Explicating hypergonadotropism in postmenopausal women: a statistical model

Pulsatility of Hypothalamo-Pituitary Hormones: A Challenge in Quantification

Neuroendocrine systems control many of the most fundamental physiological processes, e.g., reproduction, growth, adaptations to stress, and metabolism. Each such system involves the hypothalamus, the pituitary, and a specific target gland or organ. In the quantification of the interactions among these components, biostatistical modeling has played an important role. In the present article, five key challenges to an understanding of the interactions of these systems are illustrated and discussed critically.

Motivations and methods for analyzing pulsatile hormone secretion

Endocrine glands communicate with remote target cells via a mixture of continuous and intermittent signal exchange. Continuous signaling allows slowly varying control, whereas intermittency permits large rapid adjustments. The control systems that mediate such homeostatic corrections operate in a species-, gender-, age-, and context-selective fashion. Significant progress has been made in understanding mechanisms of adaptive interglandular signaling in vivo. Principal goals are to understand the physiological origins, significance, and mechanisms of pulsatile hormone secretion. Key analytical issues are: 1) to quantify the number, size, shape, and uniformity of pulses, nonpulsatile (basal) secretion, and elimination kinetics; 2) to evaluate regulation of the axis as a whole; and 3) to reconstruct dose-response interactions without disrupting hormone connections. This review will focus on the motivations driving and the methodologies used for such analyses.

Age and testosterone feedback jointly control the dose-dependent actions of gonadotropin-releasing hormone in healthy men

Healthy older men manifest combined declines in testosterone concentrations, LH secretory burst mass (amount of LH released per pulse), and feedback-sensitive regularity of unknown cause. To test a unifying hypothesis of simultaneous reductions in GnRH outflow, gonadotrope responsiveness to GnRH, and androgenic negative feedback, we monitored LH secretion 1) after bolus iv injection of a 1000-fold range of randomly ordered individual doses of GnRH on separate mornings, 2) during unmodified (eugonadal) or testosterone-withdrawn (hypoandrogenemic) negative feedback, and 3) in 16 young (age, 18-35 yr) and 15 older (age, 60-85 yr) healthy men. LH secretory burst mass and pattern regularity were quantitated by intensive blood sampling, high specificity LH beta-subunit-directed immunoradiometric assay, deconvolution analysis, and approximate entropy. GnRH dose responsiveness was assessed by four-parameter nonlinear regression analysis. We demonstrated that older men exhibit 1) delayed attainment of GnRH-evoked maximal LH secretion; 2) enhanced potency of GnRH stimulation in both the feedback-intact and feedback-withdrawn states; 3) elevated gonadotrope sensitivity to GnRH, unmasked by experimental testosterone depletion; 4) comparable young adult-like GnRH efficacy, independent of testosterone feedback milieu; and 5) diminished regularity of GnRH-induced LH release evident only during unmodified androgenic feedback. We conclude that a 3-fold interaction among GnRH dose, testosterone concentration, and age governs GnRH action, and age determines both testosterone-modulated and testosterone-independent actions of GnRH.

Endogenous ACTH concentration-dependent drive of pulsatile cortisol secretion in the human

According to current regulatory concepts, pulsatile ACTH concentrations (CON) stimulate time-lagged cortisol secretion rates (SEC) via an implicit CON-SEC dose-response relationship. The present analyses reconstruct nonlinear properties of this in vivo agonist-response interface noninvasively in order to investigate pulse-by-pulse coupling consistency and to obviate the need to infuse isotopes or exogenous effectors, which may disrupt pathway interactions. This approach required an ensemble strategy of 1) measuring ACTH and cortisol CON in plasma sampled every 10 min for 24 h in 32 healthy adults, and 2) estimating simultaneously a) variable-waveform ACTH and cortisol SEC bursts superimposed upon fixed basal SEC; b) biexponential kinetics of ACTH and cortisol disappearance; c) nonequilibrium exchange of cortisol among free and cortisol-binding globulin (CBG)- and albumin-bound moieties; d) two SEC-burst shapes demarcated by a statistically defined day/night boundary; e) feedforward efficacy, potency, and sensitivity; and f) stochastic variability in feedforward measures over time. Thereby, we estimate 1) ACTH SEC (microg.l(-1).day(-1)) of 0.27 +/- 0.04 basal and 0.87 +/- 0.07 pulsatile (means +/- SE); 2) cortisol SEC (micromol.l(-1).day(-1)) of 0.10 +/- 0.01 basal and 3.5 +/- 0.20 pulsatile; 3) free cortisol half-lives (min) of 1.8 +/- 0.20 (diffusion/advection) and 4.1 +/- 0.30 (elimination) and a half-life of total cortisol of 49 +/- 2.4 and of ACTH of 20 +/- 1.3; 4) ACTH potency (EC(50), ng/l) of 26 +/- 2.4, efficacy (nmol.l(-1).min(-1)) 10 +/- 1.8, and sensitivity (slope units) 0.65 +/- 0.09; 5) night/day augmentation of ACTH and cortisol SEC-burst mass by 2.1- and 1.7-fold (median); 6) abbreviation of the modal time to maximal ACTH and cortisol SEC rates by 4.4- and 4.3-fold, respectively, after a change point clock time of 0205 (median); 7) in vivo percentage distribution of cortisol as 6% free, 14% albumin bound, and 80% CBG bound with an absolute free cortisol CON (nmol/l) 11.5 +/- 0.54; and 8) significant (mean CV) stochastic variability in feedforward efficacy (140%), potency (38%), and sensitivity (56%) within the succession of paired ACTH/cortisol pulses of any given subject. In conclusion, the present composite formulation illustrates a platform for dissecting mechanisms of in vivo regulation of effector-response properties noninvasively in the corticotropic axis of the uninfused individual.

