Download a) Where in the cochlea would you say the process of "fourier

SOLUTIONS
Homework #3
Introduction to Engineering in Medicine and Biology
ECEN 1001
Due Tues. 9/30/03
Problem 1:
a) Where in the cochlea would you say the process of "fourier decomposition" of the
incoming sound energy occurs? Please explain your reasoning.
Fourier decomposition in this context refers to the spatial separation of the sound energy
entering the fluid-filled cochlea which occurs along the length of the basilar membrane. It is the
basilar membrane and to some degree the hair cells themselves that use mechanical tuning and
resonance to distribute the sound energy as a function of frequency over space. Structures in
the middle ear, including the tympanic membrane and ossicular system, serve only to increase
the efficiency by which the time-varying pressure (sound) in the air is conducted into the fluid of
the inner ear. No time-domain to frequency-domain organization of the sound energy occurred
in the middle ear.
b) Describe the important physical characteristics of the structure which you identified in
part a) which give it the ability to effectively "fourier transform" the sound. Explain how
each of these characteristics contributes to this frequency separation process.
The basilar membrane has several important mechanical characteristics which endow it
with what is effectively a continuum of natural mechanical resonance from very high frequencies
at the base (entrance) to low frequencies at the apex (end). These are briefly described below,
and in more detail in the text:
i.. Overall Basilar Membrane Geometry: The basilar membrane is a filmy structure
which is attached along its transverse edges by bony projections from the inner walls of the
cochlear cavity. It separates the cochlea longitudinally into the scala tympani and scala media,
and therefore vibrates with incoming sound energy. The bony projections to which the edges of
the basilar membrane are attached extend furthest at the base of the cochlea and least at the
apex. Thus, the width of the basilar progressively increases from the base to apex, while the
width of the cochlear cavity decreases.
ii. Transverse basilar fibers: The filmy basilar membrane has 20,000 to 30,000
transverse basilar fibers which are embedded within it, and are connected at one end in the
bony projection of the cochlear "modiolus", but free on their other ends. These basilar fibers
affect the local stiffness or rigidity in the membrane, and can thus contribute to the local resonant
characteristic of the basilar membrane in their proximity. These transverse fibers are
approximately 40 microns (0.04 mm) in length near the entrance (base) of the cochlea, and
increase in length progressively towards the apex, reaching 500 microns (0.5 mm) at the
deepest part of the membrane (apex).
In addition, the diameters of the shorter fibers are greater, thereby making them stiffer,
while the diameter of the longer fibers is less, thereby making them less stiff. Thus, the short,
stiff basilar fibers embedded in the filmy membrane exhibit a high mechanical resonant
frequency, while the longer, more flexible fibers at the base exhibit a low frequency resonance.
iii. Contractile Outer Hair Cells: In addition to the single row of inner hair cells which
are distributed along the length of the basilar membrane and convert the mechanical vibration of
the membrane into small electrical potentials for transmission to the brain, there are 3-4 rows of
outer hair cells which respond to signals from the brain by mechanically contracting. This allows
the brain to use a feedback path to locally adjust or tune the stiffness of the basilar membrane.
This is thought to provide a means of local mechanical tuning of the resonance characteristics of
the membrane to improve the sharpness of the separation of frequencies.
iv. Hair Cell Stereocilia: The stereocilia which project from the tops of the inner hair
cells exhibit a similar position-dependent variation as the transverse basilar fibers. At the base
(front) of the cochlea, these are shorter and stiffer, and become progressively longer and more
flexible as one approaches the base. This helps the stereocilia respond more specifically to the
frequencies which they are intended to sense.
c) Imagine that you could uncoil the cochlea and you are now "watching" the basilar
membrane vibrate in response to sound energy coming from my voice. Explain how what
you see relates to the frequency domain representation of my voice that you saw
displayed on the spectrum analyzer screen during the class demo. In other words,
compare what would you look for in the vibration of the basilar membrane to acquire
information about the frequency content of my voice (and the relative power of each
frequency) with what you would look at with a frequency domain representation provided
by the spectrum analyzer. Do these seem similar to you? Do you think it is reasonable to
say that the cochlea performs a Fourier transform of the sound energy before this
information is sent to your brain for further processing?
As discussed in part b, the basilar membrane exhibits a progressive range of natural
resonant frequencies from high (at the oval/round windows) to low, at the back of the cochlea
where the fluid from the scala vestibuli and scala tympani "communicate". Sound energy (which
is a pressure which varies as a function of time) travels along the basilar membrane, and in the
process, the energy associated with the various frequencies which compose the traveling sound
wave tend to naturally be trapped or dissipated at the place along the membrane which has the
same natural resonant frequency. Thus, it is the amplitude of the vibration of the basilar
membrane as a function of location or place where the information about the frequency
composition of the incoming sound energy is represented.
