Daniel M. Keenan

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.

Dynamic characteristics of blood glucose time series during the course of critical illness: Effects of intensive insulin therapy and relative association with mortality

Objectives:To assess the effect of intensive insulin therapy on blood glucose amplitude variation and pattern irregularity in critically ill patients. To assess the association of these blood glucose signal characteristics with hospital mortality, independent of blood glucose level. Design:Retrospective analysis of the databases of two previously published randomized controlled trials. Setting:University hospital, 56-bed adult surgical intensive care unit and 17-bed medical intensive care unit. Patients:One thousand five-hundred forty-eight surgical intensive care unit patients, admitted between February 2000 and January 2001, and 1200 medical intensive care unit patients, admitted between March 2002 and May 2005. Interventions:In the two randomized controlled trials, patients were randomized to receive either intensive insulin therapy (targeting normoglycemia, between 4.4 and 6.1mmol/L) or conventional insulin therapy (infusing insulin when blood glucose levels were >12 mmol/L and stopping at 10 mmol/L). Measurements and Main Results:Intensive insulin therapy significantly lowered mean blood glucose (5.8 vs. 8.4 mmol/L), hyperglycemic index (0.8 vs. 3.2 mmol/L), and glycemic penalty index (26 vs. 53), but it increased the mean daily difference between minimum and maximum blood glucose (mean daily &dgr; blood glucose; 4.0 vs. 3.3 mmol/L). There was no significant effect on the standard deviation of the blood glucose measurements or on jack-knifed approximate entropy. In multivariable logistic regression analysis, corrected for baseline risk factors, blood glucose levels outside the normoglycemic range, higher mean daily &dgr; blood glucose, higher standard deviation blood glucose, and higher jack-knifed approximate entropy were independently associated with hospital mortality. Conclusions:The Leuven intensive insulin therapy strategy increased mean daily &dgr; blood glucose while not affecting standard deviation blood glucose and jack-knifed approximate entropy. Increased blood glucose amplitude variation and pattern irregularity were associated with mortality, irrespective of blood glucose level. The reduced mortality observed with intensive insulin therapy in the Leuven trials cannot be attributed to an effect on blood glucose amplitude variation or entropy. Reducing amplitude variation and entropy of the blood glucose signal, irrespective of blood glucose concentration, may produce clinical benefits.

A feedback-controlled ensemble model of the stress-responsive hypothalamo-pituitary- adrenal axis

The present work develops and implements a biomathematical statement of how reciprocal connectivity drives stress-adaptive homeostasis in the corticotropic (hypothalamo-pituitary-adrenal) axis. In initial analyses with this interactive construct, we test six specific a priori hypotheses of mechanisms linking circadian (24-h) rhythmicity to pulsatile secretory output. This formulation offers a dynamic framework for later statistical estimation of unobserved in vivo neurohormone secretion and within-axis, dose-responsive interfaces in health and disease. Explication of the core dynamics of the stress-responsive corticotropic axis based on secure physiological precepts should help to unveil new biomedical hypotheses of stressor-specific system failure.

A biomathematical model of time-delayed feedback in the human male hypothalamic-pituitary-Leydig cell axis.

We develop, implement, and test a feedback and feedforward biomathematical construct of the male hypothalamic [gonadotropin-releasing hormone (GnRH)]-pituitary [luteinizing hormone (LH)]-gonadal [testosterone (Te)] axis. This stochastic differential equation formulation consists of a nonstationary stochastic point process responsible for generating episodic release of GnRH, which is modulated negatively by short-loop (GnRH) and long-loop (Te) feedback. Pulsatile GnRH release in turn drives bursts of LH secretion via an agonistic dose-response curve that is partially damped by Te negative feedback. Circulating LH stimulates (feedforward) Te synthesis and release by a second dose response. Te acts via negative dose-responsive feedback on GnRH and LH output, thus fulfilling conditions of a closed-loop control system. Four computer simulations document expected feedback performance, as published earlier for the human male GnRH-LH-Te axis. Six other simulations test distinct within-model coupling mechanisms to link a circadian modulatory input to a pulsatile control node so as to explicate the known 24-h variations in Te and, to a lesser extent, LH. We conclude that relevant dynamic function, internodal dose-dependent regulatory connections, and within-system time-delayed coupling together provide a biomathematical basis for a nonlinear feedback-feedforward control model with combined pulsatile and circadian features that closely emulate the measurable output activities of the male hypothalamic-pituitary-Leydig cell axis.We develop, implement, and test a feedback and feedforward biomathematical construct of the male hypothalamic [gonadotropin-releasing hormone (GnRH)]-pituitary [luteinizing hormone (LH)]-gonadal [testosterone (Te)] axis. This stochastic differential equation formulation consists of a nonstationary stochastic point process responsible for generating episodic release of GnRH, which is modulated negatively by short-loop (GnRH) and long-loop (Te) feedback. Pulsatile GnRH release in turn drives bursts of LH secretion via an agonistic dose-response curve that is partially damped by Te negative feedback. Circulating LH stimulates (feedforward) Te synthesis and release by a second dose response. Te acts via negative dose-responsive feedback on GnRH and LH output, thus fulfilling conditions of a closed-loop control system. Four computer simulations document expected feedback performance, as published earlier for the human male GnRH-LH-Te axis. Six other simulations test distinct within-model coupling mechanisms to link a circadian modulatory input to a pulsatile control node so as to explicate the known 24-h variations in Te and, to a lesser extent, LH. We conclude that relevant dynamic function, internodal dose-dependent regulatory connections, and within-system time-delayed coupling together provide a biomathematical basis for a nonlinear feedback-feedforward control model with combined pulsatile and circadian features that closely emulate the measurable output activities of the male hypothalamic-pituitary-Leydig cell axis.

