Approximate entropy and point correlation dimension of heart rate variability in healthy subjects

The contribution of nonlinear dynamics to heart rate variability in healthy humans was examined using surrogate data analysis. Several measures of heart rate variability were used and compared. Heart rates were recorded for three hours and original data sets of 8192 R-R intervals created. For each original data set (n=34), three surrogate data sets were made by shuffling the order of the R-R intervals while retaining their linear correlations. The difference in heart rate variability between the original and surrogate data sets reflects the amount of nonlinear structure in the original data set. Heart rate variability was analyzed by two different nonlinear methods, point correlation dimension and approximate entropy. Nonlinearity, though under 10 percent, could be detected with both types of heart rate variability measures. More importantly, not only were the correlations between these measures and the standard deviation of the R-R intervals weak, the correlation among the nonlinear measures themselves was also weak (generally less than 0.6). This suggests that in addition to standard linear measures of heart rate variability, the use of multiple nonlinear measures of heart rate variability might be useful in monitoring heart rate dynamics.     

Canonical correlations with fallible data

The technique of canonical correlation may be used to determine the extent to which two sets of measurements reflect the same underlying traits. However, if the two sets are not perfectly reliable, the unreliability may obscure the fact that they are essentially dependent on similar processes. If we attempt to determine sets of weights so as to maximize the correlation between linear composites after correction for attenuation in the composites, it turns out that the results may be obtained by determining the canonical correlations and canonical regression weights between the true score components of the measures making up the two sets. In addition, formulas are developed for calculating the correlations between the canonical variates and original measures, both corrected and uncorrected for attenuation. A numerical example relating the verbal to the performance subtests of the Wechsler Intelligence Scale for Children is presented.     

Some symmetric,invariant measures of multivariate association

A distinction is drawn between redundancy measurement and the measurement of multivariate association for two sets of variables. Several measures of multivariate association between two sets of variables are examined. It is shown that all of these measures are generalizations of the (univariate) squared-multiple correlation; all are functions of the canonical correlations, and all are invariant under linear transformations of the original sets of variables. It is further shown that the measures can be considered to be symmetric and are strictly ordered for any two sets of observed variables. It is suggested that measures of multivariate relationship may be used to generalize the concept of test reliability to the case of vector random variables.     

Heart rate variability in a binary choice reaction task: an evaluation of some scoring methods

Several scoring methods of heart rate variability have been investigated in a binary choice task. It was concluded that in this type of task the number of waves in the cardiotachogram and the sum of absolute differences between successive R-R intervals divided by the number of waves are the best indicators of the task levels (20, 30, 40, 50 and 60 binary choices per min). A detailed analysis of these scoring methods in different types of information processing tasks is recommended.     

Compassionate reappraisal and emotion suppression as alternatives to offense-focused rumination: Implications for forgiveness and psychophysiological well-being

This within subjects experiment (28 females, 26 males) examined three responses to a past interpersonal offender. We contrasted offense-focused rumination with two subsequent, counterbalanced coping strategies: compassionate reappraisal and emotion suppression. Compassionate reappraisal emphasized the offender's human qualities and need for positive change. Emotion suppression inhibited the experience and expression of negative offense-related emotions. Offense rumination was associated with negative emotion, faster heartbeats (i.e., shortened electrocardiogram R-R intervals), and lower heart rate variability (HRV; i.e., the high-frequency component of the R-R power spectrum). By contrast, both compassionate reappraisal and emotion suppression decreased negative emotion in ratings and linguistic analyses, calmed eye muscle tension (orbicularis oculi EMG, electromyography), and maintained HRV at baseline levels. Suppression inhibited negative emotion expression at the brow (corrugator EMG) and slowed cardiac R-R intervals, but without forgiveness effects. Only compassionate reappraisal significantly increased positive emotions, smiling (zygomatic EMG), and social language along with forgiveness.     

Variability in the timing of responses during repetitive tapping with alternate hands

Summary This paper addresses the question of whether a simple two-stage account of variability in timing developed for single-hand repetitive tapping is applicable to regular tapping with the hands in alternation. The task required key presses at a steady rate, previously set by a periodic auditory signal. On separate blocks of trials four subjects used the index finger of the left hand or of the right hand at intervals of 200, 400, and 800 ms or alternated between the hands at intervals of 100, 200, or 400 ms. For each subject the variability of the between-hand intervals in the 200- and 400-ms alternate-hand conditions was greater than the variability of the same interval in the single-hand conditions. In the 100-ms alternate-hand condition correlations between adjacent (between-hand) intervals were reliably less then –.5. These results are inconsistent with the simple two-stage model, and two variants are shown to provide a better qualitative fit to at least some aspects of the data.     

