Blood pressure fragmentation as a new measure of blood pressure variability: association with predictors of cardiac surgery outcomes.

Background: Fluctuations in beat-to-beat blood pressure variability (BPV) encode untapped information of clinical utility. A need exists for developing new methods to quantify the dynamical properties of these fluctuations beyond their mean and variance. Objectives: Introduction of a new beat-to-beat BPV measure, termed blood pressure fragmentation (BPF), and testing of whether increased preoperative BPF is associated with (i) older age; (ii) higher cardiac surgical risk, assessed using the Society of Thoracic Surgeons' (STS) Risk of Morbidity and Mortality index and the European System for Cardiac Operative Risk Evaluation Score (EuroSCORE II); and (iii) longer ICU length of stay (LOS) following cardiac surgery. The secondary objective was to use standard BPV measures, specifically, mean, SD, coefficient of variation (CV), average real variability (ARV), as well a short-term scaling index, the detrended fluctuation analysis (DFA) ⍺1 exponent, in the same type of analyses to compare the results with those obtained using BPF. Methods: Consecutive sample of 497 adult patients (72% male; age, median [inter-quartile range]: 67 [59-75] years) undergoing cardiac surgery with cardiopulmonary bypass. Fragmentation, standard BPV and DFA ⍺1 measures were derived from preoperative systolic blood pressure (SBP) time series obtained from radial artery recordings. Results: Increased preoperative systolic BPF was associated with older age, higher STS Risk of Morbidity and Mortality and EuroSCORE II values, and longer ICU LOS in all models. Specifically, a one-SD increase in systolic BPF (9%) was associated with a 26% (13%-40%) higher likelihood of longer ICU LOS (>2 days). Among the other measures, only ARV and DFA ⍺1 tended to be associated with longer ICU LOS. However, the associations did not reach significance in the most adjusted models. Conclusion: Preoperative BPF was significantly associated with preoperative predictors of cardiac surgical outcomes as well as with ICU LOS. Our findings encourage future studies of preoperative BPF for assessment of health status and risk stratification of surgical and non-surgical patients.

Heart rate fragmentation and brain MRI markers of small vessel disease in MESA.

INTRODUCTION: Heart rate (HR) fragmentation indices quantify breakdown of HR regulation and are associated with atrial fibrillation and cognitive impairment. Their association with brain magnetic resonance imaging (MRI) markers of small vessel disease is unexplored. METHODS: In 606 stroke-free participants of the Multi-Ethnic Study of Atherosclerosis (mean age 67), HR fragmentation indices including percentage of inflection points (PIP) were derived from sleep study recordings. We examined PIP in relation to white matter hyperintensity (WMH) volume, total white matter fractional anisotropy (FA), and microbleeds from 3-Tesla brain MRI completed 7 years later. RESULTS: In adjusted analyses, higher PIP was associated with greater WMH volume (14% per standard deviation [SD], 95% confidence interval [CI]: 2, 27%, P = 0.02) and lower WM FA (-0.09 SD per SD, 95% CI: -0.16, -0.01, P = 0.03). DISCUSSION: HR fragmentation was associated with small vessel disease. HR fragmentation can be measured automatically from ambulatory electrocardiogram devices and may be useful as a biomarker of vascular brain injury.

Method to quantify the impact of sleep on cardiac neuroautonomic functionality: application to the prediction of cardiovascular events in the Multi-Ethnic Study of Atherosclerosis.

