Noninvasive in vivo investigative probes of adaptive mechanisms of neuroendocrine regulation: the paradigm of the hypothalamo-pituitary-gonadal axis in the aging male.

Intermittent signal exchange serves to encode repeated incremental adjustments among central-neural centers and the ensemble of glands comprising any given axis. Interglandular communication proceeds dynamically via pulsatile and basal modes of hormone release, deterministic (dose-responsive) interfaces, and apparently stochastic (randomly varying) processes. Physiological investigations of the time-dependent control of neurohormone secretion and action depend upon valid reconstruction of such interactive signaling. Recent technical and experimental advances afford new and fundamental insights into such composite mechanisms that maintain precise homeostasis in health, and show susceptibility to disruption in disease. Underlying concepts are becoming more readily understandable intuitively without full rehearsal of detailed analytical and statistical facets that undergird computer-assisted methods. Accordingly, the present overview highlights core precepts that guide the implementation of sensitive, specific and utilitarian technologies to quantitate neuroendocrine adaptations in pathophysiology. The aging male gonadal axis provides a well studied paradigmatic platform to illustrate the formulation and implementation of analytical strategies in diverse systems.

Sexual dimorphism in the synchrony of joint growth hormone and cortisol dynamics in children with classic 21-hydroxylase deficiency.

In humans, growth hormone (GH) and cortisol are secreted in a pulsatile fashion and a mutual bidirectional interaction between the GH/insulin-like growth factor (IGF)-I axis and hypothalamic-pituitary-adrenal (HPA) axis has been established. Classic congenital adrenal hyperplasia (CAH) is characterized by a defect in the synthesis of glucocorticoids and often mineralocorticoids, and adrenal hyperandrogenism. In view of the sexually dimorphic pattern in GH secretion, we investigated the GH-cortisol bihormonal secretory dynamics in male and female children with classic CAH. Thirty-eight children with classic 21-hydroxylase deficiency (M: 13, F: 25; age range: 6.1-18.8 yr) were studied prospectively. Serum GH and cortisol concentrations were determined at 20 min intervals for 24 hours. The irregularity of GH and cortisol pattern was assessed using approximate entropy (ApEn), a scale- and model-independent statistic. The synchrony of joint GH-cortisol dynamics was quantified using the cross-ApEn statistic. Cross-correlation analysis of GH and cortisol concentrations was computed at various time lags covering the 24-h period. There was no gender difference in mean 24-hour serum GH (males vs females: 5.25 +/- 4.72 vs 4.44 +/- 2.64 mIU/l) or cortisol (156.2 +/- 44.6 vs 172.0 +/- 58.5 nmol/l) concentrations. For GH, ApEn values were significantly higher in females (0.66 +/- 0.14) than in males (0.53 +/- 0.16) (p = 0.009). No difference in cortisol ApEn values was noted between sexes (0.53 +/- 0.21 vs 0.54 +/- 0.12). Cross-ApEn values of paired GH-cortisol, with cortisol leading GH, were significantly higher in females (0.94 +/- 0.14) than in males (0.83 +/- 0.20) (p = 0.03). These findings suggest that females with classic 21-hydroxylase deficiency have a more irregular pattern of GH secretion and a more asynchronous joint GH and cortisol dynamics than their male counterparts.

Impact of pulsatility on the ensemble orderliness (approximate entropy) of neurohormone secretion.

Regular patterns of neurohormone secretion are driven by underlying pulsatile and subordinate (feedback sensitive) dynamics. Measures of time-series orderliness, e.g., the approximate entropy (ApEn) statistic (Pincus SM. Proc Natl Acad Sci 88: 2297-2301, 1991), vividly discriminate pathological and physiological patterns of hormone release. To investigate how specific pulsatility features impact regularity estimates, we have examined the sensitivity of the ApEn metric to systematic variations in the frequency, amplitude, and half-life of simulated neurohormone pulse trains (Veldhuis JD, Carlson ML, and Johnson ML. Proc Natl Acad Sci 84: 7686-7690, 1987) and compared the impact of a high vs. low baseline luteinizing hormone (LH) pattern regularity state mimicking the normal female luteal phase and the young male, respectively. Shortening the interpulse interval length elevated ApEn in both pulsatility models, thereby signifying greater ensemble series irregularity. The frequency sensitivity of ApEn was robust to several complementary renditions of ApEn and to variations in experimental uncertainty, basal (nonpulsatile) LH secretion, and secretory burst amplitude. ApEn rose with increasing hormone half-life, especially in the face of low baseline variability emulated by midluteal LH secretion profiles. High variability of secretory burst amplitude, pulse duration, or interpeak intervals increased ApEn in the more orderly femalelike construct; in the highly irregular malelike LH pulse model, these variability changes had little effect on ApEn. In summary, the ensemble regularity statistic, ApEn, quantifies unequal pattern orderliness in neurohormone pulse trains with minimal dependence on mean pulse amplitude, interpulse baseline, or (subthreshold) sample uncertainty. Thus ApEn monitors changing secretory event frequency and interpulse variability with sensitivity to starting pattern regularity, providing a mechanistic linkage between model evolution and statistical change.

Disruption of the synchronous secretion of leptin, LH, and ovarian androgens in nonobese adolescents with the polycystic ovarian syndrome.

