K-nearest-neighbor conditional entropy approach for the assessment of the short-term complexity of cardiovascular control

Abstract

Complexity analysis of short-term cardiovascular control is traditionally performed using entropy-based approaches including corrective terms or strategies to cope with the loss of reliability of conditional distributions with pattern length. This study proposes a new approach aiming at the estimation of conditional entropy (CE) from short data segments (about 250 samples) based on the k-nearest-neighbor technique. The main advantages are: (i) the control of the loss of reliability of the conditional distributions with the pattern length without introducing a priori information; (ii) the assessment of complexity indexes without fixing the pattern length to an arbitrary low value. The approach, referred to as k-nearest-neighbor conditional entropy (KNNCE), was contrasted with corrected approximate entropy (CApEn), sample entropy (SampEn) and corrected CE (CCE), being the most frequently exploited approaches for entropy-based complexity analysis of short cardiovascular series. Complexity indexes were evaluated during the selective pharmacological blockade of the vagal and/or sympathetic branches of the autonomic nervous system. We found that KNNCE was more powerful than CCE in detecting the decrease of complexity of heart period variability imposed by double autonomic blockade. In addition, KNNCE provides indexes indistinguishable from those derived from CApEn and SampEn. Since this result was obtained without using strategies to correct the CE estimate and without fixing the embedding dimension to an arbitrary low value, KNNCE is potentially more valuable than CCE, CApEn and SampEn when the number of past samples most useful to reduce the uncertainty of future behaviors is high and/or variable among conditions and/or groups.

Entropy Measures in the Assessment of Heart Rate Variability in Patients with Cardiodepressive Vasovagal Syncope

“…The decrease of entropy as a consequence of the sympathetic activation during orthostatic challenge was also shown by Turianikova et al [36]. On the other hand, pharmacological autonomic blockade with atropine, as well as propranolol combined with atropine have also decreased heart entropy, suggesting that vagal activity is the main modulator of heart rate complexity [37]. A recent study by Weipert [38] indicates that both vagal and sympathetic modulations contribute to heart rate complexity, and what is more, different autonomic states might result in the same value of SampEn (e.g., reciprocal changes of vagal and sympathetic systems and co-activation of both systems).…”

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

“…After one of the first attempts to elucidate the autonomic influence on HR entropy during autonomic blocking and exercise, Tulppo et al concluded that sympathetic rather than vagal efferent activity modulates HR complexity [68]. In a recent experiment the group around Porta used refined methods to estimate HR complexity and an autonomic blocking protocol to elucidate the underlying autonomic mechanisms [22]. From their results the authors concluded that vagal efferent activity is the main contributor, because high dose of atropine significantly reduced complexity compared to baseline conditions, while sympathetic blocking with propranolol did not have any effect on HR complexity.…”

“…However, many researchers found at least modest correlations for some nonlinear measures and traditional HRV indices under different conditions [5,9,19,20]. It has also been shown that complexity of short-term HRV is under control of the autonomic nervous system [21,22]. Currently, there are only few studies available that compared the cardiovascular response pattern to different exercise modes at similar HR.…”

Entropy of Entropy: Measurement of Dynamical Complexity for Biological Systems

“…In another words, complexity is different from irregularity. Similar paradox also appears in other entropies such as fuzzy entropy (FuzzyEn) [14], permutation entropy [15], and conditional entropy [16]. The paradox may be due to the fact that conventional entropies fail to account for the multiple time scales inherent in healthy physiologic dynamics.…”