Determinants and interindividual variation of R-R interval dynamics in healthy middle-aged subjects

Determinants and intersubject variations of fractal and complexity measures of R-R interval variability were studied in a random population of 200 healthy middle-aged women (age 51 +/- 6 yr) and 189 men (age 50 +/- 6 yr) during controlled conditions in the supine and sitting positions. The short-term fractal exponent (alpha(1)) was lower in women than men in both the supine (1.18 +/- 0.20 vs. 1.12 +/- 0.17, P < 0.01) and sitting position (P < 0.001). Approximate entropy (ApEn), a measure of complexity, was higher in women in the sitting position (1.16 +/- 0.17 vs. 1.07 +/- 0.19, P < 0.001), but no gender-related differences were observed in ApEn in the supine position. Fractal and complexity measures were not related to any other demographic, laboratory, or lifestyle factors. Intersubject variations in a fractal measure, alpha(1) (e.g., 1.15 +/- 0.20 in the supine position, z value 1.24, not significant), and in a complexity measure, ApEn (e.g., 1.14 +/- 0.18 in the supine position, z value 1.44, not significant), were generally smaller and more normally distributed than the variations in the traditional measures of heart rate variability (e.g., standard deviation of R-R intervals 49 +/- 21 ms in the supine position, z value 2.53, P < 0.001). These results in a large random population sample show that healthy subjects express relatively little interindividual variation in the fractal and complexity measures of heart rate behavior and, unlike the traditional measures of heart rate variability, they are not related to lifestyle, metabolic, or demographic variables. However, subtle gender-related differences are also present in fractal and complexity measures of heart rate behavior.     

Effects of exercise and passive head-up tilt on fractal and complexity properties of heart rate dynamics

tk;1Passive head-up tilt and exercise result in specific changes in the spectral characteristics of heart rate (HR) variability as a result of reduced vagal and enhanced sympathetic outflow. Recently analytic methods based on nonlinear system theory have been developed to characterize the nonlinear features in HR dynamics. This study was designed to assess the changes in the fractal and complexity measures of HR behavior during the passive head-up tilt and during exercise. Fractal exponent (alpha(1)) and approximate entropy (ApEn), measures of short-term correlation properties and overall complexity of HR, respectively, along with spectral components of HR variability were analyzed during a passive head-up tilt test (n = 10) and a low-intensity steady-state exercise (n = 20) in healthy subjects. We observed that alpha(1) increased during the tilt test (from 0.85 +/- 0.22 to 1.48 +/- 0.20; P < 0.001) and during the exercise (from 1.00 +/- 0.22 to 1.37 +/- 0. 14; P < 0.001). ApEn also increased during the exercise (from 1.04 +/- 0.11 to 1. 11 +/- 0.08; P < 0.05), but it did not change during the tilt test. The normalized high-frequency spectral component decreased and the low-frequency component increased similarly during both the exercise and the tilt test (P < 0.001 for all). Exercise and passive tilt result in an increase of short-term fractal correlation properties of HR dynamics, which is related to changes in the balance between the low- and high-frequency oscillations in controlled situations. Overall complexity of HR dynamics increases during exercise but not during passive tilt.     

Correlation properties of heartbeat dynamics

In this study, we investigate correlation properties of fluctuations in heart interbeat (RR) time series in a broad range of physiological and pathological conditions. Using detrended fluctuation analysis (DFA) method we determined short-term (alpha (1)) and long-term (alpha (2)) scaling exponent. In addition, we calculated standard deviation of RR intervals (SDRR) as the simplest variability measure. We found that the difference between alpha (1) and alpha (2) is related to RR interval length. At the shortest RR intervals, which correspond to extreme physiological and pathological conditions, we found the highest reduction of variability and the biggest difference between scaling exponents. In this case, DFA reveals a white noise over short scales (alpha (1 )about 0.5) and strongly correlated noise over large scales (alpha (2) about 1.5). With an increase in RR interval, accompanied by increased variability (increase in parasympathetic control), the difference between alpha (1) and alpha (2) decreases. The difference between scaling exponents disappeared in a state of efficient autonomic control. We suggest that the complexity in heart rhythm is achieved through coupling between intrinsically controlled heart rhythm and autonomic control, and that the model of stochastic resonance mechanism could be applied to this system.     