The present study probes putative disruption of hypothalamic control of multihormone outflow in polycystic ovarian syndrome by quantitating the joint synchrony of leptin and LH release in adolescents with this syndrome and eumenorrheic controls. To this end, hyperandrogenemic oligo- or anovulatory patients with polycystic ovarian syndrome (n = 11) and healthy girls (n = 9) underwent overnight blood sampling every 20 min for 12 h to monitor simultaneous secretion of leptin (immuno-radiometric assay), LH (immunofluorometry), and androstenedione and T (RIA). Synchronicity of paired leptin-LH, leptin-androstenedione, and leptin-T profiles was appraised by two independent bivariate statistics; viz., lag-specific cross-correlation analysis and pattern-sensitive cross-approximate entropy. The study groups were comparable in chronological and postmenarchal age, body mass index, fasting plasma insulin/glucose ratios, and serum E2 concentrations. Overnight mean (+/- SEM) serum leptin concentrations were not distinguishable in the two study groups at 30 +/- 4.8 (polycystic ovarian syndrome) and 32 +/- 7.4 microg/liter (control). Serum LH concentrations were elevated at 9.5 +/- 1.4 in girls with polycystic ovarian syndrome vs. 2.8 +/- 0.36 IU/liter in healthy subjects (P = 0.0015), androstenedione at 2.8 +/- 0.30 (polycystic ovarian syndrome) vs. 1.2 +/- 0.11 ng/ml (control) (P = 0.0002), and T at 1.56 +/- 0.29 (polycystic ovarian syndrome) vs. 0.42 +/- 0.06 ng/ml (P < 0.0001). Cross-correlation analysis shows that healthy adolescents maintained a positive relationship between leptin and LH release, wherein the latter lagged by 20 min (P < 0.01). No such association emerged in girls with polycystic ovarian syndrome. In eumenorrheic volunteers, leptin and androstenedione concentrations also covaried in a lag-specific manner (0.0001 < P < 0.01), but this linkage was disrupted in patients with polycystic ovarian syndrome. Anovulatory adolescents further failed to sustain normal time-lagged coupling between leptin and T (P < 0.01). Approximate entropy calculations revealed erosion of orderly patterns of leptin release in polycystic ovarian syndrome (P = 0.012 vs. control). Cross-entropy analysis of two-hormone pattern regularity disclosed marked disruption of leptin and LH (P = 0.0099), androstenedione and leptin (P = 0.0075) and T-leptin (P = 0.019) synchrony in girls with polycystic ovarian syndrome. In summary, hyperandrogenemic nonobese adolescents with oligo- or anovulatory polycystic ovarian syndrome manifest: 1) abrogation of the regularity of monohormonal leptin secretory patterns, despite normal mean serum leptin concentrations; 2) loss of the bihormonal synchrony between leptin and LH release; and 3) attenuation of coordinate leptin and androstenedione as well as leptin and T output. In ensemble, polycystic ovarian syndrome pathophysiology in lean adolescents is marked by vivid impairment of the synchronous outflow of leptin, LH and androgens. Whether analogous disruption of leptin-gonadal axis integration is ameliorated by therapy and/or persists into adulthood is not known.

Joint growth hormone and cortisol spontaneous secretion is more asynchronous in older females than in their male counterparts.

In humans, cortisol and GH are secreted in a pulsatile manner, and an interaction between GH and the hypothalamic-pituitary-adrenal axis has been established. In view of the sexually dimorphic pattern in GH secretion, we investigated the GH-cortisol bihormonal secretory dynamics in male and female healthy older individuals. We studied the GH and cortisol secretory patterns in 83 healthy subjects (45 men and 38 women; age range, 59.4-73.0 yr) by determining serum GH and cortisol concentrations at 20-min intervals for 24 h. The irregularity of GH and cortisol secretion was assessed using approximate entropy (ApEn), a scale- and model-independent statistic. The synchrony of joint GH-cortisol spontaneous secretion was quantified using the cross-ApEn statistic. Cross-correlation analysis of GH and cortisol patterns was computed at various time lags covering the 24-h period. Mean 24-h serum GH concentrations were significantly higher in females (mean, 1.31 mU/L; SD, 0.87) than in males (mean, 0.88 mU/L; SD, 0.42; P = 0.009), whereas mean 24-h serum total cortisol concentrations were higher in males (mean, 9.0 microg/dL; SD, 1.4) than in females (mean, 7.3 microg/dL; SD, 1.4; P = 0.0001). GH secretion was more irregular in females (mean ApEn, 0.81; SD, 0.23) than in males (mean ApEn, 0.60; SD, 0.20; P < 0.001). No significant difference in the regularity of cortisol secretion was noted between sexes. Cross-ApEn values of paired GH-cortisol were higher in females (mean, 1.15; SD, 0.18) than in males (mean, 1.01; SD, 0.16; P = 0.0003). Stepwise multiple linear regression analysis indicated that estradiol and insulin-like growth factor-binding protein-3 concentrations were independently related to GH ApEn values (r(2) = 0.14; P = 0.01), whereas cross-ApEn values of paired GH-cortisol were best predicted by FSH concentrations (r(2) = 0.37; P = 0.003). Cross-correlation analysis revealed a significant positive correlation between GH and cortisol, peaking at lag time of 4.7 h in males (r = 0.30; P < 0.0001) and 4.3 h in females (r = 0.14; P < 0.0001), with GH leading cortisol by these time intervals. In addition, a significant negative correlation between the two hormones was noted over time, peaking at 4.7 h in males (r = -0.21; P < 0.0001) and 6.3 h in females (r = -0.25; P < 0.0001), with cortisol leading GH by these time intervals. The above results indicate that in the elderly, females have a more disordered GH secretory pattern and a more asynchronous joint GH-cortisol secretion than their male counterparts. These observations most likely reflect bidirectional interactions between the GH and hypothalamic-pituitary-adrenal axis in humans as well as diminution of subsystem integrity and synchronous control of interconnected hormonal systems with advancing age.