Detecting nonlinearity in psychological data: Techniques and applications

Modern graphical and computational techniques for detecting nonlinearity in psychological data sets are presented. These procedures allow researchers to determine the information complexity of temporal data, using physiological and psychological measurements, and to provide evidence for chaos in time series contaminated by measurement noise. Problems with noise reduction and appropriate experimental control, using surrogate time series, are discussed, and applications of the technology are illustrated, using response time, handwriting, and typing data sets. In an experimental application of appropriate nonlinear analysis procedures, the results of a time series prediction experiment confirm that some subjects are sensitive to chaos. In contrast to previous attempts demonstrating sensitivity to chaos, the experiment reported here employs surrogate series to control for linear stochastic aspects of the stimulus sequences, such as autocorrelation. Recommendations for the selection of appropriate software for performing nonlinear analyses are presented, including a comprehensive list of World-Wide Web sites offering such software.     

Effects of incentive and preparatory interval on activity, heart rate, and reaction time in children.

To resolve certain empirical and theoretical difficulties concerning, primarily, the significance of phasic heart-rate deceleration prior to reaction signals, 48 children were employed to perform in simple reaction-time tasks while speed, heart rate, head movement, gross movement, and blink activity were recorded. The indeory intervals and level of incentives. Reaction time varied with incentive, with preparatory interval and mode of presentation. Phasic heart-rate deceleration varied with the intervals but not incentive or mode of presentation. There was little relation between deceleration and RT. Heart rate and somatic movement measures (especially of blinking) were roughly concordant at a group level but did not correlate.     

Examining the reliability of interval level data using root mean square differences and concordance correlation coefficients

This article introduces new statistics for evaluating score consistency. Psychologists usually use correlations to measure the degree of linear relationship between 2 sets of scores, ignoring differences in means and standard deviations. In medicine, biology, chemistry, and physics, a more stringent criterion is often used: the extent to which scores are identically equal. For each test taker (or other unit of measurement), the difference between the 2 scores is calculated. The root mean square difference (RMSD) represents the average change from 1 set of scores to the other, and the concordance correlation coefficient (CCC) rescales this coefficient to have a maximum value of 1. This article shows the relationship of the RMSD and CCC to the intraclass correlation coefficients, product-moment correlation, and standard error of measurement. Finally, this article adapts the RMSD and the CCC for linear, consistency, and absolute definitions of agreement.     

Maternal aggression as a model for acute social stress in the rat: A behavioral-electrocardiographic study

Maternal aggression of lactating rats was used to induce acute social stress in a resident-intruder paradigm. Behavioral and electrocardiographic responses of male intruders were simultaneously recorded. Cardiac electrical activity was measured by means of a telemetry system which ensured preservation of intruder's behavioral repertoire. Behavioral response to maternal attack was evaluated in terms of percent time spent in passive/submissive (p/s) and active/non-submissive (a/ns) patterns. This allowed us to classify the intruders as submissive, non-submissive, and intermediates. During the test, a significant decrease of average R-R interval (R-R) compared to baseline conditions and the occurrence of arrythmias of different nature were found. Ventricular arrhythmias, including premature ventricular beats and ventricular tachycardias, were present in all the intruders while R-R fluctuations and II degree atrioventricular (A-V) blocks only appeared in submissive and intermediate rats. Most ventricular arrhythmias occurred within the upper range of heart rate and were preceded by periods of low R-R variability. These electrocardiographic events were temporally associated with a/ns behavioral patterns and were related to an increased prevalence of sympathetic activity. On the other hand, R-R fluctuations and II degree A-V blocks preceded by high R-R variability were synchronized with p/s behavior and were ascribed to a predominant inhibitory effect of vagal activation which becomes more pronounced as the level of sympathetic activity increases. © 1995 Wiley-Liss, Inc.     

Stability of heartbeat interval distributions in chronic high altitude hypoxia.

