Frequency Distribution, Variance, and Moving Average of Left Ventricular Rhythm and Contractility during Atrial Fibrillation in Dog.

Abstract

Many groups in both basic and clinical studies [1][2][3][4][5][6][7][8][9] have long investigated basic statistical characteristics, including the frequency distribution of arrhythmic beat interval (RR), during atrial fibrillation (AF). Mean RR has been used to evaluate the average RR during AF [9][10][11]. However, the minimal number of beats from which the mean RR has been reliably obtained varied widely between only 4 beats to as many as the number of beats for 2 min among investigators and their purposes [9][10][11]. In some of these studies, mean RR was obtained to characterize the average RR even either in case of the nonnormal distribution or without testing its normality [1,5,6,[8][9][10][11].We have recently studied the frequency distributions not only of RR, but also of ventricular contractility (E max ) [12] and effective arterial elastance (E a ) [13] in in situ ejecting left ventricles during AF [14]. We have found that not only RR, but also E max , E a , and ventriculo-arterial coupling (E a /E max ) distributed nonnormally with considerable skewness (lack of symmetry of a frequency distribution) and kurtosis (peakedness or flatness of a frequency distribution) [14]. Their meanϮSD values could not uniquely characterize their nonnormal frequency distributions [14], unlike a normal frequency distribution [15,16].We recognized in the present study the necessity of isovolumic contractions to scrutinize the frequency distributions of E max during AF for the following reason. Although E a and E a /E max require ejecting contractions whether in situ or ex vivo [13,14,17] Key words: arrhythmia, statistics, histogram, normality, variance.Abstract: Mean levels of left ventricular rhythm and contractility averaged over arrhythmic beats would characterize the average cardiac performance during atrial fibrillation (AF). However, no consensus exists on the minimal number of beats for their reliable mean values. We analyzed their basic statistics to find out such a minimal beat number in canine hearts. We produced AF by electrically stimulating the atrium and measured left ventricular arrhythmic beat interval (RR) and peak isovolumic pressure (LVP). From these, we calculated instantaneous heart rate (HRϭ60,000/RR), contractility (E max ϭLVP/isovolumic volume above unstressed volume), and beat interval ratio (RR1/RR2). We found that all their frequency distributions during AF were variably nonnormal with skewness and kurtosis. Their meansϮstandard deviations alone cannot represent their nonnormal distributions. A 90% reduction of variances of E max and RR1/RR2 required a moving average of 15 and 24, respectively, arrhythmic beats on the average, whereas that of RR and HR required 60 beats on the average. These results indicate that a statistical characterization of arrhythmic cardiodynamic variables facilitates better understanding of cardiac performance during AF.

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

“…Figure 1 illustrates these variables under AF in the P-V diagram. We have described in detail the methods to calculate EW, E max , and PVA elsewhere [7,8]. Briefly, we first obtained V 0 ( Fig.…”

“…We also calculated PVA as usual on a computer as the P-V area scanned by the instantaneous P-V line connecting the instantaneous P-V point to V 0 in each arrhythmic beat [7,8]. This calculation also yielded EW and PE (shaded rectangular and triangular areas, respectively, in Fig.…”

“…We had shown that 1 min was long enough to obtain a large enough number of arrhythmic beats for statistical analyses since we had found both E max and PVA to distribute normally even within 1 min [8]. We used Microsoft Office 2004 Excel and SAS StatView 5.0 for the statistical analyses.…”

“…EW), EDV, and ESP also fluctuated simultaneously. As for these fluctuations under AF, we have already analyzed them in detail [4,5,8,[12][13][14][15]. Figure 2 plots LV EW (open circles) and its efficiency (solid circles) against the predicted LV VO 2 of arrhythmic beats for 30 s in one canine heart.…”

High Mechanical Efficiency of Left Ventricular Arrhythmic Contractions during Atrial Fibrillation

“…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.Key words: heart, arrhythmia, external work, pressure-volume area.We have been investigating the statistical characteristics of major mechanoenergetic variables of the left ventricle (LV) beating arrhythmically during atrial fibrillation (AF) in normal canine in situ hearts [1][2][3][4][5][6]. In these studies, we have found the positive correlation between E max and the preceding beat interval [5]; the apparently nonnormal or non-Gaussian frequency distributions of the beat interval, heart rate, and effective arterial elastance (E a ) [1,2]; and the normal or Gaussian distributions of the end-systolic pressure-volume (P-V) ratio or maximal elastance (E max ) as a load-independent contractility index and the systolic P-V area (PVA) as a measure of the LV total mechanical energy [3,7].…”