Traditional approaches to measuring the complexity of biological signals fail to account for the multiple time scales inherent in such time series. These algorithms have yielded contradictory findings when applied to real-world datasets obtained in health and disease states. We describe in detail the basis and implementation of the multiscale entropy (MSE) method. We extend and elaborate previous findings showing its applicability to the fluctuations of the human heartbeat under physiologic and pathologic conditions. The method consistently indicates a loss of complexity with aging, with an erratic cardiac arrhythmia (atrial fibrillation), and with a life-threatening syndrome (congestive heart failure). Further, these different conditions have distinct MSE curve profiles, suggesting diagnostic uses. The results support a general "complexity-loss" theory of aging and disease. We also apply the method to the analysis of coding and noncoding DNA sequences and find that the latter have higher multiscale entropy, consistent with the emerging view that so-called "junk DNA" sequences contain important biological information.

Following the publication of the Task Force document on heart rate variability (HRV) in 1996, a number of articles have been published to describe new HRV methodologies and their application in different physiological and clinical studies. This document presents a critical review of the new methods. A particular attention has been paid to methodologies that have not been reported in the 1996 standardization document but have been more recently tested in sufficiently sized populations. The following methods were considered: Long-range correlation and fractal analysis; Short-term complexity; Entropy and regularity; and Nonlinear dynamical systems and chaotic behaviour. For each of these methods, technical aspects, clinical achievements, and suggestions for clinical application were reviewed. While the novel approaches have contributed in the technical understanding of the signal character of HRV, their success in developing new clinical tools, such as those for the identification of high-risk patients, has been rather limited. Available results obtained in selected populations of patients by specialized laboratories are nevertheless of interest but new prospective studies are needed. The investigation of new parameters, descriptive of the complex regulation mechanisms of heart rate, has to be encouraged because not all information in the HRV signal is captured by traditional methods. The new technologies thus could provide after proper validation, additional physiological, and clinical meaning. Multidisciplinary dialogue and specialized courses in the combination of clinical cardiology and complex signal processing methods seem warranted for further advances in studies of cardiac oscillations and in the understanding normal and abnormal cardiac control processes.

Time irreversibility, a fundamental property of nonequilibrium systems, should be of importance in assessing the status of physiological processes that operate over a wide range of scales. However, measurement of this property in living systems has been limited. We provide a computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales and apply it to the human heartbeat time series in health and disease. We find that the multiscale time asymmetry index is highest for a time series from young subjects and decreases with aging or heart disease. Loss of time irreversibility may provide a new way of assessing the functionality of living systems that operate far from equilibrium.

Costa, Goldberger, and Peng Reply: The authors of the Comment [1] raise a point that was not discussed in our paper [2] due to page limitations. The multiscale entropy (MSE) [2] method is aimed at evaluating the complexity of time series. It is based on the analysis of the entropy values assigned not only to the original time series but also to coarse-grained time series, each of which represents the system's dynamics on a different scale.The entropy assigned to a time series takes into account both its standard deviation (SD) and its correlation properties. However, there is no universal relationship between entropy and SD. Signals with higher variance may or may not have higher entropy, depending on the correlation properties. We illustrate both cases: (1) Consider stochastic variables that are completely independent (without correlations). The variables with larger variances will have higher entropy.(2) Consider a periodic signal with variance jxj and a random signal with variance jyj. The entropy for the random signal is higher than the entropy for the periodic signal, even if jxj jyj.For a very simple time series, belonging to one of the two groups comprising completely ordered or completely disordered signals, it is possible to evaluate, separately, the contributions of the SD and the correlation properties to the entropy value. However, this is not the case for complex signals, which may incorporate both random and deterministic components, as Nikulin et al. imply in their Comment. In general, the degree of irregularity of a complex signal is a property measured by entropy that cannot be entirely captured by the SD or correlation measures, individually or in combination.In our Letter, we used sample entropy (SampEn) to evaluate the degree of randomness of a single time series. This algorithm requires that we specify the values of two parameters: m and r, where m defines the length of the patterns that are compared to each other, and r the similarity criterion. Two patterns of length m, ui and uj, are similar if the distance between them is r. r is defined as a percentage of the SD, and not as an absolute value. This particular implementation is commonly used in heart rate variability analysis because it is well established that SD alone can be a useful indicator of health status. Use of the parameter r, a percentage of SD, therefore probes information that is independent of the time series SD.We considered r 0:15 SD for all groups, which corresponds to normalizing all time series by their SD. Next, we coarse grained the time series and calculated their entropy. We did not renormalize the coarse-grained time series because, after the initial normalization, subsequent changes in SD of coarse-grained time series contain information about the temporal structure of the original time series that should be accounted for by an entropy measure.Using this approach, we consistently observed that 1=f noise is more complex than white noise. As applied to the

