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1 Endocrinology Research Unit and General Clinical Research Center, Mayo Clinic, Mayo Medical and Graduate Schools of Medicine, Rochester, MN, USA
2 990 Moose Hill Rd., Guilford, CT, USA
3 Department of Statistics, University of Virginia, Charlottesville, VA, USA
4 Department of Endocrinology, Leiden University Medical Center, Leiden, The Netherlands
* To whom correspondence should be addressed. E-mail: veldhuis.johannes{at}mayo.edu.
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 concentration secretion X-ApEn estimates were calculated from ACTH-cortisol pairs. X-ApEn, a scale and 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 concentration secretion compared with concentration-concentration analyses. Linking relevant 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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