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PROBLEMS
Problem 1
canal and explain why that resonance occurs.
Problem 2
Considering the areas of the stapes and the tympanic
membrane, as well as the properties of the ossicular
chain, compute the approximate ratio of pressures that
Problem 3
Focusing stimuli has been proposed by several people
(Suesserman and Spelman, 1993; Jolly et al., 1996) as
a solution to the problem of field interference between
monopole sources. Consider using dipole and quad-
rupole sources. Assume that the sources are 50 μm
hemispheres located on the surface of an insulating
carries current I, while the two flanking sources carry
current −I/2. For ease of calculation, place one of the
sources at the origin, and let the other sources lie on,
e.g., the x-axis.
Problem 4
deflection is 20 μm. The modulus of elasticity of silicone is
2.76 Mpa, and that of liquid crystal polymer is 158 MPa.
The polar moment of inertia is:
Problem 5
Izzo and Richter address the intensity of optical stim-
uli to excite the inner ear in terms of the energy density
required to stimulate neurons. They state that the energy
density well above threshold is 3 mJ/cm2 at a pulse width
of 5 μsec. Assume that the optical source is a Vertical
ANSWERS
Problem 1
The ear canal is bounded at one end by the tympanic
membrane (a closed end), at the other by the opening in
the pinna (an open end). The canal can be approximated
Problem 2
The area of the tympanic membrane is 20 times that of
the footplate of the stapes. The pressure at the footplate
of the stapes will be 20 times that applied to the tym-
panic membrane. However, the motion of the footplate
CHAPTER II.5.11
Cochlear Prostheses
e2
Problem 3
The fields can be computed by summing the potentials
produced by the sources. The potential produced by a
be 10 μA in this case; ρ is the resistivity in ohm-cm, here,
let the resistivity be 53 ohm-cm (the resistivity of peri-
lymph); r is the radial distance from the source. For a
source on an insulator, the potential field is twice that
produced by the same source in a conductive medium.
field. Note also that the quadrupole field decreases more
rapidly with distance than does the dipole field.
Problem 4
solving for P, the force necessary to deflect the beam:
P=
3EIy
max
l
3
For this beam, d = 200 μm and I = 1.57 × 10−16 m4. Thus:
This is the program Question3, that determines the potential fields 100 and 200 microns above a
dipole and quadrupole source. The sources are separated by 200 microns. In the case of the
Compute the potential fields:
voltsVd
i j,
k( ) 1
x
i
x1−
( )
2
y
j
( )
2
+
0.5
1
x
i
x2−
( )
2
y
j
( )
2
+
0.5
−
⋅:=
Vcmk rh I
2π
⋅
⋅:=AI 10
5−
:=ohmcmrh 53:=
e3
Problem 5
The energy density of the optical pulse is given as
3 mJ/cm2. The width of the pulse applied to the cochlea
papp =
w
app
tpulse
And
S
vcsel
=π
(10
−
3)
2
cm2
The applied power is the product of the power density
and the area of emission:
Now the VCSEL is 15% efficient, and the applied
power per pulse is the optical power divided by the
efficiency of the VCSEL. However, the pulsatile power
The power per stimulus channel is quite reasonable,
indeed, ten channels could be driven simultaneously with
0.00
0
0.00
0.00
0.00
0.00
Potential vs Distance for Dipole and Quadrupole Sources
FIGURE II.5.11.3 Potential pro-
duced by the dipole and quadru-