We introduce the concept of cardiac neuroautonomic renewability and a method for its quantification. This concept refers to the involuntary nervous system's capacity to improve cardiac control in response to restorative interventions, such as sleep. We used the change in heart rate fragmentation (ΔHRF), before sleep onset compared with after sleep termination, to quantify the restorative effects of sleep. We hypothesized that the ability to improve cardiac neuroautonomic functionality would diminish with age and be associated with lower risk of major adverse cardiovascular events (MACE). We analyzed the ECG channel of polysomnographic recordings from an ancillary investigation of the Multi-Ethnic Study of Atherosclerosis (MESA). In a cohort of 659 participants (mean ± SD age, 69.7 ± 8.8; 42% male), HRF was significantly (P < 0.001) lower after sleep (before: 74 ± 12%, after: 67 ± 13%). Furthermore, the magnitude of the decrease significantly (P < 0.001) diminished with cross-sectional age. In addition, a larger reduction in HRF following sleep (i.e., higher ΔHRF) was associated with lower risk of MACE, independent of traditional cardiovascular risk factors and current measures of sleep quality. Specifically, over a mean follow-up period of 6.4 ± 1.6 yr, in which 60 participants had their first MACE, a one-SD (12%) increase in ΔHRF was associated with a 36% (95% CI: 12%-53%) decrease in the risk of MACE. The results demonstrate the restorative impact of sleep on heart rate control. As such they support the concept of cardiac neuroautonomic renewability and the utility of ΔHRF for its quantification.

Prediction of Cognitive Decline Using Heart Rate Fragmentation Analysis: The Multi-Ethnic Study of Atherosclerosis.

Background: Heart rate fragmentation (HRF), a new non-invasive metric quantifying cardiac neuroautonomic function, is associated with increasing age and cardiovascular disease. Since these are risk factors for cognitive decline and dementia, in the Multi-Ethnic Study of Atherosclerosis (MESA), we investigated whether disrupted cardiac neuroautonomic function, evidenced by increased HRF, would be associated with worse cognitive function assessed concurrently and at a later examination, and with greater cognitive decline. Methods: HRF was derived from the ECG channel of the polysomnographic recordings obtained in an ancillary study (n = 1,897) conducted in conjunction with MESA exam 5 (2010-2012). Cognitive function was assessed at exam 5 and 6.4 ± 0.5 years later at exam 6 (2016-2018) with tests of global cognitive performance (the Cognitive Abilities Screening Instrument, CASI), processing speed (Digit Symbol Coding, DSC) and working memory (Digit Span). Multivariable regression models were used to quantify the associations between HRF indices and cognitive scores. Results: The participants' mean age was 68 ± 9 years (54% female). Higher HRF at baseline was independently associated with lower cognitive scores at both exams 5 and 6. Specifically, in cross-sectional analyses, a one-standard deviation (SD) (13.7%) increase in HRF was associated with a 0.51 (95% CI: 0.17-0.86) points reduction in CASI and a 1.12 (0.34-1.90) points reduction in DSC. Quantitatively similar effects were obtained in longitudinal analyses. A one-SD increase in HRF was associated with a 0.44 (0.03-0.86) and a 1.04 (0.28-1.81) points reduction in CASI and DSC from exams 5 to 6, respectively. HRF added predictive value to the Cardiovascular Risk Factors, Aging, and Incidence of Dementia (CAIDE-APOE-ε4) risk score and to models adjusted for serum concentration of NT-proBNP, an analyte associated with cognitive impairment and dementia. Conclusion: Increased HRF assessed during sleep was independently associated with diminished cognitive performance (concurrent and future) and with greater cognitive decline. These findings lend support to the links between cardiac neuroautonomic regulation and cognitive function. As a non-invasive, repeatable and inexpensive probe, HRF technology may be useful in monitoring cognitive status, predicting risk of dementia and assessing therapeutic interventions.

Fragmented sinoatrial dynamics in the prediction of atrial fibrillation: the Multi-Ethnic Study of Atherosclerosis.

