Numerical analysis of nonlinearity of outer hair cells based on comparison with measurements of DPOAEs

Distortion-product otoacoustic emissions (DPOAEs) are considered to be generated by nonlinear force of the outer hair cells (OHC), and those frequencies and levels depend on the function curve of the force. Each order of distortion component is generally generated by a different degree term of a nonlinear function which is approximated by a power series. In this study, the nonlinear force of OHC was formulated based on the distortion components detected in measurements of DPOAEs. The input/output (I/O) functions of DPOAEs were measured in normal-hearing human ears. The I/O functions of each component showed different nonlinear curve and varied by stimuli conditions. Odd-order of distortion components (2f₁-f₂ or 3f₂-2f₁) were generated in all the ears, on the other hand, even-order of distortion components (f₂-f₁ or 3f₁-f₂) were seldom detected. Thus, nonlinear curvature of the force of OHC, P_OHC was formulated as a function including both of saturability and symmetry around operating point, because even-order of distortion components were barely detected. The I/O functions of DPOAEs obtained from numerical analysis using a finite-element model of the human cochlea which includes the force were compared with the measurements in normal-hearing human ears, and validity of the force was evaluated. As a result, the I/O functions of each component obtained from the volume displacement of the stapes footplate of the model showed different nonlinear curve. If the sound pressure gains of the middle ear are assumed to be constant at a certain frequency regardless of sound pressure level, the ease of saturation of the I/O function obtained from the model is considered to be comparable to that obtained from the measurements in the human ear. The curve of the I/O functions of each component obtained from the model approximately matched that obtained from the measurements.