## Abstract

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 ∼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.

- approximate entropy
- pulsatility
- growth rate
- somatotropic axis
- humans

greater understanding of the regulation of hormonal dynamics during puberty is of vital importance both physiologically and clinically. Whereas many studies have quantified the amounts of hormone secreted by the somatotropic and gonadotropic axes during this transition (1, 5, 7, 25,30, 31), basic neuroregulatory questions remain to be clarified about the underlying control mechanisms that drive increased hormone output (3, 24). One means of assessing pulsatility changes on the basis of hormonal time-series data is approximate entropy (ApEn), a model-independent quantification of sequential irregularity (10,21). ApEn applications have allowed the endocrinologist to monitor and quantify changes in secretory patterns from a perspective complementary to that provided by output estimates or pulse detection algorithms (26). The present study explores the hypothesis that the marked pubertal enhancement of growth hormone (GH) release in boys is accompanied by shifts in the irregularity (extent of “randomness”) of GH secretory patterns, thus identifying a distinct aspect of changes in GH system control. Given that ApEn changes bear a mechanistic relationship to alterations in feedback control (discussed further below), the ensuing analyses thus allow inferential assessment of changing feedback regulation in the somatotropin release-inhibiting hormone (SRIH)/GH-releasing hormone (GHRH)-somatotropic (GH)-insulin-like growth factor I (IGF-I) axis across human puberty.

In a recent cross-sectional study of 53 boys (29), we observed that ApEn was largest (GH dynamics most irregular) at mid-to-late puberty, with a return to maximal orderliness (smallest ApEn) thereafter toward reproductive maturity. However, this study was significantly limited by its cross-sectional study design and absence of concurrent growth analysis. Thus causality of per-subject ApEn evolution could at best be inferred only indirectly and could not be related to individual growth activity. Critically from a statistical perspective, cross-subject heterogeneity often blurs longitudinal evolutionary determinations that are more apparent on a per-subject basis. Herein, we wished to determine longitudinal per-subject profiles of ApEn evolution of GH across puberty, and to assess the time association (if any) between ApEn changes and concurrently measured linear growth rate. For this purpose, we utilize the clinical model to be described in methods on the basis of GH profiles collected from 23 boys studied longitudinally at 4-mo intervals over a 6-yr period as they progressed through puberty. These data provide an uncommon, possibly unprecedented, 72-point GH time series per study date for each of ∼18 study dates for each of the 23 boys.

In addition to clarifying the evolution of ApEn transpubertally, we examine the association between ApEn values and a classical primary clinical marker of pubertal change, growth velocity (GrVel), considering both lagged and unlagged comparisons. GrVel is a well-established and relevant biological response (22), which can be measured quite accurately via standard auxological methods.

## METHODS

### Clinical Protocols

This study was approved by the University of Virginia Human Investigation Committee and performed in the General Clinical Research Center. Written informed consent was obtained from a parent or guardian, and written assent was obtained from each subject. A longitudinal study was conducted of 23 prepubertal and early pubertal normally growing boys. Each volunteer was observed for ≥6 yr as he entered and progressed through pubertal development, i.e., from prepuberty, as defined by Tanner Stage I for pubic hair and genitalia, to early postpuberty (clinical Tanner Stage V for the same characteristics). At entry, each boy was within 2 SD of height for age and was growing normally. Each boy also had a normal weight for height. None of the boys had chronic illnesses or was receiving medications chronically. Data were gathered from each boy approximately every 4 mo. Height, from which GrVel was calculated, was taken mainly by a single experienced technician by use of the mean of three early morning measurements with a Harpenden stadiometer. All measurements were made to the nearest millimeter. All volunteers underwent blood sampling at 20-min intervals for 24 h on each study date (*n* = 72 point time series). Serum GH concentrations were assayed in duplicate by immunoradiometric assay, or IRMA (Nichols Laboratories, San Juan Capistrano, CA) (6). The minimum detectable concentration was 0.5 μg/l. A detailed description of the mean intra-assay coefficients of variation (CV) across a full range of serum GH concentrations has been reported previously (4).

