Complexity-based measures inform Tai Chi's impact on standing postural control in older adults with peripheral neuropathy.

BACKGROUND: Tai Chi training enhances physical function and may reduce falls in older adults with and without balance disorders, yet its effect on postural control as quantified by the magnitude or speed of center-of-pressure (COP) excursions beneath the feet is less clear. We hypothesized that COP metrics derived from complex systems theory may better capture the multi-component stimulus that Tai Chi has on the postural control system, as compared with traditional COP measures. METHODS: We performed a secondary analysis of a pilot, non-controlled intervention study that examined the effects of Tai Chi on standing COP dynamics, plantar sensation, and physical function in 25 older adults with peripheral neuropathy. Tai Chi training was based on the Yang style and consisted of three, one-hour group sessions per week for 24 weeks. Standing postural control was assessed with a force platform at baseline, 6, 12, 18, and 24 weeks. The degree of COP complexity, as defined by the presence of fluctuations existing over multiple timescales, was calculated using multiscale entropy analysis. Traditional measures of COP speed and area were also calculated. Foot sole sensation, six-minute walk (6MW) and timed up-and-go (TUG) were also measured at each assessment. RESULTS: Traditional measures of postural control did not change from baseline. The COP complexity index (mean ± SD) increased from baseline (4.1 ± 0.5) to week 6 (4.5 ± 0.4), and from week 6 to week 24 (4.7 ± 0.4) (p=0.02). Increases in COP complexity-from baseline to week 24-correlated with improvements in foot sole sensation (p=0.01), the 6MW (p=0.001) and TUG (p=0.01). CONCLUSIONS: Subjects of the Tai Chi program exhibited increased complexity of standing COP dynamics. These increases were associated with improved plantar sensation and physical function. Although more research is needed, results of this non-controlled pilot study suggest that complexity-based COP measures may inform the study of complex mind-body interventions, like Tai Chi, on postural control in those with peripheral neuropathy or other age-related balance disorders.

Nonlinear phase interaction between nonstationary signals: a comparison study of methods based on Hilbert-Huang and Fourier transforms.

Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.

Complex dynamics of human red blood cell flickering: alterations with in vivo aging.

Human red blood cells (RBCs) exhibit vibratory motions, referred to as "flickering." Their dynamical properties, classically attributed to thermal mechanisms, have not been fully characterized. Using detrended fluctuation analysis and multiscale entropy methods, we show that the short-term flickering motions of RBCs, observed under phase contrast microscopy, have a fractal scaling exponent close to that of 1f noise and exhibit complex patterns over multiple time scales. Further, these dynamical properties degrade with in vivo aging such that older cells that have been in the circulation longer generate significantly (p<0.003) less complex flickering patterns than newly formed cells. Quantitative assessment of multiscale flickering may provide a way of measuring RBC functionality. Membrane models need to account for the complex properties of these motions and their changes with in vivo senescence.

Altered Phase Interactions between Spontaneous Blood Pressure and Flow Fluctuations in Type 2 Diabetes Mellitus: Nonlinear Assessment of Cerebral Autoregulation.

Cerebral autoregulation (CA) is an important mechanism that involves dilation and constriction in arterioles to maintain relatively s cerebral blood flow in response to changes of systemic blood pressure. Traditional assessments of CA focus on the changes of cerebral blood flow velocity in response to large blood pressure fluctuations induced by interventions. This approach is not feasible for patients with impaired autoregulation or cardiovascular regulation. Here we propose a newly developed technique-the multimodal pressure-flow (MMPF) analysis, which assesses CA by quantifying nonlinear phase interactions between spontaneous oscillations in blood pressure and flow velocity during resting conditions. We show that CA in healthy subjects can be characterized by specific phase shifts between spontaneous blood pressure and flow velocity oscillations, and the phase shifts are significantly reduced in diabetic subjects. Smaller phase shifts between oscillations in the two variables indicate more passive dependence of blood flow velocity on blood pressure, thus suggesting impaired cerebral autoregulation. Moreover, the reduction of the phase shifts in diabetes is observed not only in previously-recognized effective region of CA (<0.1Hz), but also over the higher frequency range from ~0.1 to 0.4Hz. These findings indicate that Type 2 diabetes alters cerebral blood flow regulation over a wide frequency range and that this alteration can be reliably assessed from spontaneous oscillations in blood pressure and blood flow velocity during resting conditions. We also show that the MMPF method has better performance than traditional approaches based on Fourier transform, and is more sui for the quantification of nonlinear phase interactions between nonstationary biological signals such as blood pressure and blood flow.

