The motion along the basilar membrane in the cochlea is due to the interaction between the microm... more 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 micromechanic...
ABSTRACT The pressure distribution in each of the fluid chambers of the cochlea can be decomposed... more ABSTRACT The pressure distribution in each of the fluid chambers of the cochlea can be decomposed into a 1D, or plane wave, component and a near field component, which decays rapidly away from the excitation point. The transverse motion of the basilar membrane, BM, for example, generates both a 1D pressure field, which couples into the slow wave, and a local near field pressure, proportional to the BM acceleration, that generates an added mass on the BM due to the fluid motion. When the organ of Corti, OC, undergoes internal motion, due for example to outer hair cell activity, this motion will not itself generate any 1D pressure if the OC is incompressible and the BM is constrained not to move volumetrically, and so will not directly couple into the slow wave. This motion will, however, generate a near field pressure, proportional to the OC acceleration, which will act on the OC and thus increases its effective mass. The near field pressure due to this OC motion will also act on the BM, generating a force on the BM proportional to the acceleration of the OC, and thus create a “coupling mass” effect. By reciprocity, this coupling mass is the same as that acting on the OC due to the motion of the BM. This near field fluid coupling is initially observed in a finite element model of a slice of the cochlea. These simulations suggest a simple analytical formulation for the fluid coupling, using higher order beam modes across the width of the cochlear partition. It is well known that the added mass due to the near field pressure dominates the overall mass of the BM, and thus significantly affects the micromechanical dynamics. This work not only quantifies the added mass of the OC due its own motion in the fluid, and shows that this is important, but also demonstrates that the coupling mass effect between the BM and OC significantly affects the dynamics of simple micromechanical models.
Journal of the Royal Society, Interface / the Royal Society, 2016
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivi... more 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 t...
A 2D box model of the cochlea has been used to predict the basilar membrane, BM, velocity and the... more A 2D box model of the cochlea has been used to predict the basilar membrane, BM, velocity and the fluid flow caused by two components of bone conduction: due to inertia of the middle ear and due to inertia of the cochlear fluids. A finite difference approach has been used with asymmetric fluid chambers, that enables an investigation of the effect of varying window stiffness, due to otosclerosis for example. The BM is represented as a series of locally reacting single degree of freedom systems, with graded stiffness along the cochlea to represent the distribution of natural frequencies and with a damping representative of the passive cochlea.
ABSTRACT The complicated, three dimensional geometry of the fluid chambers in the cochlea is ofte... more ABSTRACT The complicated, three dimensional geometry of the fluid chambers in the cochlea is often represented in models of its mechanics by a box with a uniform area along its length. In this paper we use previous measurements of the variation in area of the two fluid chambers along the length of the cochlea in various mammals, to calculate the variation in the "effective area" that determines the 1D fluid coupling, which is given by the harmonic mean of the two chamber areas. The square root of this effective area is found to vary surprisingly linearly along the cochlea length in several mammalian species. This suggests a variation of the box model in which the width and height of the two fluid chambers are still equal, but now decrease linearly along its length. The width of the basilar membrane, BM, is assumed to increase linearly along the length of the model. The analytic form of the 1D fluid pressure distribution due to elemental BM motion is derived for this tapered box model. The added mass due to the near field acoustic coupling can also be computed, which surprisingly turns out to be almost constant along the length of the BM. The coupled response of the box model with a passive BM can then be readily calculated. Although the pressure distributions due to elemental fluid coupling are very different in the uniform and tapered box models, the distribution of the passive BM response in the coupled models are very similar in the two cases, although the overall level of the response in the tapered model is about 10 dB greater than that in the uniform model.
ABSTRACT Most cochlear models used to describe the basilar membrane vibration along the cochlea a... more ABSTRACT Most cochlear models used to describe the basilar membrane vibration along the cochlea are concerned with macromechanics, and often assume that the organ of Corti moves as a single unit, ignoring the individual motion of different components. New experimental technologies provide the opportunity to measure the dynamic behaviour of different components within the organ of Corti, but only for certain types of excitation. It is thus still difficult to directly measure every aspect of cochlear dynamics, particularly for acoustic excitation of the fully active cochlea. The present work studies the dynamic response of a model of the cross-section of the cochlea, at the microscopic level, using the finite element method. The elastic components are modelled with plate elements and the perilymph and endolymph are modelled with inviscid fluid elements. The individual motion of each component within the organ of Corti is calculated with dynamic pressure loading on the basilar membrane and the motions of the experimentally accessible parts are compared with measurements. The reticular lamina moves as a stiff plate, without much bending, and is pivoting around a point close to the region of the inner hair cells, as observed experimentally. The basilar membrane shows a slightly asymmetric mode shape, with maximum displacement occurring between the second-row and the third-row of the outer hair cells. The dynamics responses is also calculated, and compared with experiments, when driven by the outer hair cells. The receptance of the basilar membrane motion and of the deflection of the hair bundles of the outer hair cells is thus obtained, when driven either acoustically or electrically. In this way, the fully active linear response of the basilar membrane to acoustic excitation can be predicted by using a linear superposition of the calculated receptances and a defined gain function for the outer hair cell feedback.
