Heart rate variability (HRV) decreases in patients with diabetic neuropathy and in those at increased risk for myocardial infarction . Measurement of short-term HRV may have clinical relevance to anesthesiology . For example, respiratory sinus arrhythmia predicts emergence from anesthesia . Also, spectral analysis of HRV suggests autonomic nervous system impairment after cardiac surgery .
Newer HRV measures are model independent, suitable for nonlinear processes, and measure aspects of HRV different from the traditional methods such as standard deviation or spectral analysis . One of these nonlinear measures, approximate entropy (ApEn), correlates with postoperative ventricular dysfunction . However, the new nonlinear methods of HRV measurement have not been applied in the operating room. We wanted to determine whether these methods could be used as tools to detect changes in HRV which occur during the anesthetic management of patients.
We compared the effect of the induction of anesthesia on HRV as measured by two nonlinear methods, ApEn and point correlation dimension (PD2). ApEn is a modification of traditional informational entropy measures designed to measure "regularity" in small amounts of noisy data, even in chaotic systems [4-6]. In essence, it is calculated by identifying patterns within a time series (e.g., groups of two consecutive R-R intervals) and determining the effect of increasing pattern size (e.g., from two to three consecutive R-R intervals) on the likelihood that patterns repeat themselves. PD2 estimates the "dimension" at each point in a series (e.g., the number of independent variables affecting heart beat generation), even if it changes during the measurement period (i.e., the data is nonstationary) [4,7]. Its calculation is complex, but is based on breaking a times series (e.g., R-R interval series) into vectors of many dimensions (e.g., different numbers of consecutive R-R intervals), determining the vector lengths and relating the number of vector length differences within a certain tolerance level to the size of the tolerance level.
With institutional review board approval, we recorded electrocardiograms (ECGs) from 12 patients undergoing cardiac surgery by a single surgeon. Enrollment in the study did not alter patient management. Two patients had atrial fibrillation. Patients received morphine (0.1 mg/kg) and scopolamine (6 micro gram/kg) for premedication. Fentanyl (50-60 micro gram/kg) induced anesthesia and pancuronium (0.1 mg/kg) provided muscle relaxation for endotracheal intubation. Shortly before and 10-15 min after anesthesia induction, 15-min ECGs were recorded on FM tape (Vetter model 420). A microcomputer-based waveform analysis system (Experimenter's Workbench; DataWave, Longmont, CO) subsequently digitized the ECG signal at 2000 Hz and determined heart beat periods (the R-R interval, in ms). Occasional noisy periods which defied proper analysis by our software were identified by outlier detection and visual inspection. HRV analysis proceeded with two series of 700 sequential R-R intervals, one series before and one after the induction of anesthesia.
ApEn calculation, using the method of Pincus et al. , utilized parameters of m = 2, r = 7.5 ms (which was 15% of the standard deviation of all R-R intervals in the experimental population), and n = 700. To calculate ApEn independently of the standard deviation, the ApEn calculation was repeated over a wide range of r values (0-40 ms) and the maximum ApEn value obtained was designated the Peak ApEn Figure 1. PD2-02 software from Neurotech Laboratories (Bangor, PA) calculated PD2 following the algorithm of Skinner et al.  utilizing the default values (tau = 1, interval = 4, linearity = 0.30, convergence = 0.40, plot length = 0.15). PD2 is calculated for individual points in the time series. For each series of 700 R-R intervals, the mean of individual PD2s calculated for that series characterized the entire series. After data transformation from an R-R duration versus an R-R number series to a heart rate versus time series, using a method similar to Berger et al. , calculation of total power used a fast Fourier transformation with subsequent integration of the power spectrum from 0.03 to 0.5 Hz using MATLAB software (Math Works, Natick, MA). After testing for normality, paired t-tests or Wilcoxon signed rank tests were used as appropriate. Data are presented as means +/- SE with P < 0.05 considered significant.
There were no significant changes after the induction of anesthesia in the mean R-R interval or the standard deviation of the R-R intervals Table 1. The r value at which Peak ApEn occurred also did not differ with anesthesia induction (before, 8.2 +/- 2.5 ms; after, 6.6 +/- 3.3 ms). However, total power, ApEn, Peak ApEn, and mean PD2 decreased significantly after the induction of anesthesia Table 1. The percent decreases after anesthesia induction of ApEn (37% +/- 8.3%) and mean PD2 (32% +/- 5.5%) were similar, but both were greater than the percent decrease in Peak ApEn (13% +/- 5.5%). ApEn and Peak ApEn decreased in all but one patient (who had atrial fibrillation), whereas mean PD2 decreased in all 12 patients.
Both ApEn and PD2 revealed changes in HRV which occur after the induction of anesthesia. Although the opioid was likely responsible for a decrease in HRV , other drugs, such as muscle relaxants, and changes in ventilation also may have affected the HRV as measured by ApEn and PD2.
Like ApEn, Peak ApEn decreased significantly after the induction of anesthesia. Although Peak ApEn changed less with induction than ApEn, it also varied less. An advantage of Peak ApEn is that it can be calculated independently for each time series, whereas ApEn relies on the SD of the entire experimental population to fix the calculation variable r. Further analysis of the characteristics of ApEn versus r curves may reveal other advantages of Peak ApEn calculation.
This study included patients with atrial fibrillation because nonlinear measures such as ApEn and PD2, being model independent, should thus be robust. Indeed, exclusion of these patients from the analysis yields similar results: ApEn, Peak ApEn, and mean PD2 detect significant differences in HRV after anesthesia induction.
In agreement with previous reports , total power also decreased after anesthesia induction. Even though all the measures of HRV used here (power spectra, ApEn, and PD2) decreased with anesthesia induction, they calculate variability differently and cannot be considered equivalent measures. For example, the power spectrum is very sensitive to periodic changes such as respiratory sinus arrhythmia, which is affected by patient position and respiratory rate. However, the magnitude of periodic change does not affect ApEn, making it a preferred measure of HRV when changes in position and respiratory rate are confounding factors. Although PD2 requires the most data for precise calculation, it is appropriate for nonstationary data and thus may detect transient changes in the complexity of the cardiovascular system.
ApEn and PD2 monitor perioperative heart rate changes that are not reflected by changes in the mean or SD of R-R intervals. These nonlinear measures may supplement spectral analysis of HRV. Clinical application of both linear and nonlinear measures of HRV deserve continued investigation.
We are grateful for the excellent assistance of Viet-Nhan Nguyen in performing portions of the data analysis.
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