Computer Methods and Programs in Biomedicine 183 (2020) 105094 Contents lists available at ScienceDirect Computer Methods and Programs in Biomedicine journal homepage: www.elsevier.com/locate/cmpb Analysis of linear lung models based on state-space models Esra Saatci a,∗ , Ertugrul Saatci a , Aydin Akan b a Department of Electrical and Electronics Engineering, Istanbul Kultur University, Bakirkoy, Istanbul b Department of Biomedical Engineering, Izmir Katip Celebi University, Izmir a r t i c l e i n f o Article history: Received 10 May 2019 Revised 22 August 2019 Accepted 23 September 2019 Keywords: Linear parametric respiratory system models State-space analysis Stability and sensitivity analysis Desensitized linear Kalman filter a b s t r a c t Background and Objectives: Linear parametric respiratory system models have been used in the model- based analysis of the respiratory system. Although there are studies exploring the physiological correct- ness and fitting accuracy of the models, they are not analysed in terms of interaction between param- eters and dynamics of the model. In this study we propose to use state-space modelling to yield the time-varying nature of the system incorporated by the parameters. Methods: We tested controllability, observability and stability characteristics of the equation of motion, 2-comp. parallel, 2-comp. series, vis- coelastic, 6-element and mead models while using the parameters given in the literature. In the sensitiv- ity analysis we proposed to use dual Desensitized Linear Kalman Filter (DKF) and Extended Kalman Filter (EKF) method. In this method, state error covariance revealed the parameter sensitivities for each model. Results: Results showed that all models, except 2-comp. parallel and mead models, are both controllable and observable models. On the other hand all models, except mead model, are stable models. Regarding to the sensitivity analysis, dual DKF - EKF method estimated states of the models successfully with a low estimation error. Sensitivity analysis results showed that airway parameters have higher effects on the state estimation than the other parameters have. Conclusion: We proved that state-space evaluation of the previously proposed parametric models of the respiratory system led us to quantitative and qual- itative assessments of the respiratory models. Moreover parameter values found in the literature have different effects on the models. © 2019 Elsevier B.V. All rights reserved. 1. Introduction Researchers proposed the respiratory system models to param- eterise the mechanic lung function and lung tissue properties; thereby deviations from the normal numeric values of the param- eters would indicate the malfunction of the system. For this pur- pose, models in time or frequency domain are fit to measured pressure and flow signals by minimising the power of leftovers (in other word error variance). In this step, researchers employed deterministic or stochastic methods to either calculate or estimate the unknown parameters [1–3]. Even if the underlying property of the system is the nonlinear composition of physical laws and parameters, general linear and nonlinear parametric and non-parametric models have been used in the model-based analysis of the respiratory system. Comprehen- sive review with reasonable mathematical analysis can be found in [1]. If we focus on respiratory mechanics determination problem, in parametric linear models, pressure and flow relationship is mod- ∗ Corresponding author. E-mail addresses: esra.saatci@iku.edu.tr (E. Saatci), e.saatci@iku.edu.tr (E. Saatci), aydin.akan@ikc.edu.tr (A. Akan). elled by linear either electrical or fluidic parameters in both time and frequency domain. The interest to these models are downturn after the revelation of constant phase model (model defined by fractional order differential equations). However, parametric linear models, especially viscoelastic model, are still used to determine the detailed physiologic function or anatomic modelling of the sys- tem. Interestingly, to our knowledge, none of the researchers di- rected his approach to comprehensive analysis of the respiratory models, which define the unknown continuous time system. Thus, our objective is to explore parametric linear models in control sys- tems point of view. The specific aim we pursue was to understand link between information bearing parameters and dynamics of the system and to gain new insights in respiration modelling. At the end of this study, we will answer the following ques- tions: 1. Which of the linear lung models are controllable and observ- able for the estimated parameter values in the literature? 2. Is the asymptotic stability an issue for the estimated param- eter values in linear lung models? 3. If we relax the Gaussian noise assumption on the model fit- ting errors, how do parameter variations affect the estima- tions? https://doi.org/10.1016/j.cmpb.2019.105094 0169-2607/© 2019 Elsevier B.V. All rights reserved.