## Abstract

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.

- age
- reproduction
- human
- male
- pituitary
- hypothalamus
- androgen

healthy aging occursinsidiously, making causal mechanisms difficult to discern (6,12, 17, 22). However, recent studies suggest that older humans exhibit subtle deterioration of regulatory and integrative hormonal control (22), consistent with an aging hypothesis of impaired neuroendocrine feedback adaptations. The present studies use the male reproductive axis as a dynamic neurointegrative system to examine the latter thesis further. In this networklike (feedback and feedforward coupled) axis, hypothalamic gonadotropin-releasing hormone (GnRH) neurons impose pulsatile drive on luteinizing hormone (LH) secretion (2, 4, 11, 16, 18, 20). Available clinical observations suggest that the GnRH-LH pulsing mechanism offers a possible prototype of early disruption of neurointegrative control in aging (3, 4, 19). To test this notion, we have quantified the daily GnRH-LH pulsing rate (frequency), the LH pulse mass, the regularity of serial LH burst amplitude and interpulse-interval sequences, and the frequency-independent variability of the latter measures in healthy young and older men.

## METHODS

#### Overview.

Hormone concentration profiles in peripheral blood arise from episodic secretory bursts (or pulses), which decay in the circulation due to dilution, distribution, and subsequent metabolic elimination (2,4, 7-9, 11, 16, 19, 20, 22). We here examine LH pulse generation in 13 young (ages 18–25 yr) and 13 older (ages 60–80 yr) healthy men. Under the assumption that LH pulses reflect corresponding GnRH inputs (see discussion), we formulate statistical inferences regarding LH secretion pulse timing independently of hormone kinetics.

#### Clinical protocol.

Volunteers underwent blood sampling at 10-min intervals for 24 h. Sera (145 samples/subject) were analyzed in duplicate for LH content (First International Reference Preparation) by two-site monoclonal immunoradiometric assay (IRMA), as reported earlier (13). Observed serum LH concentration time series are illustrated in Fig.1. In parallel experiments, we infused 50 IU recombinant human LH (Serono Laboratories; equal to 20 IU First International Reference Preparation) every 2 h intravenously as 6-min square-wave pulses in seven young (ages 21–35 yr) and seven older (ages 60–80 yr) men 3–4 wk after downregulation of LH secretion with leuprolide acetate (3.75 mg im). Blood was sampled every 10 min from 0800 to 2400 from a contralateral forearm vein for later assay of LH time series by IRMA, thereby allowing direct validation of model-based estimates of LH “secretory” burst mass.

#### Conditional pulse-time model.

To quantify LH secretion and elimination simultaneously from available serum LH concentration time series (above), we used a stochastic model of pulsatile and basal hormone release, which allows for two-compartment elimination kinetics and is conditional on pulse times, as validated earlier on statistical and physiological grounds (7-9). This formulation includes burstlike hormone release of variable amplitude and skewness superimposed on an unknown rate of basal (time invariant) secretion. In this construction, the rate of change in the hormone concentration [X(t)] is described by a set of (coupled) differential equations, whose solution is

where a is the proportion of rapid elimination, α_{1} and α_{2} are the respective rate constants for the rapid and slow elimination phases, X(0) is the starting hormone concentration, β_{0} is the basal secretion rate, t is time, r is a dummy variable, and P (r) d r is the instantaneous pulsatile secretion rate over the infinitesimal time interval (r, r + d r). The observed plasma LH concentration profile is a discrete time sampling of this underlying continuous process plus observational error.

As described earlier in detail (7, 8), the foregoing biomathematical formulation allows for any of three plausible models of basal secretion: *1*) freely varying or analytically fitted β_{0} (F model, above), *2*) zero basal (Z model), or *3*) basal secretion as a fixed percentage of total secretion [C(δ) model, where δ is a literature-based population value of 11% of the mean serum LH concentration in men (8, 19, 20)]. The maximum likelihood estimators of the above parameters (as computed below;results) are asymptotically normal with statistically estimable variances and covariances (7, 8). Then, total (basal plus pulsatile) daily LH secretion is the integral of the reconstructed LH secretion rate, Z(·) = β_{0} + P(·), from 0 to 1,440 min.

