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，其结构反映了现有的知识和假设的系统，通常是非线性的，其特征在于大量的未知参数。这种模型的实例是酶动力学和药代动力学-药效学模型。在进行实验从数据中估计这些未知参数之前，出现了以下问题：我们将要收集的数据（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，通过最小二乘法或最大似然法）假设模型的所有未知参数？这个问题，设置在一个无误差的模型结构和无噪声的数据的（理论）上下文中，通常被称为先验全局可识别性问题。尽管它的理论性质，它是一个必不可少的，但往往被忽视，从真实的数据模型参数估计的先决条件。然而，可识别性问题的解决方案通常是非常困难的，因为人们需要解决一个非线性代数方程组，这是随着模型阶数的增加而增加的项和非线性度。 本申请的具体目标集中在开发一种算法和一种软件工具，以测试非线性房室模型的先验全局可识别性，这是一类基于质量守恒的非常包容的非线性常微分方程模型。这些模型广泛用于研究内源性（例如底物、激素、酶）和外源性（例如，药物、放射性示踪剂）物质。这个问题已经解决了一个非常有限的一组模型，但没有解决方案存在于一般情况下。我们将开发一种基于计算机代数的算法，该算法可以降低系统的复杂性，从而为模型的每个参数提供解决方案的数量。我们建议开发的软件将基于客户端-服务器架构模式，并将是开放源代码，用户友好和平台无关的。这样的工具在实验设计中将是非常有用的。该软件还将有助于定义最小的输入输出实验配置，以确保先验的全局可识别性：这在实验设计存在严重限制的临床研究中尤其重要，即输入和输出的数量因伦理和实际原因而受到限制。

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.