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Endocrine Sciences Research Group (M.S.G., V.T., P.E.C.), Academic Unit of Child Health, University of Manchester, Manchester M13 9PT, United Kingdom; and Department of Medicine (J.D.V.), General Clinical Research Center, University of Virginia Health Sciences Center, Charlottesville, Virginia 22908
Address all correspondence and requests for reprints to: Dr. Peter Clayton, Endocrine Sciences Research Group, Department of Medicine, Stopford Building, University of Manchester, Oxford Road, Manchester M13 9PT, United Kingdom. E-mail: pclayton{at}man.ac.uk
Abstract
GH is the principal hormone driving growth throughout childhood, but the mechanism by which changing GH secretion is translated into height (Ht) remains undefined. We previously demonstrated that variability in urinary GH (uGH) output over weeks is an important statistical determinant of stature in normal children. We now examine the relationship between the temporal pattern of uGH output and growth using approximate entropy (ApEn) in 29 healthy prepubertal children, monitored serially three times a week from September to June [13 males and 16 females; age, 5.7–7.8 yr; Ht SD score, -2.9 to +2.3; median, 85 measurements per subject]. ApEn is a measure of process irregularity, with low values indicating strong regularity or subpattern persistence and high values indicating greater irregularity. The bivariate extension of this method, cross (X)-ApEn, provides a measure of the strength of interaction between two paired time series (joint signal synchrony). Low values of X-ApEn indicate synchrony, whereas high values indicate asynchrony.
Weekly Ht gain, weight (Wt) gain, and uGH output showed significant orderliness in 20 of 29, 26 of 29, and 29 of 29 subjects, respectively, with weekly changes in uGH output being significantly more ordered than Ht gain (P < 0.001) and Wt gain (P < 0.01). ApEn(GH) was positively correlated with Ht gain over the whole year (r = 0.42) and Ht velocity SD score (r = 0.42; both, P < 0.05). Thus, increased irregularity in successive weekly GH output was associated with increased Ht gain and growth rate. There was significant synchrony between Ht and uGH, Wt and uGH, and Ht and Wt in 16 of 29, 22 of 29, and 25 of 29 subjects, respectively, as measured by X-ApEn. The degree of synchrony between Ht and GH output [X-ApEn(Ht:GH)] was inversely correlated with Ht SD score (r = -0.45) and Ht velocity SD score (r = -0.40; both P < 0.05), indicating that increased joint signal synchrony between Ht and GH accompanies tall stature and increased growth rate.
These results extend the concept that variability in GH output over time is an important determinant of growth in normal children by indicating that an irregular temporal pattern of GH contributes to growth. Furthermore, synchrony between GH output and short-term Ht increments is associated with tall stature and good growth.
CHILDHOOD GROWTH IS a nonlinear process, comprising periods of rapid growth (growth spurts) occurring over a number of weeks, separated by periods of little or no growth (growth stasis) (1). Variation in height (Ht) increments has also been described at daily, weekly, monthly, and annual intervals (2, 3, 4, 5, 6), but few studies have attempted to relate short-term growth to the underlying pattern of hormone output. Postnatal growth is dependent on normal GH secretion, which is pulsatile at an ultradian scale, with further variation occurring over days, months, and years (7, 8, 9, 10). In most studies nonetheless, GH output over only 1 d has been related to change in Ht over months or years (11, 12, 13). Accordingly, the significance of longer term changes in GH secretion to growth has not been addressed.
Urinary GH (uGH) measurements provide an alternative method of appraising GH output longitudinally that is practical and noninvasive (14, 15, 16). In this way, we have previously examined weekly uGH output and growth in a group of healthy school children over a 1-yr period (17). This study revealed that the variability in uGH output over the whole year, expressed as coefficient of variation (CV), was an important determinant of stature, whereas the relative constancy of short-term changes in GH influenced Ht gain. However, these findings were based on summary attributes of the GH excretion profiles and growth endpoints such as stature and annual Ht velocity. We were unable to demonstrate a coincident relationship between the temporal pattern of GH and the pattern of short growth.
The approximate entropy (ApEn) statistic offers a model-free measure of order or disorder within a series (18). An important feature of this index is that it reflects the temporal organization of a complex time series, unlike the CV, which simply captures the degree of variability in a process. An extension of this method, cross (X)-ApEn analysis, examines the bivariate pattern relationships between two complex processes (19). This can be considered as a measure of cross-correlation or covariance between two series without the need to impose a structure on either series. These statistics therefore offer a new opportunity to examine whether the pattern of GH output is associated with the dynamics of short-term growth in a group of normal healthy prepubertal children.
