Audoly S, Bellu G, D'Angiò L, Saccomani M P, Cobelli C
Department of Structural Engineering, University of Cagliari, 09100 Cagliari, Italy.
IEEE Trans Biomed Eng. 2001 Jan;48(1):55-65. doi: 10.1109/10.900248.
A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. In this paper, we present a new algorithm for testing global identifiability of nonlinear dynamic models, based on differential algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer algebra techniques are used to solve the resulting set of nonlinear algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.
生物和生理系统参数估计适定性的一个先决条件是先验全局可识别性，这一特性涉及未知模型参数解的唯一性。对于非线性动态模型，评估先验全局可识别性尤为困难。文献中已经提出了各种方法，但在一般情况下不存在解决方案。在本文中，我们提出了一种基于微分代数的测试非线性动态模型全局可识别性的新算法。以高效的方式计算与动态方程相关的特征集，并使用计算机代数技术来求解由此产生的非线性代数方程组。该算法能够处理生物系统模型中出现的许多特征，包括零初始条件和时变参数。给出了该算法用于分析生物和生理系统非线性模型先验全局可识别性的使用示例。
