Nonlinear analysis of heart rate variability signals in meditative state: a review and perspective

INTRODUCTION

In recent times, an upsurge in the investigation related to the effects of meditation in reconditioning various cardiovascular and psychological disorders is seen. In majority of these studies, heart rate variability (HRV) signal is used, probably for its ease of acquisition and low cost. Although understanding the dynamical complexity of HRV is not an easy task, the advances in nonlinear analysis has significantly helped in analyzing the impact of meditation of heart regulations. In this review, we intend to present the various nonlinear approaches, scientific findings and their limitations to develop deeper insights to carry out further research on this topic.

RESULTS

Literature have shown that research focus on nonlinear domain is mainly concentrated on assessing predictability, fractality, and entropy-based dynamical complexity of HRV signal. Although there were some conflicting results, most of the studies observed a reduced dynamical complexity, reduced fractal dimension, and decimated long-range correlation behavior during meditation. However, techniques, such as multiscale entropy (MSE) and multifractal analysis (MFA) of HRV can be more effective in analyzing non-stationary HRV signal, which were hardly used in the existing research works on meditation.

CONCLUSIONS

After going through the literature, it is realized that there is a requirement of a more rigorous research to get consistent and new findings about the changes in HRV dynamics due to the practice of meditation. The lack of adequate standard open access database is a concern in drawing statistically reliable results. Albeit, data augmentation technique is an alternative option to deal with this problem, data from adequate number of subjects can be more effective. Multiscale entropy analysis is scantily employed in studying the effect of meditation, which probably need more attention along with multifractal analysis.

METHODS

Scientific databases, namely PubMed, Google Scholar, Web of Science, Scopus were searched to obtain the literature on "HRV analysis during meditation by nonlinear methods". Following an exclusion criteria, 26 articles were selected to carry out this scientific analysis.

Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

The 1/f-like gait cycle variability, characterized by temporal changes in stride-time intervals during steady-state human walking, is a well-documented gait characteristic. Such gait fractality is apparent in healthy young adults, but tends to disappear in the elderly and patients with neurological diseases. However, mechanisms that give rise to gait fractality have yet to be fully clarified. We aimed to provide novel insights into neuro-mechanical mechanisms of gait fractality, based on a numerical simulation model of biped walking. A previously developed heel-toe footed, seven-rigid-link biped model with human-like body parameters in the sagittal plane was implemented and expanded. It has been shown that the gait model, stabilized rigidly by means of impedance control with large values of proportional (P) and derivative (D) gains for a linear feedback controller, is destabilized only in a low-dimensional eigenspace, as P and D decrease below and even far below critical values. Such low-dimensional linear instability can be compensated by impulsive, phase-dependent actions of nonlinear controllers (phase resetting and intermittent controllers), leading to the flexible walking with joint impedance in the model being as small as that in humans. Here, we added white noise to the model to examine P-value-dependent stochastic dynamics of the model for small D-values. The simulation results demonstrated that introduction of the nonlinear controllers in the model determined the fractal features of gait for a wide range of the P-values, provided that the model operates near the edge of stability. In other words, neither the model stabilized only by pure impedance control even at the edge of linear stability, nor the model stabilized by specific nonlinear controllers, but with P-values far inside the stability region, could induce gait fractality. Although only limited types of controllers were examined, we suggest that the impulsive nonlinear controllers and criticality could be major mechanisms for the genesis of gait fractality.

Complexity matching and coordination in individual and dyadic performance

Complexity matching is a measure of coordination based on information exchange between complex networks. To date, studies have focused mainly on interpersonal coordination, but complexity matching may generalize to interacting networks within individuals. The present study examined complexity matching in a double, coordinated Fitts' perceptual-motor task with comparable individual and dyadic conditions. Participants alternated touching targets with their left and right hands in the individual condition, or analogously with the left hand of one partner and the right hand of another in the dyadic condition. In Experiment 1, response coupling was manipulated by making targets drift either randomly or contingently based on prior responses. Here, drift refers to the variability in the target movements between response locations. Long-range correlations in time series of inter-response intervals exhibited complexity matching between the left and right hands of dyads and individuals. Response coupling was necessary for complexity matching in dyads but not individuals. When response coupling was absent in the dyadic condition, the degree of complexity matching was significantly reduced. Experiment 2 showed that the effect of coupling was due to interactions between left and right responses. Results also showed a weak, negative relationship between complexity matching and performance as measured by total response time. In conclusion, principles and measures of complexity matching apply similarly within and between individuals, and perceptual-motor performance can be facilitated by loose response coupling.

Years of running experience influences stride-to-stride fluctuations and adaptive response during step frequency perturbations in healthy distance runners

RESEARCH QUESTION

The current study investigated stride-to-stride fluctuations of step rate and contact time in response to enforced step frequency perturbations as well as adaptation and de-adaptation behavior.

METHODS

Forty distance runners ran at a self-selected speed and were asked to match five different enforced step frequencies (150, 160, 170, 180, and 190 beats per min). The influence of experience was explored, because running is a skill that presumably gets better with practice, and increased years of running experience is protective against injury. Detrended fluctuation analysis was used to determine the strength of long-range correlations in gait fluctuations at baseline, during the perturbation, and post-perturbation. Adaptive response was measured by the ability to match, rate of matching, and aftereffect of step frequency perturbations.

