Secretory process regularity monitors neuroendocrine feedback and feedforward signaling strength in humans

¹ Division of Endocrinology, Departments of Internal Medicine and Pharmacology, General Clinical Research Center, Center for Biomathematical Technology, University of Virginia School of Medicine, Charlottesville 22908-0202; ² Endocrine Section, Medical Service, Salem Veterans Affairs Medical Center, Salem 24153; ³ Geriatrics and Extended Care Service, McGuire Veterans Affairs Medical Center, Richmond, Virginia 23249; ⁴ Endocrine Section, Medical Service, Veterans Affairs Medical Center, Ann Arbor, Michigan 48105; and ⁵ Guilford, Connecticut 06437

	ABSTRACT

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The present experiments examine the neuroregulatory hypothesis that the degree of sample-by-sample regularity of hormone output by an interlinked hypothalamopituitary target-organ system monitors the strength of feedback and/or feedforward signaling. To test this postulate and assess its generality, we implemented a total of nine thematically complementary perturbation experiments. In particular, we altered feedback or feedforward signaling selectively in two distinct neuroendocrine systems; namely, the growth hormone (GH) insulin-like growth factor type I (IGF-I) and the luteinizing hormone-testosterone axes. Four experimental paradigms comprised preferential reduction vs. enhancement of IGF-I or testosterone feedback signal strength; and, conversely, five others entailed selective attenuation vs. augmentation of GH-releasing hormone and gonadotropin-releasing hormone feedforward signal intensity. In these independent interventions, quantitation of subordinate (nonpulsatile) secretory pattern reproducibility via the approximate entropy statistic unmasked salient changes (P values typically <10³) in the conditional regularity of serial hormone output with high consistency (96-100%). In particular, approximate entropy quantified degradation of secretory subpattern orderliness under either muted feedback restraint or heightened feedforward drive. Assuming valid interpretation of the biological constraints imposed, these experimental observations coincide with earlier reductionist mathematical predictions, wherein increased irregularity of coupled parameter output mirrors attenuated feedback and/or augmented feedforward coupling within an integrative system.

neuroregulation; growth hormone; luteinizing hormone; insulin-like growth factor type I; testosterone; thyrotropin; thyroxine; ACTH; cortisol; hormone

	INTRODUCTION

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UNDER PHYSIOLOGICAL CONDITIONS, neuroendocrine axes are believed to operate as complex feedforward and feedback control systems (55, 66). For example, in the case of the growth hormone (GH) insulin-like growth factor type I (IGF-I) axis, hypothalamic peptidergic signals exert stimulatory or inhibitory effects on anterior pituitary somatotropes, and secreted GH and IGF-I impose time-delayed negative feedback on hypothalamopituitary feedforward drive (7, 11). Likewise, in relation to the male and female reproductive axes, the arcuate-nucleus neuropeptide gonadotropin-releasing hormone (GnRH) activates pituitary secretion of luteinizing hormone (LH), which stimulates gonadal sex-steroid hormone production. Androgens and estrogen, in turn, feed back negatively to restrain output of the GnRH-gonadotrope unit (8, 23, 54). Such dynamically coupled neuroendocrine systems presumptively achieve homeostasis via axis-specific, nonlinear, time-delayed, and dose-responsive feedback and feedforward linkages. An implicit corollary thesis is that such interactive properties dictate the unique time-dependent secretory patterns of each axis (22). According to this perspective, pathophysiological disruption of hormone secretion could arise from defects within a control locus itself and/or by way of failure of internodal (pathway level) communication (40, 42, 62).

Assessing alterations in the behavior of integrated biological networks is critical, especially to an understanding of pathophysiology. Unfortunately, direct experimental assessment of complex systems is generally remarkably difficult, particularly in multinodal neuroendocrine axes (1, 2, 6, 9, 23, 33, 40-42, 45, 62). Full or multisite network data are rarely available. Moreover, even when several network components are measurable simultaneously, acquiring multiple concurrent data sets may be prohibitively expensive and/or invasive, thereby limiting analyses and/or disrupting normal system behavior. Yet quantitation of system-level change is crucial to elucidating the nature of potential network disruptions, whether due to alterations in feedback and/or feedforward signaling pathways (34, 35). Thus an important issue in integrative physiology is whether one can appraise system feedback changes indirectly and in a statistically valid manner simply by observing a single variable.

Thematically, the approximate entropy (ApEn) measure quantifies feedback changes within a closed but interactive system, as validated in several reductionist mathematical contexts (23, 33, 34, 39, 41). ApEn is a two-parameter family of regularity statistics, designed to contrast the degree of subordinate regularity in system output, as quantified by subpattern reproducibility in time series (METHODS). In various numerically coupled model forms, the quantifiable irregularity (and, thus ApEn) of signal output increases with increasing positive feedback and, conversely, decreases with increasing negative feedback (DISCUSSION). On the basis of this background, herein we examine whether quantitation of secretory pattern orderliness with ApEn can monitor feedback alterations in a variety of human neuroendocrinologic networks. In corollary, we explore how consistently ApEn-quantified changes in serial hormone regularity match theoretical predictions.