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory.

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals.

The newly inaugurated Research Resource for Complex Physiologic Signals, which was created under the auspices of the National Center for Research Resources of the National Institutes of Health, is intended to stimulate current research and new investigations in the study of cardiovascular and other complex biomedical signals. The resource has 3 interdependent components. PhysioBank is a large and growing archive of well-characterized digital recordings of physiological signals and related data for use by the biomedical research community. It currently includes databases of multiparameter cardiopulmonary, neural, and other biomedical signals from healthy subjects and from patients with a variety of conditions with major public health implications, including life-threatening arrhythmias, congestive heart failure, sleep apnea, neurological disorders, and aging. PhysioToolkit is a library of open-source software for physiological signal processing and analysis, the detection of physiologically significant events using both classic techniques and novel methods based on statistical physics and nonlinear dynamics, the interactive display and characterization of signals, the creation of new databases, the simulation of physiological and other signals, the quantitative evaluation and comparison of analysis methods, and the analysis of nonstationary processes. PhysioNet is an on-line forum for the dissemination and exchange of recorded biomedical signals and open-source software for analyzing them. It provides facilities for the cooperative analysis of data and the evaluation of proposed new algorithms. In addition to providing free electronic access to PhysioBank data and PhysioToolkit software via the World Wide Web (http://www.physionet. org), PhysioNet offers services and training via on-line tutorials to assist users with varying levels of expertise.

Genomic classification using an information-based similarity index: application to the SARS coronavirus.

Measures of genetic distance based on alignment methods are confined to studying sequences that are conserved and identifiable in all organisms under study. A number of alignment-free techniques based on either statistical linguistics or information theory have been developed to overcome the limitations of alignment methods. We present a novel alignment-free approach to measuring the similarity among genetic sequences that incorporates elements from both word rank order-frequency statistics and information theory. We first validate this method on the human influenza A viral genomes as well as on the human mitochondrial DNA database. We then apply the method to study the origin of the SARS coronavirus. We find that the majority of the SARS genome is most closely related to group 1 coronaviruses, with smaller regions of matches to sequences from groups 2 and 3. The information based similarity index provides a new tool to measure the similarity between datasets based on their information content and may have a wide range of applications in the large-scale analysis of genomic databases.

Multiscale entropy analysis of biological signals.

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.

Diurnal and ultradian dynamics of serum adiponectin in healthy men: comparison with leptin, circulating soluble leptin receptor, and cortisol patterns.

Adiponectin is an abundant serum adipokine secreted exclusively from differentiated adipocytes, which plays an important role in regulating insulin sensitivity. The dynamics of circulating adiponectin concentrations have yet to be systematically investigated. We sought to determine whether serum adiponectin levels exhibit diurnal or ultradian rhythms in healthy normal-weight men and to compare the 24-h profile of adiponectin fluctuations with those of leptin, leptin-binding protein (sOB-R), and cortisol. We collected blood samples at 15-min intervals over 24 h from six subjects receiving an isocaloric diet, and we measured adiponectin, leptin, sOB-R, and cortisol levels. Fourier and cross-correlation analyses were performed on these time series to study diurnal variations, and the Cluster7 program was used for pulsatility analysis. Circulating adiponectin and sOB-R levels exhibited ultradian pulsatility as well as a diurnal variation with a significant decline at night, reaching a nadir in the early morning. The 24-h variations of serum adiponectin and sOB-R were nearly identical and followed those of cortisol after a few hours, but were out-of-phase with leptin diurnal rhythms. These data suggest that adiponectin and sOB-R levels might be influenced by common regulatory factors and challenge the notion that cortisol may have a direct inhibitory effect on adiponectin in humans.

