Department of Pharmaceutical Sciences, University at Buffalo, 370 Kapoor Hall, Buffalo, NY, 14214, USA.
J Pharmacokinet Pharmacodyn. 2019 Feb;46(1):53-63. doi: 10.1007/s10928-018-09618-z. Epub 2019 Jan 7.
In many models of pharmacodynamic systems with delays, a delay of an input is introduced by means of the convolution with the gamma distribution. An approximation of the convolution integral of bound functions based on a system of ordinary differential equations that utilizes properties of the binomial series has been introduced. The approximation converges uniformly on every compact time interval and an estimate of the approximation error has been found [Formula: see text] where [Formula: see text] is the number of differential equations and [Formula: see text] is the shape parameter of the gamma distribution. The accuracy of approximation has been tested on a set of input functions for which the convolution is known explicitly. For tested functions, [Formula: see text] has resulted in an accurate approximation, if [Formula: see text]. However, if [Formula: see text] the error of approximation decreases slowly with increasing [Formula: see text], and [Formula: see text] might be necessary to achieve acceptable accuracy. Finally, the approximation was applied to estimate parameters for the distributed delay model of chemotherapy-induced myelosuppression from previously published WBC count data in rats treated with 5-fluorouracil.
在许多具有时滞的药效动力学系统模型中，通过与伽马分布的卷积来引入输入的时滞。已经引入了一种基于利用二项式级数性质的常微分方程组来逼近有界函数卷积积分的方法。该逼近在每个紧致时间区间上一致收敛，并找到了逼近误差的估计[公式：见正文]，其中[公式：见正文]是微分方程的数量，[公式：见正文]是伽马分布的形状参数。在卷积显式已知的一组输入函数上测试了逼近的准确性。对于测试函数，如果[公式：见正文]，则[公式：见正文]导致了准确的逼近。然而，如果[公式：见正文]，则逼近误差随[公式：见正文]的增加缓慢减小，并且可能需要[公式：见正文]才能达到可接受的准确性。最后，该逼近方法被应用于从先前发表的用 5-氟尿嘧啶处理的大鼠的白细胞计数数据中估计化疗诱导的骨髓抑制的分布式时滞模型的参数。