	METHODS

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Overview

The following published experiments were used to examine the utility of ApEn to discriminate differences in the orderliness of hormone secretory patterns induced by selected experimentally imposed variations in feedback and/or feedforward signaling: 1) exogenously imposed feedback enhancement, as achieved by constant peripheral intravenous infusion of IGF-I to suppress GH production (19) and of testosterone to repress pulsatile LH secretion (64); 2) muted endogenous negative feedback signaling, as accomplished in the GH axis by systemic IGF-I depletion (3) and in the GnRH-LH axis by inhibition of testosterone biosynthesis (64, 67); 3) augmented exogenous feedforward drive, as imposed by pulsatile fixed-dose and fixed-interval intravenous infusions of the hypothalamic releasing factors GH-releasing hormone (GHRH) or GnRH to augment GH and LH output (17, 30); and 4) attenuated endogenous hypothalamic feedforward input, as enforced by infusion of somatostatin or a selective peptidyl antagonist of the GHRH receptor in the GH axis and of a downregulating agonist of the GnRH receptor in the case of the LH axis (18).

Specific Clinical Protocols

IGF-I and testosterone feedback augmentation. Serum GH concentration time series were obtained by frequent (10 min) blood sampling for 24 h during paired and randomly ordered saline vs. recombinant human (rh) IGF-I infusions (10 µg · kg¹ · h¹) in eight young men and seven young women, as published earlier (19). No ApEn data have been reported for these studies. Serum GH concentrations were quantitated in each sample by ultrasensitive chemiluminescence-based assay, which detected GH in all samples (15, 60).

Serum LH concentration profiles were obtained by sampling blood every 10 min during the second 24 h of the randomly ordered administration of placebo or 1,600 mg ketoconazole (KTCZ) given orally daily for 48 h in eight healthy young men to block androgen biosynthesis. In a subset of six individuals, a continuous intravenous infusion of saline or 8.0 mg testosterone was used to replete androgen during KTCZ ingestion (64, 67). LH was measured by two-site immunoradiometric assay (IRMA) (53).

IGF-I and testosterone feedback withdrawal. Plasma IGF-I concentrations were lowered experimentally in eight young midluteal-phase women by imposing a 2.5-day fast (3). Blood was sampled every 10 min during the last 24 h of the randomly ordered paired fed vs. fasting sessions. Serum GH concentrations were measured by chemiluminescence assay (above).

GHRH and GnRH feedforward augmentation. GHRH feedforward was accentuated in 19 men by infusing GHRH (0.33 µg/kg bolus) vs. saline intravenously every 90 min for 3 days. Blood was sampled at 10-min intervals for 24 h on the third day for later chemiluminescence-based assay of serum GH concentrations (17).

GnRH's stimulation of LH secretion was augmented in five other young men by pulsatile infusion of this decapeptide (100 ng/kg bolus) vs. saline given intravenously every 90 min for 14 days via a portable pump. LH was assayed by IRMA in sera collected every 10 min for 24 h on day 14 (30).

GHRH and GnRH feedforward inhibition. GHRH feedforward was antagonized by a bolus intravenous injection followed by continuous infusion of a specific antagonist of the GHRH receptor or saline for 8 h overnight in six young men (18). In other experiments, GHRH feedforward was opposed via a constant 3-h intravenous infusion of somatostatin-14 (30 ug · 1.73 m² · h¹) in 10 postmenopausal women (5). Serum GH samples were collected every 10 min and later assayed by chemiluminescence (above).

GnRH feedforward was impeded in six young men by subcutaneous injection of an LH-downregulating dose of a long-acting GnRH agonist (leuprolide acetate 3.75 mg) 3-4 wk before blood sampling. Blood was withdrawn at 10-min intervals for 12 h (0800-2000). Serum LH concentration time series were compared with those obtained in 13 other age-matched, saline-treated men, who underwent an identical blood-sampling protocol. Serum LH concentrations were measured by IRMA (31, 53).

All samples contained uniformly detectable serum GH or LH concentrations in each of the above nine studies.

ApEn

ApEn is a translation- and scale-independent regularity measure that quantifies the serial regularity or degree of recurrence of subordinate patterns in both mathematical sequences and empirical time series (33, 34, 39, 41). Precisely, ApEn is a model-free, two-parameter family of statistics: ApEn (m, r), with m a run length, and r, a de facto tolerance width (see Refs. 33 and 41 for practical examples). ApEn parameters of m = 1 and r = 20% of each intraseries standard deviation (SD) were used here for 24-h 10-min data, as previously described for various neurohormone profiles of this length (12, 17, 27, 38, 40, 56, 61, 63). Corresponding values of r were applied for shorter time series, as recently validated (40). ApEn monitors sample-by-sample irregularity and is thus distinguished from conventional analyses of pulsatility, circadian rhythmicity, or short-term (ultradian) periodicity (4, 50, 51, 56, 62). Higher ApEn values denote greater irregularity (or higher process randomness) of repetitive (successive) measurements as reported for the following: GH, ACTH, and prolactin time series in patients with acromegaly, Cushing's Disease, and prolactinomas compared with age- and sex-matched controls (12, 46, 65); GH patterns in boys in mid-to-late puberty and in boys and girls after sex-steroid hormone administration (10, 32, 43, 61, 63); GH secretion in females compared with males (13, 38, 61, 63); and ACTH, LH, GH, cortisol, testosterone, and insulin time series in aging vs. younger humans (17, 27, 28, 42, 43, 56, 60).