### Quantification of Irregularity

To quantify irregularity, we utilize ApEn, a model-independent statistic defined in Ref. 10, with further mathematical properties and representative biological (including endocrinological) applications given in Refs. 8, 9, 12, 13, 15, 17, 19-21, 23, and 28. ApEn assigns a nonnegative number to a time series, with larger values corresponding to greater apparent process randomness or serial irregularity and smaller values corresponding to more instances of recognizable features or patterns in the data. Two input parameters, a run length *m* and a tolerance window *r*, must be specified to compute ApEn. Briefly, ApEn measures the logarithmic likelihood that runs of patterns that are close (within *r*) for *m* contiguous observations remain close (within the same tolerance width *r*) on next incremental comparisons; the precise mathematical definition is given in Ref. 10.

For this study, we calculated ApEn values for all data sets, *m*= 1 and *r *= 20% of the standard deviation (SD) of the individual subject time series. Normalizing *r* to each time- series SD gives ApEn a translation and scale invariance to absolute serum concentration levels (12). Additionally, ApEn provides a direct barometer of feedback system change in many coupled systems (11, 18). Further technical discussion of mathematical and statistical properties of ApEn can be found elsewhere (14, 16).

### Analytic Strategy

#### Challenges in forming statistical tests.

The goal of this study is to deduce typical and general characteristics of longitudinal per-subject ApEn(GH) curves transpubertally. This requires a careful analytic strategy for several reasons. First, the primary per-subject inputs are ApEn and GrVel curves (longitudinal point sets), rather than single numerical values; thus a means to aggregate these correlated data for suitable statistical testing is not straightforward. Reducing each per-subject curve to a several-parameter set via a low-order best-fit polynomial (or other elementary function) seems inappropriate, because many of the per-subject longitudinal data sets are highly nonmonotonic; i.e., they show numerous changes in direction (as in Fig. 1). Virtually no low-parameter models are characterized by such frequent shifts in direction (manifesting many first derivative sign changes) across time. Second, pooling the data is not so straightforward, even upon*z*-transformation standardization (see below), because subjects were not sampled on common dates and had differing start and end study dates relative to their date of maximal GrVel and unequal numbers of studies. Third, GrVel itself does not smoothly increase to a maximal value, thereafter subsequently showing monotonic decrease (see Fig. 1), so that comparisons of ApEn values to the clinical reference GrVel must at least accommodate this irregular variation.

To address these issues, we chose to analyze the data via several different and complementary, although thematically related, assessments to establish robustness and generality to the findings.

#### Statistical tests: ApEn(GH) evolution.

On the basis of previous cross-sectional study (29), we hypothesized that per-subject ApEn values would be at a midlevel prepubertally, would tend to increase toward maximal ApEn at or near the time of maximal GrVel, and then generally and steadily decrease to a very low value at maturity, markedly smaller than the initial study value, indicating very regular GH dynamics at the final test date. To evaluate this notion in a robust manner that did not require model-based assumptions for the ApEn longitudinal curves, we performed the following calculations. First, for a given subject, denote the ApEn(GH) value on the *i*
^{th} study date as ApEn_{i} and denote the GrVel value on the*i*
^{th} study date as GrVel_{i}. Denote the study date for which GrVel is maximal for the subject as*t*
_{max}, with corresponding ApEn value ApEn_{vmax}; also, denote by *t*
_{1} and*t*
_{fin} the subject study start and final dates, respectively, with corresponding ApEn values denoted ApEn_{1}and ApEn_{fin}. Last, define *t*
_{early} as the study date midway between *t*
_{1} and*t*
_{max}, and define *t*
_{late} as the study date midway between *t*
_{max} and*t*
_{fin}. Thus the five study dates*t*
_{1}, *t*
_{early},*t*
_{max}, *t*
_{late}, and*t*
_{fin} can be seen as a per-subject increasing time sequence of markers segmenting the start date-maximal growth date-final date continuum.

One-way ANOVA was then applied to evaluate the null hypothesis that the ApEn values were statistically unrelated to pubertal development across the five epochs *t*
_{1},*t*
_{early}, *t*
_{max},*t*
_{late}, and *t*
_{fin}. ANOVA was applied to both the raw ApEn values and to the standardized (*z*-transformed) ApEn values.

