《藥物動力學模型的修正》是2020年經濟管理出版社出版的圖書，作者是劉欠寧。
基本介紹
- 中文名：藥物動力學模型的修正
- 作者：劉欠寧
- 出版社：經濟管理出版社
- ISBN：9787509661864
內容簡介,圖書目錄,作者簡介,
內容簡介
傳統藥物動力學的房室模型，通過對比預測數據與實際數據，已經推導出了很多有用的結論。然而，在臨床操作中，藥物在胃中的停留時間可能隨胃排空的時間而變化。後者受食物攝取，其他藥物，輔藥和其他因素的影響。此外，真正的藥理過程總是受到不確定性因素的影響，忽略這些現象建模可能影響模型參數的估計和所得出的結論。因此，越來越需要將確定性模型擴展到包括隨機元素的模型。再者，測量值也不可能完全準確。為了做出更加可靠的分析，本書對傳統模型做了修正，建立了帶有*控制的隨機微分方程模型並對新模型進行定性、定量分析、R語言算法分析、參數估計及模型擬合。此模型可對用藥安全及合理性研究有一定的參考價值。
圖書目錄
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
作者簡介
劉欠寧，美國新墨西哥州立大學數理統計學博士。現任職於江西財經大學統計學院。教授本科、碩土、博士課程包括貝葉斯統計、隨機微分方程、數學分析。2007年參編教材《線性代數》，中國農業出版社出版。2018年任SCI期刊International Journal of Biomathematics審稿人。本專著為本人原創作品。
