Guangjian Ni

Fluid coupling in a discrete model of cochlear mechanics

A discrete model of cochlear mechanics is introduced that includes a full, three-dimensional, description of fluid coupling. This formulation allows the fluid coupling and basilar membrane dynamics to be analyzed separately and then coupled together with a simple piece of linear algebra. The fluid coupling is initially analyzed using a wavenumber formulation and is separated into one component due to one-dimensional fluid coupling and one comprising all the other contributions. Using the theory of acoustic waves in a duct, however, these two components of the pressure can also be associated with a far field, due to the plane wave, and a near field, due to the evanescent, higher order, modes. The near field components are then seen as one of a number of sources of additional longitudinal coupling in the cochlea. The effects of non-uniformity and asymmetry in the fluid chamber areas can also be taken into account, to predict both the pressure difference between the chambers and the mean pressure. This allows the calculation, for example, of the effect of a short cochlear implant on the coupled response of the cochlea.

A wave finite element analysis of the passive cochlea.

Current models of the cochlea can be characterized as being either based on the assumed propagation of a single slow wave, which provides good insight, or involve the solution of a numerical model, such as in the finite element method, which allows the incorporation of more detailed anatomical features. In this paper it is shown how the wave finite element method can be used to decompose the results of a finite element calculation in terms of wave components, which allows the insight of the wave approach to be brought to bear on more complicated numerical models. In order to illustrate the method, a simple box model is considered, of a passive, locally reacting, basilar membrane interacting via three-dimensional fluid coupling. An analytic formulation of the dispersion equation is used initially to illustrate the types of wave one would expect in such a model. The wave finite element is then used to calculate the wavenumbers of all the waves in the finite element model. It is shown that only a single wave type dominates the response until this peaks at the best place in the cochlea, where an evanescent, higher order fluid wave can make a significant contribution.

Modelling Cochlear mechanics

The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map sounds of different frequencies onto corresponding characteristic positions on the basilar membrane (BM). Sounds enter the fluid-filled cochlea and cause deflection of the BM due to pressure differences between the cochlear fluid chambers. These deflections travel along the cochlea, increasing in amplitude, until a frequency-dependent characteristic position and then decay away rapidly. The hair cells can detect these deflections and encode them as neural signals. Modelling the mechanics of the cochlea is of help in interpreting experimental observations and also can provide predictions of the results of experiments that cannot currently be performed due to technical limitations. This paper focuses on reviewing the numerical modelling of the mechanical and electrical processes in the cochlea, which include fluid coupling, micromechanics, the cochlear amplifier, nonlinearity, and electrical coupling.

Aero-engine Blade Fatigue Analysis Based on Nonlinear Continuum Damage Model Using Neural Networks

Fatigue life and reliability of aero-engine blade are always of important significance to flight safety. The establishment of damage model is one of the key factors in blade fatigue research. Conventional linear Miner’s sum method is not suitable for aero-engine because of its low accuracy. A back propagation neutral network (BPNN) based on the combination of Levenberg-Marquardt (LM) and finite element method (FEM) is used to describe process of nonlinear damage accumulation behavior in material and predict fatigue life of the blade. Fatigue tests of standard specimen made from TC4 are carried out to obtain material fatigue parameters and S-N curve. A nonlinear continuum damage model (CDM), based on the BPNN with one hidden layer and ten neurons, is built to investigate the nonlinear damage accumulation behavior, in which the results from the tests are used as training set. Comparing with linear models and previous nonlinear models, BPNN has the lowest calculation error in full load range. It has significant accuracy when the load is below 500 MPa. Especially, when the load is 350 MPa, the calculation error of the BPNN is only 0.4%. The accurate model of the blade is built by using 3D coordinate measurement technology. The loading cycle in fatigue analysis is defined from takeoff to cruise in 10 min, and the load history is obtained from finite element analysis (FEA). Then the fatigue life of the compressor blade is predicted by using the BPNN model. The final fatigue life of the aero-engine blade is 6.55×104 cycles (10 916 h) based on the BPNN model, which is effective for the virtual design of aero-engine blade.

Finite element model of the active organ of Corti

The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback.

Effect of basilar membrane radial velocity profile on fluid coupling in the cochlea

The effects of different radial distributions of basilar membrane velocity on the fluid coupling in the cochlea are studied. Different mode shapes across the width of the basilar membrane, modeled as a beam, are simulated by assuming various boundary conditions. The results suggest that the fluid coupling is insensitive to the resulting differences in mode shape. This validates the assumption commonly made in cochlear models that the fluid coupling can be reasonably well predicted by assuming a single modal shape across the basilar membrane width, even if the exact form of the radial profile is not known.

Comparing methods of modeling near field fluid coupling in the cochlea

As well as generating the far field pressure, which allows wave propagation in the cochlea, the vibration of an individual element of the basilar membrane (BM) will also generate a near field pressure, which increases its mass and gives rise to local longitudinal coupling. This paper compares the efficiency and accuracy of a number of different methods of calculating the near field pressure distribution, and explores the connections between them. In particular it is shown that a common approximation to the wavenumber description of the near field pressure is equivalent, in the spatial domain, to an exponential decay away from the point of excitation. Two important properties of the near field pressure are its maximum amplitude, which is finite if the vibrating element has a finite length, and the value of its spatial integral, which determines the added mass on the BM due to the fluid loading. These properties are calculated as a function of the BM width relative to the width of the fluid chamber. By parameterizing the near field pressure variation in this way, it can be readily incorporated into coupled models of the cochlea, without the considerable computational expense of calculating the full three dimensional pressure field.

Finite element modelling of cochlear electrical coupling

The operation of each hair cell within the cochlea generates a change in electrical potential at the frequency of the vibrating basilar membrane beneath the hair cell. This electrical potential influences the operation of the cochlea at nearby locations and can also be detected as the cochlear microphonic signal. The effect of such potentials has been proposed as a mechanism for the non-local operation of the cochlear amplifier, and the interaction of such potentials has been thought to be the cause of the broadness of cochlea microphonic tuning curves. The spatial extent of influence of these potentials is an important parameter for determining the significance of their effects. Calculations of this extent have typically been based on calculating the longitudinal resistance of each of the scalae from the scala cross sectional area, and the conductivity of the lymph. In this paper, the range of influence of the electrical potential is examined using an electrical finite element model. It is found that the range of influence of the hair cell potential is much shorter than the conventional calculation, but is consistent with recent measurements.

Finite Element Modelling of Fluid Coupling in the Coiled Cochlea

A finite element model is first used to calculate the modal pressure difference for a box model of the cochlea, which shows that the number of fluid elements across the width of the cochlea determines the accuracy with which the near field, or short wavenumber, component of the fluid coupling is reproduced. Then results are compared with the analytic results to validate the accuracy of the FE model. It is, however, the far field, or long wavelength, component of the fluid coupling that is most affected by the geometry. A finite element model of the coiled cochlea is then used to calculate fluid coupling in this case, which has similar characteristics to the uncoiled model.

An elemental approach to modelling the mechanics of the cochlea

&NA; 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. HighlightsGeneral formulation of an elemental model for cochlear mechanics.Reduce to the transmission line model for locally‐reacting micromechanical and 1D fluid coupling.Incorporation of non‐uniform areas, 3D fluid coupling and non locally‐reacting micromechanics.MATLAB programs for the elemental model in the frequency domain and time domain.