Human acoustics: from vocal chords to inner ear
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Part I covers the vocal chords, more accurately known as the vocal folds (VF). Modeling efforts are split into two areas: the VF tissue and the airflow. There are multiple existing models of the VF, with varying ranges of complexity for both the tissue and the airflow. In our model, the tissue is based on a recent two-mass model of Bogaert’s , while the airflow is quasione-dimensional and is derived from the two-dimensional compressible NavierStokes equations. Our model is more accurate than Bernoulli’s law (quasisteady approximation), yet less complex than the full Navier-Stokes system. The model is shown to reproduce important transient behaviour intrinsic in vocal fold motion, such as pressure peaks before and after vocal fold closure. Part II concerns the inner ear, or cochlea. Again the modeling effort is split into two areas: the cochlear tissue and the cochlear fluid. We model the cochlear fluid with the well known two-dimensional box model of the cochlea, derived from the three-dimensional compressible Navier-Stokes equations. The cochlear tissue structure is where the complexity takes place. We start with Neely and Kim’s  linear active model for the cochlear structure and modify vi their active gain parameter into a nonlinear nonlocal functional. The nonlinearity forces us to work in the time domain, which is prone to dispersive instabilities if one uses a frequency domain middle ear model. The middle ear’s role as a transient absorber is discussed and its time domain formulation is shown to reduce the dispersive instability. We perform simulations on the full system and show that the model recovers many important nonlinear phenomena, such as suppression and difference tones. A spectrogram based on the cochlear response is created and compared with the spectrogram of the input waveform. In both Part I and Part II, the emphasis is on time dependent modeling and numerical implementation.