具并行一级和希尔消除药物动力学模型的稳态药动学分析  

Steady-state Pharmacokinetic Analysis of Drugs with Parallel First-order and Hill Elimination

作　　者：蒋家豪 金中 李军 吴孝钿 JIANG JIAHAO;JIN ZHONG;LI JUN;WU XIAOTIAN(School of Science,Shanghai Maritime University,Shanghai 201306,China;Faculté de Pharmacie,Universitéde Montréal,Montreéal,QC,H3C3J7,Canada)

机构地区：[1]上海海事大学理学院,上海201306 [2]蒙特利尔大学药学院,加拿大H3C3J7

出　　处：《应用数学学报》2024年第5期770-788,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(基金号:12271346,12071300)资助项目。

摘　　要：基于微分方程数学模型的药物动力学的理论研究在药物研发、临床给药方案设计等方面具有重要的作用.本文通过考虑具并行一级和饱和希尔(n=2)双通道消除的单仓室非线性药物动力学模型,研究了周期静脉注射用药下的稳态药物暴露量和稳态平均血药浓度的变化规律.首先,本文从理论上证明了任意给药方案下脉冲微分方程模型稳态周期解的存在唯一性,并严格推导了两个重要药动学指标的计算公式:稳态药物暴露量和稳态平均血药浓度.其次,运用数值模拟和理论证明,预测了不同给药方案下的稳态平均血药浓度的变化趋势.不同于现有的具一级和米氏消除通道的非线性药物动力学模型的单一趋势,本文模型结果显示随着给药频率的增加,稳态平均血药浓度呈现多样化变化趋势:(ⅰ)单调递减趋于极限值;(ⅱ)单调递增趋于极限值;(ⅲ)先递减后递增趋于极限值.最后,通过对重组粒细胞集落刺激因子的实际药物非格司亭(Filgrastim)的案例分析,本文给出了不同给药方案下的稳态平均血药浓度的数值解析表达式并定量计算了相应的稳态平均血药浓度和稳态最低血药浓度.Mathematical analysis of pharmacokinetic models plays an important role in drug researches.In this paper,considering a one-compartment pharmacokinetic model with parallel first-order and Hill(n=2)elimination under different dosage designs with periodic intravenous bolus administrations,we have mathematically studied the steady-state pharmacokinetics.As a result,we have proved that the pharmacokinetic model,represented by an impulsive differential equation,admits a unique steady-state periodic solution.Then we have derived the analytical formulas for two important pharmacokinetic indexes:steady-state drug exposure and steady-state average plasma concentration.Moreover,different to the existing the pharmacokinetic model with parallel first-order and Michaelis elimination pathways,we have been able to discover,both numerically and theoretically,the diversity in the steady-state average plasma concentration for different dose regimens.That is,by increasing the dosing frequency,three circumstances can occur for the steady-state average drug concentration:(i)monotonically decreases and converges to a limit value;(i)monotonically increases and converges to a limit value;and(ii)decreases first and then increases and eventually converges to a limit value.Finally,we have applied the results to a real drug model of recombinant granulocyte colony-stimulating factor(Filgrastim),for which we have provided the analytical formulas of the steady-state average plasma concentrations using different dose regimens and calculated the steady-state average plasma concentration and minimum plasma concentration.

关 键 词：脉冲微分方程 并行一级和希尔消除 药物动力学模型 稳态药物暴露量 稳态平均血药浓度 

分 类 号：R969.1[医药卫生—药理学] O175.14[医药卫生—药学]