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This Article Full Text Full Text (PDF) Supplemental Data All Versions of this Article: 297/5/R1215    most recent 90800.2008v1 Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Google Scholar Articles by Keenan, D. M. Articles by Veldhuis, J. D. PubMed PubMed Citation Articles by Keenan, D. M. Articles by Veldhuis, J. D.

Articles

Age-dependent regression analysis of male gonadal axis

¹Department of Statistics, University of Virginia, Charlottesville, Virginia; and ²Endocrine Research Unit, Department of Internal Medicine, Mayo School of Graduate Medical Education, Clinical Translational-Research Unit, Mayo Clinic, Rochester, Minnesota

Submitted September 22, 2008 ; accepted in final form July 2, 2009

The mechanisms by which aging progressively depletes testosterone (Te) availability in the male are unknown. Accordingly, the objective was to estimate brain gonadotropin-releasing hormone (GnRH) outflow (release and action), which cannot be observed directly, on the basis of downstream effects on pituitary luteinizing hormone (LH) secretion. LH, in turn, feeds forward on (stimulates) gonadal Te secretion, which then feeds back on (inhibits) GnRH-driven LH secretion. LH and Te concentrations were measured repetitively (every 10 min) over 18 h during graded pharmacological blockade of endogenous GnRH outflow in 24 healthy 20- to 72-yr-old men. Data were analyzed using a new age-dependent regression model of GnRH-LH-Te interactions to estimate pulsatile LH secretion and elimination, GnRH outflow, LH feedforward, and Te feedback. By incorporating regression on age within the dose-response model, we show that aging erodes all three primary forward and reverse pathways linking the brain, pituitary gland, and testes. Aging is associated with concomitant deficits in GnRH LH feedforward, LH Te feedforward, and Te GnRH/LH feedback. The analytical formalism should be generalizable to other ensemble regulatory systems, such as those that control growth, reproduction, stress adaptations, and glucose metabolism.

gonadotropin; men; human; testosterone; testis; model

Abbreviations: a_L and (1 – a_L), Fast and slow fractions of biexponential LH elimination • a_Te and (1 – a_Te), Fast and slow fractions of free Te elimination • A_G^k,j, Random-effect component of jth GnRH pulse mass for series k • A_L^k,j, Random-effect component of the jth LH pulse mass for series k • ED₅₀, ED₅₀ coefficient for LH secretion as a dose-response function of GnRH and free Te • f₁, Coefficient for free Te inhibition of LH efficacy on GnRH • F_L^(k)(t), LH feedforward signal (on Te secretion rate) • G^(k)(t), Unobserved GnRH signal, acting on the pituitary, at time t • _i^(k)(i = 1,..., n), Reconstruction of unobserved GnRH signal, based on estimated LH secretion rate and estimated free Te concentrations • [GRX^(k)] and K_d^GRX, GRX concentration (k = 0, 1, 2, 3) and GRX dissociation constant • IPI, Interpulse interval (min) • k, Index for k = 0, 1, 2, 3 (i.e., 4 levels of GRX for each subject) • K_a^S, Association constant for Te binding to SHBG (2 binding sites) • MLE, Maximum-likelihood expectation • n^AK_a^A, (Apparent) association constant for Te binding to albumin (multiple binding sites) • t, Time (min) • T^k,1, T^k,2,..., T^k,m, LH pulse times (same as GnRH pulse times) for k = 0, 1, 2, 3 • [totalTe], [TeS], [TeA], and [FrTe], Concentrations at time t (left implicit) of total Te, Te bound to SHBG (S), Te bound to albumin (A), and free (Fr) Te • X_L^(k)(t), LH concentration at time t for series k • X_Te^(k)(t) = [X_FrTe^(k)(t), X_TeS^(k)(t), X_TeA^(k)(t)], 3 components of Te concentration for series k • X_Te^(k)(t), True (i.e., without measurement error) Te concentration at time t for series k • _FrTe,i^(k), Estimated free Te concentration at time t_i • Y_Te,i^(k)= X_Te^(k)(t_i) + _Te,i^(k)(1 = 1,..., n), Observed total Te concentrations • Z_L^(k)(t), LH secretion rate (mass·unit volume^–1·unit time^–1) • Z_Te^(k)(t), Te secretion rate (mass·unit volume^–1·unit time^–1) • _L,i^(k)(i = 1,..., n), Estimated LH secretion rate, reconstructed as the conditional expectation of the unobserved LH secretion rate (at the MLE), given the observed LH concentrations • _Te,i^(k)(i = 1,..., n), Estimated Te secretion rate, reconstructed as the conditional expectation of the unobserved Te secretion rate (at the MLE), given the observed Te concentrations • _L¹ and _L², Fast and slow LH elimination rates (min^–1) • _Te⁽¹⁾ and _Te⁽²⁾, Fast and slow free Te elimination rates (min^–1) • β_L^(k), Basal LH secretion rate (mass·unit volume^–1·unit time^–1) • β_Te, Basal Te secretion rate (mass·unit volume^–1·unit time^–1) • _Te,i^(k)(1 = 1,..., n), Measurement error at time t_i for total Te concentration • _0,L^(k) and _1,L^(k), Parameters for mean pulse mass, i.e., coefficients for a linear function of the preceding IPI [e.g., the jth IPI (T^k,j – T^k,j–1)] • _0,Te, _1,Te, and _2,Te, Potency, sensitivity, and efficacy parameters of the logistic dose-response function for Te secretion, driven by the LH feedforward signal • _0,G and _1,G, Parameters for mean GnRH pulse mass, i.e., coefficients for a linear function of the preceding IPI [e.g., the jth IPI (T^k,j – T^k,j–1)] • ₁^S, _–1^S, ₁^A, and _–1^A, On- and off-binding rate coefficients for free Te to SHBG (S) and albumin (A) • ₁^S and ₁^A, Forward binding rates for free Te to SHBG (S) and albumin (A) • _L(t – T^k,j), 3-Parameter (probability density) function representing normalized pulse mass secretion at time t for pulse beginning at time T_L^k,j • _G(t – T^k,j), 3-Parameter (probability density) function representing normalized GnRH pulse mass secretion at time t for pulse beginning at time T^k,j • ^(k), Estimated frequency for IPI length under the Weibull model of IPI