Time-Varying Respiratory Mechanics as a Novel Mechanism Behind Frequency Dependence of Impedance: A Modeling Approach

Frequency dependence of respiratory mechanics is a well-established behavior of the respiratory system and is known to be an indicator of severity of obstructive disease, attributed to both tissue viscoelasticity and heterogeneity of airflow in the lung. Despite the fact that respiratory parameters are known to vary in time, often amplified in disease, all analysis methods assume stationarity or short-time stationarity in the parameters used to describe the respiratory system, and the effects of this assumption have not yet been examined in any detail. Here, using a generalized approach, we developed a theory for time-varying respiratory mechanics in time-frequency domain for analysis of linear time-varying systems, then, we analyzed the same respiratory system model with time-varying parameters in the time domain. Both time-frequency domain and time-domain derivations revealed a striking correlation between time-varying behavior of the respiratory system and frequency dependence of resistance. Remarkably, this phenomenon arose from the amplitude of time variations of the elastance. This links two mechanisms that are known to increase in obstructive disease: apparent low frequency increases in resistance and the time variations of reactance.