Sensitivity and specificity of pulse detection using a new deconvolution method

Quantifying pulsatile secretion from serial hormone concentration measurements (deconvolution analysis) requires automated, objective, and accurate detection of pulse times to ensure valid estimation of secretion and elimination parameters. Lack of validated pulse identification constitutes a major deficiency in the deconvolution field, because individual pulse size and number reflect regulated processes that are critical for the function and response of secretory glands. To evaluate deconvolution pulse detection accuracy, four empirical models of true-positive markers of pituitary (LH) pulses were used. 1) Sprague-Dawley rats had recordings of hypothalamic arcuate nucleus multiunit electrical activity, 2) ovariectomized ewes underwent sampling of hypothalamo-pituitary gonadotropin-releasing hormone (GnRH pulses), 3) healthy young men were infused with trains of biosynthetic LH pulses after GnRH receptor blockade, and 4) computer simulations of pulsatile LH profiles were constructed. Outcomes comprised sensitivity, specificity, and receiver-operating characteristic curves. Sensitivity and specificity were 0.93 and 0.97, respectively, for combined empirical data in the rat, sheep, and human (n = 156 pulses) and 0.94 and 0.92, respectively, for computer simulations (n = 1,632 pulses). For simulated data, pulse-set selection by the Akaike information criterion yielded slightly higher sensitivity than by the Bayesian information criterion, and the reverse was true for specificity. False-positive errors occurred primarily at low-pulse amplitude, and false-negative errors occurred principally with close pulse proximity. Random variability (noise), sparse sampling, and rapid pulse frequency reduced pulse detection sensitivity more than specificity. We conclude that an objective automated pulse detection deconvolution procedure has high sensitivity and specificity, thus offering a platform for quantitative neuroendocrine analyses.

A Stochastic Biomathematical Model of the Male Reproductive Hormone System

A stochastic biomathematical model for the male reproductive hormone system (gonadotropin-releasing hormone, luteinizing hormone, and testosterone) is developed. Hormone secretion occurs as either a continuous release, a pulsatile release, or a combination thereof; in the latter two, hormone molecules are stored and later released. Each form of release is represented within the male system. The model begins at the cellular level of hormone synthesis, aggrandizes to the level of the gland and secretion, and finally to the level of elimination and circulation in the blood. The model consists of a system of stochastic integrodifferential equations which describe the nonlinear time-delayed feedback from concentrations (of the various hormones) on their rates of hormone synthesis. A stochastic formulation is established, showing that the various imposed structures are consistent with one another. Computer experiments are performed and compared to analogous clinical experiments (where components are decoupled v...

The aging male hypothalamic–pituitary–gonadal axis: Pulsatility and feedback

Aging results in insidious decremental changes in hypothalamic, pituitary and gonadal function. The foregoing three main anatomic loci of control are regulated by intermittent time-delayed signal exchange, principally via gonadotropin-releasing hormone (GnRH), luteinizing hormone (LH) and testosterone/estradiol (Te/E(2)). A mathematical framework is required to embody these dynamics. The present review highlights integrative adaptations in the aging male hypothalamic-pituitary-gonadal axis, as assessed by recent objective ensemble models of the axis as a whole.

Joint recovery of pulsatile and basal hormone secretion by stochastic nonlinear random-effects analysis.

