Bayesian deconvolution analysis of pulsatile hormone concentration profiles

Many hormones are secreted into the circulatory system in a pulsatile manner and are cleared exponentially. The most common method of analyzing these systems is to deconvolve the hormone concentration into a secretion function and a clearance function. Accurate estimation of the model parameters depends on the number and location of the secretion pulses. To date, deconvolution analysis assumes the number and approximate location of these pulses are known a priori. In this article, we present a novel Bayesian approach to deconvolution that jointly models the number of pulses along with all other model parameters. Our method stochastically searches for the secretion pulses. This is accomplished by viewing the set of parameters that define the pulses as a point process. Pulses are determined by a birth-death process which is embedded in Markov chain Monte Carlo algorithm. This idea originated with Stephens (2000, Annals of Statistics 28, 40-74) in the context of finite mixture model density estimation, where the number of mixture components is unknown. There are several advantages that our model enjoys over the traditional frequentist approaches. These advantages are highlighted with four datasets consisting of serum concentration levels of luteinizing hormone obtained from ovariectomized ewes.     

A Bayesian approach to modeling associations between pulsatile hormones

Summary .  Many hormones are secreted in pulses. The pulsatile relationship between hormones regulates many biological processes. To understand endocrine system regulation, time series of hormone concentrations are collected. The goal is to characterize pulsatile patterns and associations between hormones. Currently each hormone on each subject is fitted univariately. This leads to estimates of the number of pulses and estimates of the amount of hormone secreted; however, when the signal-to-noise ratio is small, pulse detection and parameter estimation remains difficult with existing approaches. In this article, we present a bivariate deconvolution model of pulsatile hormone data focusing on incorporating pulsatile associations. Through simulation, we exhibit that using the underlying pulsatile association between two hormones improves the estimation of the number of pulses and the other parameters defining each hormone. We develop the one-to-one, driver–response case and show how birth–death Markov chain Monte Carlo can be used for estimation. We exhibit these features through a simulation study and apply the method to luteinizing and follicle stimulating hormones.     

Detecting pulsatile hormone secretions using nonlinear mixed effects partial spline models

Neuroendocrine ensembles communicate with their remote and proximal target cells via an intermittent pattern of chemical signaling. The identification of episodic releases of hormonal pulse signals constitutes a major emphasis of endocrine investigation. Estimating the number, temporal locations, secretion rate, and elimination rate from hormone concentration measurements is of critical importance in endocrinology. In this article, we propose a new flexible statistical method for pulse detection based on nonlinear mixed effects partial spline models. We model pulsatile secretions using biophysical models and investigate biological variation between pulses using random effects. Pooling information from different pulses provides more efficient and stable estimation for parameters of interest. We combine all nuisance parameters including a nonconstant basal secretion rate and biological variations into a baseline function that is modeled nonparametrically using smoothing splines. We develop model selection and parameter estimation methods for the general nonlinear mixed effects partial spline models and an R package for pulse detection and estimation. We evaluate performance and the benefit of shrinkage by simulations and apply our methods to data from a medical experiment.     

Modeling of hormone secretion-generating mechanisms with splines: a pseudo-likelihood approach

A flexible and robust approach is proposed for the investigation of underlying hormone secretion-generating mechanisms. Characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by slow decay. We model hormone concentration as a filtered counting process where the intensity function of the counting process is modeled nonparametrically using periodic splines. The intensity function and parameters are estimated using a combination of weighted least squares and pseudo-likelihood based on the first two moments. Our method uses concentration measurements directly, which avoids the difficult task of estimating pulse numbers and locations. Both simulations and applications suggest that our method performs well for estimating the intensity function of the pulse-generating counting processes.     

Measurement of pulsatile insulin secretion in the rat: direct sampling from the hepatic portal vein

It has previously been shown that insulin is secreted in discrete secretory bursts by sampling directly from the portal vein in the dog and humans. Deficient pulsatile insulin secretion is the basis for impaired insulin secretion in type 2 diabetes. However, while novel genetically modified disease models of diabetes are being developed in rodents, no validated method for quantifying pulsatile insulin secretion has been established for rodents. To address this we 1) developed a novel rat model with chronically implanted portal vein catheters, 2) established the parameters to permit deconvolution of portal vein insulin concentrations profiles to measure insulin secretion and resolve its pulsatile components, and 3) measured total and pulsatile insulin secretion compared with that in the dog, the species in which this sampling and deconvolution approach was validated for quantifying pulsatile insulin secretion. In rats, portal vein catheter patency and function were maintained for periods up to 2-3 wk with no postoperative complications such as catheter tract infection. Rat portal vein insulin concentration profiles in the fasting state revealed distinct insulin oscillations with a periodicity of approximately 5 min and an amplitude of up to 600 pmol/l, which was remarkably similar to that in the dogs and in humans. Deconvolution analysis of portal vein insulin concentrations revealed that the majority of insulin ( approximately 70%) in the rat is secreted in distinct insulin pulses occurring at approximately 5-min intervals. This model therefore permits direct accurate measurements of pulsatile insulin secretion in a relatively inexpensive animal. With increased introduction of genetically modified rat models will be an important tool in elucidating the underlying mechanisms of impaired pulsatile insulin secretion in diabetes.     