Recent studies of nonlinear dynamics of the long-term variability of heart rate have identified nontrivial long-range correlations and scale-invariant power-law characteristics (l/f noise) that were remarkably consistent between individuals and were unrelated to external or environmental stimuli (Meyer et al., 1998a). The present analysis of complex nonstationary heartbeat patterns is based on the sequential application of the wavelet transform for elimination of local polynomial nonstationary behavior and an analytic signal approach by use of the Hilbert transform (Cumulative Variation Amplitude Analysis). The effects of chronic high altitude hypoxia on the distributions and scaling functions of cardiac intervals over 24 hr epochs and 4 hr day/nighttime subepochs were determined from serial heartbeat interval time series of digitized 24 hr ambulatory ECGs recorded in 9 healthy subjects (mean age 34 yrs) at sea level and during a sojourn at high altitude (5,050 m) for 34 days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The results suggest that there exists a hidden, potentially universal, common structure in the heterogeneous time series. A common scaling function with a stable Gamma distribution defines the probability density of the amplitudes of the fluctuations in the heartbeat interval time series of individual subjects. The appropriately rescaled distributions of normal subjects at sea level demonstrated stable Gamma scaling consistent with a single scaled plot (data collapse). Longitudinal assessment of the rescaled distributions of the 24 hr recordings of individual subjects showed that the stability of the distributions was unaffected by the subject's exposure to a hypobaric (hypoxic) environment. The rescaled distributions of 4 hr subepochs showed similar scaling behavior with a stable Gamma distribution indicating that the common structure was unequivocally applicable to both day and night phases and, furthermore, did not undergo systematic changes in response to high altitude. In contrast, a single function stable over a wide range of time scales was not observed in patients with congestive heart failure or patients after cardiac transplantation. The functional form of the scaling in normal subjects would seem to be attributable to the underlying nonlinear dynamics of cardiac control. The results suggest that the observed Gamma scaling of the distributions in healthy subjects constitutes an intrinsic dynamical property of normal heart function that would not undergo early readjustment or late acclimatization to extrinsic environmental physiological stress, e.g., chronic hypoxia.     

Stability of heartbeat interval distributions in chronic high altitude hypoxia

Recent studies of nonlinear dynamics of the long-term variability of heart rate have identified nontrivial long-range correlations and scale-invariant power-law characteristics (1/f noise) that were remarkably consistent between individuals and were unrelated to external or environmental stimuli (Meyer et al., 1998a). The present analysis of complex nonstationary heartbeat patterns is based on the sequential application of the wavelet transform for elimination of local polynomial nonstationary behavior and an analytic signal approach by use of the Hilbert transform (Cumulative Variation Amplitude Analysis). The effects of chronic high altitude hypoxia on the distributions and scaling functions of cardiac intervals over 24 hr epochs and 4 hr day/nighttime subepochs were determined from serial heartbeat interval time series of digitized 24 hr ambulatory ECGs recorded in 9 healthy subjects (mean age 34 yrs) at sea level and during a sojourn at high altitude (5,050 m) for 34 days (Ev-K2-CNR Pyramid Laboratory, Sagarmatha National Park, Nepal). The results suggest that there exists a hidden, potentially universal, common structure in the heterogeneous time series. A common scaling function with a stable Gamma distribution defines the probability density of the amplitudes of the fluctuations in the heartbeat interval time series of individual subjects. The appropriately rescaled distributions of normal subjects at sea level demonstrated stable Gamma scaling consistent with a single scaled plot (data collapse). Longitudinal assessment of the rescaled distributions of the 24 hr recordings of individual subjects showed that the stability of the distributions was unaffected by the subject’s exposure to a hypobaric (hypoxic) environment. The rescaled distributions of 4 hr subepochs showed similar scaling behavior with a stable Gamma distribution indicating that the common structure was unequivocally applicable to both day and night phases and, furthermore, did not undergo systematic changes in response to high altitude. In contrast, a single function stable over a wide range of time scales was not observed in patients with congestive heart failure or patients after cardiac transplantation. The functional form of the scaling in normal subjects would seem to be attributable to the underlying nonlinear dynamics of cardiac control. The results suggest that the observed Gamma scaling of the distributions in healthy subjects constitutes an intrinsic dynamical property of normal heart function that would not undergo early readjustment or late acclimatization to extrinsic environmental physiological stress, e.g., chronic hypoxia.     

Physiological and subjective measures of anxiety during flooding

Patterns of physiological arousal and subjective reports of anxiety were examined during individual sessions of imaginal flooding of five phobic subjects. A curvilinear pattern of increased, followed by decreased, arousal characterized changes in heart rate, respiration rate and subjective anxiety. Heart rate tended to reach its peak level before respiration rate and subjective anxiety. Intercorrelations between these measures were generally positive and significant. Comparisons between periods of high and low subjective arousal revealed a significantly greater correlation for low than for high arousal only for the subjective anxiety by respiration-rate correlation.     

Ordinal properties of perceived average duration: simultaneous and sequential presentations

When a subject evaluates the duration of two simultaneous events, the perceived durations are combined in a nonlinear manner, whereas comparable evaluations of successive events yield linear combinations. Fifty-four subjects rated average durations of pairs of time intervals ranging from 0.5 s to 10.0 s. The intervals making up a pair were presented successively and simultaneously on separate occasions within the same presentation sequence. The order of data was consistent with models previously proposed for perceived average duration. A nonmetric analysis of the combined ordinal data from both conditions yielded a single set of measures of perceived duration with ratio-scale properties. The common scale for the two conditions is consistent with differences in results from simultaneous and successive monitoring of time intervals, stemming from differences in the way duration information is combined rather than how it is perceived. the derived scale is related to physical time by a power function with a 1.06 exponent.     

