RESEARCH ON THE DISTRIBUTION OF PRESSURE FIELD ON THE BASILAR MEMBRANE IN THE PASSIVE SPIRAL COCHLEA

2014 ◽  
Vol 14 (04) ◽  
pp. 1450061 ◽  
Author(s):  
JIANWEI MA ◽  
WENJUAN YAO
Keyword(s):  
Velocity Potential ◽  
Pressure Field ◽  
Basilar Membrane ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Low Frequency ◽  
Helical Structure ◽  
Hearing Ability ◽  
Leading Role ◽  
First Case

The cochlea is the important auditory organ of the inner ear. It is responsible for transforming the acoustic signals into neural impulses that travel along the auditory nerve to the brain. The role of, perhaps, the most characteristic feature of the cochlea, its three-dimensional (3D) helical structure, has remained elusive. To address this problem, the present paper develops a 3D spiral cochlea mathematical model using orthogonal coordinate system. Based on the method of separation of variables and conformal transformation, equations of three cases for the velocity potential are derived to solve the steady flow problem of lymph in the cochlea. Then, the distribution of pressure field on the basilar membrane (BM) is obtained. By comparing the analytical results with FE analyses results, the derived formulas are demonstrated to be accurate and reliable. The conclusion can be drawn that the spiral shape and physical dimension of the cochlea have a significant influence on the distribution of pressure field. Interestingly, near the helicotrema, the velocity potential of the first case plays a leading role in pressure distribution on the BM. Therefore, it may enhance the vibration of BM and improve hearing ability in the low-frequency parts of human ears. The proposed model could provide an approach for further investigation of fluid-structure interaction problem in the cochlea.

An Experimental Study of the Flow and Wall Pressure Field Around a Wing-Body Junction

1986 ◽  
Vol 108 (3) ◽  
pp. 308-314 ◽  
Author(s):  
M. A. Z. Hasan ◽  
M. J. Casarella ◽  
E. P. Rood
Keyword(s):  
Pressure Gradient ◽  
Pressure Field ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Adverse Pressure Gradient ◽  
Horseshoe Vortex ◽  
Wall Pressure ◽  
Frequency Content ◽  
Wall Pressure Fluctuations

The flow and wall-pressure field around a wing-body junction has been experimentally investigated in a quiet, low-turbulence wind tunnel. Measurements were made along the centerline in front of the wing and along several spanwise locations. The flow field data indicated that the strong adverse pressure gradient on the upstream centerline causes three-dimensional flow separation at approximately one wing thickness upstream and this induced the formation of the horseshoe root vortex which wrapped around the wing and became deeply embedded within the boundary layer. The wall-pressure fluctuations were measured for their spectral content and the data indicate that the effect of the adverse pressure gradient is to increase the low-frequency content of the wall pressure and to decrease the high-frequency content. The wall pressure data in the separated region, which is dominated by the horseshoe vortex, shows a significant increase in the low-frequency content and this characteristic feature prevails around the corner of the wing. The outer edge of the horseshoe vortex is clearly identified by the locus of maximum values of RMS wall pressure.

Determination of Transmission Loss in Slightly Distorted Circular Mufflers Using a Regular Perturbation Method

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Subhabrata Banerjee ◽  
Anthony M. Jacobi
Keyword(s):  
Helmholtz Equation ◽  
Exact Solutions ◽  
Green’S Function ◽  
Green's Function ◽  
Velocity Potential ◽  
Pressure Field ◽  
Transmission Loss ◽  
General Procedure ◽  
Separation Of Variables ◽  
Fourier Series Expansion