Acute and short-term administration of a sulfonylurea (gliclazide) increases pulsatile insulin secretion in type 2 diabetes.

The high-frequency oscillatory pattern of insulin release is disturbed in type 2 diabetes. Although sulfonylurea drugs are widely used for the treatment of this disease, their effect on insulin release patterns is not well established. The aim of the present study was to assess the impact of acute treatment and 5 weeks of sulfonylurea (gliclazide) treatment on insulin secretory dynamics in type 2 diabetic patients. To this end, 10 patients with type 2 diabetes (age 53 +/- 2 years, BMI 27.5 +/- 1.1 kg/m(2), fasting plasma glucose 9.8 +/- 0.8 mmol/l, HbA(1c) 7.5 +/- 0.3%) were studied in a double-blind placebo-controlled prospective crossover design. Patients received 40-80 mg gliclazide/placebo twice daily for 5 weeks with a 6-week washout period intervening. Insulin pulsatility was assessed by 1-min interval blood sampling for 75 min 1) under baseline conditions (baseline), 2) 3 h after the first dose (80 mg) of gliclazide (acute) with the plasma glucose concentration clamped at the baseline value, 3) after 5 weeks of treatment (5 weeks), and 4) after 5 weeks of treatment with the plasma glucose concentration clamped during the sampling at the value of the baseline assessment (5 weeks-elevated). Serum insulin concentration time series were analyzed by deconvolution, approximate entropy (ApEn), and spectral and autocorrelation methods to quantitate pulsatility and regularity. The P values given are gliclazide versus placebo; results are means +/- SE. Fasting plasma glucose was reduced after gliclazide treatment (baseline vs. 5 weeks: gliclazide, 10.0 +/- 0.9 vs. 7.8 +/- 0.6 mmol/l; placebo, 10.0 +/- 0.8 vs. 11.0 +/- 0.9 mmol/l, P = 0.001). Insulin secretory burst mass was increased (baseline vs. acute: gliclazide, 43.0 +/- 12.0 vs. 61.0 +/- 17.0 pmol. l(-1). pulse(-1); placebo, 36.1 +/- 8.4 vs. 30.3 +/- 7.4 pmol. l(-1). pulse(-1), P = 0.047; 5 weeks-elevated: gliclazide vs. placebo, 49.7 +/- 13.3 vs. 37.1 +/- 9.5 pmol. l(-1). pulse(-1), P < 0.05) with a similar rise in burst amplitude. Basal (i.e., nonoscillatory) insulin secretion also increased (baseline vs. acute: gliclazide, 8.5 +/- 2.2 vs. 16.7 +/- 4.3 pmol. l(-1). pulse(-1); placebo, 5.9 +/- 0.9 vs. 7.2 +/- 0.9 pmol. l(-1). pulse(-1), P = 0.03; 5 weeks-elevated: gliclazide vs. placebo, 12.2 +/- 2.5 vs. 9.4 +/- 2.1 pmol. l(-1). pulse(-1), P = 0.016). The frequency and regularity of insulin pulses were not modified significantly by the antidiabetic therapy. There was, however, a correlation between individual values for the acute improvement of regularity, as measured by ApEn, and the decrease in fasting plasma glucose during short-term (5-week) gliclazide treatment (r = 0.74, P = 0.014, and r = 0.77, P = 0.009, for fine and coarse ApEn, respectively). In conclusion, the sulfonylurea agent gliclazide augments insulin secretion by concurrently increasing pulse mass and basal insulin secretion without changing secretory burst frequency or regularity. The data suggest a possible relationship between the improvement in short-term glycemic control and the acute improvement of regularity of the in vivo insulin release process.

Phase I dose escalation study of topotecan combined with alternating schedules of paclitaxel and carboplatin in advanced solid tumors.

BACKGROUND: Combining topotecan with other cytotoxics has been problematic due to marrow suppression. A phase I trial was initiated to identify the optimal sequence and maximum-tolerated dose of topotecan in combination with paclitaxel and carboplatin. PATIENTS AND METHODS: Patients with advanced cancer and performance status ECOG < or = 2. The starting dose was paclitaxel 175 mg/m2 day 1, carboplatin AUC 6.0 day 1, and topotecan 0.5 mg/m2 daily day 1-5 (early sequence). The next course of paclitaxel and carboplatin administration was delayed to day 5 (late sequence). Treatment was repeated every three weeks. After determining maximum-tolerated dose without cytokines, granulocyte colony-stimulating factor (G-CSF) was added and further dose escalation was pursued. RESULTS: Fifty-one patients were entered; men: women ratio 30:21. Dose-limiting toxicity (DLT) for the early sequence was neutropenia at doses paclitaxel mg/m2/carboplatin AUC 5/topotecan mg/m2 (PCT) 175/5/0.75 for four to five days. DLT for the late sequence was neutropenia at PCT doses of 175/5/ 1.0 for four days. G-CSF 5 microg/kg subcutaneously starting day 6 permitted further topotecan dose escalation. After adding G-CSF, late sequence DLT was neutropenia at doses 175/5/1.25 for four days. Forty-six patients were evaluable for response and of those, there were thirteen partial responses. CONCLUSIONS: The late sequence resulted in less toxicity and was better tolerated. The early sequence maximum-tolerated dose (MTD) was 175/6/0.5 for five days. The late sequence MTD was PCT 175/5/0.75 for five days. The late sequence MTD with G-CSF was 175/5/1.0 for four days. The recommended phase II PCT dose is the late sequence 175/5/1.0 for four days with G-CSF.

