INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODOLOGY RESULTS DISCUSSION APPENDIX REFERENCES

IN VIVO AND IN VITRO STUDIES of endocrine glands suggest the existence of two physiologically distinguishable modes of regulated secretion, namely, time-invariant basal hormone secretion and secretagogue-driven pulsatile hormone release (15). The basal mode may represent a constitutive, unregulated, or slowly varying hormone release process (3, 12, 19, 34, 39, 40). In contrast, pulsatile secretion likely reflects rapid exocytosis of previously accumulated neurohormone (19, 43).

Pulsatile hormone release was recognized shortly after the development of RIAs in the early 1970s. Subsequent studies revealed that, in some cases, the magnitude and/or frequency of a pulse signal is critical to its tissue actions; e.g., in the gonadotropin releasing hormone-luteinizing hormone (GnRH-LH)-gonadal axis; for insulin secretion and action; in the growth hormone-insulin-like growth factor-I (GH-IGF-I) axis, and, for the actions of parathyroid hormone (PTH), oxytocin, or glucagon (15, 17, 29, 31, 35, 36, 38, 41). In contrast, knowledge of the mechanisms underlying basal hormone secretion and its tissue impact has lagged considerably. Indeed, in the case of several hormones, such as GH, physiological basal secretion was not demonstrable until the recent emergence of ultrahigh-sensitivity assays (14). On the other hand, apparently elevated basal hormone release is evident in various neuroendocrine pathologies, such as GH, ACTH, and prolactin-secreting pituitary tumors (12) and aldosteronomas (39).

A variable admixture of basal and pulsatile secretion seems to typify the release of some neurohormones, e.g., prolactin, GnRH during the preovulatory LH surge, and PTH, wherein 30-70% of hormone release appears to be nonpulsatile (10, 14, 23, 34).

Admixed basal and pulsatile hormone release also seems to characterize feedback withdrawn states, e.g., hypersecretion of PTH in hypocalcemia (34) or LH in response to testosterone withdrawal (49). Thus accurately partitioning basal versus pulsatile hormone secretion, albeit technically challenging (44, 47), should aid in separating normal physiology (low basal release), pathophysiology (jointly increased basal and pulsatile secretion), and pathology (elevated basal hormone production). To date, reliable segmentation of basal versus pulsatile release has been confounded technically by strong correlations among hormone half-life and basal and pulsatile secretion rates (44, 47). A recent step toward addressing this impasse is nonparametric or waveform-free half-life-dependent deconvolution techniques (7, 16, 24), which to date have received limited or no validated application to extended hormone profiles. As an alternative strategy, here we illustrate a physiologically motivated analytic construct that embodies variably combined basal and pulsatile hormone release, random secretory bursting, and fitted estimates of slow and fast half-lives.

	METHODOLOGY

TOP ABSTRACT INTRODUCTION METHODOLOGY RESULTS DISCUSSION APPENDIX REFERENCES

Overall model. Our general formulation defines Z(t) as the hormone secretion rate at time t (units for LH = IU · l¹ · min¹)

(1)

where ₀ is the unknown basal secretion rate and P(·) is the (nonconstant) pulsatile secretion rate. As a disappearance model, we allow for a fast and slow elimination component, where a and 1  a are their respective proportions. In Ref. 21 we show that rate of change in the blood hormone concentration [X(t)] is then described by differential equations, whose solution is

(2)

Clinical methods. Serum immunoreactive LH concentration time series were obtained and reported previously by sampling blood in healthy women at 10-min intervals for 24 h, after provision of written informed consent approved by the Human Investigation Committee (8, 32). Six volunteers were studied in each of the following categories: for each of three separate phases of the normal menstrual cycles [early follicular (EF), late follicular (LF), and midluteal (MI) phases] and estrogen-unreplaced postmenopausal women (ages 55-75). The ranges of the intra- and interassay coefficients of variations in the LH immunoradiometric assay (IRMA) are 4.5-8.3% and 6.8-10%, and assay sensitivity is 0.8 IU/l (First International Reference Preparation).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODOLOGY RESULTS DISCUSSION APPENDIX REFERENCES

