How inhomogeneities and airway walls affect frequency dependence and separation of airway and tissue properties

It has been proposed that during mild-to-moderate bronchoconstriction one can partition airway and tissue properties on the basis of input impedance (Zin) acquired from 0.1 to 5 Hz (K. R. Lutchen, B. Suki, Q. Zhang, F. Petak, B. Daroczy, and Z. Hantos. J. Appl. Physiol. 77: 373-385, 1994). The approach is to apply a homogeneous lung model that contains airway resistance and viscoelastic tissue damping and elastance parameters. The tissue parameters account for the frequency dependence in lung resistance (RL) and elastance (EL). We present an anatomically consistent asymmetrically branching airway model to address two key questions: 1) How will lung inhomogeneities, airway wall shunting, and tissue viscoelasticity contribute to increased frequency dependence and levels of RL and EL during lung constriction? and 2) How much can lung inhomogeneities and airway wall shunting contribute to our assessment of airway, tissue, and overall lung properties derived from Zin? The model incorporates nonrigid airway walls and allows for explicit control over the type and degree of inhomogeneous airway constriction or tissue changes. Our results indicate that, from 0.1 to 5 Hz, airway wall shunting does not become important unless the entire lung periphery experiences significant constriction. Mild-to-moderate inhomogeneous peripheral airway constriction produces a relatively minor additional frequency dependence in RL and EL beyond that due to the tissues alone. With more extreme constriction, however, there is a marked frequency-dependent increase in EL. This phenomenon may render it impossible to distinguish from a single frequency measurement whether an increase in EL during bronchoconstriction is a consequence of a true increase in tissue stiffening or simply a consequence of airway phenomena. Finally, Zin from 0.1 to 5 Hz can be used to provide a reasonable separation of airway and tissue properties for mild-to-moderate homogeneous or inhomogeneous lung constriction. However, during more severe disease, inhomogeneities and/or wall shunting will produce substantial overestimation of tissue damping and hysteretic properties. In fact, the only reliable indicator of a real change in the tissues may be a change in the estimate of tissue elastance that is based on data extending to a sufficiently low frequency.