Basal, pulsatile, entropic, and 24-hour rhythmic features of secondary hyperprolactinemia due to functional pituitary stalk disconnection mimic tumoral (primary) hyperprolactinemia.

Under physiological conditions, PRL secretion is regulated precisely by various stimulating and inhibiting factors. Hyperprolactinemia may arise as a primary consequence of a PRL-secreting pituitary adenoma. Secondary hyperprolactinemia (SH) may emerge in patients with hypothalamic disease, hypophyseal stalk compression, or suprasellar extension of a (nonlactotrope) pituitary adenoma. The latter may reflect diminished delivery of dopamine or other inhibitory factors to normal lactotropes. We hypothesized that diurnal and ultradian rhythms of PRL secretion would differ in secondary (e.g. hypothalamic) and primary (e.g. tumoral states) hyperprolactinemia (PH), assuming that the underlying pathophysiologies differ. To test this clinical postulate, we investigated the patterns of 24-h PRL release in eight patients with SH associated with functional hypothalamo-pituitary disconnection and in eight patients with PH attributable to microprolactinoma. Data in each group were compared with values in healthy gender-matched controls. PRL time series were obtained by repetitive 10-min blood sampling, followed by high- precision immunofluorometric assay. PRL concentration profiles were analyzed by the complementary tools of model-free discrete peak detection, waveform-independent deconvolution analysis, cosinor regression, and the approximate entropy metric to quantitate pulsatile, basal, 24-h rhythmic, and pattern-dependent (entropic) PRL secretion. Patients with tumoral hyperprolactinemia (PH) showed a 2-fold higher 24-h mean serum PRL concentration than patients with SH (62 +/- 13 microg /L vs. 30 +/- 6.9 microg/L, respectively, P = 0.029). Estimated PRL pulse frequency (events/24 h) was similar in the two patient groups (18.5 +/- 0.7 vs. 17.6 +/- 0.8; P = 0.395) but elevated over that in euprolactinemic controls (P < 0.0001 for both). Deconvolution analysis disclosed a mean daily PRL secretion rate of 790 +/- 170 microg in PH patients vs. 380 +/- 85 microg in SH patients (P = 0.030). Nonpulsatile PRL secretion comprised nearly 70% of total secretion in both patient groups and 50% in controls (P < 0.0001). Cosinor analysis revealed similar acrophases in all three study cohorts. The mean skewness of the statistical distribution of the individual PRL sample secretory rates was reduced, compared with controls (P < 10 (-5) for each), but equivalent in SH and PH patients (0.83 +/- 0.12 vs. 0.78 +/- 0.08, respectively), denoting a loss of the normal spectrum of low- and higher-amplitude secretion rates. Approximate entropy, a regularity statistic, was markedly elevated in both patient groups over controls (P < 10 (-6) for each) and was slightly higher in PH patients than in SH patients (1.639 +/- 0.029 vs. 1.482 +/- 0.067, P = 0.048). In summary, patterns of PRL secretion in PH and SH states exhibit an equivalently increased frequency of PRL pulses, a comparably marked rise in nonpulsatile (basal) PRL secretion. Despite overlap, the regularity of PRL release patterns is disrupted even more profoundly in PH (tumoral), compared with SH. Assuming that the orderliness of serial PRL output monitors normal integration within a feedback-controlled neurohormone axis, then the more disorderly patterns of tumoral PRL secretion point to greater regulatory disruption in PH. The latter may reflect abnormal secretory behavior associated with lactotrope neoplastic transformation and/or isolation of the tumor cell mass from normal hypothalamic controls.

Disruption of the joint synchrony of luteinizing hormone, testosterone, and androstenedione secretion in adolescents with polycystic ovarian syndrome.

The present study explores the postulate that the polycystic ovarian syndrome (PCOS) is marked by failure of physiological feedforward and feedback signaling between pituitary LH and ovarian androgens. To this end, we appraised the 3-fold simultaneous overnight release of LH (assayed by high precision immunofluorometry), testosterone (RIA), and androstenedione (RIA) in 12 an- or oligoovulatory adolescents with PCOS (mean +/- SEM age, 16.4 +/- 0.47 yr) and 10 eumenorrheic girls (age, 16.5 +/- 0.45 yr). Gynecological (postmenarchal) ages (years) were also comparable at 4.8 +/- 0.39 (PCOS) and 4.0 +/- 3.6 (control; P = NS). Body mass index and fasting serum insulin and estradiol concentrations were indistinguishable in the two study cohorts. Mean overnight serum concentrations of LH (assayed by both immunofluorometry and Leydig cell bioassay), testosterone, androstenedione, and 17alpha-hydroxyprogesterone were each elevated significantly in patients with PCOS (all P

Developmentally delimited emergence of more orderly luteinizing hormone and testosterone secretion during late prepuberty in boys.