To further appraise the longitudinal ApEn trajectory, we also calculated *1*) the percentage of dates *i* <*t*
_{max} for which ApEn_{i} > ApEn_{1}, and *2*) the percentage of dates*i* > *t*
_{max} for which ApEn_{i} < ApEn_{vmax}. Both of these calculations were performed per subject and were subsequently pooled.*Calculation 1* assesses the extent and consistency of increases in GH irregularity from study onset to the time of maximal GrVel, and *calculation 2* assesses the extent and consistency of decreases in GH irregularity from the time of maximal GrVel to study completion.

#### Statistical tests: joint ApEn(GH), GrVel associations.

We performed several sets of calculations to determine linear correlation between ApEn and GrVel. First, both per subject and subsequently pooled, we calculated the correlation between ApEn_{i} and GrVel_{i}._{.}Next, we performed led and lagged correlations and calculated the correlation between ApEn_{i} and GrVel_{i}
_{-N} for each of*N* = 1, 2, 3, −1, −2, and −3.

The above overall correlation calculations have the limitation that they are affected by cross-subject variation and heterogeneity. One major hypothesis of this study is that, on a per-subject basis, ApEn correlates strongly and positively with GrVel. To assess this hypothesis by using the power of the pooled data base, yet in a manner free of cross-subject heterogeneity, we also calculated pooled overall correlations between standardized (*z*-transformed) ApEn_{i} and GrVel_{i} values. The *z*-transformations were performed on each subject's ApEn and GrVel values. We also performed led and lagged correlations of the pooled *z*-transformed data, identically to the nontransformed comparisons, for the lead and/or lag times described.

#### Low final date ApEn values.

We tested the postulate that, and determined the degree to which, final date ApEn values are low, relative to the maximal growth date on a per-subject analysis, in a robust, nonparametric manner as follows. First, rank for each subject the final test date ApEn value among all (*N*) ApEn_{i} values for that subject, denoting this as Aprank_{fin}, which has a value between 1 (lowest) and *N* (largest). Then normalize this ranking by nAprank_{fin} = (Aprank_{fin} − 1)/(*N *− 1), producing a range between 0 and 1. Under the null hypothesis of identical ApEn distributions on all dates, the mean nAprank_{fin} should have a mean of 0.5 (i.e., the final date ApEn value would on average equal the median subject ApEn value). A value of nAprank_{fin} substantially below 0.5 would indicate a final date ApEn value that is among the lowest of that subject's ApEn values.

We also calculated both the percentage of subjects for which ApEn_{1} > ApEn_{fin} and the percentage of subjects for which ApEn_{vmax} > ApEn_{fin}, as another pair of assessments to evaluate the hypothesized very regular GH dynamics at the final test date.

### Statistical Analysis

All statistical comparisons below for discrimination between two groups employed the two-sided *t*-test with unknown variance. Linear correlation was assessed via the Pearson *r *statistic. One-way ANOVA was performed as we have discussed.

## RESULTS

Representative longitudinal ApEn(GH) and GrVel plots for four boys are shown in Fig. 1. In Fig. 2, representative GH serum concentration-time series are shown for the five indicated study dates for the boy whose longitudinal ApEn values are depicted in Fig. 1
*A*.

As summarized in Table 1 and displayed in Fig. 3
*A*, the comparison of raw ApEn values at the five study dates*t*
_{1},*t*
_{early},*t*
_{max},*t*
_{late}, and *t*
_{fin} showed the largest irregularity at *t*
_{early} and a minimum ApEn (greatest orderliness) at *t*
_{fin} (ANOVA,*P* < 0.0001). The corresponding analyses based on the standardized (*z*-transformed) ApEn values show the same general pattern of evolution (Table 1, Fig. 3
*B*), with the same significance (*P* < 0.0001). In addition, the standardized data analysis indicates a slight, although not statistically significant, rise in ApEn values at*t*
_{max} compared with *t*
_{1}, following the maximum at *t*
_{early}.

To further evaluate longitudinal curve characteristics, assessing increases in GH irregularity from study onset to the time of maximal GrVel showed that, pooled, ApEn_{i} > ApEn_{1} for 64% of dates *i* <*t*
_{max}. Assessment of decreases in GH irregularity from the time of maximal GrVel to study completion indicated that, pooled, ApEn_{i} < ApEn_{vmax} for 90% of dates *i* >*t*
_{max}.