In the five LH-suppressed men infused with variable but known amounts of recombinant human LH, we estimated the several masses of LH infused (known amounts were 7.5, 15, 30, 50 and 75 IU/pulse; Serono). To this end, we applied each of the three separate formulations of "basal" LH secretion: 1) freely varying or analytically fitted (F model); 2) zero basal (Z model); 3a) constrained by the preinjection steady-state [C(SS) model] measured serum LH concentration or 3b) constrained by a percentage of total secretion [C(11) model: e.g. 11% for men (30)]. For any model, the calculated slope of the plot of infused LH dose (IU) versus estimated LH pulse mass (IU/l) is the reciprocal of the LH distribution volume, which was determined independently earlier (46). As illustrated in Fig. 1, the slopes for the four models predict LH distribution volumes of 3.7 (F model), 4.2 (Z model), 4.6 [C(SS) model], and 4.8 liters [C(11) model]. The values fall within the estimated adult male range of 3-5 liters based on highly purified human pituitary LH extracts (46), although this could vary depending on LH isoforms and/or gender. The application of all four models of freely varying, zero, and constrained (steady state and 11%) basal secretion is shown. Figure 2 illustrates that, in the experimentally known basal [C(SS)] model, the second (slow)-component LH half-life is proportionate (r = +0.93, P = 0.02) to the dose of recombinant human LH injected.

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Plots of linear fits of dose (mass) of recombinant human luteinizing hormone (LH) injected (IU) vs. calculated mass (IU/l) of LH recovered in 5 leuprolide-suppressed men given 1 or 8 min intravenous infusions of 7.5, 15, 30, 50, or 75 IU of LH. LH distribution volume (V0) is estimated by reciprocal of slope.

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Plots of mass of human recombinant LH infused vs. first (rapid)- or second (slow)-phase LH half-lives (t1/2) calculated for steady-state constrained (pre-LH injection) model of basal LH secretion for experiment defined in Fig. 1. Linear regression analyses are shown with corresponding correlation coefficients and P values in 5 men evaluated.

Serum LH time series in women sampled every 10 min over 24 h were analyzed next according to the foregoing three formulations of basal secretion: freely varying, zero, or constrained. On the basis of earlier published GnRH antagonist studies in women, constrained basal secretion rates (basal secretion as percentages of total secretion) were taken as nominally 24% in premenopausal females (EF, LF, and ML, respectively) and 34% in postmenopausal women (6, 11). ANOVA applied to the resultant data revealed several major points summarized in Fig. 3, A-E, which shows slow-component LH half-lives; LH pulse frequency; and daily basal, pulsatile, and total LH secretory rates. Illustrative individual women's data (parameter estimates with corresponding estimated SEs) are given in Tables 1-3.

View larger version (3034232314K): [in this window] [in a new window]   Fig. 3.   Estimates of daily pulsatile LH secretion (A), slow-component LH half-lives (B), daily basal (absolute) LH secretion (C), daily total (pulsatile plus basal) LH secretion (D), and LH pulse frequency (E) in individual healthy premenopausal women studied in early follicular (EF), late follicular (LF), or midluteal (ML) phases of menstrual cycle and postmenopausal (PM) women. Data are means ± SE of separate estimates for the 3 (or 2) principal models of basal LH secretion 1) zero basal; 2) freely varying (fitted or analytically estimated); and 3) constrained (residual LH secretion continuing after gonadotropin-releasing hormone (GnRH)-antagonist administration; namely, 24% in young and 34% in older women; METHODOLOGY). Each woman underwent blood sampling at 10-min intervals for 24 h beginning at 0800 (clock time). LH measures by IRMA are IU/l (First International Reference Preparation). For each model, P values were determined by ANOVA after logarithmic transformation of data in 4 study groups. Different letters denote significantly different means by post hoc testing by Duncan's new multiple-range test.

