Collaborative Research: Efficient Methods for Identifiability of Dynamic Models

协作研究：动态模型可识别性的有效方法

• 批准号: 1853032
• 负责人: Marisa Eisenberg
• 金额: $ 24.9万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1853032&HistoricalAwards=false
• 关键词: Collaborative; Research; Efficient; Methods; Identifiability

The goal of the project is to analyze and improve the calibration of dynamic models developed by researchers in biology and other sciences to model real-world processes. Mathematical models are used broadly across biology to understand mechanisms, make predictions, and guide intervention strategies. To do so, the model parameters often must be calibrated using data; the estimated parameters can have significant implications for reliability of insights generated from the model and data. This raises the important question of whether the calibration process is well posed, i.e. is it possible to uniquely estimate model parameters from a given type or set of data? Identifiability analysis is the study of these issues, and this project will improve and expand the currently available set of algebraic identifiability methods to set them on a firmer theoretical basis and address new types of models used broadly in many biological settings. Beyond academia, the algorithms to be developed will allow researchers to successfully link models and experiments to generate model-based insights that improve real-world treatment strategies. Training will be provided to two Ph.D. students working on research for this project. The training component will also include interdisciplinary course development as well as a conference with tutorial lectures and problem sessions to educate industrial and academic participants in the theory, algorithms, and software developed in this project. This project is supported jointly by the Division of Mathematical Sciences Mathematical Biology and Division of Computing and Communication Foundations Algorithmic Foundations programs.More specifically, the investigators will develop, analyze, and implement symbolic and symbolic-numeric algorithms that perform identifiability analysis of dynamic models (including ordinary differential (ODE), delay, and difference equation models) that appear in biology and other sciences. Using these algorithms, they will also carry out identifiability analysis for a range of models drawn from cellular signaling and physiology applications. The proposed algorithms will be based on differential-difference algebra, which connects to identifiability in the common case of rational ODEs/delay/difference equations by applying differential-difference elimination algorithms to the model equations. Such symbolic methods for ODE models have proven to be productive in the area of parameter identifiability. The proposed methods would allow a large class of models to be analyzed for structural identifiability, allowing one to assess which parameters can be estimated and tailor experiment design to answer the questions of interest for treatment strategies and mechanistic insights. For the first time, rigorously justified and analyzed efficient algorithms will be available for identifiability problems in delay and difference equation models. Certified and more efficient algorithms will appear for global identifiability problems in ODE models. To carry out the proposed research, new advances in the algebraic theory of differential/difference equations will be made.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的目标是分析和改进生物学和其他科学研究人员开发的动态模型的校准，以模拟真实世界的过程。数学模型被广泛应用于生物学领域，以了解机制、做出预测和指导干预策略。要做到这一点，通常必须使用数据校准模型参数；估计的参数可能对模型和数据产生的见解的可靠性产生重大影响。这就提出了一个重要的问题，即校准过程是否适合，即是否有可能从给定的类型或数据集中唯一地估计模型参数？可辨识性分析是对这些问题的研究，该项目将改进和扩展目前可用的一套代数可辨识性方法，以使它们建立在更坚实的理论基础上，并解决在许多生物学环境中广泛使用的新型模型。在学术界之外，将开发的算法将允许研究人员成功地将模型和实验联系起来，以生成基于模型的见解，从而改进现实世界的治疗策略。将为两名从事该项目研究的博士生提供培训。培训部分还将包括跨学科课程开发以及一次会议，其中包括辅导讲座和问题会议，以教育工业界和学术界参与者在该项目中开发的理论、算法和软件。该项目由数学科学数学生物学分部和计算与通信基础算法基础分部联合支持。更具体地说，研究人员将开发、分析和实现符号和符号-数字算法，对生物和其他科学中出现的动态模型(包括常微分模型、延迟模型和差分方程式模型)进行可辨识性分析。使用这些算法，他们还将对从细胞信号和生理学应用中提取的一系列模型进行可识别性分析。所提出的算法将基于微分差分代数，通过将微分差分消去算法应用于模型方程，从而与有理常微分方程组/时滞/差分方程组的常见情况下的可辨识性相联系。这种常微分方程组模型的符号方法已被证明在参数可辨识性领域是有成效的。建议的方法将允许对一大类模型进行结构可识别性分析，使人们能够评估哪些参数可以估计，并量身定做实验设计，以回答治疗策略和机制洞察方面感兴趣的问题。第一次，严格证明和分析的有效算法将可用于时滞和差分方程模型的可辨识性问题。对于ODE模型中的全局可辨识性问题，将出现经过认证的更高效的算法。为了开展拟议的研究，将在微分/差分方程组的代数理论方面取得新的进展。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Predicting the second wave of COVID-19 in Washtenaw County, MI

• DOI: 10.1016/j.jtbi.2020.110461
• 发表时间: 2020-12-21
• 期刊: JOURNAL OF THEORETICAL BIOLOGY
• 影响因子: 2
• 作者: Renardy, Marissa;Eisenberg, Marisa;Kirschner, Denise
• 通讯作者: Kirschner, Denise

The role of time-varying viral shedding in modelling environmental surveillance for public health: revisiting the 2013 poliovirus outbreak in Israel

• DOI: 10.1098/rsif.2022.0006
• 发表时间: 2022-05-18
• 期刊: JOURNAL OF THE ROYAL SOCIETY INTERFACE
• 影响因子: 3.9
• 作者: Brouwer, Andrew F.;Eisenberg, Marisa C.;Eisenberg, Joseph N. S.
• 通讯作者: Eisenberg, Joseph N. S.

Mechanistic inference of the metabolic rates underlying $$^{13}$$C breath test curves

$$^{13}$$C 呼吸测试曲线基础代谢率的机械推断

• DOI: 10.1007/s10928-023-09847-x
• 发表时间: 2023
• 期刊: Journal of Pharmacokinetics and Pharmacodynamics
• 影响因子: 2.5
• 作者: Brouwer, Andrew F.;Lee, Gwenyth O.;Schillinger, Robert J.;Edwards, Christine A.;Wyk, Hannah Van;Yazbeck, Roger;Morrison, Douglas J.
• 通讯作者: Morrison, Douglas J.