Table 2 indicates the linear correlation between ApEn_{i} and GrVel_{i}
_{-N} for each of*N* = 1, 2, 3, −1, −2, and −3 for the pooled ensemble data, both raw and standardized. All the indicated correlations are positive, with high significance (*P* < 10^{−10}for all but the lag +3 correlations). For both standardized and raw data comparisons, the largest positive correlation between ApEn_{i} and GrVel_{i}
_{-N} was seen for the lag −1 data (standardized Pearson *r *= 0.510, raw data Pearson *r *= 0.494), with next largest positive correlation seen for the lag −2 data (standardized Pearson *r *= 0.487, raw data Pearson *r *= 0.467). Interestingly, both lag −1 and lag −2 data show more pronounced positive correlation than lag 0, and, importantly, all negative lag correlations (ApEn leading GrVel comparisons) were larger than any positive lag correlation.

In general, on a per-subject basis, correlation is generally moderately large and positive for each of the studied lags. Table3 summarizes the per-subject correlations of ApEn to GrVel at the indicated lags. For time lags −3, −2, −1, and 0, 91% of the correlations were positive; for time lag 0, 87% were positive; for time lag +2, 83% were positive; and for time lag +3, 65% of the per-subject correlations were positive. From an alternative viewpoint, the percentages of subjects with linear correlations that were ≥0.4 (and positive) were 74% for lags −1 and −2; 65% for lags 0 and +1; 56% for lag −3; 48% for lag +2; and 13% for lag +3.

As another calculation pertinent to determining whether ApEn leads or follows GrVel, define *t*
_{Apmax} as the study date with maximal ApEn value. We found that*t*
_{Apmax} < *t*
_{max} for 18 of 23 subjects, indicating that maximal ApEn values occurred earlier than maximal GrVel in 78% of subjects. As well, for three of the remaining five subjects, *t*
_{Apmax} is either only one or two test periods (4–8 mos) delayed from*t*
_{max}.

Final date ApEn values were quite low. As seen in Table 1, cross-sectional ApEn_{fin} = 0.380 ± 0.152 is approximately one-half of ApEn at*t*
_{early} = 0.786 ± 0.186. Thus the difference in the relative orderliness of GH release between early puberty to midpuberty and maturity is great. This is suggested by and consistent with the longitudinal plots shown as Fig. 1. However, the degree to which final-date ApEn values are low (GH secretion quite regular) relative to maximal growth date is most evident by per-subject analysis via calculation of the nAprank_{fin} values described above. The mean nAprank_{fin} (over the 23 subjects) of 0.1269, i.e., the 13th percentile, is smaller (*P* < 10^{−10}) than the expected mean nAprank_{fin} of 0.5 under the null hypothesis. Moreover, for 9 of the 23 subjects, the final date had the lowest ApEn, whereas for five additional subjects, the final date was either second or third lowest.

Complementary evidence of the apparently very regular GH dynamics at the final test date is that ApEn_{1} > ApEn_{fin} for 96% of subjects, whereas ApEn_{vmax} > ApEn_{fin} for 100% of subjects.

## DISCUSSION

Summarizing the results, we have established that on a per-subject basis, 24-h serum GH concentration time series show pronounced variation in their sequential irregularity transpubertally, with maximal secretory disorderliness (ApEn) in pre- and mid-to-late puberty, followed by a steep decline in ApEn to maximal orderliness in postpubertal adolescence. Moreover, we determined that, in general, ApEn(GH) elevations precede GrVel increases, with a time-frame lead of one to two study periods (4–8 mo) providing the most pronounced correlations, as seen in Tables 2 and 3. This time delay is also consistent with visual inference given by Fig. 1, and by the finding that for 78% of boys, the date of maximal ApEn preceded that of maximal GrVel. As discussed below, there may be added clinical and experimental utility in knowing that high ApEn(GH) values typically predict high GrVel values in 4–8 mo, beyond the strictly diagnostic or confirmatory perspective that positive unlagged correlation conveys.

Statistically, per-subject standardization sharpens the (lagged and led) correlations between ApEn and GrVel by a modest, albeit significant, amount compared with raw data comparisons. More notably, one critical utility of the longitudinal study design applied here is to clarify that the hormonal dynamics precede the (accelerated) physical growth. In contrast, whereas the cross-sectional study in Ref.29 gives qualitatively relatively similar results regarding ApEn(GH) evolution with increasing age (compare Fig. 1 of Ref. 29 with Fig. 3here), the data available in Ref. 29 preclude any direct comparison of hormonal dynamics, e.g., ApEn, with either GrVel or an alternative measure of physical growth.