An unexpected finding was a high within-subject agreement (low variability) among estimates of LH pulse mass (and daily pulsatile LH secretion) across the various basal-secretion models. For example, the median (and range) coefficients of variation (SD/mean × 100%) among the four model-based estimates of LH burst mass within subjects were 3.2 (1.5-9.2%) in EF, 5.4 (3.8-14%) in LF, and 5.8 (2.3-16%) in ML phase young women and 4.5 (1.7-5.0%) in postmenopausal women.

Second, according to all three models, daily pulsatile (and total) LH secretion was maximal in postmenopausal women, and minimal in the ML phase of the menstrual cycle (Fig 3A). Third, two-component LH half-life values fell within the published normal range in the human, namely, for the (freely varying) rapid and slow components, respectively, 7-36 and 46-240 min (8, 46; Fig. 3B). These estimates in women compare with (mean ± SD) values of 18 ± 5 and 90 ± 22 min reported earlier for rapid- and slow-phase LH half-lives in four LH-injected hypopituitary men (46). The corresponding LH half-life ranges were 7-25 (rapid phase) and 58-130 min (slow phase) in the C(SS) model using literature-based GnRH-antagonist data to estimate the percentage basal.

In both non-zero basal models, the calculated percentage basal LH secretion ranged absolutely from 1 to 54% within the four groups of woman studied here (see Tables 1-3). In postmenopausal women, percentage basal LH release (variable, analytically estimated) was 2-52%, similar to the values in younger women (1-54%). Thus (in the non-zero basal models) increased absolute basal LH secretion (but not greater fractional partitioning of basal versus pulsatile LH release) characterized post (versus pre-)-menopausal women (Fig. 3C).

The highest daily total LH secretion rates (freely varying basal model) were attained in older women (260-980 IU · l¹ · 24 h¹). The range of values in LF phase premenopausal women was 47-850 IU · l¹ · 24 h¹, in the EF phase was 63-140 IU · l¹ · 24 h¹, and in ML phase was 25-150 IU · l¹ · 24 h¹ (Fig. 3D).

On the assumption of zero basal LH secretion (daily) LH pulse mass estimates remained remarkably similar to those in the two other models (freely varying vs. literature-constrained basal secretion). In the zero basal model, estimated second-component LH half-lives also tended (P = not significant by ANOVA, P < 0.05 by the Kruskal-Wallis test) to be longer in postmenopausal women and shorter in ML phase young women (Fig. 3B).

Use of a literature-constrained (GnRH antagonist predicted) percentage basal rate of LH secretion sometimes predicted lower basal secretion than freely varying (fitted) estimates and lower slow-phase LH half-lives than the zero basal model. The calculated daily LH pulse mass was similar to those in the other two models (Fig. 3A). Pulse frequency estimates were model independent and showed slowing only in the ML phase (Fig. 3E).

Illustrative observed 24-h serum LH concentration profiles, calculated (fitted) profiles, and estimated pulsatile and basal LH secretion curves are given in Fig. 4 for each of the three different formulations of basal LH release. The individual profiles highlight 1) variability among menstrual contexts and 2) distinctions among the three analytic constructs of basal (LH) secretion.

View larger version (41K): [in this window] [in a new window]   Fig. 4.   Illustrative 24-h serum LH concentration profiles in 3 of 18 healthy premenopausal women respectively, 1 individual in each of EF, LF, and ML phases of menstrual cycle) and 1 of 6 PM individuals. There are 2 subpanels for EF, top left; LF, top right; ML, bottom left; and PM, bottom right. Each pair of subpanels shows measured and fitted serum LH concentrations obtained by sampling every 10 min for 24 h beginning at 0800 (clock time) (top line), as well as the model-calculated LH secretory rates (bottom line). Three constructs of basal LH secretion are illustrated by various interrupted lines: dotted, zero basal; dashed-dotted, constrained basal; and dashed, freely varying basal (METHODOLOGY).

