Abstract:Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementati… Show more
“…7 . Readers could use this code as a template in order to incorporate different types of nonlinearity, for example, or to include modification to increase the computational efficiency ( Pan et al., 2015 ). Fig.…”
The motion along the basilar membrane in the cochlea is due to the interaction between the micromechanical behaviour of the organ of Corti and the fluid movement in the scalae. By dividing the length of the cochlea into a finite number of elements and assuming a given radial distribution of the basilar membrane motion for each element, a set of equations can be separately derived for the micromechanics and for the fluid coupling. These equations can then be combined, using matrix methods, to give the fully coupled response. This elemental approach reduces to the classical transmission line model if the micromechanics are assumed to be locally-reacting and the fluid coupling is assumed to be entirely one-dimensional, but is also valid without these assumptions. The elemental model is most easily formulated in the frequency domain, assuming quasi-linear behaviour, but a time domain formulation, using state space method, can readily incorporate local nonlinearities in the micromechanics. Examples of programs are included for the elemental model of a human cochlea that can be readily modified for other species.
“…7 . Readers could use this code as a template in order to incorporate different types of nonlinearity, for example, or to include modification to increase the computational efficiency ( Pan et al., 2015 ). Fig.…”
The motion along the basilar membrane in the cochlea is due to the interaction between the micromechanical behaviour of the organ of Corti and the fluid movement in the scalae. By dividing the length of the cochlea into a finite number of elements and assuming a given radial distribution of the basilar membrane motion for each element, a set of equations can be separately derived for the micromechanics and for the fluid coupling. These equations can then be combined, using matrix methods, to give the fully coupled response. This elemental approach reduces to the classical transmission line model if the micromechanics are assumed to be locally-reacting and the fluid coupling is assumed to be entirely one-dimensional, but is also valid without these assumptions. The elemental model is most easily formulated in the frequency domain, assuming quasi-linear behaviour, but a time domain formulation, using state space method, can readily incorporate local nonlinearities in the micromechanics. Examples of programs are included for the elemental model of a human cochlea that can be readily modified for other species.
“…2.2, we applied the nonuniform grid scheme to the macro mechanical model, which is independent of the micro mechanical model. Furthermore, specific fast solvers for cochlear models [8][9][10][11] can be applied to the nonuniform grid scheme. Therefore, this method can increase the efficiency of most cochlear models.…”
Section: Applying a Nonuniform Grid To Other Cochlearmentioning
confidence: 99%
“…To improve the efficiency of cochlear models, some groups have attempted to develop specific solvers [8][9][10][11]. In this study, we consider a way to increase the efficiency by a different method.…”
In this study, a two-dimensional (2D) mechanical model of the cochlea, discretized by a nonuniform grid, is applied to investigate the mechanisms that limit the increase in the computational efficiency. To amount for experimental findings, cochlear models have become complicated. A cochlear model consists of micro-and macro mechanical models. Many types of micro mechanical model have been proposed. However, macro mechanical models are described by the Laplace equation and show various patterns of the cochlear response depending on the location. Therefore, an efficient step width depends on the location in the cochlea. To resolve this issue, a numerical calculation has been applied to divide the space of a cochlear model into a nonuniform grid and to achieve improved efficiency of the model. However, the limitation of this method remains unclear. To investigate this point, we develop a state space model for 2D cochlear mechanics with a nonuniform gird. Stability analysis and simulations are conducted for the cochlear model with nonuniform and uniform grids. As a result, the number of segments is reduced by 29%. In addition, the execution time is reduced by 10-fold. Therefore, it is shown that a nonuniform grid can efficiently divide the space for cochlear modeling.
“…A two-port network model of the ear canal and middle ear, based on the model in [12] and programmed in [13], is also included. Model responses are computed in the time domain using a fast modified state-space method [14], which is about 40 times more efficient than the original state-space method [10].…”
Models of the mammalian cochlea have been proposed in a number of ways and they have varying degree of realism and complexity. The transmission-line (TL) models are faithful to the physiology, particularly in terms of cochlear nonlinearity, but are computationally demanding. The pole-zero filter cascade (PZFC) model, however, is much more efficient to implement, but the nonlinearity is included implicitly, using an automatic gain control network. In this study, the connection between the linear responses of these two models is first discussed, followed by a comparison of their nonlinear responses in terms of self-suppression and two-tone suppression on the level of the basilar membrane. Both models are capable of simulating dynamic range compression as measured on the cochlear partition, but the TL model is more reasonable in representing twotone suppression, with the PZFC having lower suppression thresholds and over-predicting the suppression due to high-side suppressors. Further tuning of its parameters and structure, especially the automatic gain control (AGC) network may be possible to make it more compatible with these experimental observations. After adapting the PZFC model to have a more realistic nonlinear behavior, its use for investigating auditory signal processing such as masking effects, and hence as a front-end processor for acoustic signals can be enhanced, while retaining its computational efficiency.
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