RESULTS

The structure of stride-to-stride fluctuations for step rate and contact time did not change during the perturbation or post-perturbation compared to baseline. However, fluctuations in step rate were affected by the level of perturbation. Runners with the most experience had a less persistent structural gait pattern for both step rate and contact time at baseline. Highly experienced runners also demonstrated the best adaptive response. They better matched the enforced step frequency, reached the enforced step frequency sooner, and returned to preferred step frequency more quickly following removal of the perturbation.

SIGNIFICANCE

These findings indicate baseline locomotor flexibility may be beneficial to achieve task demands and return to a stable state once the task is complete. Increased locomotor flexibility may also be a contributing factor for reduced injury risk in experienced runners.

Effect of whole-body vibration on center-of-mass movement during standing in children and young adults

Whole body vibration (WBV) can affect postural control and muscular activation. The purpose of this study was to investigate the center-of-mass (COM) movement of children and young adults before, during, immediately after, and 5min after 40-s WBV in quiet standing. Fourteen young adults (mean age 24.5 years) and fourteen children (mean age 8.1 years) participated in the study. A full-body 35-marker set was placed on the participants and used to calculate COM. Forty-second standing trials were collected before, during, immediately after, and 5min after WBV with an frequency of 28Hz and an amplitude of <1mm. Two visual conditions were provided: eyes-open (EO) and eyes-closed (EC). COM variables included time-domain measures (average velocity, range, sway area and fractal dimension), frequency-domain measures (total power and median frequency), and detrended fluctuation analysis (DFA) scaling exponent in both anterior-posterior (AP) and medial-lateral (ML) directions. Results show that during WBV both children and adults increased average velocity and median frequency, but decreased range and the DFA scaling exponent. Immediately after WBV both groups increased the range, but showed pre-vibration values for most of the COM variables. Comparing to adults, children displayed a higher COM velocity, range, fractal dimension, and total power, but a lower DFA scaling exponent at all phases. The results suggest that both children and adults can quickly adapt their postural control system to WBV and maintain balance during and after vibration. Children display some adult-like postural control during and after WBV; however, their postural development continues into adolescence.

Uncertainty quantification of environmental performance metrics in heterogeneous aquifers with long-range correlations

We investigate how the uncertainty stemming from disordered porous media that display long-range correlation in the hydraulic conductivity (K) field propagates to predictions of environmental performance metrics (EPMs). In this study, the EPMs are quantities that are of relevance to risk analysis and remediation, such as peak flux-averaged concentration, early and late arrival times among others. By using stochastic simulations, we quantify the uncertainty associated with the EPMs for a given disordered spatial structure of the K-field and identify the probability distribution function (PDF) model that best captures the statistics of the EPMs of interest. Results indicate that the probabilistic distribution of the EPMs considered in this study follows lognormal PDF. Finally, through the use of information theory, we reveal how the persistent/anti-persistent correlation structure of the K-field influences the EPMs and corresponding uncertainties.

The effects of altering attentional demands of gait control on the variability of temporal and kinematic parameters

The purpose of this study was to investigate the effects of cognitive and visuomotor tasks on gait control in terms of the magnitude and temporal structure of the variability in stride time and lower-limb kinematics measured using inertial sensors. Fourteen healthy young subjects walked on a treadmill for 15min at a self-selected gait speed in the three conditions: normal walking without a concurrent task; walking while performing a cognitive task; and walking while performing a visuomotor task. The time series data of stride time and peak shank angular velocity were generated from acceleration and angular velocity data recorded from both shanks. The mean, coefficient of variation, and fractal scaling exponent α of the time series of these variables and the standard deviation of shank angular velocity over the entire stride cycle were calculated. The cognitive task had an effect on long-range correlations in stride time but not on lower-limb kinematics. The temporal structure of variability in stride time became more random in the cognitive task. The visuomotor task had an effect on lower-limb kinematics. Subjects controlled their swing limb with greater variability and had a more complex adaptive lower-limb movement pattern in the visuomotor task. The effects of the dual tasks on gait control were different for stride time and lower-limb kinematics. These findings suggest that the temporal structure of variability and lower-limb kinematics are useful parameters to detect a change in gait pattern and provide further insight into gait control.

The effect of footwear and footfall pattern on running stride interval long-range correlations and distributional variability

The presence of long-range correlations (self-similarity) in the stride-to-stride fluctuations in running stride interval has been used as an indicator of a healthy adaptable system. Changes to footfall patterns when running with minimalist shoes could cause a less adaptable running gait. The purpose of this study was to investigate stride interval variability and the degree of self-similarity of stride interval in runners wearing minimalist and conventional footwear. Twenty-six trained habitual rearfoot footfall runners, unaccustomed to running in minimalist footwear, performed 6-min sub-maximal treadmill running bouts at 11, 13 and 15 km·h(-1) in minimalist and conventional shoes. Force sensitive resistors were placed in the shoes to quantify stride interval (time between successive foot contacts). Footfall position, stride interval mean and coefficient of variation (CV), were used to assess performance as a function of shoe type. Long-range correlations of stride interval were assessed using detrended fluctuation analysis (α). Mean stride interval was 1-1.3% shorter (P=0.02) and 27% of runners adopted a midfoot footfall (MFF) in the minimalist shoe. There was a significant shoe effect on α and shoe*speed*footfall interaction effect on CV (P<0.05). Runners that adopted a MFF in minimalist shoes, displayed reduced long-range correlations (P<0.05) and CV (P<0.06) in their running stride interval at the 15 km·h(-1) speed. The reduced variability and self-similarity observed for runners that changed to a MFF in the minimalist shoe may be suggestive of a system that is less flexible and more prone to injury.