Low frequency constant-phase behavior in the respiratory impedance

The paper presents an underpinning theory and modeling approach for determining the origins of the constant-phase behavior in the input impedance of the respiratory system. The theory and model structure are validated using (i) simulations of the intrinsic airway anatomy and (ii) measurements in 10 healthy subjects. By means of an electrical equivalent of the air flow dynamics from trachea to alveoli, a recurrent ladder network is developed and simulated with nominal morphological values available from the literature. The result of the simulated model using morphological data was similar to the measured impedance values in 23 healthy subjects in the 4–48 Hz frequency range, suggesting that it is a suitable candidate model. In this paper, we propose to use an augmented ladder network model to identify the respiratory impedance from 10 healthy subjects in the 0.9–5.7 Hz frequency range. The identification is done by means of upper airway tract (a series RLC circuit) in cascade with the recurrent ladder network described by their initial values (i.e. trachea) and corresponding recurrent ratios for resistance, inertance and compliance. The results show that (i) the identified values are close to the conditions imposed by the theory and (ii) the constant phase appearing at lower frequencies in the measured data from the volunteers is well captured by the proposed modeling approach. We conclude that next to viscoelastic and diffusion properties, the fractal geometry plays an important role in determining the phase-constancy in the input respiratory impedance. We also speculate that pathology affecting the morphology of the lungs will lead to variations in the identified model parameters, enabling thus a classification of model parameters with disease.