( t ) to S m is 15 times more than that of α. Thus, we can assume α as constant without sacrificing accuracy. S m is effectively determined by E( t ) and is achieved at the beginning of the ejection phase. This is compatible with in vivo findings. In this study (Figures 2 B, 2 C, and 3 B) and also in previous studies, S m is usually reached early in the ejection phase.
According to the value of R 2 , the theoretical model can predict 79% of S m variation. The residual variation, 21%, remains to be explained. Although it is possible that variation among animals of α in equation 1 may contribute to this residual variation, the CV of α in eight dogs was <5% in a previous study, suggesting that variation among animals of α plays a minor role in the residual variation. The variation may be caused by factors not included in the model. A previous study indicated that dynamic arterial properties such as aortic compliance have direct effects on S m . Further studies to address these issues are required in the future.
LV contractility determines the magnitude of S m . The R 2 value of 0.64 between S m and E es ′ in this study was comparable with those observed between S m and other LV functional indexes, such as LV dP/dt max , in previous studies. Borlaug et al. reported that S m was not correlated with indexes of LV contractility including, E es ′, in patients with hypertension. However, because they excluded patients with heart failure with depressed LV contractility from the study population and did not actively stimulate LV inotropy in their protocol, LV contractile indexes were well preserved with small variations among patients. This might be a reason they did not detect a significant correlation between S m and indexes of LV contractility.
S m is inversely related to LV afterload. Previous clinical studies have yielded contrasting results of dependence and independence of S m on afterload. Oki et al. reported that S m was reduced in response to an increase in LV afterload after angiotensin infusion in healthy subjects. In contrast, Amà et al. reported that S m did not change when E a and SVR were changed by phenylephrine or nitroglycerine infusion in patients undergoing cardiac surgery. However, they did not attempt to directly associate S m with the afterload indexes. Similar to their results, we also noted that S m did not change in response to phenylephrine infusion, whereas E a or SVR significantly increased ( Table 1 ). However, we further analyzed the associations between S m and afterload indexes using mixed-model procedures. In the previous studies, conducting statistical analyses similar to those we performed in this study would have been useful to evaluate association between the afterload and S m .
Unexpectedly, V ed and EJT did not affect S m independently. Both V ed and EJT are components of our theoretical model of S m . Furthermore, previous studies suggested that S m was affected by LV preload and EJT. In this study, the CVs for V ed 1/3 and EJT −1 were small compared with those for E es ′ and E a −1 . Moreover, E es ′ was correlated inversely with V ed 1/3 , and E a −1 was correlated inversely with EJT −1 . These suggest that because of the low variability of V ed 1/3 and EJT −1 and the antagonizing effects of the covariates (E es ′ and E a −1 ), the analysis might fail to detect significant correlations of V ed 1/3 and EJT −1 with S m . However, V ed also was not correlated with S m in this study (data not shown), although the CVs for V ed and E es ′ were comparable (41% and 49%). It would be ideal to change V ed or EJT individually while keeping all other parameters constant. Although impedance loading on ex vivo heart preparation would realize such protocols, this preparation is inappropriate for the study of LV longitudinal function, because it requires resection of the mitral valve and subvalvular apparatus (papillary muscles), which are critical components of longitudinal function. Taken together, although we cannot completely exclude significant contributions of LV preload and EJT to S m , their effects may be small and easily reversed by the effects of LV contractility and afterload, that is, effectively negligible compared with the status of ventricular-arterial coupling.
