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.

Emergence of dynamical complexity related to human heart rate variability.

We apply the refined composite multiscale entropy (MSE) method to a one-dimensional directed small-world network composed of nodes whose states are binary and whose dynamics obey the majority rule. We find that the resulting fluctuating signal becomes dynamically complex. This dynamical complexity is caused (i) by the presence of both short-range connections and long-range shortcuts and (ii) by how well the system can adapt to the noisy environment. By tuning the adaptability of the environment and the long-range shortcuts we can increase or decrease the dynamical complexity, thereby modeling trends found in the MSE of a healthy human heart rate in different physiological states. When the shortcut and adaptability values increase, the complexity in the system dynamics becomes uncorrelated.

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.

A systems biology approach to studying Tai Chi, physiological complexity and healthy aging: design and rationale of a pragmatic randomized controlled trial.

INTRODUCTION: Aging is typically associated with progressive multi-system impairment that leads to decreased physical and cognitive function and reduced adaptability to stress. Due to its capacity to characterize complex dynamics within and between physiological systems, the emerging field of complex systems biology and its array of quantitative tools show great promise for improving our understanding of aging, monitoring senescence, and providing biomarkers for evaluating novel interventions, including promising mind-body exercises, that treat age-related disease and promote healthy aging. MATERIAL AND METHODS: An ongoing, two-arm randomized clinical trial is evaluating the potential of Tai Chi mind-body exercise to attenuate age-related loss of complexity. A total of 60 Tai Chi-naïve healthy older adults (aged 50-79) are being randomized to either six months of Tai Chi training (n=30), or to a waitlist control receiving unaltered usual medical care (n=30). Our primary outcomes are complexity-based measures of heart rate, standing postural sway and gait stride interval dynamics assessed at 3 and 6months. Multiscale entropy and detrended fluctuation analysis are used as entropy- and fractal-based measures of complexity, respectively. Secondary outcomes include measures of physical and psychological function and tests of physiological adaptability also assessed at 3 and 6months. DISCUSSION: Results of this study may lead to novel biomarkers that help us monitor and understand the physiological processes of aging and explore the potential benefits of Tai Chi and related mind-body exercises for healthy aging.

Physiological complexity and system adaptability: evidence from postural control dynamics of older adults.

The degree of multiscale complexity in human behavioral regulation, such as that required for postural control, appears to decrease with advanced aging or disease. To help delineate causes and functional consequences of complexity loss, we examined the effects of visual and somatosensory impairment on the complexity of postural sway during quiet standing and its relationship to postural adaptation to cognitive dual tasking. Participants of the MOBILIZE Boston Study were classified into mutually exclusive groups: controls [intact vision and foot somatosensation, n = 299, 76 ± 5 (SD) yr old], visual impairment only (<20/40 vision, n = 81, 77 ± 4 yr old), somatosensory impairment only (inability to perceive 5.07 monofilament on plantar halluxes, n = 48, 80 ± 5 yr old), and combined impairments (n = 25, 80 ± 4 yr old). Postural sway (i.e., center-of-pressure) dynamics were assessed during quiet standing and cognitive dual tasking, and a complexity index was quantified using multiscale entropy analysis. Postural sway speed and area, which did not correlate with complexity, were also computed. During quiet standing, the complexity index (mean ± SD) was highest in controls (9.5 ± 1.2) and successively lower in the visual (9.1 ± 1.1), somatosensory (8.6 ± 1.6), and combined (7.8 ± 1.3) impairment groups (P = 0.001). Dual tasking resulted in increased sway speed and area but reduced complexity (P < 0.01). Lower complexity during quiet standing correlated with greater absolute (R = -0.34, P = 0.002) and percent (R = -0.45, P < 0.001) increases in postural sway speed from quiet standing to dual-tasking conditions. Sensory impairments contributed to decreased postural sway complexity, which reflected reduced adaptive capacity of the postural control system. Relatively low baseline complexity may, therefore, indicate control systems that are more vulnerable to cognitive and other stressors.

ADAPTIVE DATA ANALYSIS OF COMPLEX FLUCTUATIONS IN PHYSIOLOGIC TIME SERIES.

We introduce a generic framework of dynamical complexity to understand and quantify fluctuations of physiologic time series. In particular, we discuss the importance of applying adaptive data analysis techniques, such as the empirical mode decomposition algorithm, to address the challenges of nonlinearity and nonstationarity that are typically exhibited in biological fluctuations.

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.

Nonlinear pressure-flow relationship is able to detect asymmetry of brain blood circulation associated with midline shift.

Reliable and noninvasive assessment of cerebral blood flow regulation is a major challenge in acute care monitoring. This study assessed dynamics of flow regulation and its relationship to asymmetry of initial computed tomography (CT) scan using multimodal pressure flow (MMPF) analysis. Data of 27 patients (38 +/- 15 years old) with traumatic brain injury (TBI) were analyzed. Patients were selected from bigger cohort according to criteria of having midline shift on initial CT scan and intact skull (no craniotomy or bone flap). The MMPF analysis was used to extract the oscillations in cerebral perfusion pressure (CPP) and blood flow velocity (BFV) signals at frequency of artificial ventilation, and to calculate the instantaneous phase difference between CPP and BFV oscillations. Mean CPP-BFV phase difference was used to quantify pressure and flow relationship. The TBI subjects had smaller mean BP-BFV phase shifts (left, 8.7 +/- 9.6; right 10.2 +/- 8.3 MCAs, mean +/- SD) than values previously obtained in healthy subjects (left, 37.3 +/- 7.6 degrees; right, 38.0 +/- 8.9 degrees; p < 0.0001), suggesting impaired blood flow regulation after TBI. The difference in phase shift between CPP and BFV in the left and right side was strongly correlated to the midline shift (R = 0.78; p < 0.0001). These findings indicate that the MMPF method allows reliable assessment of alterations in pressure and flow relationship after TBI. Moreover, mean pressure-flow phase shift is sensitive to the displacement of midline of the brain, and may potentially serve as a marker of asymmetry of cerebral autoregulation.