The Journal of the Acoustical Society of America, 2015
As well as generating the far field pressure, which allows wave propagation in the cochlea, the v... more 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...
ABSTRACT The cochlea is an organ of the hearing system, whose basic function is to map sounds of ... more ABSTRACT The cochlea is an organ of the hearing system, whose basic function is to map sounds of different frequencies onto corresponding characteristic positions along the basilar membrane (BM). Sound-induced BM vibration is transformed into deflection of stereocilia on the hair cells, which then encodes the sound as neural signals for perception. Most cochlear models used to describe the BM vibration patterns or the pressure distributions along the cochlea are concerned with macromechanics, which often assumes the organ of Corti moves as a single unit and ignores individual motion of different components. New technologies provide the opportunity to measure the dynamic behaviour of different components within the organ of Corti. However, it is still difficult to measure every aspect of cochlear dynamics. The present work studies the behaviour of a radial slice of the cochlea at the microscopic level using finite element method. The individual motion of each component within the organ of Corti is calculated with static pressure loading on the BM and the motions of the experimentally accessible parts are compared with experiments. The elastic components are modelled with plate/beam element and perilymph and endolymph are modelled with fluid element. The reticular lamina moves as a stiff plate without much bending and is pivoting around a point close to the region of the inner hair cells and the basilar membrane shows an asymmetric mode shape with maximum displacement occurring between the second-row and the third-row of the outer hair cells, in agreement with experimental observations.
CITATIONS 0 READS 23 2 authors: Some of the authors of this publication are also working on these... more CITATIONS 0 READS 23 2 authors: Some of the authors of this publication are also working on these related projects: Augmenting Urban Soundscapes: Design Tools, Noise Mitigation System, and Evaluation of the Urban Sound Environment -Phase 1 View project Abating traffic noise through a holistic approach of noise monitoring, analytics and control (MAC) View project The effect of a cochlear implant on residual, low frequency, hearing is complex and poorly understood. This research focuses on the mechanical effect of a cochlear implant on the cochlear mechanics by comparing the predicted basilar membrane, BM, response before and after the implantation. Audiograms measured from pre-and post-implant users are used as input of a computational model of the passive cochlea, proposed by Elliott et al. (Elliott et al., 2011), which are then used to study the mechanical effect of the implantation. In the model, a short cochlea implant, designed to electrically stimulate the basal regions at high frequencies while allowing normal hearing at low frequencies (Cochlear, 2008), is introduced into the lower cochlear fluid chamber. The active amplification of the cochlea is not considered,
The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map s... more 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.
The motion along the basilar membrane in the cochlea is due to the interaction between the microm... more 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 micromechanic...
ABSTRACT The pressure distribution in each of the fluid chambers of the cochlea can be decomposed... more ABSTRACT The pressure distribution in each of the fluid chambers of the cochlea can be decomposed into a 1D, or plane wave, component and a near field component, which decays rapidly away from the excitation point. The transverse motion of the basilar membrane, BM, for example, generates both a 1D pressure field, which couples into the slow wave, and a local near field pressure, proportional to the BM acceleration, that generates an added mass on the BM due to the fluid motion. When the organ of Corti, OC, undergoes internal motion, due for example to outer hair cell activity, this motion will not itself generate any 1D pressure if the OC is incompressible and the BM is constrained not to move volumetrically, and so will not directly couple into the slow wave. This motion will, however, generate a near field pressure, proportional to the OC acceleration, which will act on the OC and thus increases its effective mass. The near field pressure due to this OC motion will also act on the BM, generating a force on the BM proportional to the acceleration of the OC, and thus create a “coupling mass” effect. By reciprocity, this coupling mass is the same as that acting on the OC due to the motion of the BM. This near field fluid coupling is initially observed in a finite element model of a slice of the cochlea. These simulations suggest a simple analytical formulation for the fluid coupling, using higher order beam modes across the width of the cochlear partition. It is well known that the added mass due to the near field pressure dominates the overall mass of the BM, and thus significantly affects the micromechanical dynamics. This work not only quantifies the added mass of the OC due its own motion in the fluid, and shows that this is important, but also demonstrates that the coupling mass effect between the BM and OC significantly affects the dynamics of simple micromechanical models.
Journal of the Royal Society, Interface / the Royal Society, 2016
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivi... more 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 t...
A 2D box model of the cochlea has been used to predict the basilar membrane, BM, velocity and the... more A 2D box model of the cochlea has been used to predict the basilar membrane, BM, velocity and the fluid flow caused by two components of bone conduction: due to inertia of the middle ear and due to inertia of the cochlear fluids. A finite difference approach has been used with asymmetric fluid chambers, that enables an investigation of the effect of varying window stiffness, due to otosclerosis for example. The BM is represented as a series of locally reacting single degree of freedom systems, with graded stiffness along the cochlea to represent the distribution of natural frequencies and with a damping representative of the passive cochlea.