#### Model of pulse waiting times.

To compare pulsing patterns requires a statistical model of the GnRH-LH pulse generator, which can accommodate a broad range of pulse-timing behavior. For example, here we wish to quantitate contrasts in the variability in interpulse-interval lengths independently of frequency differences. To this end, we distinguish irregularity (order-dependent reproducibility) from variability (order-independent dispersion about the mean). As a *regularity* statistic, we applied the approximate entropy (ApEn) measure to quantitate the process randomness of serial interpulse interval and pulse-mass values (14,15). ApEn is a family of three-parameter regularity statistics, which are specified by m (pattern length), r (tolerance threshold for successive comparisons), and N (total data series length). ApEn specifically quantifies the relative degree of order-dependent subpattern recurrence in numerical or biological time series (14, 15). Second, we examine*variability* of the set of GnRH (LH) pulse waiting times (interpulse-interval lengths) and pulse mass values, wherein the*order* of their successive occurrence is irrelevant. Thus regularity and variability provide complementary but distinct insights.

A renewal process plausibly describes the apparent randomness of GnRH-LH pulse times. Mathematically, a renewal process (T^{k}) results from the partial sums of incremental, independent, and identically distributed positive random variables (S_{i})
Equation 2If one views the GnRH pulse generator as an ensemble of randomly synchronized neurons (2, 4, 10, 18-20), then a renewal process would reasonably embody such intermittently coherent behavior. The Poisson process is the most basic renewal process, in which the random variables S_{i} have an exponential distribution with mean interval length of 1/λ. Albeit powerful, the Poisson model is limited in flexibility, because mean and standard deviation of the interpulse-interval length are equal definitionally. Thus low variability in pulsing becomes less likely. For instance, a Poisson model with a mean interval of 90 min (1/λ) has a correspondingly large variability (SD = 1/λ) of 100% compared with expected [expressed as a coefficient of variation (CV) physiological variability of 20–40% expected for LH interpulse intervals in men (13, 19, 20)].

To address the limitation inherent in the fixed variability of a Poisson model, we use the Weibull distribution. The latter is a simple nonlinear (i.e. power) transformation of the exponentially distributed intervals in a Poisson process (S_{i} replaced by S
, where γ is a parameter that scales variability). To illustrate this application, we first consider the CV of a set of interpulse-interval values. The CV decorrelates frequency (reciprocal of interpulse-interval length) from variance (square of SD). Thereby, two time series with different mean frequencies may exhibit the same or unequal degrees of interpulse variabilities. The CV is independent of the order of interpulse-interval values and thus complements the order-sensitivity measure, ApEn (above). The Weibull distribution further formalizes the CV notion of pulse-generator firing variability in a simple way (below).

In a Weibull renewal process, the conditional densities for T^{k} given T^{k−1} are given by
where λ is a probabilistic rate (expected number of pulses/day) and γ is a variability scaling parameter. The Poisson process is the special case of γ = 1. For γ > 1 in the Weibull distribution, variability is less than that for the Poisson process. Thus, γ defines the degree of variability of the interpulse-interval lengths. The mean, variance, and CV for the Weibull distribution are
where Γ(·) is the classical mathematical Gamma function. [The Gamma function Γ(·) and the parameter γ have no relationship to one another.] Accordingly, in the Weibull distribution, the CV depends only on γ (and not λ, frequency) and is a strictly decreasing function of γ.