Dynamic analysis of heart rate may predict subsequent ventricular tachycardia after myocardial infarction.

Dynamics analysis of RR interval behavior and traditional measures of heart rate variability were compared between postinfarction patients with and without vulnerability to ventricular tachyarrhythmias in a case-control study. Short-term fractal correlation of heart rate dynamics was better than traditional measures of heart rate variability in differentiating patients with and without life-threatening arrhythmias.

Heart rate dynamics in patients with stable angina pectoris and utility of fractal and complexity measures.

Dynamic analysis techniques may uncover abnormalities in heart rate (HR) behavior that are not easily detectable with conventional statistical measures. However, the applicability of these new methods for detecting possible abnormalities in HR behavior in various cardiovascular disorders is not well established. Conventional measures of HR variability were compared with short-term (< or = 11 beats, alpha1) and long-term (> 11 beats, alpha2) fractal correlation properties and with approximate entropy of RR interval data in 38 patients with stable angina pectoris without previous myocardial infarction or cardiac medication at the time of the study and 38 age-matched healthy controls. The short- and long-term fractal scaling exponents (alpha1, alpha2) were significantly higher in the coronary patients than in the healthy controls (1.34 +/- 0.15 vs 1.11 +/- 0.12 [p <0.001] and 1.10 +/- 0.08 vs 1.04 +/- 0.06 [p <0.01], respectively), and they also had lower approximate entropy (p <0.05), standard deviation of all RR intervals (p <0.01), and high-frequency spectral component of HR variability (p <0.05). The short-term fractal scaling exponent performed better than other heart rate variability parameters in differentiating patients with coronary artery disease from healthy subjects, but it was not related to the clinical or angiographic severity of coronary artery disease or any single nonspectral or spectral measure of HR variability in this retrospective study. Patients with stable angina pectoris have altered fractal properties and reduced complexity in their RR interval dynamics relative to age-matched healthy subjects. Dynamic analysis may complement traditional analyses in detecting altered HR behavior in patients with stable angina pectoris.

Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction. TRACE Investigators. TRAndolapril Cardiac Evaluation.

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.

Heart rate dynamics before spontaneous onset of ventricular fibrillation in patients with healed myocardial infarcts.

The traditional methods of analyzing heart rate (HR) variability have failed to predict imminent ventricular fibrillation (VF). We sought to determine whether new methods of analyzing RR interval variability based on nonlinear dynamics and fractal analysis may help to detect subtle abnormalities in RR interval behavior before the onset of life-threatening arrhythmias. RR interval dynamics were analyzed from 24-hour Holter recordings of 15 patients who experienced VF during electrocardiographic recording. Thirty patients without spontaneous or inducible arrhythmia events served as a control group in this retrospective case control study. Conventional time- and frequency-domain measurements, the short-term fractal scaling exponent (alpha) obtained by detrended fluctuation analysis, and the slope (beta) of the power-law regression line (log power - log frequency, 10(-4)-10(-2) Hz) of RR interval dynamics were determined. The short-term correlation exponent alpha of RR intervals (0.64 +/- 0.19 vs 1.05 +/- 0.12; p <0.001) and the power-law slope beta (-1.63 +/- 0.28 vs -1.31 +/- 0.20, p <0.001) were lower in the patients before the onset of VF than in the control patients, but the SD and the low-frequency spectral components of RR intervals did not differ between the groups. The short-term scaling exponent performed better than any other measurement of HR variability in differentiating between the patients with VF and controls. Altered fractal correlation properties of HR behavior precede the spontaneous onset of VF. Dynamic analysis methods of analyzing RR intervals may help to identify abnormalities in HR behavior before VF.

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait.