Deconvolution as a novel approach to analyze moment-to-moment free fatty acid release

Objective: Recent studies have shown that free fatty acid (FFA) release is pulsatile and that this pattern is controlled by the sympathetic nervous system. It is, then, necessary to understand and characterize adipose tissue lipolysis to elucidate its effect on metabolism. In this study, we introduce deconvolution as a method to detect and quantify pulsatile FFA release. Research Methods and Procedures: Octanoate, a medium‐chain fatty acid, was infused in male mongrel dogs (n = 7) to mimic the pulsatile appearance of plasma FFAs. Deconvolution analysis was used to reconstruct the number and timing of infused octanoate pulses from plasma FFA concentrations. Results: Deconvolution analysis was able to reconstruct the exogenously infused pulses of octanoate used to mimic pulsatile appearance of FFAs (pulse frequency, 8 per hour; interpulse interval, 7 minutes). However, determination of pulse mass was less accurate (1.0 ± 0.0 vs. 0.54 ± 0.1 mM). The addition of varying levels of Gaussian noise to non‐oscillatory FFA time series did not lead to detection of extraneous FFA pulses. However, goodness of fit declined with increasing variability. Discussion: These results support the use of deconvolution as an accurate approach to determine the temporal sequence of endogenous FFA release.     

Glucose ingestion acutely lowers pulsatile LH and basal testosterone secretion in men

Chronic hyperglycemia inhibits the male gonadal axis. The present analyses test the hypothesis that acute glucose ingestion also suppresses LH and testosterone (T) secretion and blunts the LH-T dose-response function. The design comprised a prospectively randomized crossover comparison of LH and T secretion after glucose vs. water ingestion in a Clinical Translational Research Center. The participants were healthy men (n = 57) aged 19-78 yr with body mass index (BMI) of 20-39 kg/m(2). The main outcome measurements were deconvolution and LH-T dose-response analyses of 10-min data. LH-T responses were regressed on glucose, insulin, leptin, adiponectin, age, BMI, and CT-estimated abdominal visceral fat. During the first 120 min after glucose ingestion, for each unit decrease in LH concentrations, T concentrations decreased by 86 (27-144) ng/dl (r = 0.853, P < 0.001). Based upon deconvolution analysis, glucose compared with water ingestion reduced 1) basal (nonpulsatile; P < 0.001) and total (P < 0.001) T secretion without affecting pulsatile T output and 2) pulsatile (P = 0.043) but not basal LH secretion. By multivariate analysis, pulsatile LH secretion positively predicted basal T secretion after glucose ingestion (r = 0.374, P = 0.0042). In addition, the glucose-induced fall in pulsatile LH secretion was exacerbated by higher fasting insulin concentrations (P = 0.054) and attenuated by higher adiponectin levels (P = 0.0037). There were no detectable changes in the analytically estimated LH-T dose-response curves (P > 0.30). In conclusion, glucose ingestion suppresses pulsatile LH and basal T secretion acutely in healthy men. Suppression is influenced by age, glucose, adiponectin, and insulin concentrations.     

Pulsatile Release from Microencapsulated Liposomes

Abstract

Ideally, release profiles of drugs from drug delivery systems should be designed to meet specific demands, such as release at a specific time points and predetermined doses; however most systems lack these capabilities. Liposomes are an example of a delivery system that generally release its contents in a continuous fashion. We have pursed two approaches of pulsatile release- that is, release of bursts of incorporated drug at specific time points- with microencapsulated liposomes. In the first approach our studies revealed that the encapsulation of certain liposomes within alginate-poly (L-lysine) microcapsules produce systems that release their contents in a pulsatile manner. In the second approach, enzymatically controlled pulsatile release from microencapsulated liposomes was achieved by incorporating phospholipase A₂ into the systems. In both systems, the number of pulses and duration between the pulses could be regulated by selecting lipid composition, enzyme concentration and type, and other parameters, such as polyelectrolyte (alginate, poly(L-lysine)) and calcium ion concentrations.     

Deconvolution of Serum Cortisol Levels by Using Compressed Sensing

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R ² above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.     

Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

An Adaptive Location‐Scale Test

Increasing locations are often accompanied by an increase in variability. In this case apparent heteroscedasticity can indicate that there are treatment effects and it is appropriate to consider an alternative involving differences in location as well as in scale. As a location‐scale test the sum of a location and a scale test statistic can be used. However, the power can be raised through weighting the sum. In order to select values for this weighting an adaptive design with an interim analysis is proposed: The data of the first stage are used to calculate the weights and with the second stage's data a weighted location‐scale test is carried out. The p‐values of the two stages are combined through Fisher's combination test. With a Lepage‐type location‐scale test it is illustrated that the resultant adaptive test can be more powerful than the ‘optimum’ test with no interim analysis. The principle to calculate weights, which cannot be reasonably chosen a priori, with the data of the first stage may be useful for other tests which utilize weighted statistics, too. Furthermore, the proposed test is illustrated with an example from experimental ecology.     

Implied Spatial Meaning and Visuospatial Bias: Conceptual Processing Influences Processing of Visual Targets and Distractors

Concepts with implicit spatial meaning (e.g., "hat", "boots") can bias visual attention in space. This result is typically found in experiments with a single visual target per trial, which can appear at one of two locations (e.g., above vs. below). Furthermore, the interaction is typically found in the form of speeded responses to targets appearing at the compatible location (e.g., faster responses to a target above fixation, after reading "hat"). It has been argued that these concept-space interactions could also result from experimentally-induced associations between the binary set of locations and the conceptual categories with upward and downward meaning. Thus, rather than reflecting a conceptually driven spatial bias, the effect could reflect a benefit for compatible cue-target sequences that occurs only after target onset. We addressed these concerns by going beyond a binary set of locations and employing a search display consisting of four items (above, below, left, and right). Within each search trial, before performing a visual search task, participants performed a conceptual task involving concepts with implicit upward or downward meaning. The search display, in addition to including a target, could also include a salient distractor. Assuming a conceptually driven visual bias, we expected to observe, first, a benefit for target processing at the compatible location and, second, an increase in the cost of the salient distractor. The findings confirmed both predictions, suggesting that concepts do indeed generate a spatial bias. Finally, results from a control experiment, without the conceptual task, suggest the presence of an axis-specific effect, in addition to the location-specific effect, suggesting that concepts might cause both location-specific and axis-specific spatial bias. Taken together, our findings provide additional support for the involvement of spatial processing in conceptual understanding.     

Models of the pulsatile hydrodynamics of cerebrospinal fluid flow in the normal and abnormal intracranial system

Images obtained from magnetic resonance imaging have helped to ascertain that both the cerebrospinal fluid (CSF) and brain move in a pulsatile manner within the cranium. However, these images are not able to reveal any quantitative information on the physiological forces that are associated with pulsatile motion. Understanding both the pressure and velocity flow field of CSF in the ventricles is important to help understand the mechanics of hydrocephalus. Four separate fluid structure interaction models of the ventricular system in the sagittal plane were created for this purpose. The first model was of a normal brain. The second and third models were pathological brain models with aqueductal stenosis at various locations along the fluid pathway. The fourth model was of a hydrocephalic brain. Results revealed the hydrodynamics of CSF pulsatile flow in the ventricles of these models. Most importantly, it has also revealed the different changes in CSF pulsatile hydrodynamics caused by the various locations of fluid flow obstructions.     

AutoDecon, a deconvolution algorithm for identification and characterization of luteinizing hormone secretory bursts: description and validation using synthetic data

Hormone signaling is often pulsatile, and multiparameter deconvolution procedures have long been used to identify and characterize secretory events. However, the existing programs have serious limitations, including the subjective nature of initial peak selection, lack of statistical verification of presumed bursts, and user-unfriendliness of the application. Here we describe a novel deconvolution program, AutoDecon, which addresses these concerns. We validate AutoDecon for application to serum luteinizing hormone (LH) concentration time series using synthetic data mimicking real data from normal women and then comparing the performance of AutoDecon with the performance of the widely employed hormone pulsatility analysis program Cluster. The sensitivity of AutoDecon is higher than that of Cluster (∼ 96% vs. 80%, P = 0.001). However, Cluster had a lower false-positive detection rate than did AutoDecon (6% vs. 1%, P = 0.001). Further analysis demonstrated that the pulsatility parameters recovered by AutoDecon were indistinguishable from those characterizing the synthetic data and that sampling at 5- or 10-min intervals was optimal for maximizing the sensitivity rates for LH. Accordingly, AutoDecon presents a viable nonsubjective alternative to previous pulse detection algorithms for the analysis of LH data. It is applicable to other pulsatile hormone concentration time series and many other pulsatile phenomena. The software is free and downloadable at http://mljohnson.pharm.virginia.edu/home.html.     

