Hearing

 

Alexander Liss

 

11/03/2008

 

 

Morphological description of hearing mechanism often gets in the way of understanding of its functioning. Following provides description of this mechanism from functional point of view.

 

Resonating System

 

Middle Ear and Inner Ear comprise one Resonating System and reactions of this System to vibrations of bones and air are detected and converted into a stream of electrical signals of various intervals passed in parallel through a set of neural pathways.

 

Elements

 

Following are morphological Elements of the Resonating System, which resonate not separately but in concert, while each element has its own set of free vibrations:

 

·        Air Cavity of the Middle Ear

·        A Three Bones Assembly in the Middle Ear

·        Liquid Filled Channel (spiral) of the Inner Ear

·        Sensing Sealed Tube inside this Channel

·        Outer Membrane separating the Middle Ear and Outer Ear.

 

Outer Membrane is connected to the Air Cavity and the Three Bones Assembly and its vibrations induced by vibrations of air outside the Outer Ear affect vibrations of entire Resonating System, not only vibrations of the Air Cavity or the Three Bones Assembly.

 

The Liquid Filled Channel has:

 

·        one end connected to the three bones assembly of the Middle Ear via an Oval Window, with the end of one if these bones serving as a cover of this Window with three degree of freedom of motion

·        Another end connected to the Air Cavity of the Middle War via a Round Window with a membrane separating them; this membrane has a large set of forms of free vibrations

·        Sensing Sealed Tube is separated from the Liquid Filled Channel with flexible membranes, which have a large set of forms free vibrations.

 

Two opposing walls of the Sensing Sealed Tube are membranes separating it from the Liquid Filled Channel; two other opposing walls are bones. Membranes are connected to walls and have a form of (twisted) trapezoid.

External vibrations could reach the Sensing Sealed Tube via air through the Liquid Filled Channel and via bones.

 

     The Liquid Filled Channel is bent around the Sensing Sealed Tube and has two compartments: one adjacent to one membrane of the Sensing Sealed Tube and to the Oval Window, and the other adjacent to the other membrane and to the Round Window.

     The Liquid Filled Channel has a large set of asymmetric forms of free vibrations, which vary more near the Round Window and less near the Oval Window.

 

     The membrane separating the Sensing Sealed Tube and the Liquid Filled Channel at the Round Window is a Basilar Membrane; it has sensors attached inside the Sensing Sealed Tube.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


     There are two muscles inside the Middle Ear, which control the tension the Outer Membrane and the state of the Three Bones Assembly. One muscle is large and attached close to the Outer Membrane the other is small and attached to the middle of the Three Bones assembly.

 

Control

 

     Actions of these muscles affect forms of free vibrations of the Outer Membrane. This alone affects the forms of free vibrations of the Resonating System. In addition, they change the form of the Air Chamber and hence the set of its free vibrations and the tension and the form of the Three Bones Assembly and hence it’s set of free vibrations.

     There are many reasons why the body would like to modify the stream of sensory information:

 

·        Throttling the intensity of the signal

·        Throttling the information stream

·        Focusing the sensory system on a particular type signals

·        Introducing variability in a monotonous signal to keep focus on it.

 

Close analogy could be found in the way visual signal is controlled. There is:

 

 

     It is reasonable to assume that the large ear muscle provides action similar to large scale eye movement and the small ear muscle provides “scanning” to assure variability of the perceived signal.

 

     Creatures, which do not have a second small ear muscle, should have difficulties perceiving monotonous sounds and should compensate with ear or head movement.

 

     A resonating system with control could have cases of Auto Vibrations when the control system produces a positive feedback. It seems that tinnitus (nose in the ear) is the case of Auto Vibration, when the control system focuses on the vibration not induced by the external vibrations, and perpetuates this vibration.

    

 

Sensory Mechanism

 

     The Sensing Sealed Tube is filled with liquid and it houses a Sensory Mechanism.

 

Cross Section

 

It consists of the Basilar Membrane on which sits one row of Inner Hair Cells and at some distance from this row a three cell wide belt of Outer Hair Cells.

Hair Cells are sensors, Inner and Outer Hair Cells are different types of sensors.

     In the middle of the Sensing Sealed Tube is a Ridge protruding from the bonny wall of the Tube. This Ridge is not cellular tissue and Hair Cells have their other end “touching” it with various degree of attachment.

 

 

 

 

 

Basilar Membrane

    

     The Basilar Membrane is a (twisted) trapezoid with its broad end facing the Round Window. Its edge is rigidly attached to the bone. There is one row of Inner Hair Cells and a belt of tree rows of Outer Hair Cells. They provide information about vibration of the membrane.

 

 

 

 

 

 

 

     Its broad end is more rigid than its narrow end, this causes the amplitude of vibrations be of comparable size over the surface if the membrane. The consequence of this is higher response of the broad end to higher frequencies of vibrations and higher response of narrow end to low frequencies.

