Fig. 1. Model of the respiratory system with a parallel arrangement of N branches, each consisting of equivalent linear resistance ( R ) and inertance ( I ) elements and subtended by a viscoelastic tissue element. The tissue elements have equivalent hysteresivity parameters (η) but distinct tissue elastance parameters ( H1 , H2 , …, HN ) that may vary from branch to branch in a probabilistic manner. The exponent α depends on η: α= (2/π)tan−1(1/η); ω: angular frequency; and j : unit imaginary number ( i.e. ,√−1) .