Heart rate fragmentation (HRF), a marker of abnormal sinoatrial dynamics, was shown to be associated with incident cardiovascular events in the Multi-Ethnic Study of Atherosclerosis (MESA). Here, we test the hypothesis that HRF is also associated with incident atrial fibrillation (AF) in the MESA cohort of participants who underwent in-home polysomnography (PSG) and in two high-risk subgroups: those ≥70 yr taking antihypertensive medication and those with serum concentrations of NH2-terminal prohormone B-type natriuretic peptide (NT-proBNP) >125 pg/ml (top quartile). Heart rate time series (n = 1,858) derived from the ECG channel of the PSG were analyzed using newly developed HRF metrics, traditional heart rate variability (HRV) indices and two widely used nonlinear measures. Eighty-three participants developed AF over a mean follow-up period of 3.83 ± 0.87 yr. A one-standard deviation increase in HRF was associated with a 31% (95% CI: 3-66%) increase in risk of incident AF, in Cox models adjusted for age, height, NT-proBNP, and frequent premature supraventricular complexes. Furthermore, HRF added value to the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE)-AF models. Traditional HRV and nonlinear indices were not significantly associated with incident AF. In the two high-risk subgroups defined above, HRF was also significantly associated with incident AF in unadjusted and adjusted models. These findings support the translational utility of HRF metrics for short-term (∼4-yr) prediction of AF. In addition, they support broadening the concept of atrial remodeling to include electrodynamical remodeling, a term used to refer to pathophysiological alterations in sinus interbeat interval dynamics.NEW & NOTEWORTHY This study is the first demonstration that heart rate fragmentation (HRF), a marker of anomalous sinoatrial dynamics, is an independent predictor of atrial fibrillation (AF). Traditional measures of heart rate variability and two widely used nonlinear measures were not associated with incident AF in the Multi-Ethnic Study of Atherosclerosis. Fragmentation measures added value to the strongest contemporary predictors of AF, including ECG-derived parameters, coronary calcification score, serum concentrations of NH2-terminal prohormone B-type natriuretic peptide, and supraventricular ectopy. The computational algorithms for quantification of HRF could be readily incorporated into wearable ECG monitoring devices.

Comparison of Invasive and Noninvasive Blood Pressure Measurements for Assessing Signal Complexity and Surgical Risk in Cardiac Surgical Patients.

BACKGROUND: Continuous arterial blood pressure (ABP) is typically recorded by placement of an intraarterial catheter. Recently, noninvasive ABP monitors have been shown to be comparable in accuracy to invasive measurements. In a previous study, we showed that the fluctuations in beat-to-beat ABP measurements were not random variations but had a complex dynamical structure, and that ABP dynamical complexity was inversely associated with surgical risk estimated using the Society of Thoracic Surgeons (STS) index. Dynamical complexity is a mathematical construct that reflects the capacity of a physiological system to adapt to stimuli. The objectives of present study were to: (1) determine whether noninvasive beat-to-beat ABP measurements also exhibit a complex temporal structure; (2) compare the complexity of noninvasive versus invasive ABP time series; and (3) quantify the relationship between the complexity of noninvasive ABP time series and the STS risk scores. METHODS: Fifteen adult patients undergoing coronary artery bypass graft, valve, or combined coronary artery bypass graft/valve surgery were enrolled in this observational study. Preoperative ABP waveforms were simultaneously recorded for ≥15 minutes using a radial artery catheter (invasive) and a continuous noninvasive arterial pressure monitor. Beat-to-beat systolic blood pressure (SBP), diastolic blood pressure (DBP), pulse pressure (PP), and mean arterial pressure (MAP) time series were extracted from the continuous waveforms. Complexity was assessed using the multiscale entropy method. The Wilcoxon signed-rank test was used to compare the mean ranks of indices derived from invasive versus noninvasive ABP time series. Spearman correlation coefficients were used to quantify the relationship between invasive and noninvasive indices. Linear regression analysis was used to quantify the association between each of the complexity indices and the STS risk scores. RESULTS: Beat-to-beat fluctuations in noninvasive ABP measurements were not random but complex; however, their degree of complexity was lower than that of fluctuations in invasively obtained ABP signals (SBP: 7.05 vs 8.66, P < .001; DBP: 7.40 vs 8.41, P < .001; PP: 6.83 vs 8.82, P < .001; and MAP: 7.17 vs 8.68, P < .005). Invasive and noninvasive indices for MSEΣ·slope showed good correlation (rs) (0.53 for SBP, 0.79 for DBP, 0.42 for PP, 0.60 for MAP). The complexity of noninvasive ABP time series (-0.70 [-1.28 to -0.11]; P = .023 for DBP), like that of invasive time series (-0.94 [-1.52 to -0.35]; P = .004 for DBP), was inversely associated with estimated surgical risk in patients undergoing cardiovascular operations. CONCLUSIONS: Our results support the use of noninvasive ABP monitoring in computations of complexity-based indices that correlate with estimated surgical risk.