As a general modeling comment, which is applicable to Tables 2 and 3, for those parameters that describe the pulsatile structure, mass accumulation (₀, ₁), pulse shape (₁, ₂, ₃), and the variance of pulse mass random effects (²_A), the precision of their estimators is determined as much by the number of pulses as by the actual number of observations. In Tables 2 and 3, illustrating the individual parameter estimates for an EF female and a postmenopausal female, the number of pulse times were 10 and 16, respectively. In Table 2, particularly, some of the (estimated) SEs are large enough that several of the above parameters could not be individually rejected from being zero. In part, this is the consequence of allowing for the flexibility necessary for describing the broad range of profiles encountered in practice; for example, sometimes two of the three pulse shape parameters will suffice, but which two of the three can vary among individuals, and, in some women, there appears to be large basal secretion, whereas for others there is not. The modeling implication of all of this is somewhat dependent on one's specific goal. If the purpose is to find the most parsimonious model for a particular individual, then one might attempt to eliminate potential parameters in a manner analogous to stepwise regression. However, in the present context, these structural parameters are, in some sense, more like nuisance parameters, whose importance rests in their combination allowing one to soundly estimate total daily pulsatile secretion and to assign a justified SE (Table 1). These resulting aggregates are in general well separated from zero.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODOLOGY RESULTS DISCUSSION APPENDIX REFERENCES

We here present, validate, and then apply a random-effects and maximum-likelihood methodology to evaluate hormone biexponential elimination and pulsatile and basal neurohormone secretion according to different renditions of basal secretory behavior. This new analytic formulation extends our earlier efforts by 1) delineating three distinct possible notions of basal secretion; 2) implementing biexponential kinetics; 3) requiring independent biological validation using recombinant human LH infusions; and 4) analyzing full 24-h-long serum LH concentration profiles in women in different menstrual contexts to clarify normal physiology. Indeed, evaluating LH secretion in a relatively large cohort (n = 24) of healthy pre- and postmenopausal women unmasked an unanticipated, remarkably robust within-subject uniformity of estimates of LH secretory burst mass across the three analytically distinct strategies for defining basal gonadotropin release: 1) zero basal and thus purely pulsatile LH secretion; 2) freely varying analytically estimated basal LH secretion; or 3) constrained or putatively non-GnRH-dependent basal LH release. In particular, in any given menstrual context, the three structurally distinct assumptions regarding basal LH secretion predicted a similar mean mass of LH secreted in pulses for any woman. The median within-subject coefficients of variation of estimated LH pulse mass among the three models fell within the range of 3-6%. This primary observation suggests the thesis that, for a fitted two-compartment LH elimination process, the investigator's choice of a particular model of basal LH secretion does not uniquely dictate the estimate of endogenous LH secretory pulse mass. In accordance with this inference, daily pulsatile LH secretion can be estimated robustly within subject independently of the basal secretion analytic construct, conditional on determinable LH pulse frequency and two-component LH half-lives.

Model-independent within-subject estimation of LH pulse mass has several important implications. First, the pulsatile mode of LH secretion, presumptively activated by hypothalmic GnRH impulses, should be a more robust measurable endpoint of neuroendocrine regulation. Second, unlike our own and other earlier highly parameterized constructs (21), the present more parsimonious formulation of basal and pulsatile LH secretion along with biexponential kinetics obviates some of the strong mathematical confounds that impede maximum-likelihood estimates (44). Third, because the sum of the estimated random mass effects within any given time series is (theoretically) zero (21), we can calculate by maximum-likelihood analysis statistically valid confidence intervals for pulsatile and basal LH secretion and LH half-lives. We showed earlier that this cannot be accomplished reliably for a one-component disappearance idiom (21, 44). Fourth, by comparing basal and pulsatile secretion of LH among reproductive states in healthy women, we could examine gonadotropin regulation across the normal adult human female lifetime.

Comparison of LH profiles disclosed that postmenopausal women have a pronounced augmentation of LH secretory burst mass. In principle, such unleashing of pulsatile LH release in the gonadoprival state may reflect an expanded gonadotroph-cell secretory capacity and/or enhanced endogenous GnRH drive (8). In contrast, in premenopausal women, LH pulse mass remained nearly constant across the menstrual cycle, except for the ML phase.

