UCLA, Department of Mathematics, Los Angeles, CA 90095, USA.
Math Biosci. 2009 Dec;222(2):61-72. doi: 10.1016/j.mbs.2009.08.010. Epub 2009 Sep 6.
The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the 'simplest' globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.
动态系统 ODE 模型的参数可识别性问题已经得到了广泛的研究。然而，除了线性 ODE 模型之外，当模型不可识别时，确定可识别的参数组合的问题并没有得到太多关注，并且这个问题对于非线性 ODE 也没有得到完全解决。可识别的参数组合是有用的，例如，对于将不可识别的 ODE 模型重新参数化为可识别的模型。我们将现有的用于找到非线性 ODE 模型全局可识别参数的算法扩展到使用 Gröbner 基来生成“最简单”的全局可识别参数组合。我们还为该方法提供了工作的充分条件，演示了我们的算法，并为几个线性和非线性不可识别的生物模型找到了相关的可识别的重新参数化。