    

 

Types of Hair Cells and Their Distribution

 

     Amplitude of vibration near the edge of the membrane is the smallest. This could be a pattern reinforcing existence of two types of Hair Cells and their placement: Inner at the edge of the membrane and Outer closer to the membrane’s middle.

     Other creatures have Hair Cells of different types and some have these sensors placed over entire surface of the membrane.

 

Sensors Directionality

 

     Some of types of Hair Cells have a bunch of hairs (stereocilia) on top; they do not exhibit directionality in motion detection. However human Hair Cells have hairs neatly placed in rows and this should cause clear directionality of motion detection.

     Hairs of Inner Hair Cell are in the row parallel to the edge of the membrane; hence it is most sensitive to displacement perpendicular to the edge:

 

 

 

 

    

 

     Hairs of Outer Hair Cell are in two perpendicular rows, which should cause more unidirectional sensitivity:

 

 

 

    

     Signals from one row are added to signals from perpendicular row of hairs.

 

Cumulative Signal

 

     The Basilar Membrane vibrates with high frequency (human ear easily detects 20,000 cycles per second). Neurons could fire with frequency not more than 1,000 per second. Hence, the assembly of Hair Cell and an attached neuron should work on the principle of accumulation: a few cycles of stimulation of a Hair Cell cause its firing and a few firing of a Hair Cell cause firing of the attached neuron.

     Number of cycles causing firing of the Hair Cell should vary depending on the amplitude of stimulation: higher amplitude of stimulation should cause larger deformation of “hairs” in the Hair Cell and quicker accumulation of ions in the cell. Hence, higher amplitude should lead to more frequent firing of the Hair Cell. In response, the attached nerve cell should fire more frequently.

     Frequency of the attached nerve firing characterizes the vibration in the given place on a Basilar Membrane. The set of such data characterizes the shape of two dimensional vibration of the membrane.

 

Hair Cells Response

 

     In biological systems the increase of response is proportional to the increase of the stimulus, i.e. amplitude of the Basilar Membrane vibrations.

 

     If

 

r - a Hair Cell response,

a – amplitude of membrane vibration and

a0 - a threshold of sensitivity of the Hair Cell

 

then

 

r = log(a – a0), when a > a0

 

 

    

Outer Hair Cells Disengagement

 

     Outer Hair Cells have unique ability to contract at command from the attached nerve cells and on mechanical stimulation - motility.

     Outer Hair Cells move in space and have to adjust their height that their hairs are not crashed by the Ridge. This could be the reason of their mechanical motility – automatic height adjustment as a response to a mechanical stimulus.

     Most likely, the same mechanism used for dampening the monotonous signal, especially when such contraction is caused by the nerve signals.

     When Outer Hair Cells contract, they become wider, this should make the Basilar membrane stiffer and shift the resonance pattern.

 

Vibrations which Matter

 

     Hairs have to bend to generate signal, they cannot be “squashed” or “stretched” and they are placed upright on a “flat” top of a Hair Cell.

     Hence they essentially detect an equivalent of two dimensional movement of a Hair Cell, even when it moves in three dimensions.

     For the purpose of signal analysis, only projection of the movement of the top of the Hair Cell on the surface of the calm Basilar Membrane matters.

     Had the Basilar Membrane been flat, one would say that only the projection on the plane of Membrane matters, i.e. all variety of sounds is present in the family of vibrations, where displacement of the Membrane is a transformation of the Membrane in its plane. This set of vibrations is easier to analyze than one, which allow movements of the Membrane outside its plane.

 

 

 

Model of Perception

 

     The sensor detects vibrations of the Basilar Membrane and the Ridge. Different forms of the Basilar Membrane vibrations cause different patterns of signals from the Hair Cells.

    

 

Probing

 

     To probe reactions of the hearing mechanism, simple air pressure vibrations are used, which have a front (a crest of the wave) of a simple form, usually a sphere, and changes in time as a sine function.

     This is definitely a “monotonous” vibration, which perception could be quickly suppressed by the system, unless it has a compensating mechanism as one described above.

     Properly used, these probes are useful.

     They cause the Basilar Membrane resonate with a clear maximum  of the amplitude, which depends on the frequency of forcing vibration – the higher frequency the closer the maximum to a broad end of the Basilar Membrane.

     A major property of hearing system is ability to differentiate vibrations with different shapes of the front, to probe this ability one needs more sophisticated set of probes.

    

    

Insufficiency of Traditional Sound Presentation

 

     Traditional presentation of sound as one dimensional vibration is too simple to describe this phenomenon. It reflects an important part of this presentation, and this is a cause of its usefulness, but it is not sufficient.  

     Had it been only one row of sensors – Inner Hair Cells, one-dimensional model would be adequate. However, there are other sensors on the membrane and they provide additional characterization of the vibration. There are theories claiming that Outer Hair Cells serve only as sound amplifiers, but this is highly unlikely. If one looks at the Basilar Membrane covered with sensors in Inner Ear of some creatures, it is obvious that they are used to detect vibrations of a membrane, a two dimensional object.