Complex fluctuations of unknown origin appear in the normal gait pattern. These fluctuations might be described as being 1) uncorrelated white noise, 2) short-range correlations, or 3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series, we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that successfully accounts for the experimentally observed long-range correlations.

Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations.

Fractal dynamics were recently detected in the apparently "noisy" variations in the stride interval of human walking. Dynamical analysis of these step-to-step fluctuations revealed a self-similar pattern: fluctuations at one time scale are statistically similar to those at multiple other time scales, at least over hundreds of steps, while healthy subjects walk at their normal rate. To study the stability of this fractal property, we analyzed data obtained from healthy subjects who walked for 1 h at their usual, slow, and fast paces. The stride interval fluctuations exhibited long-range correlations with power-law decay for up to 1,000 strides at all 3 walking rates. In contrast, during metronomically paced walking, these long-range correlations disappeared; variations in the stride interval were random (uncorrelated) and nonfractal. The long-range correlations observed during spontaneous walking were not affected by removal of drifts in the time series. Thus the fractal dynamics of spontaneous stride interval are normally quite robust and intrinsic to the locomotor system. Furthermore, this fractal property of neural output may be related to the higher nervous centers responsible for the control of walking rhythm.

Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease.

Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.

Heart rate dynamics during three forms of meditation.

OBJECTIVE: This study was designed to quantify and compare the instantaneous heart rate dynamics and cardiopulmonary interactions during sequential performance of three meditation protocols with different breathing patterns. BACKGROUND: We analyzed beat-to-beat heart rate and continuous breathing signals from 10 experienced meditators (4 females; 6 males; mean age 42 years; range 29-55 years) during three traditional interventions: relaxation response, breath of fire, and segmented breathing. RESULTS: Heart rate and respiratory dynamics were generally similar during the relaxation response and segmented breathing. We observed high amplitude, low frequency (approximately 0.05-0.1 Hz) oscillations due to respiratory sinus arrhythmia during both the relaxation response and segmented breathing, along with a significantly (p<0.05) increased coherence between heart rate and breathing during these two maneuvers when compared to baseline. The third technique, breath of fire, was associated with a different pattern of response, marked by a significant increase in mean heart rate with respect to baseline (p<0.01), and a significant decrease in coherence between heart rate and breathing (p<0.05). CONCLUSIONS: These findings suggest that different meditative/breathing protocols may evoke common heart rate effects, as well as specific responses. The results support the concept of a "meditation paradox," since a variety of relaxation and meditative techniques may produce active rather than quiescent cardiac dynamics, associated with prominent low frequency heart rate oscillations or increases in mean resting heart rate. These findings also underscore the need to critically assess traditional frequency domain heart rate variability parameters in making inferences about autonomic alterations during meditation with slow breathing.

Exaggerated heart rate oscillations during two meditation techniques.

We report extremely prominent heart rate oscillations associated with slow breathing during specific traditional forms of Chinese Chi and Kundalini Yoga meditation techniques in healthy young adults. We applied both spectral analysis and a novel analytic technique based on the Hilbert transform to quantify these heart rate dynamics. The amplitude of these oscillations during meditation was significantly greater than in the pre-meditation control state and also in three non-meditation control groups: i) elite athletes during sleep, ii) healthy young adults during metronomic breathing, and iii) healthy young adults during spontaneous nocturnal breathing. This finding, along with the marked variability of the beat-to-beat heart rate dynamics during such profound meditative states, challenges the notion of meditation as only an autonomically quiescent state.

Fractals in biology and medicine.

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

Self-reported coping behavior in health and disease: assessment with a card sort game.

The authors tested the hypothesis that individuals with a variety of severe chronic illnesses and the healthy elderly exhibit a loss of flexibility in their response to a variety of stressors, compared with healthy adults. A card sort game designed to assess self-reported coping behavior under different stressful life situations was used to compare healthy adults with individuals with multiple sclerosis, rheumatoid arthritis, systemic lupus erythematosus, and the elderly. The healthy adults were found to exhibit more variability than any of the illness groups or the elderly. Healthy function is marked by a complex type of variability.