To quantitate changing feedback control in the GnRH-LH/FSH-testosterone axis in male puberty, we here quantitate the orderliness of hormone release patterns using the regularity (pattern-sensitive) statistic, approximate entropy (ApEn), in 46 eugonadal boys representing 6 genitally defined stages of normal puberty. ApEn is a single variable, model-free, and scale-independent barometer of coordinate signaling or integrative regulation within a coupled neuroendocrine axis. Accordingly, we quantitated ApEn of LH profiles obtained by immunofluorometric assay of sera sampled every 20 min for 24 h. LH ApEn declined remarkably between early prepuberty (genital stage I-A: mean bone age, 4.6 +/- 1.6 yr; testis volume, <3 mL for at least 3 succeeding yr) and late prepuberty (genital stage I-C: bone age, 8.7 +/- 1.8 yr; testis volume, <3 mL for up to 1 yr thereafter; P: = 0.00019), which indicates the acquisition of more regular LH release patterns in late prepuberty. Maximal LH orderliness occurred in puberty stage II (bone age, 10.7 +/- 1.0 yr; testis volume, 2.8 +/- 0.4 mL). The LH secretory process was more disorderly in mid- and later puberty (Tanner stages III and IV). Transpubertal variations in testosterone ApEn manifested a similar tempo, i.e. the greatest regularity of testosterone secretion (lowest ApEn) emerged in Tanner genital stage II (P: < 10(-)(7)), with less orderly patterns evident both earlier and later in sexual development. In contrast, FSH ApEn values remained invariant of pubertal status. Analysis of bihormonal coupling using the theoretically related bivariate cross-ApEn statistic disclosed maximal 2-hormone synchrony for LH and testosterone secretion in genital stage II (P: = 0.031), with relative deterioration of coordinate LH and testosterone release patterns both before and after. LH and FSH release became maximally synchronous at the end of prepuberty (genital stage I-C; P: = 0.029), and FSH and testosterone synchrony peaked in pubertal stage III (P: = 0.037). As mean 24-h serum concentrations of LH, FSH, and testosterone rose transpubertally by 35-fold (LH), 68-fold (FSH), and 70-fold (testosterone), respectively, we infer that pubertal developmental stage per se rather than level of hormone output dictates coordinate GnRH-LH/FSH-testosterone secretion. In summary, in eugonadal boys, the regularity of 24-h LH and testosterone secretory patterns undergoes well defined pubertal stage-specific control. No sexually developmentally delimited regulation is inferable for FSH. The concept of temporally biphasic puberty-dependent variations in neurohormone secretory regularity contrasts with the unidirectional rise in daily hormone output. Accordingly, we infer that late prepuberty and early puberty (Tanner genital stages IC and II) embody a physiologically unique sexual developmental window, marked by transiently enhanced LH and testosterone feedback stability in boys. Whether analogous plasticity of hypothalamo-pituitary-gonadal interactions unfolds during female adolescence is not known.

Hyperleptinemia in women with Cushing's disease is driven by high-amplitude pulsatile, but orderly and eurhythmic, leptin secretion.

The episodicity of 24 h leptin release was studied in seven women (mean age 39 years, range 22-56 years) with pituitary-dependent hypercortisolism and in seven age- and body mass index (BMI)-matched female controls. Pulsatile leptin release was quantified by model-free cluster analysis and deconvolution, the orderliness of leptin patterns by the approximate entropy statistic (ApEn), and nyctohemeral leptin rhythmicity by cosinor analysis. Blood samples were taken at 10 min intervals for 24 h. Both cluster and deconvolution analysis revealed 2.4-fold increased leptin secretion in patients, caused by combined and equal amplification of basal and pulsatile secretion. Cluster analysis identified 7.1+/-1.5 peaks per 24 h in patients and 6.0+/-0.5 in controls (not significant). The statistical distribution of the individual sample secretory rates was similarly skewed in patients and controls (0.55+/-0.12 vs 0.52+/-0.07). The acrophase (timing of the nyctohemeral leptin peak) in patients occurred at 2314 h (+/-76 min) and at 0058 h (+/-18 min) in controls (not significant). The approximate entropy of leptin release was equivalent in patients and controls (1.67+/-0.03 vs 1.61+/-0.05). The approximate entropy (ApEn) for cortisol in patients was 1.53+/-0.09 and in controls was 0.93+/-0.07 (P<0.0005). Cross-ApEn showed significant pattern synchrony between leptin and cortisol release, which (unexpectedly) was not disrupted by the cortisol excess (patients, 2.02+/-0.04; controls, 1.88+/-0.09; P=0.233). Insulin levels in fasting patients ('fasting insulin') were 27+/-5.7 mU/l vs 14+/-1.6 mU/l in controls (P=0.035). Leptin secretion correlated with fasting insulin levels (R(2)=0.34, P=0.028) and with the cortisol production rate (R(2)=0.33, P=0.033) when patients and controls were combined. In summary, Cushing's disease in women increases leptin production about twofold in an amplitude-specific way. The pulse-generating, nyctohemeral phase-determining, and entropy-control mechanisms that govern the 24 h leptin release are not altered. The increased secretion is not explained by BMI and is probably only partly explained by increased insulin production, suggesting a cortisol-dependent change in adipose leptin secretion.

Irregular circulating insulin concentrations in type 2 diabetes mellitus: an inverse relationship between circulating free fatty acid and the disorderliness of an insulin time series in diabetic and healthy individuals.

