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中文摘要：
药物动力学模型的解析求解公式在新药设计特别是药物动力学参数确定等方面具有非常重要的意义．近年来，由于非线性米氏消除速率过程确定的药物动力学模型解析求解公式的获得，使得大多数单房室模型的解析解基本确定．但是，由于刻画血管外给药的非线性米氏药物动力学模型是一个非自治系统，进而不可能寻求其解析求解公式．该文的目的是讨论一次性血管外给药和周期血管外给药下非线性药物动力学模型解的逼近问题．采用微分方程和脉冲微分方程的比较定理并借助LambertW函数的定义以及相关性质给出模型的不同上下界，估计模型解的逼近程度，并通过数值模拟进行验证．
英文摘要：
The analytical solution to the pharmacokinetics model plays a key role in the design of new drugs, especially in determining the pharmacokinetic parameters. In recent years, the analytical formulae for most of the pharmacokinetics models decided by the nonlinear Michaelis-Menten elimination process, were investigated and solved. However, the pharmacokinetics model with nonlinear Michaelis-Menten elimination rate for extravascular administration was a non-autonomous system, which resulted in difficulties in seeking its analytical solutions. Therefore, the problem of approximation to the solutions to the non-autonomous nonlinear pharmacokinetics models in the cases of single or periodic extravascular administrations was adressed. Different upper and lower bounds were given based on the comparison theorems for differential equations and impulsive differential equations, with the definition and related properties of the Lambert W function employed. Numerical simulations show the effectiveness of the proposed approximation method.
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