Keenan D M, Veldhuis J D, Yang R
Division of Statistics, University of Virginia, Charlottesville 22903, Virginia, USA.
Am J Physiol. 1998 Dec;275(6):R1939-49. doi: 10.1152/ajpregu.1998.275.6.R1939.
We present a nonlinear random-effects stochastic differential equation (SDE) model of combined basal and pulsatile hormone secretion with a series-specific hormone half-life and conditional pulse times. The construct uses a three-parameter pulse shape (generalized gamma function) to allow variably skewed secretory bursts superimposed on a finite basal hormone secretion rate. The analysis imbeds stochastic elements at three levels: a variable mass of hormone accumulation (of which the random effect is a part) during interpulse intervals, nonuniform secretion with hormone admixture into the circulation, and technical (sampling and assay) experimental uncertainty. We implement maximum likelihood estimates of secretory parameters (basal and pulsatile secretion and half-life) with asymptotic standard errors. The model applied to illustrative human luteinizing hormone (LH) time series suggests contrasts in basal LH secretion rates (e.g., greater in postmenopausal women than men) and LH secretory burst mass (e.g., higher in older women), but not LH burst frequency or distributional LH half-lives (7-40 min). For validation, in two infused (human recombinant) LH profiles, we implement partially constrained mono- and biexponential versions of the model with fixed (a priori assumed) versus variable LH basal secretion rates. We conclude that a statistically supported, nonlinear, random effects, SDE-based construct can evaluate jointly basal and pulsatile LH secretory rates and LH half-life in 24 h, episodically varying serum LH concentration profiles. This new reduced-parameter analytic strategy should be useful to explore further the pathophysiological mechanisms of altered neurohormone secretion.
我们提出了一种非线性随机效应随机微分方程（SDE）模型，用于描述基础激素分泌和脉冲式激素分泌的组合，该模型具有特定系列的激素半衰期和条件脉冲时间。该模型使用三参数脉冲形状（广义伽马函数），以允许在有限的基础激素分泌率之上叠加可变偏态的分泌脉冲。该分析在三个层面嵌入了随机因素：脉冲间期内激素积累的可变质量（随机效应是其中一部分）、激素混合进入循环的不均匀分泌以及技术（采样和测定）实验不确定性。我们采用具有渐近标准误差的分泌参数（基础分泌和脉冲分泌以及半衰期）的最大似然估计。应用于示例性人类促黄体生成素（LH）时间序列的模型表明基础LH分泌率存在差异（例如，绝经后女性高于男性）以及LH分泌脉冲质量存在差异（例如，老年女性更高），但LH脉冲频率或分布性LH半衰期（7 - 40分钟）没有差异。为了进行验证，在两个注入（重组人）LH的实验中，我们采用了模型的部分受限单指数和双指数版本，分别具有固定（先验假设）和可变的LH基础分泌率。我们得出结论，一种基于统计支持的、非线性、随机效应、基于SDE的模型能够联合评估24小时内基础和脉冲式LH分泌率以及LH半衰期，适用于血清LH浓度随时间变化的情况。这种新的参数简化分析策略对于进一步探索神经激素分泌改变的病理生理机制应该是有用的。