Of course, it is imperative to note that growth is a multifactor-dependent phenomenon, and that the present analysis reflects only one correlate (GH), albeit an important one. We anticipate that, ultimately, forecasts based on multiple physiological (including hormonal) characteristics will provide enhanced accuracy in predicting periods of very rapid linear growth. To reinforce this point, in modeling the growth velocity of these boys, we have found marked effects of testosterone concentration in addition to the mean GH level (32). In addition to age (either chronological or bone), the interaction between the mean GH level and testosterone concentration has a significant effect on the GrVel. The maximal rise in circulating testosterone concentration (and perhaps its conversion to biologically effective estrogens) precedes the maximal mean GH concentration and peak GrVel by ∼3 mo (32), commensurate with the findings of the present study.

The longitudinal analyses allow a first-order, clinically applicable, predictive relationship between ApEn and GrVel. Across all subjects, an ApEn value of >0.8 for the 24-h GH time series (which occurred in ∼20% of measurements) produced a mean GrVel in the subsequent measurement period of 7.33 ± 2.95 cm/yr, which is significantly larger than the overall mean GrVel, which is 5.43 ± 3.36 cm/yr (*P* < 0.0001). The GrVel of 7.33 cm/yr is the 68th percentile of pooled GrVel values. The decision rule that an ApEn value >0.8 generally predicts a high GrVel in the next 4-mo period is relatively easy to implement in potential applications, in that it is an overall population rule (rather than a per-subject determinant), thus incorporating cross-subject variation.

ApEn values of GH time series on each boy's final test date (0.380 ± 0.152) were insignificantly different (*P*> 0.4) from comparable 20-min sampled GH ApEn values (0.425 ± 0.183) in healthy young men (mean age 25 yr; age range 22–28 yr) reported in Ref. 13. Thus we infer that, from a secretory irregularity perspective, in the present analysis, healthy postpubertal boys exhibit a fully mature GH subnetwork by the mean per-subject final study age of 17.3 (±0.9) yr.

One issue should be clarified concerning statistical study design. For statistical reasons, we chose to avoid fitting unimodal functions (or splines) to either the ApEn or GrVel longitudinal data. In principle, if such best-fit functions were established, then characteristics of each curve, such as the date of maximal growth rate from such a GrVel curve, could be inferred algebraically. However, given the nonmonotonicity of each of ApEn and GrVel as a function of time (see comments in *Analytical Strategy*), we expect that such fitting procedures could produce somewhat equivocal or arbitrary results. Indeed, the ApEn-GrVel correlations as assessed herein provided a robust, and we believe biologically realistic, quantification of the association of ApEn and transpubertal growth.

### Neuroendocrine Considerations

We have previously linked ApEn changes to a mechanistic understanding via theoretical modeling studies (11,18). In particular, for diverse mathematical network models, greater regularity (lower ApEn) typically corresponds to greater component and subsystem autonomy and, conversely, greater irregularity corresponds to increased external influences, increased coupling strength, and/or accelerated positive feedback. On the basis of the present analysis, we thus propose that the increased GH irregularity observed before and near peak GrVel reflects more critical interacting factors within the GH feedback axis, or a greater intensity of particular interactions, e.g., among GHRH-SRIH-GH-IGF-I. Specific, yet distinct, mechanistic explanations consistent with this interpretation are proposed and discussed in Ref. 29, although as noted there, further clinical and interventional studies will be required to distinguish among several theoretically plausible alternatives. Additionally, the very low ApEn values seen at maturity are consistent with a relatively closed GH subnetwork, in which some of the inter-system interactions that are enhanced in puberty have diminished substantially.

Two additional clinical investigations (29) support the hypothesis that estradiol in particular, or testosterone acting after its aromatization to estradiol, can govern the feedback regulation of GH release during puberty and in young adulthood. In the first study, clinical experiments in prepubertal girls with gonadal dysgenesis (Turner's syndrome) showed that treatment with a small dose of ethinyl estradiol orally for 5 wk increases GH ApEn significantly. In the second study, ApEn of GH increased in response to short-term parenteral testosterone administration to clinically prepubertal boys with constitutionally delayed adolescence, yet showed no increase upon treatment with a nonaromatizable androgen, 5 α-dihydrotestosterone (DHT).

A minority of children born with intrauterine growth retardation have a propensity for the metabolic syndrome as adults (2). Theoretically, the disordered intrauterine environment had reprogrammed intermediary metabolism. Large doses of GH given for 2 yr leads to marked catch-up growth in the majority of those who fail to catch up on their own. Those that do catch up to their target height percentile often remain along that growth trajectory even without additional GH. One interpretation of this observation is that the metabolic syndrome is again reprogrammed toward normalcy by this treatment. It is likely that altering GH secretion is pivotal in this extrauterine treatment phase. Analyses such as those discussed in this report may then provide explicit numerical support of the hypothesis that feedback mechanisms have been altered in this metabolic reprogramming.

### Potential Applications and Follow-Up Studies

Some follow-up studies are suggested by the present findings. For example, clinically one would like to predict, as well as possible, stature at maturity, and as an important intermediate point, the time of maximal linear growth. In addition to GH input, one might develop a multivariate predictive model utilizing concurrent (e.g., testosterone, IGF-I, and/or estradiol) measurements when they are available. Furthermore, if time-series data per study date became available for two or more hormones, e.g., GH and testosterone, one could calculate cross-ApEn values (19, 21) on paired hormonal time series to determine changes in bihormonal synchrony across the peripubertal years. Such information could aid in determining effective intervention modalities, e.g., whether and when treatment with testosterone would be necessary to augment linear growth.

Additionally, there may be practical applicability in determining whether administering GH on the basis of some secretory irregularity threshold, e.g., current ApEn(GH) >0.8, achieves more efficient growth per unit GH dosage compared with dosages given either at random times or uniformly over a longer regimen.

Whether the ApEn variations in GH across pubertal development are unique to the somatotropic axis, or also apply to other hormonal subsystems transpubertally, is not yet known. An earlier finding is that aging well beyond the young adult years results in a slowly increasing rise in GH ApEn (28), indicating a progressively more disorderly GH release pattern, also seen for luteinizing hormone/testosterone (19), ACTH/cortisol (27), and insulin (8). Hence, one could hypothesize that ApEn changes in hormonal secretory patterns may in part detect broader alterations in neuroregulatory control.

The present study was conducted in healthy boys only. Accordingly, the extent to which analogous secretory irregularity changes are present in boys with growth-related pathophysiology, in young girls in the peripubertal time frame, and in nonhuman species remains a very important, yet open, area for future research.

## Acknowledgments

We thank Sandra Jackson and the nursing staff at the General Clinical Research Center for their expert patient care, Melanie Bishop Harlow and Margaret Wood Ball for research coordination, and Catherine Kern and Ginger Bauler for technical assistance with the assays. Our long-term colleague Dr. Robert M. Blizzard is acknowledged for foresight and for development of the concept and the patient protocol. We thank a large number of pediatric endocrine fellows at the University of Virginia for the clinical care of the boy subjects. Without the remarkable generosity of these boys and their parents, the studies could not have been completed.

## Footnotes

This work was supported in part by National Institutes of Health (NIH) NCRR Grant RR-00847 (to the Clinical Research Center of the University of Virginia); NIH National Institute of Child Health and Human Development Research Career Development Award 1-KO4-HD-00634 (to J. D. Veldhuis); the University of Virginia Pratt Foundation; the National Science Foundation (NSF) Center for Biological Timing (NSF Grant DIR-89–20162); NIH U-54 Specialized Cooperative Centers Program for Reproduction Research (NICHD) HD-28934; Postdoctoral Research Training in Diabetes and Hormone Grants 5T32-DK-07320 and DK-07642 (to the University of Virginia); NIH National Institute on Aging R01 AG-14799 and R03 AG-14873 (to J. D. Veldhuis); and NIH R01 HD-32631 (to A. D. Rogol).

Address for reprint requests and other correspondence: S. M. Pincus, 990 Moose Hill Road, Guilford, CT 06437 (E-mail:stevepincus{at}alum.mit.edu).

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- Copyright © 2000 the American Physiological Society