Zhang L Q, Collins J C, King P H
Department of Biomedical Engineering, Vanderbilt University, Nashville, Tennessee 37235.
Math Biosci. 1991 Feb;103(1):77-95. doi: 10.1016/0025-5564(91)90092-w.
Two compartmental model structures are said to be indistinguishable if they have the same input-output properties. In cases in which available a priori information is not sufficient to specify a unique compartmental model structure, indistinguishable model structures may have to be generated and their attributes examined for relevance. An algorithm is developed that, for a given compartmental model, investigates the complete set of models with the same number of compartments and the same input-output structure as the original model, applies geometrical rules necessary for indistinguishable models, and test models meeting the geometrical criteria for equality of transfer functions. Identifiability is also checked in the algorithm. The software consists of three programs. Program 1 determines the number of locally identifiable parameters. Program 2 applies several geometrical rules that eliminate many (generally most) of the candidate models. Program 3 checks the equality between system transfer functions of the original model and models being tested. Ranks of Jacobian matrices and submatrices and other criteria are used to check patterns of moment invariants and local identifiability. Structural controllability and structural observability are checked throughout the programs. The approach was successfully used to corroborate results from examples investigated by others.
如果两个隔室模型结构具有相同的输入输出特性，则称它们是不可区分的。在现有先验信息不足以指定唯一隔室模型结构的情况下，可能不得不生成不可区分的模型结构，并检查它们的属性是否相关。开发了一种算法，对于给定的隔室模型，该算法研究具有与原始模型相同隔室数量和相同输入输出结构的完整模型集，应用不可区分模型所需的几何规则，并测试满足传递函数相等几何标准的模型。该算法还会检查可识别性。该软件由三个程序组成。程序1确定局部可识别参数的数量。程序2应用几个几何规则，消除许多（通常是大多数）候选模型。程序3检查原始模型和被测试模型的系统传递函数之间的相等性。使用雅可比矩阵和子矩阵的秩以及其他标准来检查矩不变量模式和局部可识别性。在整个程序中检查结构可控性和结构可观测性。该方法已成功用于证实其他人研究的示例结果。
