Gain-Delay Decoupling in Human Stimulus Frequency Otoacoustic Emissions Reveals Constraints on Cochlear Nonlinear Amplification

Purpose: The nonlinear cochlear amplifier, driven by outer hair cells, underlies the remarkable sensitivity and frequency selectivity of the mammalian auditory system. Stimulus frequency otoacoustic emissions (SFOAEs) provide a noninvasive window into these active cochlear processes, yet the relationship between emission gain and delay across stimulus levels remains incompletely understood. This study examined the level dependence of SFOAEs in normal-hearing human listeners to characterize cochlear nonlinear response properties. We tested how emission gain and delay vary with stimulus level and estimated the frequency of the apical-basal transition associated with the breakdown of the approximate local scaling symmetry. Methods: SFOAEs were recorded from a cohort of normal-hearing participants (n = 20; females = 13) across a range of stimulus levels. A time-frequency filtering approach was applied to isolate single-reflection components and improve signal-to-noise ratio, yielding stable and unbiased estimates of emission level and phase-gradient delay. The relationships between stimulus level, gain, and delay were analyzed and normalized using a general relation derived from the fundamental physical properties of linear two-dimensional cochlear model. Results: The results confirm the nonlinear dependence of SFOAE level and delay on stimulus level. However, when the variations in gain and delay were compared to the predictions of a linear and a nonlinear 2D cochlear model, the discrepancy with the linear model predictions was evident. Measurements also revealed no stimulus-level dependence of the apical-basal transition frequency, consistent with a fixed apical cochlear region associated with the breakdown of the approximate scaling symmetry. Conclusion: The relative decoupling between gain and delay indicates that changes in cochlear amplification do not produce proportionate changes in emission timing, revealing constraints on the relationship between amplification and phase behavior in human cochlear responses. These findings indicate that SFOAE delay may remain informative about cochlear tuning, but nonlinear cochlear models could be constrained by the observed decoupling between gain and delay.