Heart rate fragmentation: using cardiac pacemaker dynamics to probe the pace of biological aging.

This perspectives article discusses the use of a novel set of dynamical biomarkers in the assessment of biological versus chronological age. The basis for this development is a recently delineated property of altered sinoatrial pacemaker-neuroautonomic function, termed heart rate fragmentation (HRF). Fragmented rhythms manifest as an increase in the density of changes in heart rate acceleration sign, not mechanistically explicable by physiological cardiac vagal tone modulation. We reported that HRF increased monotonically with cross-sectional age and that HRF measures, but not conventional heart rate variability metrics, were significantly associated with major incident cardiovascular events in the Multi-Ethnic Study of Atherosclerosis (MESA). Furthermore, HRF measures added value to both Framingham and MESA cardiovascular risk indices. Here, we propose that interventions that fundamentally slow or reverse the pace of biological aging, via system-wide effects, should be associated with a decrease in the degree of HRF and possibly with a reemergence of the nonfragmented ("fluent") patterns associated with more youthful heart rate dynamics.

Complexity of preoperative blood pressure dynamics: possible utility in cardiac surgical risk assessment.

Complexity measures are intended to assess the cardiovascular system's capacity to respond to stressors. We sought to determine if decreased BP complexity is associated with increased estimated risk as obtained from two standard instruments: the Society of Thoracic Surgeons' (STS) Risk of Mortality and Morbidity Index and the European System for Cardiac Operative Risk Evaluation Score (EuroSCORE II). In this observational cohort study, preoperative systolic, diastolic, mean (MAP) and pulse pressure (PP) time series were derived in 147 patients undergoing cardiac surgery. The complexity of the fluctuations of these four variables was quantified using multiscale entropy (MSE) analysis. In addition, the traditional time series measures, mean and standard deviation (SD) were also computed. The relationships between time series measures and the risk indices (after logarithmic transformation) were then assessed using nonparametric (Spearman correlation, rs) and linear regression methods. A one standard deviation change in the complexity of systolic, diastolic and MAP time series was negatively associated (p < 0.05) with the STS and EuroSCORE indices in both unadjusted (21-34%) and models adjusted for age, gender and SD of the BP time series (15-31%). The mean and SD of BP time series were not significantly associated with the risk index except for a positive association with the SD of the diastolic BP. Lower preoperative BP complexity was associated with a higher estimated risk of adverse cardiovascular outcomes and may provide a novel approach to assessing cardiovascular risk. Future studies are needed to determine whether dynamical risk indices can improve current risk prediction tools.

Heart Rate Fragmentation as a Novel Biomarker of Adverse Cardiovascular Events: The Multi-Ethnic Study of Atherosclerosis.