## RESULTS

Stochastic differential equation-based deconvolution analysis revealed comparable pulsatile, basal, and total daily LH secretory rates and LH elimination kinetics in young and older men, for all three models of basal LH secretion (methods; Table1). However, mean LH pulse frequency (events/24 h) was higher (P < 0.001) and the mass of LH secreted per pulse (IU/l distribution volume) was lower (P = 0.038) in older men in the freely varying basal model, whether pulse mass was normalized to the length of the preceding or following interpulse interval (Fig.2). The age-related reduction in LH pulse mass was corroborated in the zero basal (3.40 ± 0.62 vs. 5.57 ± 0.63 IU/l) and basal (3.51 ± 0.65 vs. 5.47 ± 0.66 IU/l) LH secretion models (both P < 0.038). In contrast, analyses of pulsatile LH profiles created via controlled intravenous infusions of recombinant human LH in leuprolide-downregulated young and older men (methods) yielded comparable (P = NS) estimates of *1*) injected LH pulse mass [7.8 ± 0.58 (older) and 6.9 ± 0.82 (young) IU/l]; *2*) rapid LH half-lives (7.2 ± 0.08 and 7.2 ± 0.05 min); *3*) delayed LH half-lives (97 ± 8.5 and 93 ± 6.6 min); and *4*) ApEn values [1.215 ± 0.032 (young) and 1.317 ± 0.045 (older) (P = NS)].

The regularity of observed 24-h serum LH concentration time series and of successive LH pulse-mass or interpulse-interval values was evaluated by the ApEn statistic (methods). The latter measure used a vector length of m = 1 and tolerance of r = 20% (for LH concentrations) and r = 75% (for the shorter pulse mass or waiting-time series). ApEn of serum LH concentration profiles was increased markedly in older men (1.579 ± 0.041) compared with young volunteers (1.071 ± 0.071; P < 10^{−3}). Because ApEn is a family of statistics defined also by N (number of observations), we compared the ratios of observed to random ApEn (mean of 1,000 randomly shuffled versions of each data series) in the two age cohorts. Parametric and nonparametric (Wilcoxon) statistical testing revealed an elevated ApEn ratio of successive LH pulse mass values (whether or not normalized to the previous or succeeding interpulse interval) in older men (P < 0.01; Fig.3
*A*). In contrast, the ApEn ratio of serial LH interpulse intervals did not differ by age (Fig.3
*B*).

The Weibull distribution was used to evaluate the behavior of pulse waiting times (interpulse-interval lengths) in the two age groups. Figure4
*A*illustrates schematically how the mean and SD of a set of interpulse-interval lengths depend upon λ (frequency) and γ (variability). Figure 4
*B* shows simulations for different values of λ (25, 20, 15, 10, and 5 pulses/day) in relation to each of three values of γ [1 (≡ Poisson process), 2, and 5]. Specifically, the Weibull model accommodates both regular (large γ) and irregular (small γ) pulsing patterns. Figure 4
*C*illustrates the estimated Weibull distributions for the sets of interpulse intervals observed in one young and one older man. This plot highlights how the parameter γ mirrors pulsing variability. Figure5 gives all 26 estimates of λ and γ and corresponding plots of the estimated Weibull densities (interpulse-interval distributions) and their individual CVs.

We performed generalized likelihood ratio tests of the two groups of Weibull functions. The full parameter space would consist of four parameters: a λ and γ for each group. A test of the null hypothesis that both age groups have a common γ suggests a trend toward unequal (higher) γ in older men (P = 0.08), which denotes reduced interpulse waiting-time variability. Lambda values are highly different in the two age cohorts (P values numerically <10^{−6}), whether one considers distinct or identical γs for the two groups. Elevated λ signifies an increased mean LH pulsing rate in the aging male.

## DISCUSSION

The present analyses unveiled threefold disruption of the GnRH-LH pulsing system in healthy aging men. First, quantitation of LH secretion by way of a stochastic differential equation-based deconvolution model disclosed an accelerated frequency and reduced amplitude of LH pulses in elderly males. Second, statistical analysis of the regularity of LH pulse-mass sequences by the ApEn measure revealed a significantly more disorderly succession of LH pulse mass over 24 h in older men. And, third, modeling of pulse-generator timing via the Weibull probability distribution pointed to reduced variability of interpulse-interval lengths in aging males. Thus the foregoing comparisons delineate defects in amplitude-dependent LH secretion and in both frequency-dependent and frequency-independent GnRH-LH pulse-generator timing in older men.

