分形药动学建模研究-应用统计专业论文.docxVIP

华中科技大学硕士学位论文 华 中 科 技 大 学 硕 士 学 位 论 文 II II 摘 要 房室模型广泛应用到生物工程、药学等学科上，特别是药动学和药效学，房室 模型的建立几乎可以说是研究它们的基础，通过实验数据建立房室模型，利用模型 中的数学公式、方程解释药物在生物体内的过程。传统的药物动力学一般是假设在 均匀状态下研究的，特别是经典的房室模型就是假定在均匀介质中的运动及基础上 的建模。 但是，现在普遍认为整个生物系统是一种分形，尤其在微观环境下发现药物分 子与膜界面、酶、受体等的相互运动是非均匀的、受空间限制的，也属于几何分形。 因此传统药物动力学假定的均匀状态是不现实的，经典的房室模型需要重新审视。 经过对参数的估计、速率常数的记录、大量不同药物的试验、对应的生物的反应的 探索，可以发现所有的 PK 建模方法都属于特殊情况下的分形药动学。所以本文主要 是利用分形的思想对药动学的房室模型展开研究。 首先介绍了一些准备知识，包括药动学的一些基本知识，经典房室模型的大致 介绍和一些其他需要用到的理论。其次重点介绍了分形的相关理论。最后将分形的 思想加入到房室模型中，将模型优化，使模型变得更普适更现实。 关键词：分形药动学 分形 房室模型 速率常数 II III Abstract compartmental model has been widely used on biological engineering, medicine and other subjects, especially in the pharmacokinetic and pharmacodynamic, the establishment of compartmental model is nearly the foudation of studying them .compartmental model is established by experimental data,and then we can explain the process of dugs in the body by the model of mathematical formulas and equations .The classical pharmacokinetics research is generally done in the uniform condition ,especially the classical compartmental model is assumed on the basis of movement in the homogeneous medium. It is accepted now that the biological system is a kind of fractal , however , especially the micro environment where drug molecules react with membrane interface.enzymes and receptors of mutual movement .Therefore , the homogeneous environment which was artf icially supposed in advance is not realistic when we deal with the reality of reaction of dru gs in the body .So the classical compartmental models need to review.In fact , exploring th e full range of parametric possibilitiess and taking care of the different drugs and respectiv e biological concentrations , it may be found that all PK modelling ways are some cases of the fractal PK theory .So this article is mainly using the ideas of fractal to get some reserch of the pharmacokinetic compartmental model. Firstly it introduces some knowledge of preparation, including some basic knowledge of