Thus if you were watching the fourier decomposition of my voice on the spectrum
analyzer, as we did in class, you would see the relative amplitude of each of the frequency
components displayed on the screen at any given moment as a function of position. The
frequency axis could be linear, or logarithmic. Similarly, if you were "watching" the movement
of the basilar membrane in response to my voice, you would see the relative amplitude of each
of the frequency components represented by the amplitude of the membrane vibration at
different points or places along its length. In the case of the basilar membrane, the distribution
of the frequency response is not linear, but is logarithmic, as discussed in class and in the text. It
is also “reversed” from the normal frequency representation, in that the highest frequencies
appear at the entrance to the cochlea, and the lowest frequencies at the rear. Nevertheless, it is
quite reasonable to say that the basilar membrane effectively performs a Fourier transform of the
incoming time-varying sound pressure, utilizing mechanical resonance of the various membrane
and hair cell structures.
2. You are examining a person who exhibits a hearing impairment of unknown origin.
(a)
What are the two major classes of hearing impairment? Identify the basic
structures which are responsible for the impairment in each class.
Conduction System of the Middle Ear: Any condition leading to restriction of
movement of the tympanic membrane and ossicular system will result in increased thresholds
(decreased sensitivity). This is often associated with fibrosis (in-growth of fibrous tissue) which
may be caused by chronic inflammation accompanying infection or response to trauma.
Particularly in cases where chronic conditions are present, fibrosis may also be accompanied by
the degeneration of the ossicular bone tissue. Generally, decreased sensitivity due to conduction
impairment is comparatively greater in response to low frequency acoustic stimuli, since these
require relatively greater excursions (displacement) of the ossicular system for adequate
conduction to the inner ear.
Sensorineural (Inner Ear):
Any condition leading to the degradation or destruction
of the hair cells along the organ of corti will result in increased thresholds. Hair cell damage/loss
may be due to ototoxic action of antibiotics on certain individuals, trauma, exposure to
excessive acute or long term noise, etc. Less frequently, sensorineural impairment may be
attributed to damage to the cochlear nerve bundle or to higher level auditory processing regions
in the CNS (e.g. following tumor removal). Animal models have suggested that destruction of
the hair cells by either acute noise exposure or antibiotic reaction leads to subsequent
degeneration of the associated ganglia and cochlear nerve fibers over a period of months or
years. This is a somewhat discouraging observation in the context of the design of implantable
cochlear electrodes, which depend on the stimulation of existing surviving nerve fibers through
which to deliver speech information.
As noted in lecture, these two major classes of hearing sensitivity impairment may occur
alone, or in combination in different individuals. The degree to which a given amount of
sensitivity loss (due to any physiological impairment) translates to a functional impairment (e.g.
speech discrimination) varies greatly among individuals. Certain people appear to exhibit
exceptional capability to extract vital speech information despite very limited acoustic input.
(b)
What tests would you perform to distinguish the origin of this person's
impairment? Explain the procedure, using representative sketches, and how you
interpret the results
One of the basic tests compares the threshold or sensitivity to pure tones as a function
of frequency when delivered through the air vs. through bone conduction. Reference
sensitivities across the audio range have been established, and these are used as a comparison
to the sensitivity exhibited by the person being tested. The results are plotted and are generally
referred to as audiograms. Examples of two audiograms are shown in chapter 52 of the text one consistent with fibrosis of the middle ear, and one consistent with moderate sensorineural
impairment typically exhibited as people age. The degree of loss of sensitivity (and the
frequency response) may vary greatly depending on the individual, and in the case of the
profoundly deaf, may be essentially total. Such persons may be candidates for the cochlear
implant if they have retained some viable nerve fibers. As noted in class, if the frequencydependent sensitivity is significantly different for bone conduction than for air, this result suggests
a conduction problem. If the decreased sensitivity is similar for both air and bone conduction,
this suggests sensorineural pathology.
3. You are contemplating the design of a cochlear implant device with the goal of
restoring human speech perception in people with sensorineural (loss of hair cell
function) impairment.
(a) Sketch a block diagram, identifying the major components of the system, and
describe the basic function of each.