The lower LH secretory burst mass estimates and the higher daily GnRH-LH secretory burst frequency inferred here in older men might arise secondarily from a reduction in gonadal sex-steroid negative feedback and/or primarily from an intrinsic hypothalamic defect in GnRH neuronal pulse generation (1, 5, 6, 12, 19, 20, 22). In relation to secondary causes, clinical experiments and biomathematical models indicate that muting of testosterone's negative feedback will reduce LH secretory burst mass, elevate mean GnRH-LH pulse-generator frequency and also heighten the irregularity of LH secretory patterns (20). However, the degree of testosterone deprivation required to initiate such adaptations is not known and may itself be age dependent. In relation to primary dysregulation of the GnRH neuronal pulse generator in aging, an accelerated frequency pulsing could arise from blunted repression and/or heightened activation of relevant neurotransmitter pathways, which govern episodic outflow of the synchronized GnRH neuronal ensemble (16, 19). However, the nature of any imbalance between inhibitory and excitatory control mechanisms inferred here in older men is not known.

The age-dependent increase in daily GnRH-LH pulse frequency was substantial (an ∼50% median increment) and mechanistically specific, because total daily LH secretion and LH kinetics were comparable in the two study cohorts. Accelerated GnRH-LH pulse frequency in older men is reminiscent of that observed in ovariprival women. However, in the postmenopausal female, the calculated mass of LH secreted per pulse is elevated significantly (8), in contradistinction to the 50% reduction observed here. From a mechanistic perspective, lower-amplitude LH secretory bursts in the aging male could reflect several pathophysiologies. First, reduced hypothalamic GnRH release has been inferred indirectly in aged animals and humans (1, 5, 19,20). Second, an excessive feedback action of androgens might repress GnRH-LH output in older men (5, 21). Third, a higher GH stimulus frequency per se can diminish the amount of LH secreted per pulse (4). Fourth, in principle, impaired gonadotrope responsiveness to GnRH could limit LH secretory burst mass in older men. However, measurable pituitary stores of LH are actually increased in older humans (1), and the potency of GnRH is higher (5, 13, 19, 23). Last, systematic alterations in the distribution volume or metabolic clearance rate of LH were excluded as a trivial explanation for reduced LH pulse size in aging men (13, 23). Thus impoverished LH secretory burst mass most likely mirrors reduced hypothalamic GnRH feedforward drive of pulsatile LH output in the elderly male.

The regularity of successive LH pulse-mass values, as quantitated by the ApEn statistic (14, 15), was significantly disrupted in older men. More disorderly LH pulse-mass sequences in aging may denote nonuniform hypothalamic release of GnRH or inconsistent actions of GnRH on gonadotropes over 24 h. Normalizing LH pulse mass to each preceding (or following) interpulse-interval length did not nullify the age-related irregularity in serial LH pulse mass. Thus anomalous regulation of successive LH burst amplitudes in aging is frequency-independent at least on statistical grounds.

The present analysis assumes that the timing of statistically identifiable LH release episodes provides a valid (noncritically censored) index of intermittently synchronized GnRH neuronal secretion (2, 4, 5, 8, 11, 19-22). Under this assumption, we infer that aging alters the probabilistic structure of GnRH pulse generation, as monitored by LH interpulse waiting times (intervals between successive bursts). To decorrelate interpulse-interval variability from the elevated mean GnRH-LH pulse firing rate in older men, we used a Weibull model of a stochastic renewal-like process for the timing behavior of the GnRH pulse generator. The Weibull (member of the generalized Gamma) distribution allows for a full spectrum of interpulse-interval variabilities at any given mean pulsing frequency. Thereby, we show that LH pulse waiting-time variability in both age groups studied is considerably less than that predicted by a simple Poisson process (i.e., Gamma typically exceeded unity in the Weibull formulation; methods). The degree of departure of interpulse-interval variability from a Poisson model tended to be greater in older men (P = 0.08). This apparent age distinction would denote relative repression of normal waiting-time variability. The consistency and the cause of such presumptive aging-related (and frequency independent) quenching of normal young-adult variability in the renewal behavior of the GnRH-LH pulse generator in older men are not known.