Background: A major objective of precision medicine is the elucidation of non-invasive biomarkers of cardiovascular (CV) risk. Recently, we introduced a new dynamical marker of sino-atrial instability, termed heart rate fragmentation (HRF), which outperformed traditional and nonlinear heart rate variability metrics in separating ostensibly healthy subjects from patients with coronary artery disease. Accordingly, we hypothesized that HRF may be a dynamical biomarker of adverse cardiovascular events (CVEs). Methods: This study employed data from a cohort of participants in the Multi-Ethnic Study of Atherosclerosis (MESA), a prospective study of sub-clinical heart disease. Interbeat interval time series (n = 1963), derived from the electrocardiographic channel of the polysomnogram study, were analyzed using the newly introduced metrics of fragmentation, as well as traditional heart rate variability (HRV) indices and the short-term detrended fluctuation analysis exponent. Cox regression analysis was used to assess the association between HR dynamic indices and CV outcomes in unadjusted and adjusted models. Results: The mean (± SD) follow-up time was 2.97 ± 0.63 years. In adjusted models, higher fragmentation was significantly associated with incident CVEs (number of events; hazard ratio [95% confidence interval]: n = 72, 1.43 [1.16-1.76]) and CV death (n = 21; 1.65 [1.15-2.36]). The traditional HRV and the fractal indices were not associated with CVEs or CV death. The most discriminatory fragmentation indices added significant value to Framingham and MESA CV risk indices in all analyses. Conclusion: Our findings show that HRF has promise as a non-invasive, automatable biomarker of CV risk. The basic mechanisms underlying fragmentation remain to be delineated. Its association with incident outcomes raises the possibility of connections to degenerative changes in the multisystem network controlling SAN function.

Elevations in neutrophils with obstructive sleep apnea: The Multi-Ethnic Study of Atherosclerosis (MESA).

BACKGROUND: Obstructive sleep apnea (OSA) associates with increased risk of cardiovascular diseases (CVD). Immune abnormalities and surges in sympathetic activity accompany OSA and CVD. We hypothesized that OSA associates with leukocytosis partially by abnormalities in autonomic nervous system (ANS) function that would suggest a pathway linking OSA and CVD. METHODS: Participants from the Multi-Ethnic Study of Atherosclerosis (MESA), a prospective cohort of individuals initially without overt CVD, underwent polysomnography and assays for white blood cells (WBC) and subsets. Heart rate (HR) and heart rate variability (HRV), indirect measurements of ANS, were obtained from overnight electrocardiography. A formal statistical mediation analysis tested the indirect effect that mean HR and HRV measures contribute to associations between OSA and leukocytosis. RESULTS: The analytical sample consisted of 1298 participants (54% female), ages 54-93years, 14% with severe OSA (apnea-hypopnea-index, AHI≥30). Severe OSA associated with a higher prevalence of obesity, diabetes, and increased levels of WBC total and subsets. Neutrophil count associated with severe OSA after adjusting for confounders (p=0.017). Mean HR positively associated with OSA indices and neutrophils. A mediation analysis revealed an "indirect" effect of mean HR that explained an estimated 11% of the association between AHI and neutrophils. Overnight hypoxia also associated with neutrophil count (p=0.009), and mean HR explained 14% of the association between neutrophils and hypoxia. CONCLUSIONS: In the MESA cohort, OSA measures associate with elevated neutrophil counts and increases in overnight mean HR. These data link innate immune dysregulation with OSA and provide a potential pathophysiologic pathway between CVD and OSA.

Heart Rate Fragmentation: A Symbolic Dynamical Approach.

Background: We recently introduced the concept of heart rate fragmentation along with a set of metrics for its quantification. The term was coined to refer to an increase in the percentage of changes in heart rate acceleration sign, a dynamical marker of a type of anomalous variability. The effort was motivated by the observation that fragmentation, which is consistent with the breakdown of the neuroautonomic-electrophysiologic control system of the sino-atrial node, could confound traditional short-term analysis of heart rate variability. Objective: The objectives of this study were to: (1) introduce a symbolic dynamical approach to the problem of quantifying heart rate fragmentation; (2) evaluate how the distribution of the different dynamical patterns ("words") varied with the participants' age in a group of healthy subjects and patients with coronary artery disease (CAD); and (3) quantify the differences in the fragmentation patterns between the two sample populations. Methods: The symbolic dynamical method employed here was based on a ternary map of the increment NN interval time series and on the analysis of the relative frequency of symbolic sequences (words) with a pre-defined set of features. We analyzed annotated, open-access Holter databases of healthy subjects and patients with CAD, provided by the University of Rochester Telemetric and Holter ECG Warehouse (THEW). Results: The degree of fragmentation was significantly higher in older individuals than in their younger counterparts. However, the fragmentation patterns were different in the two sample populations. In healthy subjects, older age was significantly associated with a higher percentage of transitions from acceleration/deceleration to zero acceleration and vice versa (termed "soft" inflection points). In patients with CAD, older age was also significantly associated with higher percentages of frank reversals in heart rate acceleration (transitions from acceleration to deceleration and vice versa, termed "hard" inflection points). Compared to healthy subjects, patients with CAD had significantly higher percentages of soft and hard inflection points, an increased percentage of words with a high degree of fragmentation and a decreased percentage of words with a lower degree of fragmentation. Conclusion: The symbolic dynamical method employed here was useful to probe the newly recognized property of heart rate fragmentation. The findings from these cross-sectional studies confirm that CAD and older age are associated with higher levels of heart rate fragmentation. Furthermore, fragmentation with healthy aging appears to be phenotypically different from fragmentation in the context of CAD.

