Identifiability of Nonlinear Biological Models

描述（由申请人提供）：生物系统的数学模型对于定量理解人类和动物的生理和病理生理机制至关重要。生理上合理的模型，其结构反映了对系统的现有知识和假设，通常是非线性的，并以大量未知参数为特征。这种模型的例子是酶动力学和药代动力学-药效学模型。在进行从数据中估计这些未知参数的实验之前，出现了以下问题：我们即将收集的数据（通常花费很大）是否包含足够的信息来精确和明确地估计（例如，通过最小二乘或最大似然）假设模型的所有未知参数？这个问题，设置在（理论）背景下的无错误的模型结构和无噪声的数据，通常被称为先验的全局可识别性问题。尽管它具有理论性质，但它是从实际数据估计模型参数的必要前提，但往往被忽视。然而，可辨识性问题的求解通常是非常困难的，因为需要求解一个非线性代数方程组，该方程组的项数和非线性程度随着模型阶数的增加而增加。

DESCRIPTION (provided by applicant): Mathematical models of biological systems are essential to the quantitative understanding of physiological and pathophysiological mechanisms in humans and animals. Physiologically plausible models, the structure of which reflect available knowledge and assumptions about the systems, are usually nonlinear and characterized by a large number of unknown parameters. Examples of such models are enzyme kinetics and pharmacokinetic-pharmacodynamic models. Before performing an experiment to estimate these unknown parameters from the data, the following question arises: will the data we are about to collect (usually at a substantial expense) contain enough information to precisely and unequivocally estimate (for example, via least squares or maximum likelihood) all the unknown parameters of the postulated model? This question, set in the (theoretical) context of an error-free model structure and noise-free data, is usually referred to as the a priori global identifiability problem. Despite its theoretical nature, it is an essential, but often overlooked, prerequisite for model parameter estimation from real data. The solution of the identifiability problem is however in general very difficult, since one needs to solve a system of nonlinear algebraic equations which is increasing in number of terms and nonlinearity degree with the model order. The specific aims of this application focus on the development of an algorithm and a software tool to test a priori global identifiability of nonlinear compartmental models, a very inclusive class of ordinary nonlinear differential equation models based on conservation of mass. These models are widely used to study the kinetics of endogenous (e.g. substrates, hormones, enzymes) and exogenous (e.g., drugs, radiotracers) substances in living systems. The problem has been solved for a very limited set of models, but no solution exists in the general case. We will develop an algorithm based on computer algebra which allows to decrease the system complexity, thus providing the number of solutions for each parameter of the model. The software we propose to develop will be based on the client-server architecture paradigm, and will be open source, user-friendly and platform-independent. Such a tool would be very useful in experiment design. The software will also help in defining minimal input-output experimental configurations to assure a priori global identifiability: this is particularly important in clinical studies where severe constraints exist on experiment design, i.e. the number of inputs and outputs is limited for ethical and practical reasons.