Insulin is released in a high-frequency pulsatile secretory pattern, which is reflected as quantifiable oscillations in peripheral circulating insulin concentrations. Type 2 diabetes mellitus is characterized by a broad spectrum of abnormalities in beta-cell function, including disturbed pulsatile insulin secretion as assessed by autocorrelation analysis. To achieve further insight into beta-cell pathophysiology in type 2 diabetes, we examined the orderliness of the baseline serum insulin time series (blood collection every minute for 75 minutes) in 16 type 2 diabetics (fasting plasma glucose, 170 +/- 10 mg/dL [mean +/- SE]; serum free fatty acid [FFA], 0.794 +/- 0.083 mmol/L; and known diabetes duration, 6 +/- 2 years) and 15 healthy controls (serum FFA, 0.523 +/- 0.055 mmol/L). We used approximate entropy (ApEn), a recently introduced scale- and model-independent measure of serial irregularity. ApEn was significantly increased in the type 2 diabetics compared with the controls (0.671 +/- 0.016 v 0.653 +/- 0.008, P = .04), indicating more irregular serum insulin time series in diabetics. Autocorrelation also discriminated between groups, although only when the data were pooled. Interestingly, an inverse relationship between ApEn and serum FFA was observed in the controls (r = -.63, P = .01) and diabetics (r = -.65, P < .01), whereas no relationships were found between ApEn and the age, body mass index (BMI), or plasma glucose. In conclusion, type 2 diabetes is characterized by an increased disorderliness of the fasting serum insulin time series, strongly suggesting perturbed rapid oscillatory insulin release. An inverse relationship between ApEn and fasting serum FFA among both groups might suggest a hitherto unknown stabilizing action of FFA on the high-frequency pulsatile insulin release process. This hypothesis needs to be tested in experimental designs that more specifically focus on this issue, eg, during changes in serum FFA.

Assessing serial irregularity and its implications for health.

Approximate entropy (ApEn) is a recently formulated family of parameters and statistics quantifying regularity (orderliness) in serial data, with developments within theoretical mathematics as well as numerous applications to multiple biological contexts. We discuss the motivation for ApEn development, from the study of inappropriate application of dynamical systems (complexity) algorithms to general time-series settings. ApEn is scale invariant and model independent, evaluates both dominant and subordinant patterns in data, and discriminates series for which clear feature recognition is difficult. ApEn is applicable to systems with at least 50 data points and to broad classes of models: it can be applied to discriminate both general classes of correlated stochastic processes, as well as noisy deterministic systems. Moreover, ApEn is complementary to spectral and autocorrelation analyses, providing effective discriminatory capability in instances in which the aforementioned measures exhibit minimal distinctions. Representative ApEn applications to human aging studies, based on both heart rate and endocrinologic (hormonal secretory) time series, are featured. Heart rate (HR) studies include gender- and age-related changes in HR dynamics in older subjects, and analyses of "near-SIDS" infants. Endocrinologic applications establish clear quantitative changes in joint LH-testosterone secretory dynamics in older versus younger men (a "partial male menopause"), via cross-ApEn, a related two-variable asynchrony formulation; a disruption in LH-FSH-NPT (penile tumescence) synchrony in older subjects; and changes in LH-FSH secretory dynamics across menopause. The capability of ApEn to assess relatively subtle disruptions, typically found earlier in the history of a subject than mean and variance changes, holds the potential for enhanced preventative and earlier interventionist strategies.

Apparently complete restoration of normal daily adrenocorticotropin, cortisol, growth hormone, and prolactin secretory dynamics in adults with Cushing's disease after clinically successful transsphenoidal adenomectomy.

ACTH production in Cushing's disease is characterized by a markedly elevated rate of basal (nonpulsatile) secretion, an increased mass of ACTH released per burst and an unremarkable pulse frequency. In addition, the ACTH secretory process and that of GH and PRL exhibit profoundly disordered patterns. Whether some or all of these disturbances can be reversed or normalized by transsphenoidal microadenomectomy remains unknown. We therefore investigated the detailed dynamics of ACTH, GH, and PRL in eight patients (aged 38.9+/-4.2 yr) with pituitary-dependent Cushing's disease who were in long-term (8.2+/-1.7 yr) clinical remission following transsphenoidal surgery and eight controls matched for age, gender, and body mass index. To this end, blood was sampled at 10-min intervals for 24 h for the later assay of ACTH, cortisol, GH, and PRL. Secretory activity was quantitated by deconvolution methods, and the pattern orderliness (regularity) of hormone release was determined by the approximate entropy (ApEn) statistic. The joint synchrony of ACTH and cortisol secretion was monitored by the cognate bivariate statistic, cross-ApEn. Diurnal properties of the hormonal release were appraised by cosinor analysis. Based on deconvolution analysis, postsurgical patients exhibited a normal frequency, half-life, duration, and mass of ACTH and cortisol secretory bursts. Accordingly, the 24-h production rates of both ACTH (2.5+/-0.7 microg/L in patients vs. 2.9+/-0.7 microg/L in controls; P = 0.755) and cortisol (49+/-11 micromol/L in patients vs. 73+/-15 micromol/L in controls; P = 0.217) were normal also. The acrophase of the diurnal rhythm of ACTH (patients, 0817 h +/- 37 min; controls, 0850 h +/- 38 min; P = 0.629) and cortisol (patients, 1000 h +/- 24 min; controls, 0855 h +/- 30 min; P = 0.175) was also restored by surgery. ApEn values of ACTH (patients, 1.168 +/- 0.090; controls, 0.864+/-0.122; P = 0.133) and cross-ApEn of ACTH-cortisol (patients, 1.396+/-0.087; controls, 1.170+/-0.076; P = 0.140) secretion were both normal in this cohort, denoting restoration of the secretory process regularity. Cortisol ApEn was slightly higher in patients (patients, 1.034+/-0.084; controls, 0.831+/-0.038; P = 0.048). Both GH and PRL time series manifested full reconstitution of pulsatile, 24-h rhythmic, and entropic properties. In summary, clinically successful transsphenoidal microadenomectomy in adults with Cushing's disease can fully normalize virtually all quantitative features of regulated ACTH, cortisol, GH, and PRL secretion. Further studies will be needed to establish the consistency of these findings in larger cohorts of adults with Cushing's disease and in children with this disorder and to delineate the significance, if any, of a residual, minimally detectable disruption of orderly cortisol secretion in this patient population.

