A Respiratory System Model: Parameter Estimation and Sensitivity Analysis

Abstract

In this paper we compare several approaches to identifying certain key respiratory control parameters relying on data normally available from non-invasive measurements. We consider a simple model of the respiratory control system and describe issues related to numerical estimates of key parameters involved in respiratory function such as central and peripheral control gains, transport delay, and lung compartment volumes. The combination of model-specific structure and limited data availability influences the parameter estimation process. Methods for studying how to improve the parameter estimation process are examined including classical and generalized sensitivity analysis, and eigenvalue grouping. These methods are applied and compared in the context of clinically available data. These methods are also compared in conjunction with specialized tests such as the minimally invasive single-breath CO₂ test that can improve the estimation, and the enforced fixed breathing test, which opens the control loop in the system. The analysis shows that it is impossible to estimate central and peripheral gain simultaneously without usage of ventilation measurement and a controlled perturbation of the respiratory system, such as the CO₂ test. The numerical results are certainly model dependent, but the illustrated methods, the nature of the comparisons, and protocols will carry over to other models and data configurations.