Articles in PresS. Am J Physiol Regul Integr Comp Physiol (October 14, 2004). doi:10.1152/ajpregu.00414.2004
ANALYSIS OF BIDIRECTIONAL PATTERN SYNCHRONY OF CONCENTRATIONSECRETION PAIRS: IMPLEMENTATION IN THE HUMAN TESTICULAR AND ADRENAL AXES
Peter Y. Liu1 Steven M. Pincus2 Daniel M. Keenan3 Ferdinand Roelfsema4 Johannes D. Veldhuis 1* 1
Division of Endocrinology, Department of Internal Medicine
Endocrine Research Unit and General Clinical Research Center Mayo Clinic, Mayo Medical and Graduate Schools of Medicine 200 First St. Southwest, Rochester, MN 55905
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990 Moose Hill Road, Guilford, CT 06437
Department of Statistics, University of Virginia, Charlottesville, VA 22908
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Department of Endocrinology, Leiden University Medical Center Albinusdreef 2, 2333ZA Leiden, The Netherlands.
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Corresponding author:
Telephone: (507) 255-0906
FAX: (507) 255-0901
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Short heading: Forward and reverse X-ApEn 1 Copyright © 2004 by the American Physiological Society.
Forward and reverse X-ApEn ABSTRACT The hypothalamo-pituitary-testicular and hypothalamo-pituitary-adrenal axes are prototypical coupled neuroendocrine systems. The present study contrasts in vivo linkages within and between these two axes using methods without linearity assumptions. We examined 11 young (ages 21 to 31) and 8 older (ages 62 to 74) men, who underwent frequent (every 2.5 min) blood sampling overnight for paired measurement of LH and Te, and 35 adults (17 women and 18 men) aged 26 to 77 y in whom ACTH and cortisol were measured every 10 min for 24 hr. To mirror physiological interactions, hormone secretion was first deconvolved from serial concentrations using a waveform-independent biexponential elimination model. Feedforward synchrony, feedback synchrony and the difference in feedforward-feedback synchrony were quantified by the cross-approximate entropy (X-ApEn) statistic. The latter was applied in a forward (LH concentration template, examining pattern recurrence in Te secretion), reverse (Te concentration template, examining pattern recurrence in LH secretion) and differential (forward minus reverse) manner, respectively. Analagous concentrationsecretion X-ApEn estimates were calculated from ACTH-cortisol pairs. X-ApEn, a scaleand model-independent measure of pattern reproducibility, disclosed (i) greater Te-LH feedback coordination than LH-Te feedforward synchrony in healthy men, and significant and symmetric erosion of both feedforward and feedback linkages with aging; (ii) more synchronous ACTH concentration-dependent feedforward than feedback drive of cortisol secretion independently of gender and age; (iii) enhanced detection of bidirectional physiological regulation by in vivo pairwise concentrationsecretion compared with concentration-concentration analyses. Linking relevant
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Forward and reverse X-ApEn biological input to output signals, and vice versa should have utility in dissecting reciprocal control of neuroendocrine systems or even more broadly in other nonendocrine network analyses.
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Forward and reverse X-ApEn INTRODUCTION Aging is marked by a 30-50% decline in systemic testosterone concentrations in healthy community-dwelling men, as recognized nearly 50 yr ago (11; 46). Subsequent longitudinal (5; 9; 20) and population-based cross-sectional (2; 7; 19; 37) studies have corroborated relative androgen depletion in the aging male. Other epidemiological data have correlated hypoandrogenemia with sarcopenia, osteopenia, reduced physical stamina, sexual dysfunction, impaired quality of life and (possibly) depressive mood and cognitive impairment (46). Recent interventional studies suggest that reduced testosterone availability may be relevant to frailty in the aging male (18; 36). In parallel with therapeutic notions, mechanistic investigations are required to determine why aging is associated with hypoandrogenemia. Few studies have appraised the effect of aging on nonlinear interactions, which are expected from time-delayed asymptotic doseresponse connections among GnRH, LH and testosterone. The recent development of regulatory statistics and their validation in mathematical, laboratory-based and clinical contexts may begin to address this impasse (15; 22; 26). Aging and persistent stress also appear to force subtle adaptations in integrative control of the hypothalamo-pituitary-adrenal axis (HPA) (34). In large population-based studies, late-day cortisol concentrations rise consistently with age, whereas single morning values are variable (1; 3; 4; 13; 17; 38; 39; 51). Feedback analyses based on acute administration of synthetic and natural glucocorticoids suggest diminished inhibitory efficacy in older individuals, especially in women. These data point to subtle age and gender differences in feedback regulation. Such changes may be detrimental in the long run, since the stress-responsive corticotropic axis is vital for maintenance of
