Frequency distribution, variance, and moving average of left ventricular rhythm and contractility during atrial fibrillation in dog

Mode of frequency distribution of external work efficiency of arrhythmic beats during atrial fibrillation remains normal in canine heart

The external work (EW) efficiency of individual arrhythmic beats of the left ventricle (LV) cannot directly be obtained since LV O(2) consumption (VO(2)) of each beat cannot directly be measured under beat-to-beat varying contractile and loading conditions. We, however, have recently reported that VO(2) of each arrhythmic beat can reasonably be estimated by VO(2) = aPVA + bE(max) + c even under varying PVA and E(max). Here, PVA is the LV pressure-volume (P-V) area as a measure of the LV total mechanical energy, E(max) is the LV end-systolic elastance as an index of the LV contractility, a is a constant O(2) cost of PVA, b is a constant O(2) cost of E(max), and c is the basal metabolic VO(2) of the beat, all on a per-beat basis. Using the above formula in this study, we calculated VO(2) of the individual arrhythmic beats from their measured PVA and E(max) during electrically induced atrial fibrillation (AF) in normal canine hearts. We then calculated their LV EW efficiency by dividing their measured EW with the estimated VO(2). We found that the thus calculated EW efficiency of the arrhythmic beats had a rightward skewed distribution with a mode of 15% and a maximum of 18% around a mean of 13% on average in six hearts. This mode remained comparable to the efficiency (15%) at regular tachycardia though 22% lower than mean arrhythmic tachycardia.

Single Beat Determination of Regional Myocardial Strain Measurements in Patients with Atrial Fibrillation

Atrial fibrillation (AF) and congestive heart failure share several features and often coexist in the same patients; therefore, serial assessment of regional myocardial function is important for patients with AF. However, the clinical assessment of regional myocardial function in AF is unreliable and difficult because of beat-to-beat variation. Recent reports have shown that the ratio of the preceding to the prepreceding R-R interval (RR1/RR2) can be used to assess global left ventricular systolic function. Accordingly, we tested the hypothesis that regional wall motion can be estimated from a single beat based on RR1/RR2 in patients with AF. Peak systolic strain at basal, mid, and apical segments of the septal wall was measured by Doppler tissue imaging from an apical 4-chamber view for 30 seconds in 50 patients with AF (mean ejection fraction 52.1 +/- 15.3%; mean heart rate 76.4 +/- 16.0/min). There was a positive linear relationship between peak strain and RR1/RR2 and RR1, and a negative relationship with RR2, with the correlation of peak strain to RR1/RR2 was better than that in RR1 or RR2. Furthermore, peak strain at RR1/RR2 = 1 was calculated from the linear regression and compared with the average measured value of all recorded cardiac cycles in each patient. In all cases, average peak strain showed a significant positive correlation with RR1/RR2 at each segment (r = 0.99). In conclusion, regional myocardial strain at RR1/RR2 = 1 on the linear regression represents the average value of all recorded cardiac cycles in patients with AF.

High mechanical efficiency of left ventricular arrhythmic contractions during atrial fibrillation

We analyzed the frequency distribution of the left ventricular (LV) mechanical efficiency of individual arrhythmic beats during electrically induced atrial fibrillation (AF) in normal canine hearts. This efficiency is the fraction of the external mechanical work (EW) in the total mechanical energy measured by the systolic pressure-volume area (PVA). The mean, median, and mode of this efficiency (EW/PVA) were as high as 78%, 80%, and 81%, respectively, on average in six hearts. These high efficiencies were comparable to that of the regular beats in these hearts. The frequency distribution of the EW/PVA during AF tended to skew to the higher side in all the hearts. Since the EW/PVA is directly related to both the ventriculo-arterial (or afterload) coupling ratio (E(a)/E(max); E(a) = effective arterial elastance, E(max) = end-systolic ventricular elastance) and the ejection fraction on a per-beat basis, we also analyzed their frequency distributions. We found them to skew enough to account for the rightward skewed frequency distribution of the EW/PVA during AF with the unexpectedly high mean EW/PVA. These results indicate that the LV arrhythmia during AF per se does not directly suppress the mean level of LV mechanical efficiency in normal canine hearts.