Cortisol feedback state governs adrenocorticotropin secretory-burst shape, frequency, and mass in a dual-waveform construct: time of day-dependent regulation

Quantification of in vivo pituitary hormone secretion requires simultaneous appraisal of implicit 1) secretory-burst waveform, mass, and stochastic pulse timing; 2) basal secretion; 3) biexponential elimination kinetics; and 4) random experimental error (Keenan DM, Licinio J, and Veldhuis JD. Proc Natl Acad Sci USA 98: 4028-4033, 2001). The present study extends this analytic formalism to allow for time of day-dependent waveform adaptation (burst-shape change) at statistically determinable boundary times. Thereby, we test the hypothesis that diurnal mechanisms and glucocorticoid negative feedback jointly govern distinctive facets of the burstlike secretion of ACTH. To this end, we reanalyzed intensively (10 min) sampled 24-h plasma ACTH concentration profiles collected previously under feedback-intact and drug-induced cortisol depletion in nine healthy adults. Akaiki information criterion-based model comparison favored dual (rather than single) secretory-burst representation of 24-h ACTH release in both the intact and low-cortisol setting in eight of nine subjects. Under feedback-intact conditions, analytically predicted waveform changepoints (median clock times 0611 and 1739) flanked an interval of elevated ACTH secretory-burst mass (P < 10-3). Experimental hypocortisolemia did not alter day/night boundaries, but 1) stimulated day ACTH secretory-burst mass (P < 10-3); 2) accelerated day ACTH secretory-burst frequency (P < 10-3); and 3) forced skewness of day ACTH secretory bursts toward more rapid initial release (P < 0.05). In contrast, the basal ACTH secretion rate and regularity of interpulse-interval lengths were invariant of day/night segmentation and cortisol availability. In conclusion, unknown diurnal factors and systemic cortisol concentrations codetermine ACTH secretory-burst waveform, frequency, and mass, whereas neither mechanism regulates basal ACTH release or regularity of the burst-renewal process.

Control of LH secretory-burst frequency and interpulse-interval regularity in women

Hypothalamic neurons generate discrete bursts of gonadotropin-releasing hormone (GnRH) and thereby pulses of luteinizing hormone (LH) at randomly timed intervals centered on a probabilistic mean frequency. We tested the hypothesis that physiological mechanisms govern not only the number but also the stochastic dispersion of the GnRH/LH pulse-renewal process in humans; for example, in young women in the early (EF) and late (LF) follicular and midluteal (ML) phases of the menstrual cycle (n = 18) and in postmenopausal individuals (PM, n = 16). To this end, we quantify stochastic interpulse variability by way of the order-independent, two-parameter Weibull renewal process (Keenan DM and Veldhuis J. Am J Physiol Regul Integr Comp Physiol 281: R1917-R1924, 2001) and the sequence-specific, model-free approximate-entropy statistic (ApEn) (Pincus SM. Proc Natl Acad Sci USA 88: 2297-2301, 1991). Statistical testing unveiled 1) reduced probabilistic mean LH secretory-burst frequency (lower lambda of the Weibull distribution) in ML compared with each of EF, LF, and PM (P < 0.001); 2) quantifiably more regular LH interburst-interval sets (elevated gamma of the Weibull density) in PM than in each of EF, LF, and ML (P < 0.01); 3) uniquely prolonged latency to maximal LH secretion within individual secretory bursts in ML (P < 0.01); and 4) comparably mean random, sequential LH interburst-interval and mass values (normalized ApEn) among the distinct hormonal milieus. From these data, we postulate that sex steroids and age determine daily LH secretory-burst number, quantifiable pulse-renewal variability, and secretory-waveform evolution.