A perturbation-based approach is implemented to study the sound attenuation in distorted cylindrical mufflers with various inlet/outlet orientations. Study of the transmission loss (TL) in mufflers requires solution of the Helmholtz equation. Exact solutions are available only for a limited class of problems where the method of separation of variables can be applied across the cross section of the muffler (e.g., circular, rectangular, elliptic sections). In many practical situations, departures from the regular geometry occur. The present work is aimed at formulating a general procedure for determining the TL in mufflers with small perturbations on the boundary. Distortions in the geometry have been approximated by Fourier series expansion, thereby, allowing for asymmetric perturbations. Using the method of strained parameters, eigensolutions for a distorted muffler are expressed as a series summation of eigensolutions of the unperturbed cylinder having similar dimensions. The resulting eigenvectors, being orthogonal up to the order of truncation, are used to define a Green's function for the Helmholtz equation in the perturbed domain. Assuming that inlet and outlet ports of the muffler are uniform-velocity piston sources, the Green's function is implemented to obtain the velocity potential inside the muffler cavity. The pressure field inside the muffler is obtained from the velocity potential by using conservation of linear momentum. Transmission loss in the muffler is derived from the averaged pressure field. In order to illustrate the method, TL of an elliptical muffler with different inlet/outlet orientations is considered. Comparisons between the perturbation results and the exact solutions show excellent agreement for moderate (0.4∼0.6) eccentricities.

A mathematical model of the dynamics of the inner ear

1982 ◽  
Vol 116 ◽  
pp. 59-75 ◽  
Author(s):  
Mark H. Holmes
Keyword(s):  
Cross Section ◽  
Basilar Membrane ◽  
Three Dimensional ◽  
Low Frequency ◽  
Transverse Cross Section ◽  
Frequency Theory ◽  
Slender Body Theory ◽  
High Frequencies ◽  
Hearing Range ◽  
Body Theory

A three-dimensional hydroelastic model of the dynamical motion in the cochlea is analysed. The fluid is Newtonian and incompressible, and the basilar membrane is modelled as an orthotropic elastic plate. Asymptotic expansions are introduced, based on slender-body theory and the relative high frequencies in the hearing range, which reduce the problem to an eigenvalue problem in the transverse cross-section. After this, an example is worked out and a comparison is made with experiment and the earlier low-frequency theory.

scholarly journals Far-field representation for the vertical force on a floating structure

2012 ◽  
Vol 712 ◽  
pp. 661-670 ◽  
Author(s):  
M. McIver
Keyword(s):  
Velocity Potential ◽  
Three Dimensional ◽  
Low Frequency ◽  
Exciting Force ◽  
Far Field ◽  
Vertical Force ◽  
Floating Structure ◽  
Field Representation ◽  
Reciprocity Relations ◽  
Scattering Potential

AbstractEquations are derived that relate the vertical hydrodynamic force on two- and three-dimensional structures that are floating in a fluid of infinite depth to the far-field dipole coefficient in the velocity potential. By an application of Green’s theorem to the radiation or scattering potential and a suitable test potential, the heave added mass, the heave damping and the vertical exciting force are shown to be expressible in terms of the dipole coefficient in the relevant potential. The results add to the known reciprocity relations, which relate quantities such as the damping and the exciting force to the amplitude of the far-field radiated wave. The expressions are valid at all frequencies, and their high- and low-frequency asymptotics are investigated.

scholarly journals Hydro-Elastic Oscillations of the Bottom Membrane of a Rectangular Container Filled with Fluid

2020 ◽  
Vol 399 ◽  
pp. 76-86
Author(s):  
Manuel Gascón-Pérez
Keyword(s):  
Dynamic Behaviour ◽  
Velocity Potential ◽  
Pressure Field ◽  
Separation Of Variables ◽  
Fluid Velocity ◽  
Geometrical Parameters ◽  
Elastic Interactions ◽  
Rectangular Container ◽  
Deformation Equation ◽  
Discretization Procedure