Potential Clinical Implications
A novel and important finding of this study is that S m strongly reflects the status of ventricular-arterial coupling. Ventricular-arterial coupling is a central determinant of cardiovascular performance and cardiac energetics. Normally, the left ventricle and the arterial system are optimally coupled to produce maximal stroke work, when E es /E a is near unity. Maximal energetic efficiency occurs when E es /E a approximates 2.0. In patients with heart failure, the left ventricle and the arterial system are suboptimally coupled (E es /E a becomes less than unity). Beta-blockade improves this situation. In patients with myocardial infarction, suboptimal coupling ratio is associated with poor prognosis over the next 5 years. S m as a measure of the status of ventricular-arterial coupling may allow accurate evaluations of cardiovascular pathophysiology and also predictions of prognosis in patients with cardiac disease. The ventricular-arterial coupling ratio can be predicted also by LVEF. However, LVEF assessment requires precise definition of the endocardial borders on conventional echocardiography, which is complicated by trabeculae or endocardial dropout. Precise endocardial definition is sometimes difficult, especially in obese patients, the elderly, and patients with pulmonary disease. Recording of mitral annular motion has the advantage that it is not dependent on the endocardial definition and is therefore relatively independent of image quality. S m measurement can be an alternative to LVEF assessment to predict the status of ventricular-arterial coupling in such patients.
Study Limitations
In accordance with a previous canine study, sonomicrometry consistently underestimated systolic mitral annular velocity compared with TD echocardiography ( Figure 2 D). This discrepancy may be attributed to the location of the crystals, which are implanted in the subepicardium. Although longitudinally directed myocardial fibers in both subendocardial and subepicardial layers of the left ventricle may play a major role in the magnitude of systolic mitral annular velocity, systolic shortening of subepicardial fiber is significantly smaller than that of subendocardial fiber. In humans, the absolute value of mitral annular velocity measured by TD echocardiography agreed with that measured by cardiac magnetic resonance imaging, which is the widely accepted gold standard for the assessment of LVV and function. Although sonomicrometry is useful in animal experiments for the assessment of heart motion, our data suggest that S m obtained by sonomicrometry in this study might have underestimated the true LV longitudinal shortening velocity. However, a strong correlation was observed between S m and S mTD ( Figure 2 D). Percentage changes in S m and S mTD were also correlated tightly ( Figure 2 E), indicating that S m sensitively tracked changes in S mTD . Taken together, it is fair to say that conclusions provided by sonomicrometry in this study are comparable, at least qualitatively, with those obtained by TD echocardiography.
In analyzing the experimental data, we relied on E es ′ (the P es /V es ratio) to quantify LV contractility, which can be evaluated more precisely by both the slope (E es ) and volume axis intercept (V 0 ) of the relationship between P es and V es ( Figure 1 A). It was unclear how each contributed to the magnitude of S m in this study. Despite these limitations, the P es /V es ratio as a single contractile index simplifies the statistical analysis of contractility.
Colinearity among the cardiovascular parameters as noted between E es ′ and V ed 1/3 might have affected the present results. The colinearity may be attributable to the nature of the protocols, such as heart failure induction, which depresses LV contractility and increases preload simultaneously. However, the protocols are analogous to commonly observed clinical setting or practice, that is, relevant to possible clinical application of the conclusions of this study.
Conclusions
LV contractility and afterload independently determine S m . The effects of LV preload and EJT on S m might be small, even though they are theoretically associated with S m . S m strongly reflects the status of ventricular-arterial coupling.
Appendix
Instantaneous LVP, P( t ), and LVV, V( t ), are related by the following formula:
where E( t ) is time-varying LV elastance and V 0 is the volume axis intercept of the relationship between P es and V es . S m is a parameter of the ejection phase. The left ventricle has an ellipsoid shape, and the ratio of LV longitudinal length, L( t ), to short-axis length is assumed to be constant during the ejection phase. L( t ) and its time derivative are expressed as follows:
dL ( t ) / dt = α 3 ⋅ dV ( t ) / dt ⋅ [ V ( t ) ] − 2 / 3 .
During the ejection phase, because P( t ) can be approximated to P es ( Figure 1 A), equation A 2 is rewritten as follows:
Differentiation of both sides of equation A 5 with respect to time yields
dV ( t ) / dt = − P es ⋅ dE ( t ) / dt [ E ( t ) ] 2 .
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