Aging and nonlinear heart rate control in a healthy population

In recent years more studies are using nonlinear dynamics to describe cardiovascular control. Because of the large dispersion of physiological data, it is important to have large studies with both male and female participants to establish a range of physiological healthy values. This study investigated the effect of gender and age on nonlinear indexes. Nonlinear scaling properties were studied by using 1/f slope (where f is frequency), fractal dimension, and detrended fluctuation analysis short- and long-term correlations (DFAalpha(1) and DFAalpha(2), respectively). Nonlinear complexity was described with correlation dimension (CD), Lyapunov exponent (LE), and approximate entropy (ApEn). The population consisted of 135 women and 141 men (age, 18-71 yr). Twenty-four hour ECG recordings were obtained by using Holter monitoring. The recordings were split into daytime (8 AM-9 PM) and nighttime (11 PM-6 AM). A day-night variation was present in all nonlinear heart rate variability (HRV) indexes, except for the CD in the female population. During the night the percentage of CD values of surrogate data files differing from the CD value of the original data increased. All nonlinear indexes were significantly correlated with age. Deeper analysis per age category of 10 yr showed a stabilization in the age decline of the fractal dimension and ApEn at the age of > or =40 yr. The vagal pathways seemed to be more involved in the generation of nonlinear fluctuations. Higher nonlinear behavior was evident during the night. No clear difference between men and women was found in the nonlinear indexes. Nonlinear indexes decline with age. This can be related to the concept of decreasing autonomic modulation with advancing age.     

The dynamics of EEG entropy

The scaling properties of human EEG have so far been analyzed predominantly in the framework of detrended fluctuation analysis (DFA). In particular, these studies suggested the existence of power-law correlations in EEG. In DFA, EEG time series are tacitly assumed to be made up of fluctuations, whose scaling behavior reflects neurophysiologically important information and polynomial trends. Even though these trends are physiologically irrelevant, they must be eliminated (detrended) to reliably estimate such measures as Hurst exponent or fractal dimension. Here, we employ the diffusion entropy method to study the scaling behavior of EEG. Unlike DFA, this method does not rely on the assumption of trends superposed on EEG fluctuations. We find that the growth of diffusion entropy of EEG increments of awake subjects with closed eyes is arrested only after approximately 0.5 s. We demonstrate that the salient features of diffusion entropy dynamics of EEG, such as the existence of short-term scaling, asymptotic saturation, and alpha wave modulation, may be faithfully reproduced using a dissipative, first-order, stochastic differential equation—an extension of the Langevin equation. The structure of such a model is utterly different from the “noise+trend” paradigm of DFA. Consequently, we argue that the existence of scaling properties for EEG dynamics is an open question that necessitates further studies.     

Fractal scaling properties of heart rate dynamics following resistance exercise training.

With aging and disease, there is a breakdown of the natural fractal-like organization of heart rate (HR). Fractal-like correlation properties of HR can be assessed with detrended fluctuation analysis (DFA). A short-time scaling exponent (alpha(s)) value of 1 is associated with healthy HR dynamics, whereas values that deviate away from 1, in either direction, indicate fractal collapse. The purpose of this study was to examine the effect of resistance exercise training (RT) on fractal correlation properties of HR dynamics. Resting ECG was collected at baseline, following a 4-wk time control period and 6 wk of RT (3 days per wk) in 34 men (23 +/- 1 years of age). Fractal properties of HR were assessed with DFA. There was no change in alpha(s) following either the time control period or RT (1.01 +/- 0.06 to 0.98 +/- 0.06 to 0.93 +/- 0.04, P > 0.05). Given the potential bidirectional nature of fractal collapse, subjects were retrospectively separated into two groups (higher alpha(s) and lower alpha(s)) on the basis of the initial alpha(s) by using cluster analysis. An interaction was detected for alpha(s) following RT (P < 0.05). There was no change in alpha(s) in either group following the time control, but alpha(s) increased following RT in the lower alpha(s) group (n = 18; 0.73 +/- 0.04 to 0.69 +/- 0.04 to 0.88 +/- 0.04) and alpha(s) decreased following RT in the higher alpha(s) group (n = 16; 1.20 +/- 0.04 to 1.24 +/- 0.04 to 0.98 +/- 0.04). In conclusion, RT improves fractal properties of HR dynamics.     

Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly

Heart beat fluctuations exhibit temporal structure with robust long-range correlations, fractal and nonlinear features, which have been found to break down with pathologic conditions, reflecting changes in the mechanism of neuroautonomic control. It has been hypothesized that these features change and even break down also with advanced age, suggesting fundamental alterations in cardiac control with aging. Here we test this hypothesis. We analyze heart beat interval recordings from the following two independent databases: 1) 19 healthy young (average age 25.7 yr) and 16 healthy elderly subjects (average age 73.8 yr) during 2 h under resting conditions from the Fantasia database; and 2) 29 healthy elderly subjects (average age 75.9 yr) during approximately 8 h of sleep from the sleep heart health study (SHHS) database, and the same subjects recorded 5 yr later. We quantify: 1) the average heart rate (); 2) the SD sigma(R-R) and sigma(DeltaR-R) of the heart beat intervals R-R and their increments DeltaR-R; 3) the long-range correlations in R-R as measured by the scaling exponent alpha(R-R) using the Detrended Fluctuation Analysis; 4) fractal linear and nonlinear properties as represented by the scaling exponents alpha(sgn) and alpha(mag) for the time series of the sign and magnitude of DeltaR-R; and 5) the nonlinear fractal dimension D(k) of R-R using the fractal dimension analysis. We find: 1) No significant difference in (P > 0.05); 2) a significant difference in sigma(R-R) and sigma(DeltaR-R) for the Fantasia groups (P < 10(-4)) but no significant change with age between the elderly SHHS groups (P > 0.5); and 3) no significant change in the fractal measures alpha(R-R) (P > 0.15), alpha(sgn) (P > 0.2), alpha(mag) (P > 0.3), and D(k) with age. Our findings do not support the hypothesis that fractal linear and nonlinear characteristics of heart beat dynamics break down with advanced age in healthy subjects. Although our results indeed show a reduced SD of heart beat fluctuations with advanced age, the inherent temporal fractal and nonlinear organization of these fluctuations remains stable. This indicates that the coupled cascade of nonlinear feedback loops, which are believed to underlie cardiac neuroautonomic regulation, remains intact with advanced age.     

Progressive decrease of heart period variability entropy-based complexity during graded head-up tilt.

Complexity (or its opposite, regularity) of heart period variability has been related to age and disease but never linked to a progressive shift of the sympathovagal balance. We compare several well established estimates of complexity of heart period variability based on entropy rates [i.e., approximate entropy (ApEn), sample entropy (SampEn), and correct conditional entropy (CCE)] during an experimental protocol known to produce a gradual shift of the sympathovagal balance toward sympathetic activation and vagal withdrawal (i.e., the graded head-up tilt test). Complexity analysis was carried out in 17 healthy subjects over short heart period variability series ( approximately 250 cardiac beats) derived from ECG recordings during head-up tilt with table inclination randomly chosen inside the set {0, 15, 30, 45, 60, 75, 90}. We found that 1) ApEn does not change significantly during the protocol; 2) all indices measuring complexity based on entropy rates, including ad hoc corrections of the bias arising from their evaluation over short data sequences (i.e., corrected ApEn, SampEn, CCE), evidence a progressive decrease of complexity as a function of the tilt table inclination, thus indicating that complexity is under control of the autonomic nervous system; 3) corrected ApEn, SampEn, and CCE provide global indices that can be helpful to monitor sympathovagal balance.     

Evidence for fractal correlation properties in variations of peripheral arterial tone during REM sleep

Previous studies utilizing detrended fluctuation analysis (DFA) of heart rate variability during sleep revealed a higher fractal exponent during rapid eye movement (REM) sleep than non-REM sleep. The aim of this study was to determine whether the same difference exists in the variations of peripheral arterial tone (PAT). Finger pulse wave measured by a novel plethysmographic technique was monitored during sleep in 12 chronic heart failure patients, 8 heavy snorers, and 12 healthy volunteers. For each subject, at least two 15-min time series were constructed from the interpulse intervals and from pulse wave amplitudes during REM and non-REM sleep. Fractal scaling exponents of both types of time series were significantly higher for REM than non-REM sleep in all groups. In each of the groups and in both sleep stages, the fractal scaling exponents based on pulse wave amplitude were significantly higher than those based on pulse rate variability. A repeat of the analysis for short-, intermediate-, and long-term intervals revealed that the fractal-like exponents were evident only in the short- and intermediate-term intervals. Because PAT is a surrogate of sympathetic activation, our results indicate that variations in sympathetic activation during REM sleep have a fractal-like behavior.     