The analysis of the hydro-elastic interactions of the covering membrane of fluid-filled cavities or containers has a main importance due to the solution of practical problems founded in engineering applications. In this paper the dynamic behaviour of the bottom membrane of a rectangular container filled with a non-viscous and incompressible fluid is analyzed. The fluid velocity potential is obtained first by applying a method of separation of variables and afterwards the pressure field is calculated with the momentum’s linearized equation. Taking into account the deformation equation for the membrane in contact with the fluid and by applying a discretization procedure to the associated generalized work equation, a system is obtained, for the calculus of the membrane frequencies of vibration. The influence of different geometrical parameters such as dimension, aspect ratio, container relative height, relative thickness as well as the fluid density on these frequencies is analysed. Validation of the method is made by comparing the results with those obtained by other authors and theories.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

scholarly journals Hearing at threshold intensities: by slow mechanical traveling waves or by fast cochlear fluid pressure waves

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Haim Sohmer
Keyword(s):  
Soft Tissue ◽  
Hair Cells ◽  
Traveling Wave ◽  
Basilar Membrane ◽  
Fluid Pressure ◽  
Low Frequency ◽  
Frequency Discrimination ◽  
Outer Hair Cells ◽  
Common Mechanism ◽  
Frequency Stimulation

The three modes of auditory stimulation (air, bone and soft tissue conduction) at threshold intensities are thought to share a common excitation mechanism: the stimuli induce passive displacements of the basilar membrane propagating from the base to the apex (slow mechanical traveling wave), which activate the outer hair cells, producing active displacements, which sum with the passive displacements. However, theoretical analyses and modeling of cochlear mechanics provide indications that the slow mechanical basilar membrane traveling wave may not be able to excite the cochlea at threshold intensities with the frequency discrimination observed. These analyses are complemented by several independent lines of research results supporting the notion that cochlear excitation at threshold may not involve a passive traveling wave, and the fast cochlear fluid pressures may directly activate the outer hair cells: opening of the sealed inner ear in patients undergoing cochlear implantation is not accompanied by threshold elevations to low frequency stimulation which would be expected to result from opening the cochlea, reducing cochlear impedance, altering hydrodynamics. The magnitude of the passive displacements at threshold is negligible. Isolated outer hair cells in fluid display tuned mechanical motility to fluid pressures which likely act on stretch sensitive ion channels in the walls of the cells. Vibrations delivered to soft tissue body sites elicit hearing. Thus, based on theoretical and experimental evidence, the common mechanism eliciting hearing during threshold stimulation by air, bone and soft tissue conduction may involve the fast-cochlear fluid pressures which directly activate the outer hair cells.

scholarly journals Vascular Supply of the Human Spiral Ganglion: Novel Three-Dimensional Analysis Using Synchrotron Phase-Contrast Imaging and Histology

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xueshuang Mei ◽  
Rudolf Glueckert ◽  
Annelies Schrott-Fischer ◽  
Hao Li ◽  
Hanif M. Ladak ◽  
...  
Keyword(s):  
Blood Supply ◽  
Phase Contrast ◽  
Spiral Ganglion ◽  
Three Dimensional ◽  
Vascular Anatomy ◽  
Helical Structure ◽  
Vascular Supply ◽  
Phase Contrast Imaging ◽  
Contrast Imaging ◽  
Temporal Bones

AbstractHuman spiral ganglion (HSG) cell bodies located in the bony cochlea depend on a rich vascular supply to maintain excitability. These neurons are targeted by cochlear implantation (CI) to treat deafness, and their viability is critical to ensure successful clinical outcomes. The blood supply of the HSG is difficult to study due to its helical structure and encasement in hard bone. The objective of this study was to present the first three-dimensional (3D) reconstruction and analysis of the HSG blood supply using synchrotron radiation phase-contrast imaging (SR-PCI) in combination with histological analyses of archival human cochlear sections. Twenty-six human temporal bones underwent SR-PCI. Data were processed using volume-rendering software, and a representative three-dimensional (3D) model was created to allow visualization of the vascular anatomy. Histologic analysis was used to verify the segmentations. Results revealed that the HSG is supplied by radial vascular twigs which are separate from the rest of the inner ear and encased in bone. Unlike with most organs, the arteries and veins in the human cochlea do not follow the same conduits. There is a dual venous outflow and a modiolar arterial supply. This organization may explain why the HSG may endure even in cases of advanced cochlear pathology.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

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