Wanika Linda, Egan Joseph R, Swaminathan Nivedhitha, Duran-Villalobos Carlos A, Branke Juergen, Goldrick Stephen, Chappell Mike
School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom.
Department of Biochemical Engineering, University College London, London, United Kingdom.
J Biol Eng. 2024 Mar 4;18(1):20. doi: 10.1186/s13036-024-00410-x.
Advancements in digital technology have brought modelling to the forefront in many disciplines from healthcare to architecture. Mathematical models, often represented using parametrised sets of ordinary differential equations, can be used to characterise different processes. To infer possible estimates for the unknown parameters, these models are usually calibrated using associated experimental data. Structural and practical identifiability analyses are a key component that should be assessed prior to parameter estimation. This is because identifiability analyses can provide insights as to whether or not a parameter can take on single, multiple, or even infinitely or countably many values which will ultimately have an impact on the reliability of the parameter estimates. Also, identifiability analyses can help to determine whether the data collected are sufficient or of good enough quality to truly estimate the parameters or if more data or even reparameterization of the model is necessary to proceed with the parameter estimation process. Thus, such analyses also provide an important role in terms of model design (structural identifiability analysis) and the collection of experimental data (practical identifiability analysis). Despite the popularity of using data to estimate the values of unknown parameters, structural and practical identifiability analyses of these models are often overlooked. Possible reasons for non-consideration of application of such analyses may be lack of awareness, accessibility, and usability issues, especially for more complicated models and methods of analysis. The aim of this study is to introduce and perform both structural and practical identifiability analyses in an accessible and informative manner via application to well established and commonly accepted bioengineering models. This will help to improve awareness of the importance of this stage of the modelling process and provide bioengineering researchers with an understanding of how to utilise the insights gained from such analyses in future model development.
数字技术的进步已将建模推到了从医疗保健到建筑等众多学科的前沿。数学模型通常用参数化的常微分方程组来表示，可用于描述不同的过程。为了推断未知参数的可能估计值，这些模型通常使用相关实验数据进行校准。结构和实际可识别性分析是参数估计之前应评估的关键组成部分。这是因为可识别性分析可以提供关于一个参数是否可以取单一、多个、甚至无限或可数多个值的见解，这最终会对参数估计的可靠性产生影响。此外，可识别性分析有助于确定所收集的数据是否足够或质量是否足够好以真正估计参数，或者是否需要更多数据甚至对模型进行重新参数化才能继续进行参数估计过程。因此，此类分析在模型设计（结构可识别性分析）和实验数据收集（实际可识别性分析）方面也发挥着重要作用。尽管使用数据估计未知参数值很流行，但这些模型的结构和实际可识别性分析常常被忽视。不考虑应用此类分析的可能原因可能是缺乏认识、可及性和可用性问题，特别是对于更复杂的模型和分析方法。本研究的目的是通过应用于成熟且被广泛接受的生物工程模型，以一种易于理解且信息丰富的方式介绍并进行结构和实际可识别性分析。这将有助于提高对建模过程这一阶段重要性的认识，并为生物工程研究人员提供关于如何在未来模型开发中利用从此类分析中获得的见解的理解。
