) was originally defined as the end-systolic pressure (ESP)/stroke volume (SV) ratio of the left ventricle (LV) [1][2][3]. E a is approximately equal to heart rate (HR) times total peripheral resistance (TPR) under stable hemodynamics [1][2][3]. E a has the same dimensions as an index of ventricular contractility (E max ) defined as the ESP/endsystolic volume (ESV) ratio [1][2][3][4][5][6]. E a proved to be powerful in evaluating the ventriculo-arterial coupling from the viewpoint of cardiac mechanoenergetics in regular beats [1][2][3][4][5][6]. The mechanical energy efficiency from LV total mechanical energy (PVA) to SV is maximal when E a equals E max [1][2][3][4][5][6][7][8][9][10][11]. The mechanical work efficiency from LV oxygen consumption to SV is maximal when E a is appropriately (around 50%) smaller than E max [3][4][5][6][7][8][9][10][11]. Both efficiencies are re- Abbreviations: AF, atrial fibrillation; CO, cardiac output; E a (ϭESP/SV), either effective arterial elastance conventionally, or effective afterload elastance in this study; E max , an index of ventricular contractility defined as the maximum or end-systolic elastance of the ventricle, or end-systolic pressure-volume ratio; EDP, end-diastolic pressure; EDV, end-diastolic volume; ESP, end-systolic pressure; ESV, end-systolic volume; G i (t), electrical conductance of intraventricular blood; G p , parallel conductance; HR, heart rate; LV, left ventricle; LVP, left ventricular pressure; LVV, left ventricular volume; PVA, total mechanical energy of contraction, or systolic pressure-volume area; RR, cardiac beat interval measured as the interval between two R waves of ECG; RR1 through RR6, first through sixth preceding RRs; SV, stroke volume; TPR, total peripheral resistance; V c , ventricular correction volume equivalent to parallel conductance Gp; V 0 , ventricular unstressed volume.
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.
Since March 1992, 25 neonates and small infants with HLHS have undergone a modified Norwood procedure. The mean age and weight at operation were 17 days (2 days-2 months) and 2.7 kg (1.6-3.3 kg). Isolated cerebral and/or myocardial perfusion (ICMP) with direct anastomosis of aorta and pulmonary artery was utilized since January 1995 to 16 patients. Under median sternotomy, PTFE graft (usually 3.0-3.5 mm) was anastomosed to the brachiocephalic artery and the arterial cannula was inserted to this PTFE graft. The left carotid and the left subclavian arteries were snared and a clamp was placed on the aortic arch just distal to the brachiocephalic artery. This allowed blood to enter the brain and the coronary arteries, keeping the brain perfused and the heart-beating. After reconstruction of distal aortic arch, a single dose of crystalloid cardioplesia was infused and the rest of the arch was reconstructed. There were 14 early deaths (56%) and 4 late deaths (16%). Bidirectional Glenn procedure was performed to 5 patients with 1 death. Three patients underwent modified Fontan procedure without mortality. Mean aortic cross clamp time was 24 min. and mean ICMP time was 32 min. There was no neurologic complications. In conclusion, isolated cerebral and/or myocardial perfusion may offer an advantage of protecting the brain and myocardium during arch in Norwood procedure.
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