Self-similarity in variability of human heart variability at various stages of ontogenesis

We consider the potential of applying wavelet analysis to fluctuations found in physiological systems. We focus on cardiac interbeat interval time series (RR-intervals) from a group of young adults and children and fetus heart beat rate time series (antepartum cardiotocography), because the wavelet analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. We show that all the signals analyzed are self-similar and propose a method for estimating this scaling feature.     

Identification of development and autonomic nerve activity from heart rate variability in preterm infants

Heartbeat intervals, which are determined basically by regular excitations of the sinoatrial node, show significant fluctuation referred to as the heart rate variability (HRV). The HRV is mostly due to nerve activities through the sympathetic and parasympathetic branches of the autonomic nervous system (ANS). In recent years, it has been recognized that the HRV shows a greater complexity than ever expected, suggesting that it includes much information about ANS activities. In this study, we investigated relationship between HRV and development in preterm infants. To this end, heartbeat intervals were continuously recorded from 11 preterm infants in NICU. The recording periods were ranging from several days to weeks depending on the individuals. The HRV at various ages was then characterized by several indices. They include power spectrum as well as the mean and standard deviation of the series. For the power spectrum, the low-frequency band power (LF), high-frequency band power (HF), LF/HF (the ratio between LF and HF), beta (scaling exponent of the spectrum) were estimated. The detrended fluctuation analysis (DFA) was also employed to obtain short- and long-range scaling exponents. Each of these indices showed a correlation with the age. We showed that the long-range scaling exponent, derived from the DFA, was most significantly correlated with the age, suggesting that it could be a robust index to characterize the development of preterm infants.     

基于替代数据思想的复杂度归一化方法及其在心电信号分析中的应用

基于替代数据(Surrogate)思想的复杂度归一化方法,克服了一般复杂度对信号采样长度与采样频率的敏感性。文章对在生物医学信号复杂度分析中最有潜在应用价值的近似熵和C0复杂度进行了归一化。应用该方法可以有效地反映人体心脏某些病理状态之间的差别。同时,通过比较各种复杂度指标发现,C0复杂度和近似熵对采样长度的敏感性最弱,适用于短数据量的信号分析。     

Chemical activation of pre-Bötzinger complex in vivo reduces respiratory network complexity

In the in vivo anesthetized adult cat model, multiple patterns of inspiratory motor discharge have been recorded in response to chemical stimulation and focal hypoxia of the pre-B?tzinger complex (pre-B?tC), suggesting that this region may participate in the generation of complex respiratory dynamics. The complexity of a signal can be quantified using approximate entropy (ApEn) and multiscale entropy (MSEn) methods, both of which measure the regularity (orderliness) in a time series, with the latter method taking into consideration temporal fluctuations in the underlying dynamics. The current investigation was undertaken to examine the effects of pre-B?tC-induced excitation of phasic phrenic nerve discharge, which is characterized by high-amplitude, rapid-rate-of-rise, short-duration bursts, on the complexity of the central inspiratory neural controller in the vagotomized, chloralose-anesthetized adult cat model. To assess inspiratory neural network complexity, we calculated the ApEn and MSEn of phrenic nerve bursts during eupneic (basal) discharge and during pre-B?tC-induced excitation of phasic inspiratory bursts. Chemical stimulation of the pre-B?tC using DL-homocysteic acid (DLH; 10 mM; 10-20 nl; n=10) significantly reduced the ApEn from 0.982+/-0.066 (mean+/-SE) to 0.664+/-0.067 (P<0.001) followed by recovery ( approximately 1-2 min after DLH) of the ApEn to 1.014+/-0.067; a slightly enhanced magnitude reduction in MSEn was observed. Focal pre-B?tC hypoxia (induced by sodium cyanide; NaCN; 1 mM; 20 nl; n=2) also elicited a reduction in both ApEn and MSEn, similar to those observed for the DLH-induced response. These observations demonstrate that activation of the pre-B?tC reduces inspiratory network complexity, suggesting a role for the pre-B?tC in regulation of complex respiratory dynamics.     

