马尔科夫链在药物动力学建模中的应用  

Application of Markov chain in pharmacokinetics modeling

作　　者：刘爱红[1] 杨光[1] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳航空航天大学学报》2016年第2期93-96,共4页Journal of Shenyang Aerospace University

基　　金：辽宁省科学技术厅自然基金(项目编号:2014020120);辽宁省教育厅科学研究一般项目(项目编号:L2013420)

摘　　要：研究马尔科夫链在药物动力学建模中的应用问题。首先给出单室静脉注射和血管外给药两种模型下的转移概率矩阵,根据吸收马尔科夫链的基本性质推算转移概率矩阵的t次幂,给出t时刻吸收部位和体内药量的表达式;然后将马尔科夫链与非线性回归结合起来,运用复合函数模型拟合数据,估计药物动力学模型参数;最后利用残差分析法对随机抽取的一组数据计算得出,利用马尔科夫链建立的模型比传统的药物动力学微分方程模型与实际数据拟合的程度高,从而给出一种新的药物动力学建模方法。The application of Markov chain in Pharmacokinetics modeling was researched. Firstly,transition probability matrixes under both one-compartment intravenous injection model and one-compartment extravascular administration model are presented respectively. The t-th power of the matrix was deduced based on basic natures of absorbed Markov chain,and expressions of dose in vivo and in absorption site are obtained;then,Markov chain and Nonlinear regression are linked to estimate parameters of pharmacokinetics with compound function model to simulate data; finally,residual sum of squares was employed from a set of data extracted randomly to showthe result that the model built by Markov chain has a higher degree of fitting for actual data than the model established by traditional differential equation,and a newmodeling method for Pharmacokinetics is proposed.

关 键 词：马尔科夫链 静脉注射 血管外给药 单室模型 转移概率矩阵 非线性回归 

分 类 号：O211.62[理学—概率论与数理统计]