Subjects and Methods
Subjects
Twenty-nine healthy prepubertal school children were followed from September to June [13 males and 16 females; age 5.7 to 7.8 yr; Ht SD score (HtSDS), -2.9 to +2.3] and had formed part of a larger study of short-term growth (1, 17). Subjects were recruited from local schools, with ethical approval and informed parental consent. All children were free from chronic illness. Ht and weight (Wt) were measured three times a week during the school term, at the same time of day. Measurements were made on 94 occasions, the median for one child being 85 (range 75–90). All children grew well over the period of the study (change in Ht, 5.0–7.4 cm), and mean Ht velocity SD score (HVSDS) for the year was +0.6 (range, -0.9 to +1.8). Ht and Wt measurements were expressed as a weekly average (sum of observations divided by the number of observations in the week) to generate time series of equally spaced observations.
uGH
On each measurement occasion, the children provided a timed overnight urine collection for the determination of uGH. Urine was collected into preservative-free plastic bottles, and 25-ml aliquots were frozen at -20 C in the presence of 250 µl 10% BSA/10% sodium azide. uGH was measured by immunoradiometric assay after dialysis, as previously described (20). A total of 2067 samples were analyzed for uGH, and all samples for an individual child were analyzed in the same assay. The median number of samples for one child was 71 (range, 54–86). All results fell within the detection range of the assay. The intra- and interassay CVs were 6.6–8.8 and 8.8–10.0%, respectively, over the range 6–40 pg/ml. Results were expressed as total amount excreted overnight (ng). Then, these results were expressed as the average amount excreted per week (sum of observations divided by the number of observations in the week) to generate a time series of equally spaced observations.
ApEn
ApEn was used as a model-free and scale-independent measure of process irregularity or randomness, with low values indicating strong regularity or persistence of patterns and high values indicating greater irregularity (18). The weekly Ht, Wt, and uGH profiles were detrended by differencing (Xi+1 - Xi) before analysis. The significance of each ApEn statistic was assessed by calculating the ApEn for a random shuffling of each series and examining the ratio of random ApEn to observed ApEn. X-ApEn was used to provide a measure of the relationship between the patterns of change (disorderliness) in two paired series (joint signal asynchrony) (19). A low value of X-ApEn indicates that the two variables show similar patterns (synchrony), whereas high values indicate divergent patterns (asynchrony). Each X-ApEn statistic was compared with the mean (±SD) X-ApEn from random shuffling of the series 300 times to assess significance. A value of unity denotes no difference from random.
Statistical analysis
All statistical analysis was performed using the Statistical Package for Social Sciences (SPSS, Inc., Chicago, IL). Differences between variables were assessed by paired t test, and relationships between variables were assessed by Pearson correlation coefficients.
Results
ApEn
ApEn values for weekly Ht gain [ApEn(Ht)], Wt gain [ApEn(Wt)],
and uGH [ApEn(GH)] are shown in Table 1
. Observed ApEn values were
significantly lower than random ApEn values, indicating significant
order in each series (all P < 0.001). On an individual
basis, the ratio of observed to random ApEn (mean of 300 shuffling
simulations) was nonunitary in 20 of 29 (Ht), 26 of 29 (Wt), and 29 of
29 (GH) subjects. uGH output was significantly more ordered than Ht
gain (P < 0.001) and Wt gain (P <
0.01), whereas Wt gain showed significantly more order than Ht gain
(P < 0.01). ApEn(GH) was positively correlated with Ht
gain over the year (r = 0.42; P < 0.05) and with
HVSDS (Fig. 1), indicating that increased
irregularity in GH output was associated with increased growth rate.
There was no relationship between ApEn(Ht) and ApEn(Wt) and any other
measure of growth or stature.
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Values for X-ApEn are given in Table 2. There was pairwise synchrony between
Ht and GH, Wt and GH, and Ht and Wt in 16 of 29, 22 of 29 and 25 of 29
subjects, respectively. Random X-ApEn values were significantly higher
than observed X-ApEn values for Wt and GH (P < 0.001)
and Wt and Ht (P < 0.001), but not Ht and GH
(P = 0.487). There was a significant inverse
correlation between X-ApEn(Ht:GH) and HtSDS (Fig. 2A), indicating that increased joint
signal synchrony between Ht and GH was associated with relative tall
stature. In addition, X-ApEn(Ht:GH) was inversely correlated with HVSDS
(Fig. 2B), indicating analogously that increased joint signal synchrony
between Ht and GH was also associated with an increased growth rate.
Neither X-ApEn(Wt:GH) nor X-ApEn(Ht:Wt) was correlated with any
measure of growth.