Unequal autonegative feedback by GH models the sexual dimorphism in GH secretory dynamics

Growth hormone (GH) secretion, controlled principally by a GH-releasing hormone (GHRH) and GH release-inhibiting hormone [somatostatin (SRIF)] displays vivid sexual dimorphism in many species. We hypothesized that relatively small differences within a dynamic core GH network driven by regulatory interactions among GH, GHRH, and SRIF explain the gender contrast. To investigate this notion, we implemented a minimal biomathematical model based on two coupled oscillators: time-delayed reciprocal interactions between GH and GHRH, which endow high-frequency (40-60 min) GH oscillations, and time-lagged bidirectional GH-SRIF interactions, which mediate low-frequency (occurring every 3.3 h) GH volleys. We show that this basic formulation, sufficient to explain GH dynamics in the male rat [Farhy LS, Straume M, Johnson ML, Kovatchev BP, and Veldhuis JD. Am J Physiol Regulatory Integrative Comp Physiol 281: R38-R51, 2001], emulates the female pattern of GH release, if autofeedback of GH on SRIF is relaxed. Relief of GH-stimulated SRIF release damps the slower volleylike oscillator, allowing emergence of the underlying high-frequency oscillations that are sustained by the GH-GHRH interactions. Concurrently, increasing variability of basal somatostatin outflow introduces quantifiable, sex-specific disorderliness of the release process typical of female GH dynamics. Accordingly, modulation of GH autofeedback on SRIF within the interactive GH-GHRH-SRIF ensemble and heightened basal SRIF variability are sufficient to transform the well-ordered, 3.3-h-interval, multiphasic, volleylike male GH pattern into a femalelike profile with irregular pulses of higher frequency.

Impact of pulsatility on the ensemble orderliness (approximate entropy) of neurohormone secretion

Regular patterns of neurohormone secretion are driven by underlying pulsatile and subordinate (feedback sensitive) dynamics. Measures of time-series orderliness, e.g., the approximate entropy (ApEn) statistic (Pincus SM. Proc Natl Acad Sci 88: 2297-2301, 1991), vividly discriminate pathological and physiological patterns of hormone release. To investigate how specific pulsatility features impact regularity estimates, we have examined the sensitivity of the ApEn metric to systematic variations in the frequency, amplitude, and half-life of simulated neurohormone pulse trains (Veldhuis JD, Carlson ML, and Johnson ML. Proc Natl Acad Sci 84: 7686-7690, 1987) and compared the impact of a high vs. low baseline luteinizing hormone (LH) pattern regularity state mimicking the normal female luteal phase and the young male, respectively. Shortening the interpulse interval length elevated ApEn in both pulsatility models, thereby signifying greater ensemble series irregularity. The frequency sensitivity of ApEn was robust to several complementary renditions of ApEn and to variations in experimental uncertainty, basal (nonpulsatile) LH secretion, and secretory burst amplitude. ApEn rose with increasing hormone half-life, especially in the face of low baseline variability emulated by midluteal LH secretion profiles. High variability of secretory burst amplitude, pulse duration, or interpeak intervals increased ApEn in the more orderly femalelike construct; in the highly irregular malelike LH pulse model, these variability changes had little effect on ApEn. In summary, the ensemble regularity statistic, ApEn, quantifies unequal pattern orderliness in neurohormone pulse trains with minimal dependence on mean pulse amplitude, interpulse baseline, or (subthreshold) sample uncertainty. Thus ApEn monitors changing secretory event frequency and interpulse variability with sensitivity to starting pattern regularity, providing a mechanistic linkage between model evolution and statistical change.