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The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

BackgroundSeasonal depression has generated considerable clinical interest in recent years. Despite a common belief that people in higher latitudes are more vulnerable to low mood during the winter, it has never been demonstrated that human's moods are subject to seasonal change on a global scale. The aim of this study was to investigate large-scale seasonal patterns of depression using Internet search query data as a signature and proxy of human affect.Methodology/Principal FindingsOur study was based on a publicly available search engine database, Google Insights for Search, which provides time series data of weekly search trends from January 1, 2004 to June 30, 2009. We applied an empirical mode decomposition method to isolate seasonal components of health-related search trends of depression in 54 geographic areas worldwide. We identified a seasonal trend of depression that was opposite between the northern and southern hemispheres; this trend was significantly correlated with seasonal oscillations of temperature (USA: r = −0.872, p<0.001; Australia: r = −0.656, p<0.001). Based on analyses of search trends over 54 geological locations worldwide, we found that the degree of correlation between searching for depression and temperature was latitude-dependent (northern hemisphere: r = −0.686; p<0.001; southern hemisphere: r = 0.871; p<0.0001).Conclusions/SignificanceOur findings indicate that Internet searches for depression from people in higher latitudes are more vulnerable to seasonal change, whereas this phenomenon is obscured in tropical areas. This phenomenon exists universally across countries, regardless of language. This study provides novel, Internet-based evidence for the epidemiology of seasonal depression.

BackgroundDiminished control of standing balance, traditionally indicated by greater postural sway magnitude and speed, is associated with falls in older adults. Tai Chi (TC) is a multisystem intervention that reduces fall risk, yet its impact on sway measures vary considerably. We hypothesized that TC improves the integrated function of multiple control systems influencing balance, quantifiable by the multi-scale “complexity” of postural sway fluctuations.ObjectivesTo evaluate both traditional and complexity-based measures of sway to characterize the short- and potential long-term effects of TC training on postural control and the relationships between sway measures and physical function in healthy older adults.MethodsA cross-sectional comparison of standing postural sway in healthy TC-naïve and TC-expert (24.5±12 yrs experience) adults. TC-naïve participants then completed a 6-month, two-arm, wait-list randomized clinical trial of TC training. Postural sway was assessed before and after the training during standing on a force-plate with eyes-open (EO) and eyes-closed (EC). Anterior-posterior (AP) and medio-lateral (ML) sway speed, magnitude, and complexity (quantified by multiscale entropy) were calculated. Single-legged standing time and Timed-Up–and-Go tests characterized physical function.ResultsAt baseline, compared to TC-naïve adults (n = 60, age 64.5±7.5 yrs), TC-experts (n = 27, age 62.8±7.5 yrs) exhibited greater complexity of sway in the AP EC (P = 0.023), ML EO (P<0.001), and ML EC (P<0.001) conditions. Traditional measures of sway speed and magnitude were not significantly lower among TC-experts. Intention-to-treat analyses indicated no significant effects of short-term TC training; however, increases in AP EC and ML EC complexity amongst those randomized to TC were positively correlated with practice hours (P = 0.044, P = 0.018). Long- and short-term TC training were positively associated with physical function.ConclusionMultiscale entropy offers a complementary approach to traditional COP measures for characterizing sway during quiet standing, and may be more sensitive to the effects of TC in healthy adults.Trial RegistrationClinicalTrials.gov NCT01340365