Failure of physiological plasma glucose excursions to entrain high-frequency pulsatile insulin secretion in type 2 diabetes.

Insulin is released in high-frequency pulsatile bursts at intervals of 6-13 min. Intrapancreatic mechanisms are assumed to coordinate pulsatile insulin release, but small oscillations in plasma glucose concentrations may contribute further. To gain additional insight into beta-cell (patho)physiology, we explored the ability of repetitive small glucose infusions (6 mg/kg over 1 min every 10 min) to modify rapid pulsatile insulin secretion in 10 type 2 diabetic individuals (plasma glucose 9.3 +/- 1.0 mmol/l, HbA1c 7.9 +/- 0.5%, mean +/- SE) and 10 healthy subjects. All subjects were investigated twice in randomly assigned order: during saline and during glucose exposure. Blood was collected every minute for 90 min to create a plasma insulin concentration time-series for analysis using 3 complementary algorithms: namely, spectral analysis, autocorrelation analysis, and approximate entropy (ApEn). During saline infusion, none of the algorithms were able to discriminate between diabetic and control subjects (P > 0.20). During glucose entrainment, spectral density peaks (SP) and autocorrelation coefficients (AC) increased significantly (P < 0.001), and ApEn decreased (P < 0.01), indicating more regular insulin time-series in the healthy volunteers. However, no differences were observed in the diabetic individuals between the glucose and saline conditions. Furthermore, in spite of identical absolute glucose excursions (approximately 0.3 mmol/l) glucose pulse entrainment led to a complete (SP: 4.76 +/- 0.62 [range 2.08-7.60] vs. 17.24 +/- 0.93 [11.70-20.58], P < 0.001; AC: 0.01 +/- 0.05 [0.33-0.24] vs. 0.64 +/- 0.05 [0.35-0.83], P < 0.001) or almost complete (ApEn: 1.59 +/- 0.02 [1.48-1.67] vs. 1.42 +/- 0.05 [1.26-1.74], P < 0.005) separation of the insulin time-series in diabetic and control subjects. Even elevating the glucose infusion rate in the diabetic subjects to achieve comparable relative (and hence higher absolute) glucose excursions (approximately 4.9%) failed to entrain pulsatile insulin secretion in this group. In conclusion, the present study demonstrates that failure to respond adequately with regular oscillatory insulin secretion to recurrent high-frequency and (near)-physiological glucose excursion is a manifest feature of beta-cell malfunction in type 2 diabetes. Whether the model will be useful in unmasking subtle (possible prediabetic) defects in beta-cell sensitivity to glucose drive remains to be determined.

Irregularity and asynchrony in biologic network signals.

The principal focus of this chapter has been the description of both ApEn, a quantification of serial irregularity, and of cross-ApEn, a thematically similar measure of two-variable asynchrony (conditional irregularity). Several properties of ApEn facilitate its utility for biological time series analysis: (1) ApEn is nearly unaffected by noise of magnitude below a de facto specified filter level; (2) ApEn is robust to outliers; (3) ApEn can be applied to time series of 50 or more points, with good reproducibility; (4) ApEn is finite for stochastic, noisy deterministic, and composite (mixed) processes, these last of which are likely models for complicated biological systems; (5) increasing ApEn corresponds to intuitively increasing process complexity in the settings of (4); and (6) changes in ApEn have been shown mathematically to correspond to mechanistic inferences concerning subsystem autonomy, feedback, and coupling, in diverse model settings. The applicability to medium-sized data sets and general stochastic processes is in marked contrast to capabilities of "chaos" algorithms such as the correlation dimension, which are properly applied to low-dimensional iterated deterministic dynamical systems. The potential uses of ApEn to provide new insights in biological settings are thus myriad, from a complementary perspective to that given by classical statistical methods. ApEn is typically calculated by a computer program, with a FORTRAN listing for a "basic" code referenced above. It is imperative to view ApEn as a family of statistics, each of which is a relative measure of process regularity. For proper implementation, the two input parameters m (window length) and r (tolerance width, de facto filter) must remain fixed in all calculations, as must N, the data length, to ensure meaningful comparisons. Guidelines for m and r selection are indicated above. We have found normalized regularity to be especially useful, as in the growth hormone studies discussed above; "r" is chosen as a fixed percentage (often 20%) of the subject's SD. This version of ApEn has the property that it is decorrelated from process SD--it remains unchanged under uniform process magnification, reduction, and translation (shift by a constant). Cross-ApEn is generally applied to compare sequences from two distinct yet interwined variables in a network. Thus we can directly assess network, and not just nodal, evolution, under different settings--e.g., to directly evaluate uncoupling and/or changes in feedback and control. Hence, cross-ApEn facilitates analyses of output from myriad complicated networks, avoiding the requirement to fully model the underlying system. This is especially important, since accurate modeling of (biological) networks is often nearly impossible. Algorithmically and insofar as implementation and reproducibility properties are concerned, cross-ApEn is thematically similar to ApEn. Furthermore, cross-ApEn is shown to be complementary to the two most prominent statistical means of assessing multivariate series, correlation and power spectral methodologies. In particular, we highlight, both theoretically and by case study examples, the many physiological feedback and/or control systems and models for which cross-ApEn can detect significant changes in bivariate asynchrony, yet for which cross-correlation and cross-spectral methods fail to clearly highlight markedly changing features of the data sets under consideration. Finally, we introduce spatial ApEn, which appears to have considerable potential, both theoretically and empirically, in evaluating multidimensional lattice structures, to discern and quantify the extent of changing patterns, and for the emergence and dissolution of traveling waves, throughout multiple contexts within biology and chemistry.