Half-life variations might occur in postmenopausal versus premenopausal women. In particular, according to the zero-basal and constrained-basal models, the calculated LH half-life rises postmenopausally and falls in the ML phase. The former inference was suggested recently in GnRH antagonist-based studies (37). In this regard, a recent kinetic analysis of 14 human LH isoforms in a heterologous assay disclosed up to a twofold range in their in vivo half-lives (3). Analogously, in the human and animals, gonadal status (e.g., postovariectomy) may alter evident rates of in vivo LH disappearance (1, 3, 5, 27, 47, 49, 50).

Postmenopausally increased basal LH secretion was implied only in the constrained basal model. This is in accord with the literature-based inference that the percentage of basal LH secretion, when defined as non-GnRH dependent, is elevated after a GnRH antagonist in postmenopausal women (6, 11, 30). In contrast, according to a fitted basal secretion model, the absolute, but not percentage, basal LH secretion rate is higher in postmenopausal individuals. In neither construction was the variation in basal LH secretion rate the dominant mechanism regulating total daily LH secretion and hence mean serum LH concentrations in premenopausal women. Because estrogen concentrations vary remarkably across the menstrual cycle, these analyses allow one to conjecture further that estrogen or one of its gonadal covariates controls primarily pulsatile (rather than basal) LH secretion. Estrogen may also influence the slow-component half-life of LH, because the latter is elevated in the face of estrogen withdrawal. Whereas clinical studies with GnRH antagonists have suggested a lower percentage of ostensibly GnRH-independent LH secretion in young versus older women (6, 11, 30), such measures are derived in the face of near-maximal inhibition of endogenous GnRH action and thus, by definition, do not reflect the interpulse rate of basal LH release that actually occurs in the presence of physiological endogenous GnRH drive. Indeed, GnRH itself might contribute in part to maintaining some fraction of basal or nonpulsatile gonadotrope secretory activity. In fact, our freely varying fitted basal secretion construct predicts higher LH interpulse secretion than that suggested by GnRH antagonist studies.

The present strategy of partitioning total daily hormone release into respective basal and pulsatile components, conditional on pulse times and with the inclusion of random LH pulse-mass effects, simplifies several earlier numerical deconvolution approaches (44). Here we estimate approximately seven principal parameters of hormone secretion and two of hormone elimination, rather than 20-30 parameters as required in some previous efforts (8, 44). The core estimates include basal secretion (₀); the average rate of interpulse hormone (mass) accumulation (₀) and a constant (₁) relating this value to the prior interpulse interval; (one or more of) three key features of the secretory burst shape: rate of secretory burst ascent, peakedness, and steepness of descent; a random-effects term, defining stochastic variability in pulse mass accumulation; and the rapid versus slow hormone half-lives. If one used an a priori hormone secretory pulse shape, e.g., as determined by direct venous catheterization (2), this knowledge would eliminate the fitting of pulse-shape parameters, allowing further simplification. Analogously, independent ascertainment of elimination kinetics would obviate the need to solve for these terms in the analysis. Importantly, the foregoing core parameters all mirror basic physiological processes. For example, the rapid increase and slow decrease in secretion rates within a burst would likely correspond to prompt exocytotic discharge of prestored hormone granules and delayed de novo biosynthesis and release of additional hormone, respectively (19). Similarly, the slow component of hormone (LH) removal would seem to reflect its irreversible metabolic clearance from the body (3, 46).

These analyses uncover other challenging issues in appraising basal hormone secretion. First, absolute basal LH secretion rates can vary by severalfold across the reproductive life span and among individuals. Second, independent knowledge of rapid and slow hormone half-lives would aid in distinguishing the contribution of basal secretion from that of the slower half-life to the mean hormone concentration. In addition, accurate a priori defined hormone half-lives could help to discriminate between otherwise statistically comparable models of combined pulsatile and basal secretion. In contrast, we show here that estimation of the pulse mass of hormone secreted is largely basal model free. Because kinetic values are not always easily established for an individual in any particular clinical or experimental setting, we can suggest in the future also implementing a Bayesian modification of the present approach with preconditioning on the expected population hormone half-life and/or anticipated basal secretion rate.