The overall function of this implant is to restore hearing to those who have lost the ability to
transform sound energy into stimulation of the auditory nerve fibers which carry the encoded
sound information to the brain for processing. This stimulation may be achieved by appropriate
direct electrical stimulation of the auditory nerve fibers by an array of implanted electrodes. As we
have discussed in lectures, one of the basic means by which pitch discrimination occurs is via the
so-called "place principle". This refers to the ability of the cochlea and basilar membrane in
particular to spread incoming sound energy out along the length of the membrane as a function of
frequency. Thus the cochlea first performs a mechanical Fourier transform, effectively "mapping "
the basilar membrane as a function of frequency. Greater displacement amplitudes of the
membrane in any one area translates to greater stimulation of the hair cells and associated auditory
neurons, which carry this information to auditory processing areas of the brain. The frequency is
interpreted by the brain largely (but not exclusively, as we shall see later) by virtue of the mapping
of that neuron to a specific region on the basilar membrane.
In general then, we can identify some of the most basic attributes of a cochlear implant as
follows:
• Transformation of sound energy into an electrical signal which can be further processed.
We would utilize some form of microphone or dynamic pressure transducer which converts
variations in sound pressure into a time-varying voltage.
• The ability to perform frequency analysis/decomposition. The electrical signal from the
microphone must be separated into its frequency components such that the individual components
can be used to direct the electrical stimulation to the auditory neurons in the proper region of the
basilar membrane. This is performed in the speech processor.
• An implanted electrode array which can deliver electrical stimuli to the auditory
neurons as a function of the output of the frequency analysis of the incoming sound.
• A source of energy for the functioning of the device. This is achieved using an inductive
link across the skin, i.e. electrical energy is transferred between two adjacent coils: one inside the
body, and one located on the skin adjacent to it. An electrode signal receiver/stimulator directs the
energy to the appropriate electrodes.
This system may be represented in block form as follows:
Electrode
Signal receiver
/ stimulator
Speech
Processor
External
microphone
External
coil
Internal
coil
Cochlear
electrode
array
Below is an illustration of the structure of the human ear with an implant called the Nucleus 24. It
is made by a company called Cochlear:
(b) Given that your goal is to restore speech perception, identify the region of the
basilar membrane that you will target with the electrode array.
Studies of the frequency content of the human voice have indicated that most of the important
components of speech are in the range of 500 Hz to 5KHz, and thus we would like our array to
target the nerves which are arranged along the portion of the basilar membrane corresponding to
this frequency. Based on Fig. 52-6 of the text, this corresponds to the region roughly between 8-27
mm from the stapes.
(c) How many electrodes would you use along this region? Comment on the tradeoffs with using more or fewer electrodes in terms of performance, complexity,
safety, etc.
In the basilar membrane, there are approximately 1500 inner hair cells which stimulate
approximately 25000 nerve fibers which in turn transfer auditory information to the brain. Are
1500, or perhaps 25,000 individual frequency channels (and hence individual electrodes) thus
necessary? Hopefully not, since given the space constraints, it would not be feasible to implant
such an array. Studies using simulations such as those demonstrated in class have indicated that a
minimum of about 8-10 channels (electrodes) are required for reliable speech perception. Using
more channels may increase the quality of the sound up to a point, but as the number of electrodes
increases beyond about 25, the relative improvement is outweighed by added complications, such
as high current density (due to smaller electrode area), and increased complexity to manufacture.
The high current density may damage the tissue directly, and tends to form free radicals at the
electrode surface by processes similar to electrolysis (production of hydrogen and oxygen at the
surface of electrodes in water). These free radicals are very unstable and reactive, and may damage
not only the tissue, but even the electrode surface itself. Current clinical devices use between 8 and
22, with 22 being the most popular.
(d)
How would you space the electrodes – uniformly or non-uniformly? Please
explain your reasoning.
Most of the devices that have been implanted so far have uniform spacing of electrodes, such that
the currents which are produced in the cochlear fluid around the nerves you wish to simulate is
most uniform. More recently, the trend is going towards a non-uniform spacing which attempts to
match the logarithmic spacing of frequencies along the basilar membrane, with closer spacing of
the low frequency electrodes relative to the higher frequency electrodes. Both approaches have their
merit, although the non-uniform approach is currently though to yield better results. For the nonuniform spacing, the idea is to use roughly the same number of electrodes per octave, which is a
doubling of frequency. Thus you would have approximately 7 or 8 electrodes covering the 5K2.5KHz range, 7-8 over the 2.5KHz to 1250 Hz range, and 7-8 over the 1250-625 Hz range. Here is
an illustration of the current 22-electrode array used in the Cochlear system. Note the non-uniform
spacing of the electrodes: