Analysis of bidirectional pattern synchrony of concentration-secretion pairs: implementation in the human testicular and adrenal axes

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Abstract
The hypothalamo-pituitary-testicular and hypothalamo-pituitary-adrenal axes are prototypical coupled neuroendocrine systems. In the present study, we contrasted in vivo linkages within and between these two axes using methods without linearity assumptions. We examined 11 young (21–31 yr) and 8 older (62–74 yr) men who underwent frequent (every 2.5 min) blood sampling overnight for paired measurement of LH and testosterone and 35 adults (17 women and 18 men; 26–77 yr old) who underwent adrenocorticotropic hormone (ACTH) and cortisol measurements every 10 min for 24 h. To mirror physiological interactions, hormone secretion was first deconvolved from serial concentrations with 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. These were applied in a forward (LH concentration template, examining pattern recurrence in testosterone secretion), reverse (testosterone concentration template, examining pattern recurrence in LH secretion), and differential (forward minus reverse) manner, respectively. Analogous concentration-secretion X-ApEn estimates were calculated from ACTH-cortisol pairs. X-ApEn, a scale- and model-independent measure of pattern reproducibility, disclosed 1) greater testosterone-LH feedback coordination than LH-testosterone feedforward synchrony in healthy men and significant and symmetric erosion of both feedforward and feedback linkages with aging; 2) more synchronous ACTH concentration-dependent feedforward than feedback drive of cortisol secretion, independent of gender and age; and 3) enhanced detection of bidirectional physiological regulation by in vivo pairwise concentration-secretion compared with concentration-concentration analyses. The linking of relevant biological input to output signals and vice versa should be useful in the dissection of the reciprocal control of neuroendocrine systems or even in the analysis of other nonendocrine networks.

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