Leon S. Farhy

Modeling of oscillations in endocrine networks with feedback.

Publisher Summary This chapter focuses on the mathematical approximation of endocrine oscillations in the framework of a modeling process structured in three formal phases. The mathematical methods presented are tailored to quantitatively interpret formal endocrine networks with (delayed) feedbacks. The goal is to illustrate different conditions, under which oscillations can emerge. The formal network itself consists of nodes and conduits, and is based on a qualitative analysis of available experimental data. In the presentation, the nodes are hormone concentrations in abstract pools, in which hormones are released or synthesized, under the control of other hormones. The conduits specify how the nodes interact within the network. The quantitative analysis of the formal network is based on approximation of the rate of change of a single system node. This essentially means that the dynamics of the hormone concentration is described with a single (delayed) ODE. A single half-life elimination model is used and the control of the synthesis is expressed as a combination of sigmoid Hill functions, depending on the related nodes. The derivation of the ODE is demonstrated, along with a brief analysis of the properties of its solution to facilitate the actual determination of all system parameters.

Evidence for Acyl-Ghrelin Modulation of Growth Hormone Release in the Fed State

CONTEXT The timing and frequency of GH secretory episodes is regulated by GHRH and somatostatin. This study provides evidence for amplification of these GH pulses by endogenous acyl-ghrelin. DESIGN Blood was sampled every 10 min for 26.5 h during a fed admission with standardized meals and also during the final 24 h of a 61.5-h fast. GH secretion profiles were derived from deconvolution of 10-min sampling data, and full-length acyl-ghrelin levels were measured using a newly developed two-site sandwich assay. SETTING The study was conducted at a university hospital general clinical research center. PARTICIPANTS Participants included eight men with mean (+/- sd) age 24.5 +/- 3.7 yr (body mass index 24 +/- 2.1 kg/m(2)). RESULTS Correlations were computed between amplitudes of individual GH secretory events and the average acyl-ghrelin concentration in the 60-min interval preceding each GH burst. In the fed state, the peak correlations were positive for all subjects and significantly higher than in the fasting state when acyl-ghrelin levels declined [mean (+/- sem): 0.7 (0.04) vs. 0.29 (0.08), P = 0.017]. In addition, long-term fasting was associated with an increase in the GH secretory pulse mass and amplitude but not frequency [fed vs. fasting pulse mass: 0.22 (0.05) vs. 0.44 (0.06) microg/liter, P = 0.002; amplitude: 5.2 (1.3) vs. 11.8 (1.9) microg/liter/min, P = 0.034; pulses per 24 h: 19.4 (0.5) vs. 22.0 (1.4), P = 0.1]. CONCLUSION Our data support the hypothesis that under normal conditions in subjects given regular meals endogenous acyl-ghrelin acts to increase the amplitude of GH pulses.

Sample asymmetry analysis of heart rate characteristics with application to Neonatal sepsis and systemic inflammatory response syndrome

We introduce the sample asymmetry analysis (SAA) and illustrate its utility for assessment of heart rate characteristics occurring early in the course of neonatal sepsis and systemic inflammatory response syndrome (SIRS). Conceptually, SAA describes changes in the shape of the histogram of RR intervals that are caused by reduced accelerations and/or transient decelerations of heart rate. Unlike other measures of heart rate variability, SAA allows separate quantification of the contribution of accelerations and decelerations. The application of SAA is exemplified by a study comparing 50 infants, who experienced a total of 75 episodes of sepsis and SIRS, with 50 control infants. The two groups were matched by birth weight and gestational age. RR intervals were recorded for all infants throughout their course in the Neonatal Intensive Care Unit. The sample asymmetry of the RR intervals increased in the 3–4 d preceding sepsis and SIRS, with the steepest increase in the last 24 h, from a baseline value of 3.3 (SD = 1.6) to 4.2 (SD = 2.3), p = 0.02. After treatment and recovery, sample asymmetry returned to its baseline value of 3.3 (SD = 1.3). The difference between sample asymmetry in health and before sepsis and SIRS was mainly due to fewer accelerations than to decelerations. Compared with healthy infants, infants who experienced sepsis had similar sample asymmetry in health, and elevated values before sepsis and SIRS (p = 0.002). We conclude that SAA is a useful new mathematical technique for detecting the abnormal heart rate characteristics that precede neonatal sepsis and SIRS.

