A BIOMATHEMATICAL MODEL OF TIME-DELAYED FEEDBACK IN THE HUMAN MALE HYPOTHALAMIC-PITUITARY LEYDIG-CELL AXIS

We develop, implement, and test a feedback and feedforward biomathemat ical construct of the male hypothalamic [gonadotropin-releasing hormon e (GnRH)]-pituitary [luteinizing hormone (LH)]-gonadal [testosterone ( Te)] axis. This stochastic differential equation formulation consists of a nonstationary stochastic point process responsible for generating episodic release of GnRH, which is modulated negatively by short-loop (GnRH) and long-loop (Te) feedback. Pulsatile GnRH release in turn dr ives bursts of LH secretion via an agonistic dose-response curve that is partially damped by Te negative feedback. Circulating LH stimulates (feedforward) Te synthesis and release by a second dose response. Te acts via negative dose-responsive feedback on GnRH and LH output, thus fulfilling conditions of a closed-loop control system. Four computer simulations document expected feedback performance, as published earli er for the human male GnRH-LH-Te axis. Six other simulations test dist inct within-model coupling mechanisms to link a circadian modulatory i nput to a pulsatile control node so as to explicate the known 24-h var iations in Te and, to a lesser extent, LH. We conclude that relevant d ynamic function, internodal dose-dependent regulatory connections, and within-system time-delayed coupling together provide a biomathematica l basis for a nonlinear feedback-feedforward control model with combin ed pulsatile and circadian features that closely emulate the measurabl e output activities of the male hypothalamic-pituitary-leydig cell axi s.