Investigating the nonlinear dynamics of cellular motion in the inner ear using the short-time Fourier and continuous wavelet transforms

The short-time Fourier transform (STFT) and the continuous wavelet transform (CWT) are used to analyze the time course of cellular motion in the inner ear. The velocity responses of individual outer hair cells and Hensen’s cells to sinusoidal and amplitude modulated (AM) acoustical signals applied at the ear canal display characteristics typical of nonlinear systems, including the generation of harmonic and half-harmonic components. The STFT proves to be valuable for following the time course of the frequency components generated using sinusoidal and AM input signals. The CWT is also useful for analyzing these signals: however, it is generally not as effective as the STFT when octave-hand-based CWT’s are used. For the transient response, the spectrogram (which is the squared magnitude of the STFT) and the octave-hand-based scalogram (which is the squared magnitude of the CWT) prove equally valuable, and we have used both to study the responses of these cells to step-onset tones of different frequencies. Such analyses reveal information about the preferred vibration frequencies of cells in the inner ear and are useful for deciding among alternative mathematical models of nonlinear cellular dynamics. A modified Duffing oscillator model yields results that bear some similarity to the data.