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 ( approximately 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.

AutoDecon: a robust numerical method for the quantification of pulsatile events.

This work presents a new approach to the analysis of aperiodic pulsatile heteroscedastic time-series data, specifically hormone pulsatility. We have utilized growth hormone (GH) concentration time-series data as an example for the utilization of this new algorithm. While many previously published approaches used for the analysis of GH pulsatility are both subjective and cumbersome to use, AutoDecon is a nonsubjective, standardized, and completely automated algorithm. We have employed computer simulations to evaluate the true-positive, the false-positive, the false-negative, and the sensitivity percentages of several of the routinely employed algorithms when applied to GH concentration time-series data. Based on these simulations, it was concluded that this new algorithm provides a substantial improvement over the previous methods. This novel method has many direct applications in addition to hormone pulsatility, for example, to time-domain fluorescence lifetime measurements, as the mathematical forms that describe these experimental systems are both convolution integrals.

Biomathematical Modeling of Pulsatile Hormone Secretion: A Historical Perspective

Shortly after the recognition of the profound physiological significance of the pulsatile nature of hormone secretion, computer-based modeling techniques were introduced for the identification and characterization of such pulses. Whereas these earlier approaches defined perturbations in hormone concentration-time series, deconvolution procedures were subsequently employed to separate such pulses into their secretion event and clearance components. Stochastic differential equation modeling was also used to define basal and pulsatile hormone secretion. To assess the regulation of individual components within a hormone network, a method that quantitated approximate entropy within hormone concentration-times series was described. To define relationships within coupled hormone systems, methods including cross-correlation and cross-approximate entropy were utilized. To address some of the inherent limitations of these methods, modeling techniques with which to appraise the strength of feedback signaling between and among hormone-secreting components of a network have been developed. Techniques such as dynamic modeling have been utilized to reconstruct dose-response interactions between hormones within coupled systems. A logical extension of these advances will require the development of mathematical methods with which to approximate endocrine networks exhibiting multiple feedback interactions and subsequently reconstruct their parameters based on experimental data for the purpose of testing regulatory hypotheses and estimating alterations in hormone release control mechanisms.

Age-dependent decline in acyl-ghrelin concentrations and reduced association of acyl-ghrelin and growth hormone in healthy older adults.

BACKGROUND Acyl-ghrelin is thought to have both orexigenic effects and to stimulate GH release. A possible cause of the anorexia of aging is an age-dependent decrease in circulating acyl-ghrelin levels. OBJECTIVES The purpose of the study was to compare acyl-ghrelin and GH concentrations between healthy old and young adults and to examine the relationship of acyl-ghrelin and GH secretion in both age groups. METHODS Six healthy older adults (age 62-74 y, body mass index range 20.9-29 kg/m(2)) and eight healthy young men (aged 18-28 y, body mass index range 20.6-26.2 kg/m(2)) had frequent blood samples drawn for hormone measurements every 10 minutes for 24 hours. Ghrelin was measured in an in-house, two-site sandwich ELISA specific for full-length acyl-ghrelin. GH was measured in a sensitive assay (Immulite 2000), and GH peaks were determined by deconvolution analysis. The acyl-ghrelin/GH association was estimated from correlations between amplitudes of individual GH secretory events and the average acyl-ghrelin concentration in the 60-minute interval preceding each GH burst. RESULTS Twenty-four-hour mean (±SEM) GH (0.48 ± 0.14 vs 2.2 ± 0.3 μg/L, P < .005) and acyl-ghrelin (14.7 ± 2.3 vs 27.8 ± 3.9 pg/mL, P < .05) levels were significantly lower in older adults compared with young adults. Twenty-four-hour cortisol concentrations were higher in the old than the young adults (15.1 ± 1.0 vs 10.6 ± 0.9 μg/dL, respectively, P < .01). The ghrelin/GH association was more than 3-fold lower in the older group compared with the young adults (0.16 ± 0.12 vs 0.69 ± 0.04, P < .001). CONCLUSIONS These results provide further evidence of an age-dependent decline in circulating acyl-ghrelin levels, which might play a role both in the decline of GH and in the anorexia of aging. Our data also suggest that with normal aging, endogenous acyl-ghrelin levels are less tightly linked to GH regulation.

