Inverse modeling of dog airway and respiratory system impedances

Mechanical parameters of the respiratory system are often estimated from respiratory impedances using lumped-element inverse models. One such six-element model is composed of an airway branch [with a resistance (Raw) and inertance (Iaw)] separated from a tissue branch [with a resistance (Rt), inertance (It), and compliance (Ct)] by a shunt compliance representing alveolar gas compression (Cg). Even though the airways are known to have frequency-dependent resistance and inertance, these inverse models have been composed of linear frequency-independent elements. In this study we investigated the use of inverse models where the airway branch was represented by a frequency-independent Raw and Iaw, a Raw that is linearly related to frequency and an Iaw that is independent of frequency, and a system of identical parallel tubes the impedance of which was computed from the tube radius and length. These inverse models were used to analyze airway and respiratory impedances between 2 and 1,024 Hz that were predicted from an anatomically detailed forward model. The forward model represented the airways by an asymmetrically branched network with a terminal impedance representative of known Cg, Rt, It, and Ct. For respiratory impedances between 2 and 128 Hz, all models fit the data reasonably well, and reasonably accurate estimates of Cg, Rt, It, and Ct were extracted from these data. For data above 200 Hz, however, only the multiple-tube model accurately fitted respiratory impedances (Zrs). This model fitted the Zrs data best when composed of 27 tubes, each having a radius of 0.148 cm and a length of 16.5 cm.