Variable Unstressed Volume Keeps Normal Distributions of Canine Left Ventricular Contractility and Total Mechanical Energy under Atrial Fibrillation

We have reported that the contractility index (E(max)) and the total mechanical energy (PVA) of arrhythmic beats of the left ventricle (LV) distribute normally in canine hearts under electrically induced atrial fibrillation (AF). Here, E(max) is the ventricular elastance as the slope of the end-systolic (ES) pressure-volume (P-V) relation (ESPVR), and PVA is the systolic P-V area as the sum of the external mechanical work within the P-V loop and the elastic potential energy under the ESPVR. To obtain E(max) and PVA, we had to assume the systolic unstressed volume (V(o)) as the V-axis intercept of the ESPVR to be constant despite the varying E(max), since there was no method to obtain V(o) directly in each arrhythmic beat. However, we know that in regular stable beats V(o) decreases by approximately 7 ml/100 g LV with approximately 100 times the increases in E(max) from ~0.2 mmHg/(ml/100 g LV) of almost arresting weak beats to approximately 20 mmHg/(ml/100 g LV) of strong beats with a highly enhanced contractility. In the present study, we investigated whether E(max) and PVA under AF could still distribute normally, despite such E(max)-dependent V(o) changes. The present analyses showed that the E(max) changes were only approximately 3 times at most from the weakest to the strongest arrhythmic beat under AF. These changes were not large enough to affect V(o) enough to distort the frequency distributions of E(max) and PVA from normality. We conclude that one could practically ignore the slight E(max) and PVA changes with the Emax-dependent V(o) changes under AF.

Normal distribution of ventricular pressure-volume area of arrhythmic beats under atrial fibrillation in canine heart

We previously found the frequency distribution of the left ventricular (LV) effective afterload elastance (Ea) of arrhythmic beats to be nonnormal or non-Gaussian in contrast to the normal distribution of the LV end-systolic elastance (Emax) in canine in situ LVs during electrically induced atrial fibrillation (AF). These two mechanical variables determine the total mechanical energy [systolic pressure-volume area (PVA)] generated by LV contraction when the LV end-diastolic volume is given on a per-beat basis. PVA and Emax are the two key determinants of the LV O2 consumption per beat. In the present study, we analyzed the frequency distribution of PVA during AF by its χ2, significance level, skewness, and kurtosis and compared them with those of other major cardiodynamic variables including Ea and Emax. We assumed the volume intercept (V0) of the end-systolic pressure-volume relation needed for Emax determination to be stable during arrhythmia. We found that PVA distributed much more normally than Ea and slightly more so than Emax during AF. We compared the χ2, significance level, skewness, and kurtosis of all the complex terms of the PVA formula. We found that the complexity of the PVA formula attenuated the effect of the considerably nonnormal distribution of Ea on the distribution of PVA along the central limit theorem. We conclude that mean (SD) of PVA can reliably characterize the distribution of PVA of arrhythmic beats during AF, at least in canine hearts.

Predictability of O2 consumption from contractility and mechanical energy of absolute arrhythmic beats in canine heart

Left ventricular (LV) O2 consumption (V(O2)) per minute is measurable for both regular and arrhythmic beats. LV V(O2) per beat can then be obtained as V(O2) per minute minute divided by heart rate per minute minute for regular beats, but not for arrhythmic beats. We have established that V(O2) of a regular stable beat is predictable by V(O2) = a PVA + b E(max) + c, where PVA is the systolic pressure-volume area as a measure of the total mechanical energy of an individual contraction and E(max) is the end-systolic maximum elastance as an index of ventricular contractility of the contraction. Furthermore, a is the O2 cost of PVA, b is the O2 cost of E(max), and c is the basal metabolic V(O2) per beat. We considered it theoretically reasonable to expect that the same formula could also predict LV V(O2) of individual arrhythmic beats from their respective PVA and E(max) with the same a, b, and c. We therefore applied this formula to the PVA - Emax data of individual arrhythmic beats under electrically induced atrial fibrillation (AF) in six canine in situ hearts. We found that the predicted V(O2) of individual arrhythmic beats highly correlated linearly with either their V(O2) (r = 0.96 +/- 0.01) or E(max) (0.97 +/- 0.03) while both also highly correlated linearly with each other (0.88 +/- 0.04). This suggests that the above formula may be used to predict LV Vo2 of absolute arrhythmic beats from their Emax and PVA under AF.