Sample Entropy and Traditional Measures of Heart Rate Dynamics Reveal Different Modes of Cardiovascular Control During Low Intensity Exercise

Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.

Abnormal heart rate characteristics of reduced variability and transient decelerations are present early in the course of neonatal sepsis. To investigate the dynamics, we calculated sample entropy, a similar but less biased measure than the popular approximate entropy. Both calculate the probability that epochs of window length m that are similar within a tolerance r remain similar at the next point. We studied 89 consecutive admissions to a tertiary care neonatal intensive care unit, among whom there were 21 episodes of sepsis, and we performed numerical simulations. We addressed the fundamental issues of optimal selection of m and r and the impact of missing data. The major findings are that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated. The major mechanism, surprisingly, is unrelated to the regularity of the data: entropy estimates inevitably fall in any record with spikes. We propose more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.

In order to evaluate hemodynamic predictors of myocardial oxygen consumption (MVO2), 27 normotensive men with angina pectoris were studied at rest and during a steady state at sympton-tolerated maximal exercise (STME). Myocardial blood flow (MBF) was measured by the nitrous oxide method using gas chromatography. MBF increased by 71% from a resting value of 57.4 +/- 10.2 to 98.3 +/- 15.6 ml/100 g LV/min (P less than 0.001) during STME while MVO2 increased by 81% from a resting value of 6.7 +/- 1.3 to 12.1 +/- 2.8 ml O2/100 g LV/min (P less than 0.001). MVO2 correlated well with heart rate (HR) (r = 0.79), with HR x blood pressure (BP) (r = 0.83), and, adding end-diastolic pressure and peak LV dp/dt as independent variables, slightly improved this correlation (r = .86). Including the ejection period (tension-time index) did not improve the correlation (r = 0.80). Thus, HR and HR x BP, both easily measured hemodynamic variables, are good predictors of MVO2 during exercise in normotensive patients with ischemic heart disease. Including variables reflecting the contractile state of the heart and ventricular volume may further improve the predictability.