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.

Multimodal Pressure Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation.

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique "Multi-Modal Pressure Flow method (MMPF)" that utilizes Hilbert-Huang transformation to quantify dynamic cerebral autoregulation (CA) by studying interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The influence of CA is traditionally assessed from the relationship between the well-pronounced systemic BP and BFV oscillations induced by clinical tests. Reliable noninvasive assessment of dynamic CA, however, remains a challenge in clinical and diagnostic medicine.In this brief review we: 1) present an overview of transfer function analysis (TFA) that is traditionally used to quantify CA; 2) describe the a MMPF method and its modifications; 3) introduce a newly developed automatic algorithm and engineering aspects of the improved MMPF method; and 4) review clinical applications of MMPF and its sensitivity for detection of CA abnormalities in clinical studies. The MMPF analysis decomposes complex nonstationary BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we recently showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. In addition, the new technique enables reliable assessment of CA using both data collected during clinical test and spontaneous BP/BFV fluctuations during baseline resting conditions.

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.

Nonlinear assessment of cerebral autoregulation from spontaneous blood pressure and cerebral blood flow fluctuations.

Cerebral autoregulation (CA) is an most important mechanism responsible for the relatively constant blood flow supply to brain when cerebral perfusion pressure varies. Its assessment in nonacute cases has been relied on the quantification of the relationship between noninvasive beat-to-beat blood pressure (BP) and blood flow velocity (BFV). To overcome the nonstationary nature of physiological signals such as BP and BFV, a computational method called multimodal pressure-flow (MMPF) analysis was recently developed to study the nonlinear BP-BFV relationship during the Valsalva maneuver (VM). The present study aimed to determine (i) whether this method can estimate autoregulation from spontaneous BP and BFV fluctuations during baseline rest conditions; (ii) whether there is any difference between the MMPF measures of autoregulation based on intra-arterial BP (ABP) and based on cerebral perfusion pressure (CPP); and (iii) whether the MMPF method provides reproducible and reliable measure for noninvasive assessment of autoregulation. To achieve these aims, we analyzed data from existing databases including: (i) ABP and BFV of 12 healthy control, 10 hypertensive, and 10 stroke subjects during baseline resting conditions and during the Valsalva maneuver, and (ii) ABP, CPP, and BFV of 30 patients with traumatic brain injury (TBI) who were being paralyzed, sedated, and ventilated. We showed that autoregulation in healthy control subjects can be characterized by specific phase shifts between BP and BFV oscillations during the Valsalva maneuver, and the BP-BFV phase shifts were reduced in hypertensive and stroke subjects (P < 0.01), indicating impaired autoregulation. Similar results were found during baseline condition from spontaneous BP and BFV oscillations. The BP-BFV phase shifts obtained during baseline and during VM were highly correlated (R > 0.8, P < 0.0001), showing no statistical difference (paired-t test P > 0.47). In TBI patients there were strong correlations between phases of ABP and CPP oscillations (R = 0.99, P < 0.0001) and, thus, between ABP-BFV and CPP-BFV phase shifts (P < 0.0001, R = 0.76). By repeating the MMPF 4 times on data of TBI subjects, each time on a selected cycle of spontaneous BP and BFV oscillations, we showed that MMPF had better reproducibility than traditional autoregulation index. These results indicate that the MMPF method, based on instantaneous phase relationships between cerebral blood flow velocity and peripheral blood pressure, has better performance than the traditional standard method, and can reliably assess cerebral autoregulation dynamics from ambulatory blood pressure and cerebral blood flow during supine rest conditions.

Noise and poise: Enhancement of postural complexity in the elderly with a stochastic-resonance-based therapy.

Pathologic states are associated with a loss of dynamical complexity. Therefore, therapeutic interventions that increase physiologic complexity may enhance health status. Using multiscale entropy analysis, we show that the postural sway dynamics of healthy young and healthy elderly subjects are more complex than that of elderly subjects with a history of falls. Application of subsensory noise to the feet has been demonstrated to improve postural stability in the elderly. We next show that this therapy significantly increases the multiscale complexity of sway fluctuations in healthy elderly subjects. Quantification of changes in dynamical complexity of biologic variability may be the basis of a new approach to assessing risk and to predicting the efficacy of clinical interventions, including noise-based therapies.

Statistical physics approach to categorize biologic signals: from heart rate dynamics to DNA sequences.

We recently proposed a novel approach to categorize information carried by symbolic sequences based on their usage of repetitive patterns. A simple quantitative index to measure the dissimilarity between two symbolic sequences can be defined. This information dissimilarity index, defined by our formula, is closely related to the Shannon entropy and rank order of the repetitive patterns in the symbolic sequences. Here we discuss the underlying statistical physics assumptions of this dissimilarity index. We use human cardiac interbeat interval time series and DNA sequences as examples to illustrate the applicability of this generic approach to real-world problems.

Broken asymmetry of the human heartbeat: loss of time irreversibility in aging and disease.

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.

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.

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.

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.