Estimation of respiratory system parameters using an extended equation of motion during mandatory mechanical ventilation

Mechanical ventilation is crucial for critically-ill patients, but requires continuous adjustments to prevent injuries and ensure optimal performance. Accurate estimation of respiratory parameters is essential for guiding disease-specific ventilator adjustments and optimizing respiratory support. The traditional equation of motion (EOM), widely used for this purpose, assumes linear compliance and resistance and neglects key physiological phenomena such as flow-dependent resistance and viscoelasticity, which can lead to biased estimates. In this study, we propose and validate an extended equation of motion (EEOM) that integrates nonlinear resistance and viscoelastic effects into a single framework. We fit the EEOM to simulated data, experimental data with a test lung, and clinical patient data (N=10). The accuracy of the EEOM to measure airway resistance, compliance, and viscoelasticity was improved compared to the traditional models (EOM and turbulent EOM, TEOM). In simulations, EEOM method consistently reduced estimation errors across all scenarios. For example, in estimating compliance (C_rs), EEOM achieved an average percentage error range of 0.06-1.18% across all scenarios, compared to 2.5–14.5% with EOM and 10.5–18.6% with TEOM. Across all parameters and simulations, EEOM yielded lower total mean absolute errors (3.5%) than EOM (11.5%) and TEOM (11.9%). In clinical data, EEOM estimates for viscoelastic parameters (C_d, R_d) were statistically comparable to the interrupter technique (p>0.05), additionally providing real-time estimates for nonlinear resistance terms. These results demonstrate that extended mechanical parameters, including nonlinear resistance and viscoelasticity, can be identified noninvasively using standard ventilator signals, enabling more personalized, safer and adaptive ventilator settings.