The present work also highlights an analytic distinction between order-independent variability (Fig. 4) and order-dependent regularity (Fig. 3) of relevant pulse measures. Variability was appraised via the coefficient of variation (percentage ratio of the mean to standard deviation) of the Weibull distribution of interpulse-interval values. Regularity was quantified by the ApEn statistic (14, 15). ApEn measures the reproducibility of subpatterns in time series, with the higher values denoting less orderliness. Here, we used normalized ApEn ratios (defined empirically by the mean ratio of each observed ApEn series to that of 1,000 randomly reordered versions of the same data) to compare series of different N (number of observed LH interpulse-interval or pulse-mass values). ApEn ratios for successive LH pulse-waiting times in young and older men were comparable, whereas ApEn ratios for sequential LH pulse mass values were elevated in older men (above). The foregoing findings suggest rather specific mechanistic changes in aging. For example, GnRH-LH pulse timing is governed by intermittent synchronization of multiple repressive and facilitative inputs to the GnRH neuronal ensemble. In contrast, LH pulse amplitude/mass reflects GnRH stimulus strength, instantaneous gonadotrope-cell responsiveness, the momentary availability of cellular LH stores, de novo LH biosynthesis, and concomitant hypothalamo-pituitary microvascular blood flow (7, 8,10, 18, 20). Thus more irregular LH pulse mass sequences in older men could mirror age-related disparities in one or more of the foregoing processes, which couple GnRH release to LH secretion.

In summary, the present investigations identify novel facets of altered GnRH-LH pulse regulation in healthy aging men, namely, mean accelerated GnRH-LH pulse frequency, attenuated LH pulse size, reduced serial regularity of LH secretory burst mass and a trend to impaired variability of interpulse waiting times.

### Perspectives

Complementary mechanistic models are important to enrich understanding of regulatory and integrative physiology. This need reflects the inherent adaptive complexities of networklike biological control systems, and the subtlety of some pathophysiological and transitional physiological processes, such as aging of neuroendocrine axes. The present examination of the (healthy) aging male reproductive axis thus uses three models of pulsatility to dissect age-related distinctions in GnRH-LH pulsing variability and regularity. Variability in GnRH-LH pulse waiting times (intervals between successive secretory bursts) declines in the aging male, signifying more nearly metronomic behavior of the hypothalamic neuronal renewal-like process. The quantifiable regularity of successive LH burst-mass values deteriorates concomitantly. In schematic terms, the intervals separating GnRH-LH secretory pulses are more consistent, but the amplitudes of the resultant LH pulse series are less uniform. This age-related pathophysiology thus comprises both disrupted timing and anomalous amplitude control. Such alterations probably mirror changes in hypothalamic neuronal output and the hypothalamo-pituitary interface, respectively. Accordingly, the present technical treatment of the GnRH-LH pulsing mechanism should provide a useful analytic platform for exploring analogous dynamic concepts in other complex neuroendocrine systems, e.g., hypothalamic corticotropin-releasing hormone and arginine vasopressin-dependent drive of pituitary ACTH secretion, multioscillator control of pancreatic beta-cell insulin output, etc. Analysis of the variability and regularity of waiting-time sets and pulse-amplitude series in such systems should yield new mechanistic insights complementary to mean frequency and mean amplitude data.

## Acknowledgments

Support for this study was provided by National Science Foundation Interdisciplinary Grant in the Mathematical Sciences (DMS-0107680), the Center for Biomathematical Technology, the General Clinical Research Center M01-RR-00847, and the Specialized Cooperative Center for Reproduction Research (U54 National Institute of Child Health and Development HD-28934).

## Footnotes

Address for reprint requests and other correspondence: J. D. Veldhuis, Division of Endocrinology, Dept. of Internal Medicine, PO Box 800202, Univ. of Virginia School of Medicine, Charlottesville, VA 22908 (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 “

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- Copyright © 2001 the American Physiological Society