豚鼠听神经放电的复杂性分析

运用刻划非线性动力系统复杂性的两种测算方法：复杂度和近似熵,结合替代数据法,研究豚鼠听神经单纤维放电时间间隔序列的复杂性。结果显示,听神经自发放电时间间隔序列的复杂度要高于诱发时的复杂度;听神经诱发放电时间间隔序列的近似熵低于随机重排替代数据的近似熵。提示听神经放电不是完全随机的过程,而可能是混沌的动力学行为,而且诱发放电时的规律性更强。     

Hemodynamics assessed via approximate entropy analysis of impedance cardiography time series: effect of metabolic syndrome

The metabolic syndrome (MS), a predisposing condition for cardiovascular disease, presents disturbances in hemodynamics; impedance cardiography (ICG) can assess these alterations. In subjects with MS, the morphology of the pulses present in the ICG time series is more irregular/complex than in normal subjects. Therefore, the aim of the present study was to quantitatively assess the complexity of ICG times series in 53 patients, with or without MS, through a nonlinear analysis algorithm, the approximate entropy, a method employed in recent years for the study of several biological signals, which provides a scalar index, ApEn. We correlated ApEn computed from ICG times series data during fasting and postprandial phase with the presence of alterations in the parameters defining MS [Adult Treatment Panel (ATP) III (Grundy SM, Brewer HB Jr, Cleeman JI, Smith SC Jr, Lenfant C; National Heart, Lung, and Blood Institute; American Heart Association. Circulation 109: 433-438, 2004) and the International Diabetes Federation (IDF) definition]. Results show that ApEn was significantly higher in subjects with MS compared with those without (1.81 ± 0.09 vs. 1.65 ± 0.13; means ± SD; P = 0.0013, with ATP III definition; 1.82 ± 0.09 vs. 1.67 ± 0.12; P = 0.00006, with the IDF definition). We also demonstrated that ApEn increase parallels the number of components of MS. ApEn was then correlated to each MS component: mean ApEn values of subjects belonging to the first and fourth quartiles of the distribution of MS parameters were statistically different for all parameters but HDL cholesterol. No difference was observed between ApEn values evaluated in fasting and postprandial states. In conclusion, we identified that MS is characterized by an increased complexity of ICG signals: this may have a prognostic relevance in subjects with this condition.     

Age dependency and correlation of heart rate variability,blood pressure variability and baroreflex sensitivity

Simultaneous analysis of heart rate variability (HRV), blood pressure variability (BPV) and baroreflex sensitivity (BRS) with different types of measures may provide non-duplicative information about autonomic cardiovascular regulation. Therefore, a multiple signal analysis of cardiovascular time series will enhance the physiological understanding of neuro cardiovascular regulation with deconditioning in bedrest or related gravitational physiological studies. It has been shown that age is an important determinant of HRV and BRS in healthy subjects. Whereas in the case of BPV, the effect of aging seems to depend upon the activity status of the subjects. In view of the facts that most of the previous works were dealing with only the variability of one kind of cardiovascular parameters in one study with conventional time-domain and/or frequency-domain analysis, we therefore designed the present work to compare the HRV, BPV and BRS between young and middle-aged male healthy subjects in one study with the same subjects using various techniques, including the approximate entropy (ApEn) measurement, a statistic quantifying HRV "complexity" derived from non-linear dynamics.     

