药物动力学模型的修正/江西财经大学东亿学术论丛

传统药物动力学的房室 模型，通过对比预测数据与 实际数据，已经推导出了很 多有用的结论。然而，在临 床操作中，药物在胃中的停 留时间可能随胃排空的时间 而变化。后者受食物摄取、 其他药物、辅药和其他因素 的影响。此外，真正的药理 过程总是受到不确定性因素 的影响，忽略这些现象建模 可能影响模型参数的估计和 所得出的结论。因此，越来 越需要将确定性模型扩展到 包括随机元素的模型。再者 ，测量值也不可能完全准确 。为了做出更加可靠的分析 ，本书对传统模型做了修正 ，建立了带有最优控制的随 机微分方程模型并对新模型 进行定性分析、定量分析、 R语言算法分析、参数估计 及模型拟合。此模型对用药 安全及合理性研究有一定的 参考价值。

1 Introduction 1.1 First-order 1-Compartment Model (Extravascular Administration) 1.2 First-order 2-Compartment Model (Intravenous Dose) 1.3 Pontryagin's Principle 1.3.1 Hamiltonian 1.3.2 Pontryagin's Maximum (or Minimum) Principle 1.4 White Noise 1.5 Stochastic Differential Equations (SDEs) 1.5.1 The Concept of SDEs 1.5.2 Stability of the SDEs 1.6 Magnus Expansion 1.6.1 Bernoulli Number 1.6.2 Magnus Approach and Its Interpretation 1.7 Gronwall Lemma 2 Using Optimal Control Theory to Study the First Order Compartment Models 2.1 Using Optimal Control Theory to Study the First-order 1-Compartment Model 2.2 Using Optimal Control Theory to Study the First-order 2-Compartment Model 3 The First-order Compartment Stochastic Models 3.1 The First-order 1-Compartment Stochastic Model 3.2 The First-order 2-Compartment Stochastic Model 4 Qualitative Analysis of the Stochastic Models 4.1 Qualitative Analysis of the First-order 1-Compartment Stochastic Model 4.2 Qualitative Analysis of the First-order 2-Compartment Stochastic Model 5 Quantitative Analysis of the Models 5.1 Quantitative Analysis of the First-order 1-Compartment Model (Extravascular Administration) 5.1.1 Parameter Estimation of the First-order 1-Compartment Model (Extravascular Administration) 5.1.2 Parameter Estimation of the First-order 1-Compartment Model with Optimal Control 5.1.3 Simulations of the Three First-order 1-Compartment Models 5.1.4 Using Numerical Method to Verify the Explicit Solution of the First-order 1-Compartment SDE Model 5.2 Quantitative Analysis of the First-order 2-Compartment Model (Intravenous Dose) 5.2.1 Parameters Estimation of the First-order 2-Compartment Model(Intravenous Dose) 5.2.2 Parameters Estimation of the First-order 2-Compartment Model with Optimal Control 5.2.3 Simulations of the Three First-order 2-Compartment Models 5.2.4 Stability of the Euler-Maruyama (E-M) Method for the 2-Compartment SDE Model Appendix A 1-Compartment ODE Model Simulation B 1-Compartment Optimal Control Model Simulation C 1-Compartment SDE Model Simulation D 2-Compartment ODE Model Simulation E 2-Compartment Optimal Control Model Simulation F 2-Compartment SDE Model Simulation References