     Hence, traditional presentation of sound is a model, which describes the way the brain perceives vibrations only partially. A new, more precise presentation is needed.

     For description of the human perception of vibrations one need to add differentiation provided by Outer Hair Cells.

 

 

Presentation of Sound

    

 

     For the purpose of signal processing we assume:

 

 

     The brain receives two sets of signals – from Inner and Outer Hair cells.   

     Every Inner Hair Cell responds to all sine probe vibrations, however the degree of response depends on the frequency of vibration and the function plotting the degree of response from frequency of vibration is unimodal and has a clear maximum. This is similar to reaction of light sensors to light of different wavelength.

     An Inner Hair Cell is determined by its place in a row. Degree of response of Inner Hair Cells is a function of the place in the row. Hence, from Inner Hair Cells the brain receives a set of signals similar to a function of one variable. This is a continuous function with relatively small change in its value, when change in its argument is small.

     This function is changing in time and this change is perceived as change of sound.

     Similarly, an Outer Hair Cell responds to all probe vibrations with varying degree.

     One could define a line along the belt of Outer Hair Cells and for a point in this line find three corresponding cells. Degrees of their responses are a vector-function of the place along this line.

     This is a continuous three-dimensional vector-function with relatively small change in its vector-value, when change in its argument is small.

     This function is changing in time also and this change is perceived as change of sound. This component of presentation should be sensitive to changes in the shape of the front of vibration.

 

Other Creatures

 

     Creatures, which have different types of Hair Cells or different placement of them on the Basilar Membrane, have different perception of sound. When one tries to analyze their reactions to sound or their sound based communication, one has to take this in consideration – they might operate on a kind of vibrations, which is substantially different from one, which humans used to analyze the surroundings and to communicate, and the difference could be not in the frequency of vibration but in the change of the vibration front, etc.

     One should be careful and not assume much from probing hearing of a creature with limited set of sine vibrations with a fixed shape front.

     Definitely, when a creature has entire Basilar Membrane covered with Hair Cells, it perceives vibrations differently.

 

Combining Probe Sounds

 

     Combining Probe Sounds should cause the Basal Membrane to have a set of free vibrations, which is a combination of sets of free vibrations corresponding to all Probes.

     Amplitude of vibrations of mechanical system (cavities, channels, membranes, etc.) should be a sum of amplitudes of vibrations caused by individual Probes. However, the values of functions comprising the Sound Presentation is not a sum of corresponding values for Probes separately, because the increase of Hair Cells response is proportional to the increase of the amplitude of the Basilar Membrane vibrations – dependency is not linear.

     Still, the amplitude of vibration of the ear’s mechanical system is a good description of the sound even when it does not reflect properly perception of sound loudness. Hence, we could:

     Even more, we could allow this vector of amplitudes to change in time, because when change is slow enough, the vibrations of the membrane should follow this changing in time vector of amplitudes roughly proportionally and with only imperceptible delay.

     Hence, traditional presentation of sound with its (slowly changing in time) spectrum, allows analysis of sound close to the way it is perceived by the ear, if one ignores perception of loudness.

     Obviously, the requirement of slow change is crucial. When the spectrum of sound is changing fast (as it is with some calls of birds), the membrane does not have time to adjust its pattern of resonance and the match between the spectrum and perception of the sound dissipates.

 

Health

 

     Understanding functioning of the hearing system allows immediate health improvement recommendations.

 

Mitigating Tinnitus

 

     If Tinnitus is an Auto-Vibration caused by a vicious cycle in a perception mechanism in the brain and in the mechanism of the Ear, then it has to be interrupted simultaneously in both areas.

     The solution should be a quick relaxation of the perception system (psychological relaxation), combined with listening to a pleasant sounds (music).

 

Mitigating Effects of Aging

 

     With age, muscles of the Middle Ear become less efficient and this could lead to difficulty of hearing monotonous sounds or compensating for low or high level of the sound.

     The solution should be in regular exercise of these muscles, for example regular listening to music.

 

Cochlea Implant

 

     Cochlea Implant is an implant into the Sensing Sealed Tube, which provides direct electrical stimulation of the nerves and possibly Hair Cells according to externally detected sound.

     From presented above theory of cumulative signals, it is obvious that stimulation should be in form of electrical pulses, which frequency should be proportional to the intensity of revenant sound “component”, it should not be any continuous periodic signal.

 

Improving Hearing Aide

 

     Two simple modifications should substantially improve the quality of Hearing Aid Devices.

     A Hearing Aid Device is a sound amplifier.

     First, instead of collecting sound in one point it should collect it in a few points and emit amplified sound in a set of corresponding points.

     Second, it has to have added functionality (which could be configured for each patient separately), which allow periodic shift of sound frequencies back and force, similar to one caused by muscles of the Middle Ear and Outer Hair Cells of the Inner Ear.