Statistics

Because the distribution of ApEn values is asymptotically normal (33), ApEn data were compared via the two-tailed Student's t-test with unequal variance to evaluate within- or between-subject contrasts. Primary inferences were confirmed by the nonparametric Wilcoxon signed-rank or rank sum test. Time series were also shuffled (randomly reordered without replacement) 1,000 times to generate a surrogate null distribution of "random ApEn" values.

	RESULTS

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Figure 1A depicts the impact of continuously infused saline or rh IGF-I on ApEn of 24-h serum GH concentration profiles in healthy young women and men. During saline infusion, mean GH ApEn was higher in women than men (P < 10³), confirming the previous gender distinction in this axis (12, 38, 61, 63). Intravenous rh IGF-I infusion lowered GH ApEn significantly in all seven women (P = 0.0156), with an analogous but nonsignificant trend in men (P = 0.088), again denoting a sex difference. Lower ApEn values indicate more regular GH release, here attributable to exogenously imposed IGF-I negative feedback. Figure 1B shows the corresponding impact of continuous intravenous infusion of testosterone on LH ApEn in acutely hypoandrogenemic men (METHODS). LH ApEn decreased in all six volunteers in response to enforced androgen negative feedback (P = 0.012), thus defining more orderly LH secretion patterns.

View larger version (20K): [in this window] [in a new window]   Fig. 1.   A: impact of randomly ordered intravenous infusions of saline (control) and recombinant human insulin-like growth factor type I (IGF-I) (10 µg · kg1 · h1) on paired growth hormone (GH) approximate entropy (ApEn) values in 7 women and 8 men sampled every 10 min for 24 h. B: influence of randomly ordered constant intravenous infusions of saline [ketoconazole (KTCZ)] or testosterone (KTCZ and testo) on paired luteinizing hormone (LH) ApEn measures in 6 young men treated with KTCZ for 48 h to block androgen production and then sampled every 10 min for 24 h. Numerical values are group means ± SE.

Figure 2A presents paired GH ApEn values in the fed (and, hence, IGF-I replete) state vs. fasting (IGF-I deprived) context in eight women. Fasting increased GH ApEn in all subjects, identifying greater irregularity of GH secretion (P = 0.0005). Figure 2B presents paired LH ApEn values in eight young men administered the steroidogenic inhibitor KTCZ (vs. placebo) to withdraw negative feedback by testosterone (64, 67). Hypoandrogenemia increased LH ApEn in seven of eight volunteers (P = 0.0062).

View larger version (18K): [in this window] [in a new window]   Fig. 2.   A: within-subject rise in GH ApEn in 8 young midluteal-phase women evaluated when IGF-I replete (fed) and after short-term fasting to reduce systemic IGF-I negative feedback. B: paired LH ApEn data in 8 healthy men administered placebo (control) or KTCZ for 48 h to block testosterone biosynthesis. Volunteers underwent blood sampling at 10-min intervals for 24 h. Data are group means ± SE.

Figure 3A depicts paired GH ApEn values in men infused with pulses of GHRH or saline intravenously every 90 min for 3 days. Exogenous GHRH drive augmented GH ApEn in 18 of 19 volunteers (P < 10⁴). Analogously, Fig. 3B gives paired LH ApEn values in volunteers infused with fixed pulses of GnRH or saline intravenously at 90-min intervals for 14 days. The exogenous GnRH "clamp" elevated LH ApEn in all five subjects (P = 0.036).

View larger version (20K): [in this window] [in a new window]   Fig. 3.   A: paired GH ApEn values in 19 men administered intravenous saline or pulsatile GH-releasing hormone (GHRH) (0.33 µg/kg) every 90 min for 3 days in randomized order. B: LH ApEn values in 5 young men infused intravenously in random order with saline or gonadotropin RH (GnRH) pulses (100 ng/kg) every 90 min for 14 days. Data values are group means ± SE.

