D'Argenio D Z, Schumitzky A, Wolf W
Department of Biomedical Engineering, School of Pharmacy, University of Southern California 90089-1451.
Comput Methods Programs Biomed. 1988 Jul-Aug;27(1):47-54. doi: 10.1016/0169-2607(88)90102-2.
Several techniques are evaluated for solving the linear ordinary differential equations arising from compartment models. The methods involve approximating the matrix exponential of the state matrix (i.e. the transition matrix). The computational efficiencies of these techniques, together with that of a general purpose differential equation solver, are compared for several models arising from radiopharmacokinetic studies. The matrix exponential calculations are performed using both Ward's Padé approximation method and an eigenvalue-eigenvector decomposition (QR factorization) of the matrix A. These two algorithms have been incorporated as simulation options into the programs of the ADAPT package. ADAPT consists of a set of high-level programs for simulation, parameter estimation and experiment design, developed primarily for basic and clinical research modeling and data analysis applications involving pharmacokinetic and pharmacodynamic processes. The advantages and disadvantages of these simulation strategies for solving linear kinetic models within a parameter estimation setting are illustrated and discussed.
我们评估了几种用于求解隔室模型中产生的线性常微分方程的技术。这些方法涉及对状态矩阵（即转移矩阵）的矩阵指数进行近似。针对放射性药物动力学研究中产生的几个模型，比较了这些技术以及通用微分方程求解器的计算效率。矩阵指数计算使用沃德帕德逼近法和矩阵A的特征值 - 特征向量分解（QR分解）来进行。这两种算法已作为模拟选项纳入ADAPT软件包的程序中。ADAPT由一组用于模拟、参数估计和实验设计的高级程序组成，主要是为涉及药代动力学和药效学过程的基础和临床研究建模及数据分析应用而开发的。文中说明了并讨论了这些在参数估计设置下求解线性动力学模型的模拟策略的优缺点。
