Identifiability of Nonlinear Biological Models

非线性生物模型的可识别性

• 批准号: 7025040
• 负责人: PAOLO VICINI
• 金额: $ 20.63万
• 依托单位: UNIVERSITY OF WASHINGTON
• 依托单位国家: 美国
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-01 至 2009-02-28
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7025040
• 关键词: bioengineering /biomedical engineering; computer program /software; computer system design /evaluation; mathematical model; model design /development; parallel processing

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.

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，其结构反映了系统的可用知识和假设，通常是非线性的，并且具有大量未知参数。此类模型的例子是酶动力学和药代动力学-药效模型。在进行实验以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（通常花费大量费用）是否包含足够的信息来精确且明确地估计（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？这个问题设置在无错误模型结构和无噪声数据的（理论）背景下，通常被称为先验全局可识别性问题。尽管它具有理论性质，但它是根据实际数据估计模型参数的一个重要但经常被忽视的先决条件。然而，可辨识性问题的求解通常非常困难，因为需要求解非线性代数方程组，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。 该应用程序的具体目标集中于开发一种算法和软件工具来测试非线性隔室模型的先验全局可识别性，非线性隔室模型是一类非常包容的基于质量守恒的普通非线性微分方程模型。这些模型广泛用于研究生命系统中内源性（例如底物、激素、酶）和外源性（例如药物、放射性示踪剂）物质的动力学。该问题已针对非常有限的模型集得到解决，但在一般情况下不存在解决方案。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-服务器架构范例，并且是开源的、用户友好的和平台无关的。这样的工具在实验设计中非常有用。该软件还将帮助定义最小的输入-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格限制的临床研究中尤其重要，即输入和输出的数量由于伦理和实际原因而受到限制。