Figure 4A reports calculated GH ApEn values during intravenous infusion of saline or a selective GHRH-receptor antagonist peptide. Serum GH concentrations during the last 6 h of sampling fell by ~60-85% during antagonist infusion. Neither of two statistical expressions for GH ApEn (mean observed ApEn or mean ratio of observed-to-random ApEn) changed significantly. Continuous intravenous infusion of somatostatin, a negative feedback signal on GH secretion, suppressed GH output by a mean (±SE) of 89 ± 6% and lowered GH ApEn in 8 of 10 postmenopausal women (P = 0.011) (Fig. 4B). Disabling GnRH feedforward input by prior injection of a GnRH agonist (leuprolide) compared with saline yielded a higher mean LH ApEn (P = 0.0052) and elevated the ratio of observed-to-random LH ApEn (P < 10⁴) (Fig. 4C).

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Effects of intravenous infusion of a GHRH-receptor antagonist (A) or somatostatin (SS 30; B) vs. saline, or of prior intravenous injection of a downregulating GnRH agonist (C), on GH ApEn (A and B) and LH ApEn (C), respectively, in healthy adults (METHODS). Data are presented in 2 complementary forms; viz., as individually observed ApEn values (top) and as ratios of observed-to-random ApEn (bottom). Values are group means ± SE.

	DISCUSSION

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The present interventional analyses show that experimental reduction of IGF-I negative feedback increases the serial irregularity of GH release. Likewise, muting of testosterone negative feedback increases the irregularity of sample-by-sample LH secretion. Conversely, imposition of the foregoing axis-relevant feedback signals (e.g., by continuous intravenous infusion of IGF-I or testosterone) consistently reduced the irregularity of GH and LH output patterns. In aggregate, for the 30 subjects studied in four experiments, the sensitivity of ApEn to detecting a negative feedback perturbation, whether damped or heightened, was 97%. Accordingly, we infer that negative feedback signaling strength within the GH-IGF-I and LH-testosterone axes strongly governs the quantifiable regularity of hormone secretory subpatterns.

The impact of altered feedforward drive on the orderliness of hormone secretion patterns was studied conversely; i.e., by imposing fixed GHRH and GnRH input stimuli and by opposing endogenous GHRH and GnRH actions. In the first experimental paradigm of enforced "overdrive," unvarying exogenous GHRH and GnRH pulses consistently increased ApEn (i.e., degraded the regularity) of the resultant GH and LH secretory output profiles. In the 24 subjects studied, the sensitivity of ApEn to detecting predicted regularity changes was 96%. In the second experimental paradigm of blunted GHRH and GnRH feedforward, administration of a downregulating GnRH-receptor agonist, albeit not infusion of an antagonist of the GHRH receptor, markedly attenuated the orderliness of subsequent LH release (P = 0.0052). Accordingly, three of the foregoing perturbation models that supplant endogenous adaptive signaling indicate that both externally fixed feedforward inputs and antagonism of intrinsic feedforward drive disrupt the regularity of GH and LH secretion.

The notion of feedback-dependent control of the subordinate pattern regularity of neurohormone time series was foreshadowed in an earlier analysis of the thyrotropin (TSH)-thyroidal axis. In this study, increased irregularity of 24-h serum TSH concentration profiles in hypothyroid men was reversed by imposing axis-specific negative feedback with L-thyroxine (P = 0.013) (58). In analogy, in the salt-sensitive renin-angiotensin system, short-term sodium restriction induced, whereas acute salt excess repressed, irregularity in 24-h renin secretory patterns in 11 of 12 time series so studied [unpublished analysis (52)]. In a third neuroendocrine context, primary gonadal failure elevated ApEn of 24-h follicle-stimulating hormone (FSH) release, whereas testosterone repletion normalized disorderly FSH output in all six men (59). Accordingly, ApEn analyses of a variety of distinct neuroendocrine feedback models (i.e., the GH, LH, TSH, renin, and FSH axes) indicate that the (quantifiable) reproducibility of serial hormone release patterns mirrors axis-relevant positive and negative feedback signal strength with high sensitivity (96-100%).

If the foregoing (11 separate) observations are correct and generalizable, then the apparent failure of a selective GHRH-receptor antagonist to modify GH ApEn (given significant suppression of GH release) could indicate that other nonGHRH agonistic or antagonistic signals maintain the subpattern regularity of GH secretion. In relation to other agonists, one plausible GH cosecretagogue is the recently cloned GH-releasing peptide Ghrelin (14, 25). As a pertinent GHRH antagonist, somatostatin is likely to be the critical inhibitory signal. Indeed, somatostatin infusions markedly enhanced GH regularity (Fig. 4B), consistent with a model wherein negative feedback augments orderliness. However, we cannot fully exclude incomplete suppression of endogenous GHRH drive achieved by this dose or schedule of administration of the GHRH-receptor antagonist. The last consideration would be consistent with a recent analysis of ApEn after high-sensitivity immunofluorescence assay of 24-h GH profiles in two siblings harboring a profound loss-of-function (7th intron splicing junction) mutation of the GHRH receptor. Both patients exhibited markedly elevated GH ApEn values (namely, each 5 SDs or P < 10⁶ vs. gender, body mass index, and age-matched controls) (F. Roelfsema, J. D. Veldhuis, unpublished data).

The current experiments highlight the utility of a statistically validated regularity measure to monitor variations in the strength of neuroendocrine axis-relevant feedback and feedforward control signals. Whether this inference is applicable to other integrative physiological systems is not established. However, in the stress-adaptive corticotropic axis, glucocorticoid feedback signal intensity strongly modulates the sample-by-sample orderliness of ACTH secretion. Specifically, metyrapone and KTCZ induced hypocortisolemia-stimulated ACTH secretion by 8- to 35-fold and reduced ApEn of the resultant ACTH release profiles in all 23 subjects (16, 57). The fall in ApEn signifies greater regularity of corticotropin release during relief of glucocorticoid negative feedback. The direction of this ApEn change contrasts with that in the GH, LH, TSH, renin, and FSH axes. Although the mechanistic basis for this neuroregulatory distinction is not known, it is not attributable simply to the large magnitude of stimulated ACTH secretory output, because the ApEn metric in mathematical terms is largely scale invariant and translation independent (METHODS). The orderliness of parathyroid hormone (PTH) secretion is likewise enhanced by withdrawing negative feedback, in this case by lowering the ionized calcium concentration, and conversely (47-49). On the basis of these several findings, we speculate that the unique multivalent feedforward and feedback properties of any given adaptive biological network confer their direction of regularity change. For example, the corticotropic axis is regulated by dual repressive actions of adrenal cortisol on hypothalamic and pituitary sites and complex feedforward synergy of hypothalamic arginine vasopressin and corticotropin-releasing hormone on corticotrope-ACTH secretion (7, 24, 26, 44). Precisely which dynamic network properties of this homeostatic system explicate its directionally specific regularity features are not yet evident. In any case, for both the ACTH and PTH axes, a quantifiable alteration in the orderliness of serial hormone output consistently monitors a change in cognate feedback signal strength, identified in an axis-specific direction.

Theoretical formulations of two- or three-parameter-coupled mathematical systems indicate that relative nodal isolation, or greater autonomy of variables in feedback-linked equations, enhances the orderliness of numerical outputs (34, 41). Such reductionist models thematically mirror the foregoing findings in the ACTH and PTH axes, wherein feedback withdrawal (i.e., reduced parameter coupling) facilitates time series regularity. By extension, our observations across multiple axes are consistent with the more general hypothesis that the particular structural linkages within an adaptive biological network further specify the directionality of ApEn changes induced by feedback and/or feedforward modulation (37). Additional intervention experiments and more refined network-based models of multivalent neurohormone ensembles will be required to verify this notion and to clarify the particular mechanistic basis of system-specific diversity of homeostatic control. For example, one simplified stochastic differential equation construct of the multicoupled GnRH-LH-testosterone feedback/feedforward axis predicted that withdrawal of androgen-negative feedback on GnRH and LH signaling outputs would increase the irregularity of LH and testosterone secretion, as observed empirically in healthy aging men and experimentally in KTCZ-treated (androgen withdrawn) young individuals (20-23, 29, 30, 42; D. M. Keenan, J. D. Veldhuis, unpublished observations).

In summary, the present perturbation experiments and regularity analyses demonstrate that axis-specific feedforward or feedback activity closely supervises the orderliness of resultant secretory patterns in several distinct neuroendocrine contexts. Comparisons of different hormone axes (DISCUSSION) would further suggest that the unique algorithmic structure of an adaptive neuroregulatory network specifies the actual direction of the regularity change. According to this interpretation, we hypothesize that the quantifiable orderliness of a biological time series monitors changes in within-axis signaling strength with the regularity directional preference dictated by the specialized integrative properties of the system. Further exploration of this emergent concept may aid in clarifying the mechanistic basis of selected physiological adaptations and pathophysiological perturbations in feedback and/or feedforward control in complex neurohormone networks.

Perspectives

In several rather different closed mathematical model systems (e.g., coupled logistic, autoregressive moving-average, and composite stochastic-deterministic equations), uncoupling of parameter interactions consistently increases ApEn of the simulated output signal (34, 41). In such more tractable theoretical networks, higher-series ApEn (and, hence, greater irregularity) denotes erosion of feedback control. Conversely, in these simplified model forms, lower ApEn (greater series orderliness) identifies higher-parameter coordination due to stronger negative feedback loops. The present in vivo interventional analyses corroborate such reductionistic inferences in a variety of highly complex neuroendocrine systems; i.e., the GH, LH, TSH, renin FSH, ACTH, and PTH axes. In particular, we show that altered positive or negative feedback signaling modifies ApEn consistently in an axis-specific manner. The axis-relevant directionality of the ApEn change suggests to us that the unique adaptive control properties of any particular physiological system govern the relevant direction of regularity shifts (23, 36). According to this evolving perspective, more detailed analyses of the dynamic features of feedback- and feedforward-interlinked axes should advance our mechanistic understanding of the basis for system-specific homeostatic control. New insights in this challenging arena should also help to clarify the nature of the physiological factors that drive, as well as the putative pathophysiological processes that disrupt, complicated composite stochastic and deterministic systems in health and disease.

	ACKNOWLEDGEMENTS

We thank P. Craig and O. Veldhuis for skillful preparation of the manuscript; P. P. Azimi for the ApEn analysis, data management, and graphics; B. Grisso and G. Bauler for performance of the immunoassays; and S. Jackson and the expert nursing staff at the University of Virginia General Clinical Research Center for conducting the research protocols.

	FOOTNOTES

This work was supported in part by National Institutes of Health (NIH) Grant MO1-RR00847 to the General Clinical Research Center of the University of Virginia Health Sciences Center, National Institute on Aging AG-14799 (to J. D. Veldhuis), NIH Small Business Innovative Research Award (to S. Pincus and J. D. Veldhuis), NIH Specialized Cooperative 454 Center HD-28934, and Veterans Affairs Merit Review awards (to T. Mulligan, A. Iranmanesh, J. D. Veldhuis, and A. Barkan).

This focused analysis necessarily omits many references because of editorial constraints. The authors therefore acknowledge numerous colleagues, who have made earlier observations foundational to the concepts considered here.

Address for reprint requests and other correspondence: J. D. Veldhuis, Division of Endocrinology, Dept. of Internal Medicine, P. O. Box 800202, Univ. of Virginia School of Medicine, Charlottesville, VA 22908-0202 (E-mail: JDV{at}Virginia.Edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 11 August 2000; accepted in final form 17 October 2000.

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21.   Keenan, DM, and Veldhuis JD. Stochastic model of admixed basal and pulsatile hormone secretion as modulated by a deterministic oscillator. Am J Physiol Regulatory Integrative Comp Physiol 273: R1182-R1192, 1997[Abstract/Free Full Text].

22.   Keenan, DM, and Veldhuis JD. A biomathematical model of time-delayed feedback in the human male hypothalamic-pituitary-Leydig cell axis. Am J Physiol Endocrinol Metab 275: E157-E176, 1998[Abstract/Free Full Text].

23.  Keenan DM and Veldhuis JD. Neuroendocrine mechanisms underlying aging of the human male reproductive axis: novel hypothesis formulation and testing via physiologically interlinked feedback and feedforward biomathematical construct. 11th Int Cong Endocrinol, Sydney, Australia, Oct 29-Nov 2, 2000: P178.

24.   Keller-Wood, ME, and Yates FE. Corticosteroid inhibition of ACTH secretion. Endocr Rev 5: 1-24, 1984[ISI][Medline].

25.   Kojima, M, Hosoda H, Date Y, Nakazato M, Matsuo H, and Kangawa K. Ghrelin is a growth-hormone-releasing acylated peptide from stomach. Nature 402: 656-660, 1999[Medline].

26.   Leong, DA. A complex mechanism of facilitation in pituitary ACTH cells: recent single-cell studies. J Exp Biol 139: 151-168, 1988[Abstract/Free Full Text].

27.   Meneilly, GS, Ryan AS, Veldhuis JD, and Elahi D. Increased disorderliness of basal insulin release, attenuated insulin secretory burst mass, and reduced ultradian rhythmicity of insulin secretion in older individuals. J Clin Endocrinol Metab 82: 4088-4093, 1997[Abstract/Free Full Text].

28.   Meneilly, GS, Veldhuis JD, and Elahi D. Disruption of the pulsatile and entropic modes of insulin release during an unvarying glucose stimulus in elderly individuals. J Clin Endocrinol Metab 84: 1938-1943, 1999[Abstract/Free Full Text].

29.   Mulligan, T, Iranmanesh A, Johnson ML, Straume M, and Veldhuis JD. Aging alters feed-forward and feedback linkages between LH and testosterone in healthy men. Am J Physiol Regulatory Integrative Comp Physiol 273: R1407-R1413, 1997[Abstract/Free Full Text].

30.   Mulligan, T, Iranmanesh A, Kerzner R, Demers LW, and Veldhuis JD. Two-week pulsatile gonadotropin releasing hormone infusion unmasks dual (hypothalamic and Leydig cell) defects in the healthy aging male gonadotropic axis. Eur J Endocrinol 141: 257-266, 1999[Abstract].

31.  Mulligan T, Kuno H, Clore J, Iranmanesh A, and Veldhuis JD. Pulsatile infusions of recombinant human LH in leuprolide-downregulated older vs. young men unmask an impoverished Leydig-cell secretory response in aging to mid-physiological LH stimuli. 82nd Ann Endocr Soc Mtg, Toronto, Canada, 2000, p. 181.

32.   Painson, JC, Veldhuis JD, and Tannenbaum GS. Single exposure to testosterone in adulthood rapidly induces regularity in the growth hormone release process. Am J Physiol Endocrinol Metab 278: E933-E940, 2000[Abstract/Free Full Text].

33.   Pincus, SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA 88: 2297-2301, 1991[Abstract/Free Full Text].

34.   Pincus, SM. Greater signal regularity may indicate increased system isolation. Math Biosci 122: 161-181, 1994[ISI][Medline].

35.   Pincus, SM. Quantifying complexity and regularity of neurobiological systems. Methods Neurosci 28: 336-363, 1995.

36.   Pincus, SM. Mechanisms and Biological Significance of Pulsatile Hormone Secretion. New York: Wiley, 2000, p. 82-104.

37.   Pincus, SM, Cummins TR, and Haddad GG. Heart rate control in normal and aborted SIDS infants. Am J Physiol Regulatory Integrative Comp Physiol 264: R638-R646, 1993[Abstract/Free Full Text].

38.   Pincus, SM, Gevers EF, Robinson IC, van den Berg G, Roelfsema F, Hartman ML, and Veldhuis JD. Females secrete growth hormone with more process irregularity than males in both humans and rats. Am J Physiol Endocrinol Metab 270: E107-E115, 1996[Abstract/Free Full Text].

39.   Pincus, SM, and Goldberger AL. Physiological time-series analysis: what does regularity quantify? Am J Physiol Heart Circ Physiol 266: H1643-H1656, 1994[Abstract/Free Full Text].

40.   Pincus, SM, Hartman ML, Roelfsema F, Thorner MO, and Veldhuis JD. Hormone pulsatility discrimination via coarse and short time sampling. Am J Physiol Endocrinol Metab 277: E948-E957, 1999[Abstract/Free Full Text].

41.   Pincus, SM, and Keefe DL. Quantification of hormone pulsatility via an approximate entropy algorithm. Am J Physiol Endocrinol Metab 262: E741-E754, 1992[Abstract/Free Full Text].

42.   Pincus, SM, Mulligan T, Iranmanesh A, Gheorghiu S, Godschalk M, and Veldhuis JD. Older males secrete luteinizing hormone and testosterone more irregularly, and jointly more asynchronously, than younger males. Proc Natl Acad Sci USA 93: 14100-14105, 1996[Abstract/Free Full Text].

43.   Pincus, SM, Veldhuis JD, and Rogol AD. Longitudinal changes in growth hormone secretory process irregularity assessed transpubertally in healthy boys. Am J Physiol Endocrinol Metab 279: E417-E424, 2000[Abstract/Free Full Text].

44.   Plotsky, PM, and Sawchenko PE. Hypophysial-portal plasma levels, median eminence content, and immunohistochemical staining of corticotropin-releasing factor, arginine vasopressin, and oxytocin after pharmacological adrenalectomy. Endocrinology 120: 1361-1369, 1987[Abstract].

45.   Plotsky, PM, and Vale WW. Patterns of growth hormone-releasing factor and somatostatin secretion into the hypophysial-portal circulation of the rat. Science 230: 461-463, 1985[Abstract/Free Full Text].

46.   Roelfsema, F, Pincus SM, and Veldhuis JD. Patients with Cushing's disease secrete adrenocorticotropin and cortisol jointly more asynchronously than healthy subjects. J Clin Endocrinol Metab 83: 688-692, 1998[Abstract/Free Full Text].

47.   Schmitt, CP, Schaefer F, Bruch A, Veldhuis JD, Schmidt-Gayk H, Stein G, Ritz E, and Mehls O. Control of pulsatile and tonic parathyroid hormone secretion by ionized calcium. J Clin Endocrinol Metab 81: 4236-4243, 1996[Abstract].

48.   Schmitt, CP, Schaefer F, Huber D, Maiwald J, Stein G, Veldhuis JD, Mehls O, and Ritz E. Altered instantaneous and calcium-modulated oscillatory PTH secretion patterns in patients with secondary hyperparathyroidism. J Am Soc Nephrol 9: 1832-1844, 1998[Abstract].

49.   Schmitt, CP, Schaefer F, Huber D, Zahn I, Veldhuis JD, Ritz E, and Mehsl O. 1,25(OH)₂-vitamin D₃ reduces spontaneous and hypocalcemia-stimulated pulsatile component of parathyroid hormone secretion. J Am Soc Nephrol 9: 54-62, 1998[Abstract].

50.   Shah, N, Evans WS, Bowers CY, and Veldhuis JD. Tripartite neuroendocrine activation of the human growth-hormone (GH) axis in women by continuous 24-hour GH-releasing peptide (GHRP-2) infusion: pulsatile, entropic, and nyctohemeral mechanisms. J Clin Endocrinol Metab 84: 2140-2150, 1999[Abstract/Free Full Text].

51.   Shah, N, Evans WS, and Veldhuis JD. Actions of estrogen on the pulsatile, nyctohemeral, and entropic modes of growth hormone secretion. Am J Physiol Regulatory Integrative Comp Physiol 276: R1351-R1358, 1999[Abstract/Free Full Text].