We present a nonlinear random-effects stochastic differential equation (SDE) model of combined basal and pulsatile hormone secretion with a series-specific hormone half-life and conditional pulse times. The construct uses a three-parameter pulse shape (generalized gamma function) to allow variably skewed secretory bursts superimposed on a finite basal hormone secretion rate. The analysis imbeds stochastic elements at three levels: a variable mass of hormone accumulation (of which the random effect is a part) during interpulse intervals, nonuniform secretion with hormone admixture into the circulation, and technical (sampling and assay) experimental uncertainty. We implement maximum likelihood estimates of secretory parameters (basal and pulsatile secretion and half-life) with asymptotic standard errors. The model applied to illustrative human luteinizing hormone (LH) time series suggests contrasts in basal LH secretion rates (e.g., greater in postmenopausal women than men) and LH secretory burst mass (e.g., higher in older women), but not LH burst frequency or distributional LH half-lives (7-40 min). For validation, in two infused (human recombinant) LH profiles, we implement partially constrained mono- and biexponential versions of the model with fixed (a priori assumed) versus variable LH basal secretion rates. We conclude that a statistically supported, nonlinear, random effects, SDE-based construct can evaluate jointly basal and pulsatile LH secretory rates and LH half-life in 24 h, episodically varying serum LH concentration profiles. This new reduced-parameter analytic strategy should be useful to explore further the pathophysiological mechanisms of altered neurohormone secretion.We present a nonlinear random-effects stochastic differential equation (SDE) model of combined basal and pulsatile hormone secretion with a series-specific hormone half-life and conditional pulse times. The construct uses a three-parameter pulse shape (generalized gamma function) to allow variably skewed secretory bursts superimposed on a finite basal hormone secretion rate. The analysis imbeds stochastic elements at three levels: a variable mass of hormone accumulation (of which the random effect is a part) during interpulse intervals, nonuniform secretion with hormone admixture into the circulation, and technical (sampling and assay) experimental uncertainty. We implement maximum likelihood estimates of secretory parameters (basal and pulsatile secretion and half-life) with asymptotic standard errors. The model applied to illustrative human luteinizing hormone (LH) time series suggests contrasts in basal LH secretion rates (e.g., greater in postmenopausal women than men) and LH secretory burst mass (e.g., higher in older women), but not LH burst frequency or distributional LH half-lives (7-40 min). For validation, in two infused (human recombinant) LH profiles, we implement partially constrained mono- and biexponential versions of the model with fixed (a priori assumed) versus variable LH basal secretion rates. We conclude that a statistically supported, nonlinear, random effects, SDE-based construct can evaluate jointly basal and pulsatile LH secretory rates and LH half-life in 24 h, episodically varying serum LH concentration profiles. This new reduced-parameter analytic strategy should be useful to explore further the pathophysiological mechanisms of altered neurohormone secretion.

Prolactin Secretion in Healthy Adults Is Determined by Gender, Age and Body Mass Index

Background Prolactin (PRL) secretion is quantifiable as mean, peak and nadir PRL concentrations, degree of irregularity (ApEn, approximate entropy) and spikiness (brief staccato-like fluctuations). Hypothesis Distinct PRL dynamics reflect relatively distinct (combinations of) subject variables, such as gender, age, and BMI. Location Clinical Research Unit. Subjects Seventy-four healthy adults aged 22–77 yr (41 women and 33 men), with BMI 18.3–39.4 kg/m2. Measures Immunofluorometric PRL assay of 10-min samples collected for 24 hours. Results Mean 24-h PRL concentration correlated jointly with gender (P<0.0001) and BMI (P = 0.01), but not with age (overall R2 = 0.308, P<0.0001). Nadir PRL concentration correlated with gender only (P = 0.017) and peak PRL with gender (P<0.001) and negatively with age (P<0.003), overall R2 = 0.325, P<0.0001. Forward-selection multivariate regression of PRL deconvolution results demonstrated that basal (nonpulsatile) PRL secretion tended to be associated with BMI (R2 = 0.058, P = 0.03), pulsatile secretion with gender (R2 = 0.152, P = 0.003), and total secretion with gender and BMI (R2 = 0.204, P<0.0001). Pulse mass was associated with gender (P = 0.001) and with a negative tendency to age (P = 0.038). In male subjects older than 50 yr (but not in women) approximate entropy was increased (0.942±0.301 vs. 1.258±0.267, P = 0.007) compared with younger men, as well as spikiness (0.363±0.122 vs. 0463±2.12, P = 0.031). Cosinor analysis disclosed higher mesor and amplitude in females than in men, but the acrophase was gender-independent. The acrophase was determined by age and BMI (R2 = 0.186, P = 0.001). Conclusion In healthy adults, selective combinations of gender, age, and BMI specify distinct PRL dynamics, thus requiring balanced representation of these variables in comparative PRL studies.

A Time Series Analysis of Binary Data

Abstract Binary data d 1, d 2, …, dn are assumed to be generated by an underlying real-valued, strictly stationary process, {Xk }, and a response function F. For a given monotone nondecreasing function F from R to [0, 1], Dk takes on 1 with probability F(xk ) and 0 with probability 1 - F(xk ), where Xk = xk. It is shown that all strictly stationary binary processes are characterized by such a procedure. Several approximations to the n-dimensional joint probabilities of Dk are developed when Xk is a Gaussian first-order autoregressive process. Model-building procedures and methods by which to estimate parameters of a given model are discussed. The predictor of d n + 1 that minimizes probability of error among all randomized rules is determined and for certain cases a bound for this probability is found.