Disruption of the hypothalamic luteinizing hormone pulsing mechanism in aging men

The incremental nature of neuroendocrine aging suggests that subtle system dysregulation may precede overt axis failure. The present analyses unmask threefold disruption of pulsatile gonadotropin-releasing hormone (GnRH)-luteinizing hormone (LH) secretion in the aging male. First, by way of random effects-based deconvolution analysis, we document an elevated daily GnRH-LH pulse frequency in healthy older men [namely, mean (+/-SE) 23 +/- 1 (older) vs. 15 +/- 1 (young) LH secretory bursts/24 h, P < 0.001] and lower mean LH pulse mass [3.73 +/- 0.58 (older) vs. 5.46 +/- 0.66 (young) IU/l, P = 0.038]. However, total LH secretion rates and two-compartment LH elimination kinetics were comparable in the two age cohorts. Second, using the approximate entropy statistic, we show an equivalently random order-dependent succession of LH interpulse-interval lengths in young and older men, but a marked age-related deterioration of the ad seriatim regularity of LH pulse mass series in older individuals (P = 0.0057). Third, by modeling GnRH pulse-generator output as a Weibull renewal process (generalized Gamma density) to emulate loosely coupled GnRH neuronal oscillators, we identify an age-related reduction in the frequency-independent and order-independent variability of GnRH-LH interpulse-interval sets (P = 0.08). These findings indicate that the GnRH-LH pulsing mechanism in healthy older men maintains an increased mean frequency and lower amplitude of bursting activity, a reduced uniformity of serial LH pulse-mass values, and an impaired variability among interpulse-interval lengths. Thereby, the foregoing order-dependent and order-independent alterations in GnRH-LH signal generation in the aging human suggest a general framework for exploring subtle disruption of time-sensitive regulation of other neurointegrative systems.

Corticotropin secretory dynamics in humans under low glucocorticoid feedback

To explore the mechanisms of homeostatic adaptation of the hypothalamo-pituitary-adrenal axis to an experimental low-feedback condition, we quantitated pulsatile (ultradian), entropic (pattern-sensitive), and 24-h rhythmic (circadian) ACTH secretion during high-dose metyrapone blockade (2 g orally every 2 h for 12 h, and then 1 g every 2 h for 12 h). Plasma ACTH and cortisol concentrations were sampled concurrently every 10 min for 24 h in nine adults. The metyrapone regimen reduced the amplitude of nyctohemeral cortisol rhythm by 45% (P = 0.0013) and delayed the time of the cortisol maximum (acrophase) by 7.1 h (P = 0.0002). Attenuated cortisol negative feedback stimulated a 7-fold increase in the mean (24-h) plasma ACTH concentration, which rose from 24 +/- 1.6 to 169 +/- 31 pg/ml (ng/liter) (P < 0.0001). Augmented ACTH output was driven by a 12-fold amplification of ACTH secretory burst mass (integral of the underlying secretory pulse) (21 +/- 3.1 to 255 +/- 64 pg/ml; P < 0.0001), yielding a higher percentage of ACTH secreted in pulses (53 +/- 3.5 vs. 92 +/- 1.3%; P < 0.0001). There were minimal elevations in basal (nonpulsatile) ACTH secretion (by 50%; P = 0.0049) and ACTH secretory burst frequency (by 36%; P = 0.031). The estimated half-life of ACTH (median, 22 min) and the calculated ACTH secretory burst half-duration (pulse event duration at half-maximal amplitude) (median, 23 min) did not change. Hypocortisolemia evoked remarkably more orderly subordinate patterns of serial ACTH release, as quantitated by the approximate entropy statistic (P = 0.003). This finding was explained by enhanced regularity of successive ACTH secretory pulse mass values (P = 0.032). In contrast, there was no alteration in serial ACTH interpulse-interval (waiting-time) regularity. At the level of 24-h ACTH rhythmicity, cortisol withdrawal enhanced the daily rhythm in ACTH secretory burst mass by 29-fold, elevated the mesor by 16-fold, and delayed the acrophase by 3.4 h from 0831 h to 1154 h (each P < 10(-3)). In summary, short-term glucocorticoid feedback deprivation primarily (>97% of effect) amplifies pulsatile ACTH secretory burst mass, while minimally elevating basal/nonpulsatile ACTH secretion and ACTH pulse frequency. Reduced cortisol feedback paradoxically elicits more orderly (less entropic) patterns of ACTH release due to emergence of more regular ACTH pulse mass sequences. Cortisol withdrawal concurrently heightens the amplitude and mesor of 24-h rhythmic ACTH release and delays the timing of the ACTH acrophase. In contrast, the duration of underlying ACTH secretory episodes is not affected, which indicates that normal pulse termination may be programmed centrally rather than imposed by rapid negative feedback. Accordingly, we hypothesize that adrenal glucocorticoid negative feedback controls hypothalamo-pituitary-adrenal axis dynamics via the 3-fold distinct mechanisms of repressing the mass of ACTH secretory bursts, reducing the orderliness of the corticotrope release process, and modulating the intrinsic diurnal rhythmicity of the hypothalamo-corticotrope unit.