Reading Achievement and Science Proficiency: International Comparisons From the Programme on International Student Assessment

Students need to develop scientific literacy in order to participate fully as citizens, community members, and in the globalized economy. But what is the relationship between scientific literacy and reading literacy? Three international data sets from the Programme on International Student Assessment (PISA) were used to calculate correlations between scientific literacy and reading literacy for 15-year-old students. Mean correlations at the individual student level across countries were .840 for the PISA 2000 data set, .805 for the PISA 2003 data set, and .819 for the PISA 2006 data set. In all three data sets, this correlation varied among countries, and the reading-science relationship was weakest in countries with low country mean reading scores. Three possible interpretations are discussed, favoring the interpretation that knowledge and skills that drive higher reading comprehension also drive higher science achievement.     

Comparability, reliability, and practice effects on alternate forms of the Digit Symbol Substitution and Symbol Digit Modalities tests

The present study examined the comparability of 4 alternate forms of the Digit Symbol Substitution test and the Symbol Digit Modalities (written) test, including the original versions. Male contact-sport athletes (N = 112) were assessed on 1 of the 4 forms of each test. Reasonable alternate form comparability was demonstrated through establishing normality of form distributions and conducting pairwise form comparisons of means, variability, and intraclass correlations. Nonetheless, alternate forms are likely an insufficient means of controlling practice in speeded measures at brief (1-2 weeks) retest intervals. Reliable change indices demonstrated that practice must be accounted for in individual retesting.     

Heart rate-Qt interval relationship during postural change and exercise. A possible connection to cardiac contractility

The QT interval of the electrocardiogram, although often coordinated in an inverse relationship to heart rate, appears from the existing evidence to be regulated by mechanisms separate from those that govern heart rate. The purpose of this inquiry was to explore further the relationship of the two and to test other factors that may contribute to the regulation of QT. Heart rate and QT duration were measured in healthy human subjects during postural change and exercise. The data showed that, while coordinated in an inverse relationship under some circumstances, under others heart rate and QT were discordant, leading to the inference that there is no fixed linkage between the two. Previous work by the authors and other published studies have suggested that ventricular contractility may have more predictable association with QT shortening than do increases in heart rate. Observations of force of ventricular contraction (HI and IJ velocity) as reflected in ballisto-cardiographic tracings were made using each of 12 human subjects as the authors' own control. The data revealed a highly significant correlation between the velocity measures and QT duration (p less than 0.01) but not heart rate. These findings led to the conclusion that there is clearly not a fixed relationship between heart rate and QT interval and to the hypothesis that QT may more closely reflect the degree of cardiac contractility.     

Heart rate—QT interval relationship during postural change and exercise

The QT interval of the electrocardiogram, although often coordinated in an inverse relationship to heart rate, appears from the existing evidence to be regulated by mechanisms separate from those that govern heart rate. The purpose of this inquiry was to explore further the relationship of the two and to test other factors that may contribute to the regulation of QT. Heart rate and QT duration were measured in healthy human subjects during postural change and exercise. The data showed that, while coordinated in an inverse relationship under some circumstances, under others heart rate and QT were discordant, leading to the inference that there is no fixed linkage between the two. Previous work by the authors and other published studies have suggested that ventricular contractility may have more predictable association with QT shortening than do increases in heart rate. Observations of force of ventricular contraction (HI and IJ velocity) as reflected in ballisto-cardiographic tracings were made using each of 12 human subjects as the authors’ own control. The data revealed a highly significant correlation between the velocity measures and QT duration (p<0.01) but not heart rate. These findings led to the conclusion that there is clearly not a fixed relationship between heart rate and QT interval and to the hypothesis that QT may more closely reflect the degree of cardiac contractility.     

Stability of nonlinear principal components analysis: an empirical study using the balanced bootstrap

Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate normality. For nonlinear PCA, however, standard options for establishing stability are not provided. The authors use the nonparametric bootstrap procedure to assess the stability of nonlinear PCA results, applied to empirical data. They use confidence intervals for the variable transformations and confidence ellipses for the eigenvalues, the component loadings, and the person scores. They discuss the balanced version of the bootstrap, bias estimation, and Procrustes rotation. To provide a benchmark, the same bootstrap procedure is applied to linear PCA on the same data. On the basis of the results, the authors advise using at least 1,000 bootstrap samples, using Procrustes rotation on the bootstrap results, examining the bootstrap distributions along with the confidence regions, and merging categories with small marginal frequencies to reduce the variance of the bootstrap results.