Heart Rate Fragmentation: A New Approach to the Analysis of Cardiac Interbeat Interval Dynamics.

Background: Short-term heart rate variability (HRV) is most commonly attributed to physiologic vagal tone modulation. However, with aging and cardiovascular disease, the emergence of high short-term HRV, consistent with the breakdown of the neuroautonomic-electrophysiologic control system, may confound traditional HRV analysis. An apparent dynamical signature of such anomalous short-term HRV is frequent changes in heart rate acceleration sign, defined here as heart rate fragmentation. Objective: The aims were to: (1) introduce a set of metrics designed to probe the degree of sinus rhythm fragmentation; (2) test the hypothesis that the degree of fragmentation of heartbeat time series increases with the participants' age in a group of healthy subjects; (3) test the hypothesis that the heartbeat time series from patients with advanced coronary artery disease (CAD) are more fragmented than those from healthy subjects; and (4) compare the performance of the new fragmentation metrics with standard time and frequency domain measures of short-term HRV. Methods: We analyzed annotated, open-access Holter recordings (University of Rochester Holter Warehouse) from healthy subjects and patients with CAD using these newly introduced metrics of heart rate fragmentation, as well as standard time and frequency domain indices of short-term HRV, detrended fluctuation analysis and sample entropy. Results: The degree of fragmentation of cardiac interbeat interval time series increased significantly as a function of age in the healthy population as well as in patients with CAD. Fragmentation was higher for the patients with CAD than the healthy subjects. Heart rate fragmentation metrics outperformed traditional short-term HRV indices, as well as two widely used nonlinear measures, sample entropy and detrended fluctuation analysis short-term exponent, in distinguishing healthy subjects and patients with CAD. The same level of discrimination was obtained from the analysis of normal-to-normal sinus (NN) and cardiac interbeat interval (RR) time series. Conclusion: The fragmentation framework and accompanying metrics introduced here constitute a new way of assessing short-term HRV under free-running conditions, one which appears to overcome salient limitations of traditional HRV analysis. Fragmentation of sinus rhythm cadence may provide new dynamical biomarkers for probing the integrity of the neuroautonomic-electrophysiologic network controlling the heartbeat in health and disease.

Analysis of the sleep EEG in the complexity domain.

Conventional sleep analysis relies primarily on electroencephalogram (EEG) waveform features assessed in concert with eye movements, respiration and muscle tone. We explore a complementary "complexity domain" approach based on multiscale entropy (MSE) analysis of EEG signals and discuss its relationships to standard sleep analysis and to that based on electrocardiogram (ECG)-derived cardiopulmonary coupling (CPC). We observe a progressive decrease in complexity associated with decreased arousability, as measured by both conventional sleep scoring and CPC analysis. Furthermore, complexity analysis supports the contention that stage 2 non-REM sleep has distinct sub-phases that map to CPC high- and low-frequency coupled dynamics.

Remembrance of time series past: simple chromatic method for visualizing trends in biomedical signals.

