Novel application of a multiscale entropy index as a sensitive tool for detecting subtle vascular abnormalities in the aged and diabetic

(Multiscale) Cross-Entropy Methods: A Review

Cross-entropy was introduced in 1996 to quantify the degree of asynchronism between two time series. In 2009, a multiscale cross-entropy measure was proposed to analyze the dynamical characteristics of the coupling behavior between two sequences on multiple scales. Since their introductions, many improvements and other methods have been developed. In this review we offer a state-of-the-art on cross-entropy measures and their multiscale approaches.

Multiscale entropic assessment of autonomic dysfunction in patients with obstructive sleep apnea and therapeutic impact of continuous positive airway pressure treatment

OBJECTIVE

Obstructive sleep apnea (OSA) is an independent risk factor for cardiovascular disease because of its associated autonomic nervous and vascular regulatory dysfunctions. We tested the hypothesis that the multiscale entropy (MSE) approach to heart rate variability analysis may be used for evaluating OSA severity through simultaneous assessment of these abnormalities.

METHODS

A total of 147 subjects were divided into four groups according to apnea-hypopnea index (AHI) from polysomnography (PSG): Snoring without OSA (5 > AHI, n = 31), mild (5 ≤ AHI < 15, n = 31), moderate (15 ≤ AHI < 30, n = 41), and severe (AHI ≥ 30, n = 44) OSA. Of the patients, 41 receiving continuous positive airway pressure (CPAP) treatment were included for comparison. For each subject, two segments of electrocardiographic (ECG) signals (both at stage N2) were used for R-R interval (RRI) analysis, including a 10-minute recording 10 minutes after falling asleep (ie, early phase) and another 10-minute segment at 3 hours (ie, late phase). Heart rate variability as reflected in changes in RRI between the two segments was assessed with small-scale multiscale entropy index (MEISS, sum of sample entropy from time scale from 1 to 5) and large-scale multiscale entropy index (MEILS, scale from 6 to 10).

RESULTS

Increase in MEILS in the late phase of sleep was noted in both the normal snoring and CPAP groups (P <0.01). Although the moderate OSA group exhibited MEISS drop in the late phase (P < 0.02), both MEISS and MEILS decreased in the late phase in the severe OSA group (P < 0.001, P < 0.02). However, no differences were noted in mild OSA subjects in both parameters.

CONCLUSION

The results demonstrated significant severity-dependent deterioration in autonomic and vascular regulatory function in patients with OSA as reflected in the reductions in MEISS and MEILS, respectively, and notable improvement after CPAP treatment. The MEI obtainable through PSG may indicate not only OSA severity and physiological status but also therapeutic outcome for OSA patients.

Application of multiscale entropy in arterial waveform contour analysis in healthy and diabetic subjects

We applied multiscale entropy (MSE) to assess variation in crest time (CT), a parameter in arterial waveform analysis, in diagnosing patients with diabetes. Data on digital volume pulse were obtained from 93 individuals in three groups [Healthy young (Group 1, 20 < age ≤ 40, n = 30), healthy upper-middle-aged (Group 2, age > 40, n = 30), and diabetic (Group 3, n = 33) subjects]. Crest time, normalized crest time, crest time ratio (CTR), small- and large-scale MSE on CT [MSESS(CT) and MSELS(CT), respectively] were computed and correlated with anthropometric (i.e., body weight/height, waist circumference), hemodynamic (i.e., blood pressure), and biochemical parameters (i.e., serum triglyceride, high-density lipoprotein, fasting blood sugar, and glycosylated hemoglobin). The results demonstrated higher variability in CT in healthy subjects (Groups 1 and 2) compared with that in diabetic patients (Group 3) as reflected in significantly elevated MSESS(CT) and MSELS(CT) in the former (p < 0.003 and p < 0.001, respectively). MSELS(CT) also showed significant association with waist circumference and fasting blood sugar (i.e., two diagnostic criteria of metabolic syndrome) as well as glycosylated hemoglobin concentration. In conclusion, using MSE analysis for assessing CT variation successfully distinguished diabetic patients from healthy subjects. MSESS(CT) and MSELS(CT) therefore may serve as noninvasive tools for identifying subjects with diabetes and those at risk.

Applications of dynamical complexity theory in traditional Chinese medicine

Traditional Chinese medicine (TCM) has been gradually accepted by the world. Despite its widespread use in clinical settings, a major challenge in TCM is to study it scientifically. This difficulty arises from the fact that TCM views human body as a complex dynamical system, and focuses on the balance of the human body, both internally and with its external environment. As a result, conventional tools that are based on reductionist approach are not adequate. Methods that can quantify the dynamics of complex integrative systems may bring new insights and utilities about the clinical practice and evaluation of efficacy of TCM. The dynamical complexity theory recently proposed and its computational algorithm, Multiscale Entropy (MSE) analysis, are consistent with TCM concepts. This new system level analysis has been successfully applied to many health and disease related topics in medicine. We believe that there could be many promising applications of this dynamical complexity concept in TCM. In this article, we propose some promising applications and research areas that TCM practitioners and researchers can pursue.

Multiscale cross-approximate entropy analysis as a measurement of complexity between ECG R-R interval and PPG pulse amplitude series among the normal and diabetic subjects

Physiological signals often show complex fluctuation (CF) under the dual influence of temporal and spatial scales, and CF can be used to assess the health of physiologic systems in the human body. This study applied multiscale cross-approximate entropy (MC-ApEn) to quantify the complex fluctuation between R-R intervals series and photoplethysmography amplitude series. All subjects were then divided into the following two groups: healthy upper middle-aged subjects (Group 1, age range: 41-80 years, n = 27) and upper middle-aged subjects with type 2 diabetes (Group 2, age range: 41-80 years, n = 24). There are significant differences of heart rate variability, LHR, between Groups 1 and 2 (1.94 ± 1.21 versus 1.32 ± 1.00, P = 0.031). Results demonstrated differences in sum of large scale MC-ApEn (MC-ApEn(LS)) (5.32 ± 0.50 versus 4.74 ± 0.78, P = 0.003). This parameter has a good agreement with pulse-pulse interval and pulse amplitude ratio (PAR), a simplified assessment for baroreflex activity. In conclusion, this study employed the MC-ApEn method, integrating multiple temporal and spatial scales, to quantify the complex interaction between the two physical signals. The MC-ApEn(LS) parameter could accurately reflect disease process in diabetics and might be another way for assessing the autonomic nerve function.