Mathematical Modeling Of The Indirect Effects PK-PD Model Based On Stochastic Differential Equations And Its Applications

Pharmacokinetic-pharmacodynamic model is a mathematical model to study the relationship between the dynamic process of drug in the body and its efficacy comprehensively, quantitative expression of the intrinsic relationship between the concentration, time and effect. It reflects the two-way interaction between the drug and the body. The indirect effects model is more complex model of the combined models.The commonly joint we use is an ordinary differential equation model. Due to the limitations of ordinary differential equations, scholars builded pharmacokinetic model based on tochastic differential equations and achieved satisfactory results. This paper establishes the indirect effects model based on stochastic differential equations and describes the process of obtaining model by the specific examples. Firstly, the article describes the definition of pharmacokinetic and pharmacodynamic, pharmacokinetic model based on stochastic differential equations in three common mode of administration, and describes pharmacodynamic model commonly used at this stage.Secondly, due to the model for the indirect effects of the drug, this article establishes a mathematical model based on stochastic differential equations, quantitative expression of the intrinsic relationship among the time, the effect and the concentration. This article indicates the model features of the drug under a different mechanism of action and pointes out a mathematical model based on ordinary differential equations through the icon. what’s more, it introduces the significance of the use of stochastic differential equation, and establishes the pharmacokinetic-pharmacodynamic indirect effects model based on stochastic differential equations.Thirdly, through the example of a class of indirect effects model, the methods and processes for optimum binding model is described in detail.At first, we establish the pharmacokinetic model and then fix pharmacokinetic parameters to establish the pharmacodynamic model. Besides, we get simulated datas, and fit graphics through the software of matlab. Finally, use the data fitting to evaluate the model, improve the model until the optimal model appears.Finally, in order to solve the problem of small sample size and large differences between different individuals, a non-linear mixed effect model based on stochastic differential equation is also established.