Analysis of biomedical time series plays an essential role in clinical management and basic investigation. However, conventional monitors streaming data in real-time show only the most recent values, not referenced to past dynamics. We describe a chromatic approach to bring the 'memory' of the physiologic system's past behavior into the current display window.The method employs the estimated probability density function of a time series segment to colorize subsequent data points.For illustrative purposes, we selected open-access recordings of continuous: (1) fetal heart rate during the pre-partum period, and (2) heart rate and systemic blood pressure from a critical care patient during a spontaneous breathing trial. The colorized outputs highlight changes from the 'baseline' reference state, the latter defined as the mode value assumed by the signal, i.e. the maximum of its probability density function.A colorization method may facilitate the recognition of relevant features of time series, especially shifts in baseline dynamics and other trends (including transient and longer-term deviation from baseline values) which may not be as readily noticed using traditional displays. This method may be applicable in clinical monitoring (real-time or off-line) and in research settings. Prospective studies are needed to assess the utility of this approach.

Use of multiscale entropy to facilitate artifact detection in electroencephalographic signals.

Electroencephalographic (EEG) signals present a myriad of challenges to analysis, beginning with the detection of artifacts. Prior approaches to noise detection have utilized multiple techniques, including visual methods, independent component analysis and wavelets. However, no single method is broadly accepted, inviting alternative ways to address this problem. Here, we introduce a novel approach based on a statistical physics method, multiscale entropy (MSE) analysis, which quantifies the complexity of a signal. We postulate that noise corrupted EEG signals have lower information content, and, therefore, reduced complexity compared with their noise free counterparts. We test the new method on an open-access database of EEG signals with and without added artifacts due to electrode motion.

Generalized Multiscale Entropy Analysis: Application to Quantifying the Complex Volatility of Human Heartbeat Time Series.

We introduce a generalization of multiscale entropy (MSE) analysis. The method is termed MSE n , where the subscript denotes the moment used to coarse-grain a time series. MSE µ , described previously, uses the mean value (first moment). Here, we focus on [Formula: see text], which uses the second moment, i.e., the variance. [Formula: see text] quantifies the dynamics of the volatility (variance) of a signal over multiple time scales. We use the method to analyze the structure of heartbeat time series. We find that the dynamics of the volatility of heartbeat time series obtained from healthy young subjects is highly complex. Furthermore, we find that the multiscale complexity of the volatility, not only the multiscale complexity of the mean heart rate, degrades with aging and pathology. The "bursty" behavior of the dynamics may be related to intermittency in energy and information flows, as part of multiscale cycles of activation and recovery. Generalized MSE may also be useful in quantifying the dynamical properties of other physiologic and of non-physiologic time series.

Complexity-Based Measures Inform Effects of Tai Chi Training on Standing Postural Control: Cross-Sectional and Randomized Trial Studies.

BACKGROUND: Diminished 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. OBJECTIVES: To 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. METHODS: A 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. RESULTS: At 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. CONCLUSION: Multiscale 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 REGISTRATION: ClinicalTrials.gov NCT01340365.

Dynamical glucometry: use of multiscale entropy analysis in diabetes.

Diabetes mellitus (DM) is one of the world's most prevalent medical conditions. Contemporary management focuses on lowering mean blood glucose values toward a normal range, but largely ignores the dynamics of glucose fluctuations. We probed analyte time series obtained from continuous glucose monitor (CGM) sensors. We show that the fluctuations in CGM values sampled every 5 min are not uncorrelated noise. Next, using multiscale entropy analysis, we quantified the complexity of the temporal structure of the CGM time series from a group of elderly subjects with type 2 DM and age-matched controls. We further probed the structure of these CGM time series using detrended fluctuation analysis. Our findings indicate that the dynamics of glucose fluctuations from control subjects are more complex than those of subjects with type 2 DM over time scales ranging from about 5 min to 5 h. These findings support consideration of a new framework, dynamical glucometry, to guide mechanistic research and to help assess and compare therapeutic interventions, which should enhance complexity of glucose fluctuations and not just lower mean and variance of blood glucose levels.