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Forward and reverse X-ApEn glucose and salt balance, blood pressure, well-being and normal longevity. Chronic over- or underexposure to corticosteroids impairs glucose homeostasis and CNS, bone, muscle and cardiovascular function, illustrating that tight regulation of this axis is required (35). Although basic feedforward and feedback linkages are well described, the relative stability and symmetry of in vivo ACTH-cortisol feedforward and cortisol-ACTH feedback linkages are not known in any species. The analytical challenge is to achieve accurate quantitation of partially coupled time-evolving signals in the HPA axis without disrupting endogenous interactions (below). One broad class of quantitative nonlinear, model-invariant tools to assess timevarying coordination between interlinked hormones is the approximate entropy (ApEn) statistic (22). The univariate ApEn measure discriminates relative serial regularity or recurring orderliness within different complex patterns, such as pulsatile neurohormonal output. Two relevant features of this statistical perspective are applicability to the uninfused and unstressed state without disruption of ongoing time-adaptive axis interactions, and validity independent of the absolute scale of measurement. The corresponding cross-ApEn statistic quantifies the relative synchrony of two interlinked signals, such as paired sequential hormone measurements in the gonadal axis (30). To date, only the feedforward “direction” of coupling has been investigated by this means in neurohormonal systems; i.e. LH drive of testosterone and ACTH drive of cortisol concentrations (30; 33). Therefore, the current methodology provides a model-free and scale-invariant strategy to estimate two-signal interactions in a closed and coupled neurohormone system without requiring external interventions.
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Forward and reverse X-ApEn Illustratively, we examine the hypotheses that (a) both feedforward and feedback coordination of GnRH-LH-testosterone is detectably disrupted in the aging male, as monitored in the absence of external interventions; and (b) unmodified in vivo ACTHcortisol feedforward and cortisol-ACTH feedback linkages in the aging adult are relatively stable and symmetrical.
METHODS A. Clinical sampling protocol to assess the male gonadal axis Eleven young (aged 21 to 31 yr) and 8 older (aged 62 to 74 yr) men were enrolled after providing written voluntary informed consent, as approved by the Institutional Review Board. Participants were healthy community-dwelling men within 20% of ideal body weight, who had not undertaken transmeridian travel or consumed alcohol, caffeine, prescribed medications or recreational drugs. Detailed medical inventory excluded a history of infertility, systemic disease, recent weight change, hormonal therapy or psychoactive drug use. Physical examination (including testis size, libido and potentia) and fasting morning (0800 h) biochemical tests of renal, hepatic, hematological and metabolic function (fasting plasma glucose and thyroid function) were within normal limits. Men were admitted to a single room in the General Clinical Research Center for two consecutive nights, the first night being to allow adaptation to the unit. On the second night, subjects underwent blood sampling every 2.5 min starting at 2300 h, when lights were put out, until the subject awakened, for an average duration of 7 h. Blood was withdrawn via heparin-coated long lines by a phlebotomist working in
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Forward and reverse X-ApEn an adjacent room in order to prevent sleep disturbance. Further subject details are provided elsewhere (21).
B. Clinical sampling protocol to assess the adrenal axis Thirty-five normal subjects (17 women and 18 men) aged 26 to 77 yr (mean 44 yr) were enrolled after providing written informed consent, as approved by the responsible ethics committee. Volunteers were healthy community-dwelling men and women within 20% of ideal body weight, who had not received glucocorticoids or any prescribed medications within the preceding 3 months, or undertaken transmeridian travel within 2 weeks. Detailed medical inventory excluded a history of psychiatric illness (including depression), systemic disease, recent weight change, hormonal therapy and alcohol or psychoactive drug abuse. Physical examination and fasting morning biochemical tests of renal, hepatic, hematological and metabolic function (fasting plasma glucose and thyroid function) were within normal limits. Participants were hospitalized the evening before the sampling studies and an indwelling intravenous cannula was inserted in a large vein of the forearm in the morning. Premenopausal women were studied in the early follicular phase of the menstrual cycle. Blood samples were withdrawn every 10 min for 24 hr starting at 0900 h. Subjects were allowed to ambulate freely, but not to sleep during the day. Lights were turned off between 2200-2400 h depending on individual sleep habits. Further subject details are provided elsewhere (33).
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Forward and reverse X-ApEn C. Assays Blood samples were allowed to clot at room temperature, and sera were frozen at -20C. LH concentrations were assayed in duplicate by specific LH beta subunitdirected two-site monoclonal IRMA (Nichols Laboratories, San Juan Capistrano, CA) (21; 49). The sensitivity of the LH assay is 0.2 IU/L (First International Reference Preparation) and there is < 0.03% cross-reactivity with free alpha FSH or TSH (42; 49; 50; 52). The intra- and interassay coefficients of variation (CV) are