The present LH time series were collected by blood withdrawal every 10 min for 24 h and show good precision in the estimation of daily LH secretion and several key secretory parameters, as well as the more prolonged half-life phase (see Table 1-3). Pulse shape is less well estimated, in view of relatively infrequent sampling compared with the brevity of LH secretory pulses. Similarly, the rapid half-life component can only be estimated with an adequate sampling interval, t. That is, the half-life cannot be less than log(2) × t; thus, for t = 10 min, the lower bound is 6.93 min.

Although the random-effects maximum-likelihood appraisal of basal and pulsatile LH secretion is illustrated here only in healthy women, this analytic strategem should have relevance in other contexts, e.g., in assessing LH pathophysiology in various study populations and in evaluating the secretory control of other neurohormones. In addition, by incorporating relevant physiological linkages and dose-response interfaces, e.g., as suggested earlier for the integrated male GnRH-LH-testosterone feedforward and feedback axis (20), this core construct might be extended to allow appraisal of joint secretion by coupled glands within an interconnected endocrine network.

Perspectives

	APPENDIX

TOP ABSTRACT INTRODUCTION METHODOLOGY RESULTS DISCUSSION APPENDIX REFERENCES

Structural Features of the Basal Secretion Models

General structure of secretory formulation. As defined in equation 1 (METHODOLOGY), ₀ is the basal and P( · ) the pulsatile hormone secretion rate. We reason that the cellular basis for basal secretion is constitutive hormone release and for pulsatile secretion is the discharge of available intracellular (peptide) hormone contained within secretory granules, which accumulate during the interpulse interval. Hormone molecules synthesized in the cell starting at pulse time T^j1 are stored until the next pulse time, T^j. As reviewed in Refs. 8, 19, and 47, several techniques have been validated to estimate GnRH-LH pulse times. Here, we evaluate secretion conditional on the pulse times, as determined in Ref. 19. We define the mass of the jth pulse M^j to be the amount of hormone accumulated between pulse times T^j1 and T^j. Here, we assume that the LH pulse masses are given by
where ₀ is the basal (intracellular) accumulation rate, and ₁ is a constant, which relates pulse mass accumulation to the immediately preceding interpulse interval length. This relationship reflects the fact that gonadotrope cells accumulate more LH during prolonged interpulse intervals (8). We assume that the A^js are independent and identically distributed normal random variables with mean zero and variance ²_A, thus allowing for stochastic variability (random effects) in pulse mass. To accommodate variably skewed pulse shape(s), a function ( · ) is specified, which is the normalized rate of secretion given as hormone mass per unit distribution volume per unit time, as a Generalized-Gamma family of densities (i.e., normalized to integrate to 1)

(A1)

where ₁ > 0, ₂ > 0, and ₃ > 0 are three parameters that delimit the secretory burst shape. The resulting overall secretion rate [Z(t)] is thus given by
In the case of two elimination components, the foregoing formulation results in equation 2 (METHODOLOGY). Infusions of human pituitary LH have suggested that the rapid LH half-life component is approximated by a  0.63 and a half-life of 18 min [₁ = log(2)/18] and the longer half-life component by (1  a)  0.37 and a half-life of 90 min [₂ = log(2)/90] (46). Here, we initially fix a  0.63 for the kinetic estimates.

Models of basal secretion. Given the foregoing, we next consider three models for basal secretion. In our original construction (19, 21, 51), basal secretion was free to vary (₀ was unconstrained) and we allowed a single exponential elimination process. The three models evaluated here are 1) freely varying, i.e., analytically fitted (F model); 2) zero basal (Z model); 3a) constrained by preinjection steady-state [C(SS) model] measured serum LH concentration; or 3b) constrained by a percentage of total secretion [C() model, where  is a literature-based population parameter]. The zero basal (Z) model is a minor adaptation of the estimation methodology for that of the freely varying basal model; there is one fewer parameter (no basal term: ₀), and the modifications necessary for the appropriate formulas are minor. SEs can be calculated for the parameter estimates and for such constructions as total daily secretion, mass per pulse, etc. These standard errors are given in Tables 1-3.

(A2)