ABSTRACT The complicated, three dimensional geometry of the fluid chambers in the cochlea is ofte... more ABSTRACT The complicated, three dimensional geometry of the fluid chambers in the cochlea is often represented in models of its mechanics by a box with a uniform area along its length. In this paper we use previous measurements of the variation in area of the two fluid chambers along the length of the cochlea in various mammals, to calculate the variation in the "effective area" that determines the 1D fluid coupling, which is given by the harmonic mean of the two chamber areas. The square root of this effective area is found to vary surprisingly linearly along the cochlea length in several mammalian species. This suggests a variation of the box model in which the width and height of the two fluid chambers are still equal, but now decrease linearly along its length. The width of the basilar membrane, BM, is assumed to increase linearly along the length of the model. The analytic form of the 1D fluid pressure distribution due to elemental BM motion is derived for this tapered box model. The added mass due to the near field acoustic coupling can also be computed, which surprisingly turns out to be almost constant along the length of the BM. The coupled response of the box model with a passive BM can then be readily calculated. Although the pressure distributions due to elemental fluid coupling are very different in the uniform and tapered box models, the distribution of the passive BM response in the coupled models are very similar in the two cases, although the overall level of the response in the tapered model is about 10 dB greater than that in the uniform model.
ABSTRACT Most cochlear models used to describe the basilar membrane vibration along the cochlea a... more ABSTRACT Most cochlear models used to describe the basilar membrane vibration along the cochlea are concerned with macromechanics, and often assume that the organ of Corti moves as a single unit, ignoring the individual motion of different components. New experimental technologies provide the opportunity to measure the dynamic behaviour of different components within the organ of Corti, but only for certain types of excitation. It is thus still difficult to directly measure every aspect of cochlear dynamics, particularly for acoustic excitation of the fully active cochlea. The present work studies the dynamic response of a model of the cross-section of the cochlea, at the microscopic level, using the finite element method. The elastic components are modelled with plate elements and the perilymph and endolymph are modelled with inviscid fluid elements. The individual motion of each component within the organ of Corti is calculated with dynamic pressure loading on the basilar membrane and the motions of the experimentally accessible parts are compared with measurements. The reticular lamina moves as a stiff plate, without much bending, and is pivoting around a point close to the region of the inner hair cells, as observed experimentally. The basilar membrane shows a slightly asymmetric mode shape, with maximum displacement occurring between the second-row and the third-row of the outer hair cells. The dynamics responses is also calculated, and compared with experiments, when driven by the outer hair cells. The receptance of the basilar membrane motion and of the deflection of the hair bundles of the outer hair cells is thus obtained, when driven either acoustically or electrically. In this way, the fully active linear response of the basilar membrane to acoustic excitation can be predicted by using a linear superposition of the calculated receptances and a defined gain function for the outer hair cell feedback.
The Journal of the Acoustical Society of America, 2015
As well as generating the far field pressure, which allows wave propagation in the cochlea, the v... more 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...
ABSTRACT The cochlea is an organ of the hearing system, whose basic function is to map sounds of ... more ABSTRACT The cochlea is an organ of the hearing system, whose basic function is to map sounds of different frequencies onto corresponding characteristic positions along the basilar membrane (BM). Sound-induced BM vibration is transformed into deflection of stereocilia on the hair cells, which then encodes the sound as neural signals for perception. Most cochlear models used to describe the BM vibration patterns or the pressure distributions along the cochlea are concerned with macromechanics, which often assumes the organ of Corti moves as a single unit and ignores individual motion of different components. New technologies provide the opportunity to measure the dynamic behaviour of different components within the organ of Corti. However, it is still difficult to measure every aspect of cochlear dynamics. The present work studies the behaviour of a radial slice of the cochlea at the microscopic level using finite element method. The individual motion of each component within the organ of Corti is calculated with static pressure loading on the BM and the motions of the experimentally accessible parts are compared with experiments. The elastic components are modelled with plate/beam element and perilymph and endolymph are modelled with fluid element. The reticular lamina moves as a stiff plate without much bending and is pivoting around a point close to the region of the inner hair cells and the basilar membrane shows an asymmetric mode shape with maximum displacement occurring between the second-row and the third-row of the outer hair cells, in agreement with experimental observations.
CITATIONS 0 READS 23 2 authors: Some of the authors of this publication are also working on these... more CITATIONS 0 READS 23 2 authors: Some of the authors of this publication are also working on these related projects: Augmenting Urban Soundscapes: Design Tools, Noise Mitigation System, and Evaluation of the Urban Sound Environment -Phase 1 View project Abating traffic noise through a holistic approach of noise monitoring, analytics and control (MAC) View project The effect of a cochlear implant on residual, low frequency, hearing is complex and poorly understood. This research focuses on the mechanical effect of a cochlear implant on the cochlear mechanics by comparing the predicted basilar membrane, BM, response before and after the implantation. Audiograms measured from pre-and post-implant users are used as input of a computational model of the passive cochlea, proposed by Elliott et al. (Elliott et al., 2011), which are then used to study the mechanical effect of the implantation. In the model, a short cochlea implant, designed to electrically stimulate the basal regions at high frequencies while allowing normal hearing at low frequencies (Cochlear, 2008), is introduced into the lower cochlear fluid chamber. The active amplification of the cochlea is not considered,
The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map s... more 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.
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