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The relationship between Ht and GH output has been assessed conventionally by correlating the amount of GH secreted over 1 d with growth over the preceding or following months or years. However, this approach provides only a snapshot of two dynamic processes, each of which is subject to pronounced variations over days, weeks, and months. This study extends our previous observation that variability in GH output is an important determinant of growth in normal children by demonstrating that optimal growth is associated with irregularity in the patterning of GH. In addition, the present analyses demonstrate for the first time that a synchronous relationship between the pattern of simultaneous, serial measures of Ht and GH output influences growth performance.
We have used the ApEn statistic to generate an index that encapsulates the temporal organization of a time series to examine how the dynamics of GH output and Ht gain are related. ApEn was first used in an endocrine context to describe the alterations in GH secretion that occur in acromegaly subjects (18). Twenty-four-hour GH profiles in normal subjects generated a low ApEn score, reflecting the relatively ordered process of normal pulsatile secretion. However, in acromegaly, in which basal GH secretion increases and the discrete pulses of GH are lost, ApEn scores were high, indicating disordered GH secretion. Moreover, ApEn was able to distinguish between tumoral and physiological GH profiles with high sensitivity (95%) and specificity (100%) (18). ApEn also discriminates pathophysiological changes in secretory regulation of insulin (21), ACTH (22), PRL (23), aldosterone and renin (24), FSH and LH (25), and leptin (26). The ability of ApEn to detect changes in the underlying episodic behavior of a time series without the need to define the precise peak or trough attributes makes it an attractive tool for studies, such as ours, of complex time series of unknown underlying modal structure.
We found that the patterns of Ht gain, Wt gain, and GH output were significantly nonrandom, with serial GH output significantly more ordered than Wt and Ht. There was a significant positive correlation between ApEn(GH) and HVSDS, indicating that increased irregularity in GH output was associated with increased growth rate. Our previous study had suggested that good growth and tall stature are generated by relatively large swings in GH output (high CV) of relatively uniform magnitude (low coefficient of incremental change) (17). We now extend that model by demonstrating that the temporal sequence of this variability is an important determinant of growth, with optimal growth achieved with a more irregular pattern of GH output (high ApEn). This concept is supported by the longitudinal study of GH secretion through puberty reported by Pincus et al. (27). In that study, progression through puberty was characterized by an increased irregularity in 24-h serum GH profiles (high ApEn), and more importantly, maximal ApEn was associated with peak Ht velocity. Thus, in contradistinction to some endocrine pathologies in which disorder is a feature of the disease (e.g. acromegaly), these data suggest that a degree of disorderliness in serial GH output is required for optimal growth in normal individuals.
We have previously failed to identify a direct relationship between simultaneous measures of Ht and GH output, either in terms of absolute values or changes over time, using conventional linear methods. Here, we report the use of X-ApEn, a two-variable extension of ApEn, which allows the assessment of a bivariate relationship without the need to define the underlying processes (19). Its utility has been illustrated in Cushing’s disease, in which the usual coordinate release of ACTH and cortisol is diminished and is marked by increased X-ApEn scores (22). X-ApEn indicated that there was significant synchrony between successive changes in Ht and GH output in more than half of the subjects, which was associated with increased stature and growth rate. In contrast, where X-ApEn indicated a lack of synchrony between GH output and short-term Ht gain, this was associated with shorter stature and reduced growth rate. This suggests that an alteration in the long-term pattern of GH output may lead to an uncoupling from Ht gain. We speculate that this may have important implications for the etiology of growth failure in conditions in which there is no apparent alteration in GH level. In addition, we suggest that the ability of an individual to coordinate an administered pattern of GH with Ht gain could account for some of the variable response to GH treatment in GH deficiency. This may be of particular importance with the advent of depot preparations of GH (28).
Our studies suggest that week-to-week variations in GH output are physiologically relevant to growth (16, 17). Optimal growth and tall stature are associated with large changes in GH output with a relatively irregular temporal organization, whereas small changes in GH production in a relatively ordered sequence may lead to short stature and poor growth. Furthermore, through the use of X-ApEn we have demonstrated that the degree of synchrony between the pattern of GH output and short-term Ht increments is critical for good growth. Thus, the findings in this study have fundamental implications for the way in which we think about the relationship between GH availability and linear growth.
Acknowledgments
Footnotes
M.S.G. was supported by a Medical Research Council Research Fellowship.
Present address for M.S.G.: Buck Institute, 8001 Redwood Boulevard, Novato, California 94945.
Abbreviations: ApEn, Approximate entropy; CV, coefficient of variation; Ht, height; HtSDS, Ht SD score; HVSDS, Ht velocity SD score; uGH, urinary GH; Wt, weight; X-ApEn, cross-ApEn.
Received January 3, 2001.
Accepted August 29, 2001.
References
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