Nonquasi-steady character of pulsatile flow in human coronary arteries

This experiment was conducted to determine if the pulsatile flow through the proximal portion of the left coronary artery system in man exhibits quasi-steady characteristics. Steady and pulsatile flows were passed through an idealized model whose dimensions were based on a vascular cast. The mean Reynolds number was 180 and the unsteadiness number was 2.7. Velocity profiles were measured by laser Doppler anemometry at several locations along diameters in the parent and both daughter channels in the neighborhood of the "left main" bifurcation. Analysis of the results along one diameter in the "left main" channel shows that unsteady flow in the larger coronary arteries may not be simulated by a series of steady flow experiments.     

Bayesian Semiparametric Multiple Shrinkage

Summary High‐dimensional and highly correlated data leading to non‐ or weakly identified effects are commonplace. Maximum likelihood will typically fail in such situations and a variety of shrinkage methods have been proposed. Standard techniques, such as ridge regression or the lasso, shrink estimates toward zero, with some approaches allowing coefficients to be selected out of the model by achieving a value of zero. When substantive information is available, estimates can be shrunk to nonnull values; however, such information may not be available. We propose a Bayesian semiparametric approach that allows shrinkage to multiple locations. Coefficients are given a mixture of heavy‐tailed double exponential priors, with location and scale parameters assigned Dirichlet process hyperpriors to allow groups of coefficients to be shrunk toward the same, possibly nonzero, mean. Our approach favors sparse, but flexible, structure by shrinking toward a small number of random locations. The methods are illustrated using a study of genetic polymorphisms and Parkinson's disease.     

Modification of prostaglandin F-2 alpha synthesis and release in the ewe during the initial establishment of pregnancy

Pregnant (N = 10) and non-pregnant (N = 10) ewes were bled every 2 h from Days 12 to 17 after oestrus (oestrus = Day 0). Plasma concentrations of progesterone, 15-keto-13,14-dihydro-PGF-2 alpha and 11-ketotetranor-PGF metabolites were determined in all samples. The number of PGF-2 alpha pulses in non-pregnant ewes was 8.2 +/- 0.4 (mean +/- s.e.m.) with an interpulse interval of 10.7 +/- 0.7 h. Two or 3 pulses of low frequency (interpulse interval = 13.4 +/- 1.6 h) occurred in most non-pregnant ewes before the onset of luteolysis; the interpulse interval then decreased to 7.9 +/- 0.4 h for the 6.0 +/- 0.3 pulses temporally associated with luteolysis. In contrast, the number of PGF-2 alpha pulses in pregnant ewes was lower (2.5 +/- 0.7, 0-8) and the interpulse intervals longer (18.9 +/- 6.1 h). Most pulses occurred on Days 14 and 15 in the pregnant and non-pregnant ewes. The mean concentrations of both PGF-2 alpha metabolites in non-pregnant ewes were highest on Day 15 while basal levels of both metabolites remained constant at all times. In pregnant ewes, the mean concentrations of both metabolites were highest on Day 14; basal concentrations of both metabolites were also highest on Day 14. The mean concentrations of 15-keto-13,14-dihydro-PGF-2 alpha were higher in pregnant than in non-pregnant ewes on Days 13 and 14 (P less than 0.05) and higher in non-pregnant than pregnant ewes on Day 15 (P less than 0.05). The basal concentrations of the 15-keto metabolite were higher in pregnant than non-pregnant ewes at Days 13, 14, 15, 16 and 17 (P less than 0.05). Both the mean and the basal concentrations of 11-ketotetranor-PGF metabolites were higher in pregnant than in non-pregnant ewes on Day 14 (P less than 0.05). It is concluded that uterine production of PGF-2 alpha peaks at Days 14-15 after oestrus in pregnant and non-pregnant ewes. Patterns of release differ, however, in that non-pregnant ewes have a pulsatile PGF-2 alpha pattern superimposed on a constant baseline, while pregnant ewes have an increasing basal secretory pattern which is more nearly continuous, i.e. not pulsatile in form. Modification of pulsatile PGF-2 alpha synthesis and release is therefore a key aspect of prolongation of luteal function at the beginning of pregnancy in the ewe.     

Pulsatile release of immunoreactive luteinizing hormone (irLH) in hypophysectomized male rats

The concentration of plasma luteinizing hormone (LH) was monitored every minute by radioimmunoassay in male rats that were either hypophysectomized, or castrated and hypophysectomized. Castrated rats showed a pulsatile fluctuation of plasma immunoreactive LH (irLH) concentration with an elevated basal level, confirming previous work. The hypophysectomized and castrated hypophysectomized rats also showed pulsatile changes in plasma irLH concentration. This unexpected result indicates that ectopic irLH is not only actively released after hypophysectomy, but is released in pulses. The pulse interval was approximately 20 minutes for all 3 groups. The slope of the rate of decline of plasma irLH in the castrated rats is parallel to a theoretical disappearance rate of 5 min, while these slopes in the hypophysectomized and castrated hypophysectomized rats correspond to a 1 to 2-min disappearance rate. The difference in these slopes implies that the two irLH molecules may not be identical.