Amplification of pulsatile glucagon counterregulation by switch-off of α-cell-suppressing signals in streptozotocin-treated rats

Glucagon counterregulation (GCR) is a key protection against hypoglycemia that is compromised in diabetes via an unknown mechanism. To test the hypothesis that alpha-cell-inhibiting signals that are switched off during hypoglycemia amplify GCR, we studied streptozotocin (STZ)-treated male Wistar rats and estimated the effect on GCR of intrapancreatic infusion and termination during hypoglycemia of saline, insulin, and somatostatin. Times 10 min before and 45 min after the switch-off were analyzed. Insulin and somatostatin, but not saline, switch-off significantly increased the glucagon levels (P = 0.03), and the fold increases relative to baseline were significantly higher (P < 0.05) in the insulin and somatostatin groups vs. the saline group. The peak concentrations were also higher in the insulin (368 pg/ml) and somatostatin (228 pg/ml) groups vs. the saline (114 pg/ml) group (P < 0.05). GCR was pulsatile in most animals, indicating a feedback regulation. After the switch-off, the number of secretory events and the total pulsatile production were lower in the saline group vs. the insulin and somatostatin groups (P < 0.05), indicating enhancement of glucagon pulsatile activity by insulin and somatostatin compared with saline. Network modeling analysis demonstrates that reciprocal interactions between alpha- and delta-cells can explain the amplification by interpreting the GCR as a rebound response to the switch-off. The model justifies experimental designs to further study the intrapancreatic network in relation to the switch-off phenomenon. The results of this proof-of-concept interdisciplinary study support the hypothesis that GCR develops as a rebound pulsatile response of the intrapancreatic endocrine feedback network to switch-off of alpha-cell-inhibiting islet signals.

Association of self-monitoring blood glucose profiles with glycosylated hemoglobin in patients with insulin-dependent diabetes.

Publisher Summary This chapter describes the association of self-monitoring blood glucose profiles, with glycosylated hemoglobin, in patients with insulin-dependent diabetes. Researchers have known for more than 20 years that glycosylated hemoglobin (Hb) is a marker for the glycemic control of individuals, with insulin-dependent diabetes mellitus (IDDM). Numerous studies have investigated this relationship and found that glycosylated hemoglobin generally reflects the average blood glucose (BG) levels of an IDDM patient over the past two months. However, the rapid development of home BG monitoring devices somewhat changes this conclusion. Contemporary memory meters store up to several hundred self-monitoring BG (SMBG) readings and can calculate various statistics, including the mean of these BG readings. High glycosylated hemoglobin is opposite to severe hypoglycemia (SH), as an extreme manifestation of IDDM, related to long-term complications. Contemporary memory meters store up to several hundred self-monitoring BG (SMBG) readings and can calculate various statistics, including the mean of these BG readings.

Optimizing reduction in basal hyperglucagonaemia to repair defective glucagon counterregulation in insulin deficiency.

In health, the pancreatic islet cells work as a network with highly co‐ordinated signals over time to balance glycaemia within a narrow range. In type 1 diabetes (T1DM), with autoimmune destruction of the β‐cells, lack of insulin is considered the primary abnormality and is the primary therapy target. However, replacing insulin alone does not achieve adequate glucose control and recent studies have focused on controlling the endogenous glucagon release as well. In T1DM, glucagon secretion is disordered but not absolutely deficient; it may be excessive postprandially yet it is characteristically insufficient and delayed in response to hypoglycaemia. We review our system‐level analysis of the pancreatic endocrine network mechanisms of glucagon counterregulation (GCR) and their dysregulation in T1DM and focus on possible use of α‐cell inhibitors (ACIs) to manipulate the glucagon axis to repair the defective GCR. Our results indicate that the GCR abnormalities are of ‘network origin’. The lack of β‐cell signalling is the primary deficiency that contributes to two separate network abnormalities: (i) absence of a β‐cell switch‐off trigger and (ii) increased intraislet basal glucagon. A strategy to repair these abnormalities with ACI is proposed, which could achieve better control of glycaemia with reduced hypoglycaemia risk.