|
| 內容簡介： |
|
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*控制的随机微分方程模型并对新模型进行定性、定量分析、R语言算法分析、参数估计及模型拟合。此模型可对用药安全及合理性研究有一定的参考价值。
|
| 關於作者： |
刘欠宁，美国新墨西哥州立大学数理统计学博士。现任职于江西财经大学统计学院。教授本科、硕土、博士课程包括贝叶斯统计、随机微分方程、数学分析。
2007年参编教材《线性代数》，中国农业出版社出版。
2018年任SCI期刊International Journal of Biomathematics审稿人。
本专著为本人原创作品。
|
| 目錄：
|
1Introduction
1.1First-order 1-Compartment Model Extravascular Administration
1.2First-order 2-Compartment Model Intravenous Dose
1.3Pontryagin''s Principle
1.3.1Hamiltonian
1.3.2Pontryagin''s Maximum or Minimum Principle
1.4White Noise
1.5Stochastic Differential Equations SDEs
1.5.1The Concept of SDEs
1.5.2Stability of the SDEs
1.6Magnus Expansion
1.6.1Bernoulli Number
1.6.2Magnus Approach and Its Interpretation
1.7Gronwall Lemma
2Using Optimal Control Theory to Study the First Order Compartment Models
2.1Using Optimal Control Theory to Study the First-order 1-Compartment Model
2.2Using Optimal Control Theory to Study the First-order 2-Compartment Model
3The First-order Compartment Stochastic Models
3.1The First-order 1-Compartment Stochastic Model
3.2The First-order 2-Compartment Stochastic Model
4Qualitative Analysis of the Stochastic Models
4.1Qualitative Analysis of the First-order 1-Compartment Stochastic Model
4.2Qualitative Analysis of the First-order 2-Compartment Stochastic Model
5Quantitative Analysis of the Models
5.1Quantitative Analysis of the First-order 1-Compartment Model Extravascular Administration
5.1.1Parameter Estimation of the First-order 1-Compartment Model Extravascular Administration
5.1.2Parameter Estimation of the First-order 1-Compartment Model with Optimal Control
5.1.3Simulations of the Three First-order 1-Compartment Models
5.1.4Using Numerical Method to Verify the Explicit Solution of the First-order 1-Compartment SDE Model
5.2Quantitative Analysis of the First-order 2-Compartment Model Intravenous Dose
5.2.1Parameters Estimation of the First-order 2-Compartment ModelIntravenous Dose
5.2.2Parameters Estimation of the First-order 2-Compartment Model with Optimal Control
5.2.3Simulations of the Three First-order 2-Compartment Models
5.2.4Stability of the Euler-Maruyama E-M Method for the 2-Compartment SDE Model
Appendix
A1-Compartment ODE Model Simulation
B1-Compartment Optimal Control Model Simulation
C1-Compartment SDE Model Simulation
D2-Compartment ODE Model Simulation
E2-Compartment Optimal Control Model Simulation
F2-Compartment SDE Model Simulation
References
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 聯絡我們
| 運費計算
| 幫助中心 |
加入書簽
HOME
新書上架
