Mathematical modeling of circadian cortisol concentrations using indirect response models: Comparison of several methods
Mathematical modeling of circadian cortisol concentrations using indirect response models: Comparison of several methods
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DOI：
10.1023/a:1020678628317
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发表时间：
1999-02-01
期刊：
影响因子：
--
通讯作者：
Jusko, WJ
中科院分区：
文献类型：
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作者：
Chakraborty, A;Krzyzanski, W;Jusko, WJ
六个数学函数来描述皮质醇浓度的时间生物学进行了评估。吸入性丙酸氟替卡松剂量比例研究的平均数据与使用各种生物节律函数（单余弦、双斜坡、双零阶、双余弦和具有2和n谐波的傅立叶级数）的间接反应模型拟合，用于生产率。还生成了具有已知参数和随机变化的数据，并使用ADAPT II程序进行拟合。比较拟合参数、模型估计标准和运行检验。具有预分配功能的型号：双斜坡、双零阶和双余弦提供皮质醇释放速率的最大和最小时间，适用于描述不对称的昼夜节律模式并产生IC 50值。傅立叶分析与其他方法的不同之处在于，它使用安慰剂数据来恢复皮质醇分泌率的方程，而不是通过假设。傅立叶分析的非线性回归，而不是L-2范数的方法，是有用的基线皮质醇数据的特征，但限于最大的两个谐波。除了单一的余弦函数，预测对称的皮质醇浓度，所有的方法都令人满意的描述基线和抑制皮质醇浓度。另一方面，具有L-2范数的傅立叶级数产生基线模式的最佳无偏估计。傅立叶方法灵活、准确，可推广到其他药物引起的正常周期性节律改变。
Six mathematical functions to describe the chronobiology of cortisol concentrations were assessed. Mean data from a dose-proportionality study of inhaled fluticasone propionate were fitted with an indirect response model using various biorhythmic functions (single cosine, dual ramps, dual zero-order, dual cosines, and Fourier series with 2 and n-harmonics) for production rate. Data with known parameters and random variation were also generated and fitted using the ADAPT II program. Fitted parameters, model estimation criteria, and runs tests were compared. Models with preassigned functions: the dual ramps, the dual zero-order and the dual cosines provide maximum and minimum times for cortisol release rate, were suitable for describing asymmetric circadian patterns and yielding IC50 values. Fourier analysis differs fi om the other methods in that it uses the placebo data to recover equations for cortisol secretion rate rather than by postulation. Nonlinear regression for Fourier analysis, instead of the L-2-norm method, was useful to characterize the baseline cortisol data but was restricted to a maximum of two harmonics. Apart from the single cosine function, which predicts symmetrical cortisol concentrations, all methods were satisfactory in describing the baseline and suppressed cortisol concentrations. On the other hand, Fourier series with L-2-norm produced the best unbiased estimate for baseline patterns. The Fourier method is flexible, accurate, and can be extended to other drug-induced changes ill normal periodic rhythms.