Group delays of distortion product otoacoustic emissions: relating delays measured with f1- and f2-sweep paradigms.

A theoretical analysis is presented of group delays of distortion product otoacoustic emissions (DPOAEs) measured with the phase-gradient method. The aim of the analysis is to clarify the differences in group delays D1 and D2, obtained using the f1- and the f2-sweep paradigms, respectively, and the dependence of group delays on the order of the DPOAE. Two models are considered, the place-fixed and the wave-fixed models. While in the former model the generation place is assumed to be invariant with both f1- and f2-sweeps, in the latter model the shift of generation place is fully accounted for. By making a simple local approximation of the cochlear scale invariance, a mathematical conversion from phase-place to phase-frequency gradients is incorporated in the wave-fixed model. Under the assumption that the DPOAE (as recorded at the best f2/f1 ratio) is dominated by the contribution from the generation site and not by, e.g., reflection components, the analysis leads to simple expressions for the ratio and difference between D1 and D2. Validation of the models against experimental data indicates that lower sideband DPOAEs (2f1-f2, 3f1-2f2, 4f1-3f2) are most consistent with the wave-fixed model. Upper sideband components (2f2-f1), in contrast, are not properly described by either the place-fixed or the wave-fixed model, independent whether DPOAE generation is assumed to originate at the f2 or at the more basally located f(dp) characteristic place.