RELATIONSHIP BETWEEN FREQUENCY AND AMPLITUDE DEPENDENCE IN THE LUNG - A NONLINEAR BLOCK-STRUCTURED MODELING APPROACH

During lung constriction, there is an increase in both the frequency and tidal volume (VT) dependences of lung tissue resistance (Rti) and elastance (Eti). This suggests that 1) significant alterations take place in the mechanisms contributing to both the linear and nonlinear characteristics of lung tissues; and 2) the frequency and VT dependences of Rti and Eti are coupled. We examined these issues for the case of sine wave and special pseudorandom inputs by utilizing the theory of nonlinear block-structured systems. Two basic model structures were considered: the Hammerstein and the Wiener structures. The Hammerstein structure is a cascade connection of a nonlinear zero-memory (N) system and a linear dynamic process (L). This structure predicts that frequency and VT dependences of Rti and Eti are decoupled. The Wiener structure is an inverse cascade of these two blocks (i.e., L-N) in which the frequency and VT dependences of Rti and Eti are coupled. These two structures were combined with a nonlinear airway compartment and fitted to measured airway opening and alveolar capsule pressure-flow time domain data in dogs before and after histamine-induced constriction. The best lung model was a linear airway compartment combined with a Wiener structure consisting of a constant-phase linear tissue impedance in cascade with a polynomial nonlinearity, suggesting that frequency and VT dependences of Rti and Eti are indeed coupled during control and constricted conditions. Moreover, histamine caused much larger changes in the linear tissue parameters than in the nonlinear coefficients. We suggest that the primary cause for the increased VT dependence during constriction is not a change in the nonlinear mechanisms but rather that the inherent nonlinear mechanisms become exacerbated through an increase in the magnitude of the linear tissue impedance.