52.   Siragy, HM, Vieweg WVR, Pincus SM, and Veldhuis JD. Increased disorderliness and amplified basal and pulsatile aldosterone secretion in patients with primary aldosteronism. J Clin Endocrinol Metab 80: 28-33, 1995[Abstract].

53.   Straume, M, Veldhuis JD, and Johnson ML. Model-independent quantification of measurement error: empirical estimation of discrete variance function profiles based on standard curves. Methods Enzymol 240: 121-150, 1994[ISI][Medline].

54.   Urban, RJ, Evans WS, Rogol AD, Kaiser DL, Johnson ML, and Veldhuis JD. Contemporary aspects of discrete peak detection algorithms. I. The paradigm of the luteinizing hormone pulse signal in men. Endocr Rev 9: 3-37, 1988[ISI][Medline].

55.   Veldhuis, JD. Neuroendocrinology in Physiology and Medicine. Totowa, NJ: Humana, 1999, p. 453-472.

56.   Veldhuis, JD, Iranmanesh A, Mulligan T, and Pincus SM. Disruption of the young-adult synchrony between luteinizing hormone release and oscillations in follicle-stimulating hormone, prolactin, and nocturnal penile tumescence (NPT) in healthy older men. J Clin Endocrinol Metab 84: 3498-3505, 1999[Abstract/Free Full Text].

57.  Veldhuis JD, Iranmanesh A, Naftolowitz D, and Carroll BJ. Mechanisms of ACTH neurosecretory reactivity to abrupt withdrawal of glucocorticoid negative feedback in healthy men: pulsatile, nyctohemeral, and entropic responses (Abstract). 80th Ann Endocr Soc Mtg, New Orleans, Louisiana, 1998, p. 403.

58.  Veldhuis JD, Iranmanesh A, and Pincus SM. Reduction of intrinsic negative-feedback regulation of neuroendocrine axes increases the approximate entropy (serial irregularity) of the pituitary hormone release process for TSH, GH, and LH (Abstract). Soc Neurosci Mtg, Washington, DC, 1996, p. 1884.

59.   Veldhuis, JD, Iranmanesh A, and Urban RJ. Primary gonadal failure in men selectively amplifies the mass of follicle stimulating hormone (FSH) secreted per burst and increases the disorderliness of FSH release: reversibility with testosterone replacement. Int J Androl 20: 297-305, 1997.

60.   Veldhuis, JD, Liem AY, South S, Weltman A, Weltman J, Clemmons DA, Abbott R, Mulligan T, Johnson ML, Pincus SM, Straume M, and Iranmanesh A. Differential impact of age, sex-steroid hormones, and obesity on basal versus pulsatile growth hormone secretion in men as assessed in an ultrasensitive chemiluminescence assay. J Clin Endocrinol Metab 80: 3209-3222, 1995[Abstract].

61.   Veldhuis, JD, Metzger DL, Martha PM, Jr, Mauras N, Kerrigan JR, Keenan B, Rogol AD, and Pincus SM. Estrogen and testosterone, but not a non-aromatizable androgen, direct network integration of the hypothalamo-somatotrope (growth hormone)-insulin-like growth factor I axis in the human: evidence from pubertal pathophysiology and sex-steroid hormone replacement. J Clin Endocrinol Metab 82: 3414-3420, 1997[Abstract/Free Full Text].

62.   Veldhuis, JD, and Pincus SM. Orderliness of hormone release patterns: a complementary measure to conventional pulsatile and circadian analyses. Eur J Endocrinol 138: 358-362, 1998[ISI][Medline].

63.   Veldhuis, JD, Roemmich JN, and Rogol AD. Gender and sexual maturation-dependent contrasts in the neuroregulation of growth hormone secretion in prepubertal and late adolescent males and females-a general clinical research center-based study. J Clin Endocrinol Metab 85: 2385-2394, 2000[Abstract/Free Full Text].

64.   Veldhuis, JD, Zwart AD, and Iranmanesh A. Neuroendocrine mechanisms by which selective Leydig cell castration unleashes increased pulsatile LH release. Am J Physiol Regulatory Integrative Comp Physiol 272: R464-R474, 1997[Abstract/Free Full Text].

65.   Veldman, RG, van den Berg G, Pincus SM, Frolich M, Veldhuis JD, and Roelfsema F. Increased episodic release and disorderliness of prolactin secretion in both micro- and macroprolactinomas. Eur J Endocrinol 140: 192-200, 1999[Abstract].

66.   Yates, FE. Analysis of endocrine signals: the engineering and physics of biochemical communication systems. Biol Reprod 24: 73-94, 1981[Abstract].

67.   Zwart, AD, Iranmanesh A, and Veldhuis JD. Disparate serum free testosterone concentrations and degrees of hypothalamo-pituitary-luteinizing hormone suppression are achieved by continuous versus pulsatile intravenous androgen replacement in men: a clinical experimental model of ketoconazole-induced reversible hypoandrogenemia with controlled testosterone add-back. J Clin Endocrinol Metab 82: 2062-2069, 1997[Abstract/Free Full Text].