Evidence of phase transitions in heart period dynamics

Complexity measures of non-linear dynamics are a useful tool for quantifying observed stretching, folding, scaling and mixing processes in the Takens-reconstructed state space of heart period dynamics. Although such measures are not suited to provide evidence of deterministic chaos or to estimate true fractal dimensions and Lyapunov spectra in heart period time series, they allow the classification of RR dynamics and the identification of changes in RR complexity (RRC). The aim of this study was to develop appropriate measures and examine their utility in identifying the physiological effect of changes between the sleeping and waking state. Twenty-four hour electrocardiography (ECG) recordings and diaries noting their waking/sleeping period were obtained from 78 healthy subjects, aged 20 to 55 years. The approximate information dimension (ApD1) and the approximate Kolmogorov entropy (ApEn), introduced by Pincus, Kaplan and others, were modified in order to allow the calculation of strictly local values. That is, the local or pointwise dimensions and entropies were calculated for each reference vector with respect to its symmetric neighbourhood in time. For each subject the values for the local measures were averaged for 10-min periods, resulting in 144 global values over 24 h. Similarly, low- and high-frequency spectral parameters were calculated. All measures were examined and compared for the waking and the sleeping periods. All complexity measures as well as to a lesser degree high-frequency power showed a linear dependency on mean RR interval with a large individual variation. For the RRC measures this linear correlation was separated into two different clusters corresponding to the sleeping and waking periods. In almost all cases the correlation was greater in the waking period. In particular, in many cases no correlation was observed in the sleeping period. However, the values for LF were appreciably lower and indicated solely a weak relationship to the RR interval in the waking period. Analysis of variance combining mean RR interval with RRC or spectral parameters singly and in couples revealed that the best separation with respect to physiological state could be achieved with the complexity measures, in particular with ApEn. The results show evidence of at least two dynamical regimes (phases) of heart period dynamics and a close but different functional relationship within the phases between RR interval and RR complexity. The separation between these regimes and the relatively sudden shift from one regime to the other suggest the existence of a phase transition with respect to waking and sleeping periods in terms of synergetics. Received: 5 July 1996 / Accepted in revised form: 15 September 1997     

Accuracy of the StressEraser<Superscript>®</Superscript> in the Detection of Cardiac Rhythms

StressEraser is a commercially marketed biofeedback device designed to enhance heart rate variability. StressEraser makes its internal calculations on beat-to-beat measures of finger pulse intervals. However, the accuracy and precision of StressEraser in quantifying interbeat intervals using finger pulse intervals has not been evaluated against standard laboratory equipment using R-R intervals. Accuracy was assessed by simultaneously recording interbeat intervals using StressEraser and a standard laboratory ECG system. The interbeat intervals were highly correlated between the systems. The average deviation in interbeat interval recordings between the systems was approximately 6 ms. Moreover, correlations approached unity between the systems on estimates of heart period, heart rate, and heart rate variability. Feedback from StressEraser is based on an interbeat time series that provides sufficient information to provide an excellent estimate of the dynamic changes in heart rate and heart rate variability. The slight variations between StressEraser and the laboratory equipment in quantifying heart rate and heart rate variability are due to features related to monitoring heart rate with finger pulse: (1) a lack in precision in the peak of the finger pulse relative to the clearly defined inflection point in the R-wave, and (2) contribution of variations in pulse transit time.     

Physiological time-series analysis using approximate entropy and sample entropy

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.     

Longitudinal changes in growth hormone secretory process irregularity assessed transpubertally in healthy boys

Clarifying the time evolution, and underlying neuroendocrine regulation, of hormone secretion during puberty is of pivotal importance both physiologically and clinically. We sought to determine whether clinical growth and elevated growth hormone (GH) release in pubertal boys are associated with shifts in the irregularity of GH secretory patterns. We studied GH release in 23 healthy boys longitudinally at approximately 4-mo intervals over a 6-yr period throughout puberty, by repetitive blood sampling at 20-min intervals for 24 h on each study date. To quantify serial irregularity in the GH profiles, we utilized approximate entropy (ApEn), a scale- and model-independent quantification of the extent of sequential "randomness." Complementary statistical analyses establish that on a per-subject basis, serum GH concentration-time series show greatest secretory disorderliness (maximal ApEn) in prepuberty and mid-to-late puberty, followed by a steep decline in ApEn to maximal orderliness in postpubertal adolescence (P < 0.0001, ANOVA). Pooling all subject comparisons, we observed a persistent positive correlation between ApEn and growth velocity (GrVel), Pearson r = 0.467 (P < < 10(-10)). Moreover, in general, ApEn(GH) preceded GrVel evolution, with a time frame lead of 4-8 mo providing the most pronounced correlations between ApEn and GrVel. In the setting of low postpubertal growth, per-subject ApEn values fell to approximately one-half of maximal ApEn values and, on average, were in the 13th percentile from minimal (P < < 10(-10)) for fully mature boys. Thus, in a longitudinal transpubertal analysis, greater irregularity in GH secretion corresponds to greater linear growth in boys, which culminates in highly regular GH secretory dynamics after sexual maturity. In addition to clinical utility, there may be added experimental merit in knowing that GH dynamics typically predict accelerated linear growth in 4-8 mo.