Longitudinal changes in growth hormone secretory process irregularity assessed transpubertally in healthy boys.

Clarifying the time evolution, and underlying neuroendocrine regulation, of hormone secretion during puberty is of pivotal importance both physiologically and clinically. We sought to determine whether clinical growth and elevated growth hormone (GH) release in pubertal boys are associated with shifts in the irregularity of GH secretory patterns. We studied GH release in 23 healthy boys longitudinally at approximately 4-mo intervals over a 6-yr period throughout puberty, by repetitive blood sampling at 20-min intervals for 24 h on each study date. To quantify serial irregularity in the GH profiles, we utilized approximate entropy (ApEn), a scale- and model-independent quantification of the extent of sequential "randomness." Complementary statistical analyses establish that on a per-subject basis, serum GH concentration-time series show greatest secretory disorderliness (maximal ApEn) in prepuberty and mid-to-late puberty, followed by a steep decline in ApEn to maximal orderliness in postpubertal adolescence (P < 0.0001, ANOVA). Pooling all subject comparisons, we observed a persistent positive correlation between ApEn and growth velocity (GrVel), Pearson r = 0.467 (P < < 10(-10)). Moreover, in general, ApEn(GH) preceded GrVel evolution, with a time frame lead of 4-8 mo providing the most pronounced correlations between ApEn and GrVel. In the setting of low postpubertal growth, per-subject ApEn values fell to approximately one-half of maximal ApEn values and, on average, were in the 13th percentile from minimal (P < < 10(-10)) for fully mature boys. Thus, in a longitudinal transpubertal analysis, greater irregularity in GH secretion corresponds to greater linear growth in boys, which culminates in highly regular GH secretory dynamics after sexual maturity. In addition to clinical utility, there may be added experimental merit in knowing that GH dynamics typically predict accelerated linear growth in 4-8 mo.

Growth hormone and prolactin are secreted more irregularly in patients with Cushing's disease.

OBJECTIVE: To investigate whether the spontaneous secretion of growth hormone and prolactin in adult patients with pituitary-dependent Cushing's disease is decreased. PATIENTS: Fourteen adult patients (9 women, 5 men; age: 34 +/- 3.4 years, mean +/- SEM) with pituitary-dependent Cushing's disease and 14 controls matched for age, gender and body mass index were studied. METHODS: Blood samples were withdrawn at 10 minutes intervals starting at 0900 h for 24 h. GH and PRL release were quantified with deconvolution methods. The regularity of GH and PRL release was measured with approximate entropy statistics. RESULTS: The number of GH secretory events per 24 h was higher in patients than in controls: 19 +/- 1.3 vs. 14 +/- 1.5 peaks per 24 h, respectively (P = 0.020). GH secretion rate was about one quarter lower in patients (ns), and the 24 h secretion of PRL was unchanged. Total GH production correlated negatively with the urinary excretion of free cortisol (R = 0.729, P = 0.005) and with the plasma cortisol production rate (R = 0.613; P = 0.026). The orderliness of GH and PRL secretion was appraised with the approximate entropy statistic (ApEn). For GH secretion ApEn(1,20%) in patients was 0.952 +/- 0.084 vs. 0.404 +/- 0.047 in controls, P = 1.17 x 10-4, pointing to a markedly disordered secretion in patients. Similar results were obtained for PRL secretion: patients: 1.586 +/- 0.063 vs. 1.003 +/- 0.068 in controls, P = 3.67 x 10-5. No statistically significant differences in secretory dynamics were demonstrated between the 10 patients with a microadenoma and the four with a macroadenoma. CONCLUSION: The amount of GH released spontaneously into the circulation in adult patients with pituitary-dependent Cushing's disease is inversely related to the degree of cortisol hypersecretion. However, except for severe hypercortisolism, GH secretion is relatively preserved. In addition, secretion of GH and PRL is remarkably disordered in patients with Cushing's disease. Since we could not detect differences in GH and/or PRL secretory dynamics between patients with a microadenoma and those harboring a macroadenoma, we speculate that an intrapituitary paracrine mechanism and/or elevated cortisol feedback effects may be responsible for the evident disruption of GH and PRL secretion patterns.

Orderliness of hormone release.

ApEn, approximate entropy, is a recently formulated family of parameters and statistics quantifying regularity (orderliness) in serial data, with developments both within theoretical mathematics, as well as numerous applications to multiple biological contexts. ApEn appears to have broad application to hormone pulsatility analysis within endocrinology, bringing a new perspective to the assessment of secretory patterns. ApEn is complementary to pulse detection algorithms widely employed to evaluate hormone secretion time-series--it is scale-invariant and model-independent, evaluates both dominant and subordinant patterns in data, discriminates series for which clear pulse recognition is difficult, and often provides a direct barometer of feedback between subsystems. ApEn is applicable to systems with at least 50 data points and to broad classes of models: it can be applied to discriminate both general classes of correlated stochastic processes, as well as noisy deterministic systems. Moreover, ApEn is complementary to spectral and autocorrelation analyses, providing effective discriminatory capability in instances in which the aforementioned measures exhibit minimal distinctions. We present some basic background on the above, and illustrate various facets of ApEn utility via several representative endocrinological studies.