On the model it is possible to measure the force and the force direction for each individual hair as a function of the flow direction and velocity. Measurements were made at the man flow velocity .01 m/s, which is equivalent to a flow velocity in the real ear of about 1 micrometer/s. The kinematic viscosity of the liquid used in the model was 10,000 times higher than the viscosity of perilymph to attain hydrodynamic equality. Two different geometries for the sterocilia pattern were tested. First the force distribution for a W-shaped sterocilia pattern was recorded. This is the sterocilia pattern found in all real ears. It is found that the forces acting on the hairs are very regular and perpendicular to the legs of the W when the flow is directed from the outside of the W. When the flow is reversed, the forces are not reversed, but are much more irregular. This can eventually explain the half wave rectification of the nerve signals. As a second experiment, the force distribution for a V-shaped sterocilia pattern was recorded. Here the forces were irregular both when the flow was directed into the V and when it was directed against the edge of the V

Jacobson, B. O.

English

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NASA Technical Memorandum 82773f	 .
t
A Hydrodynamic Model of an
rte. Outer Hair Cell
(NASA-rM-82713)
	 A HYL[(CLYbAE1C 60DEL CE AN
	 N84'-16743
UJiER HAJFi CELL (NASA)
	 14 p bC A021mi Ail
CEC( Out'
Uacl'_
G3/54 08804
Bo 0..iacobson	 A
Lewis Research Center
Cleveland, Ohio
Prepared for the
Tenth Annual Northeast Bioengineering Conference
cosponsored by the Thayer School of Engineering, Dartmouth
College. Dartmouth Medical School, IEEE, ASME, and the
American Society for Engineering Education
Hanover, New Hampshire, March 15-16, 1982
t
r
A HYDRODYNAMIC MODEL OF AN OUTER HAIR CELL
Bo 0. Jacobson*
*University of Lulea, Lulea, Sweden and
NRC-NASA Research Associate, Lewis Research Center,
Cleveland, Ohio 44135
ABSTRACT
A 10 000t^rs enlarged hydrodynamic model of the outer hair cell sterocila in the inner
ear was built. On the model it was possible to measure the force and the force direction
co	 for each individua l hair as a function- ?f the flow direction and velocity. Measurements
g	 were made at the mean flow velocity 10' m/s, which is equivalent to a flow velocity in
the real ear of about 1 Nm/s. The kinematic viscosity of the liquid used in the model
W	 was 10 000 times higher than the viscosity of perilymph to attain hydrodynamic equallity.
Two different geometries for the sterocilia pattern were tested. Firs the force distri-
bution for a W-shaped sterocilia pattern was recorded. This is the sterocilia pattern
found in all real ears. It was found that the forces acting on the hairs were very regu-
lar and perpendicular to the legs of the W when the flow was directed from the outside
of the W. When the flow was reversed, the forces were not reversed, but were much more
irregular. This can eventually explain the half wave rectification of the nerve signals.
As a second experiment, the force distribution for a V-shaped sterocilia pattern was re-
corded. Here the forces were irregular both when the flow was directed into the V and
when it was directed against the edge of the V.
KEYWORDS
Hydrodynamic, model, outrr hair cell, force measurements, sterocilia.
INTRODUCTION
Since vonk^experimental research (3-9) about the geometry of and nerve signals
from the inner ear, many authors have described both theoretical and experimental work
about cochlear mechanics. (1-2, 10-15) There have been mathematical models of the basilar
membrane vibrations showing some correlation between the location of the maximum vibration
amplitude and the frequency of the exitation. There has also been a lot of work done n
the area of measuring the actual nerve signals from ears of different animals includir,,
humans.
The gap to fill now, is to connect the mechanical side of the sensory cells with the nerve
signals from the cell.. one way to explain the strange nerve signals coming out of the
inner ear is to look at the individual forces, acting upon each hair of ail outer hair
cell, and see if. the rectification of the nerve signals can be explained by the hydro-
dynamic forces on the sterocilia.
Another important question to answer is: why are the sterocilia of the outer hair cells
placed in the form of W:s. In the present hydrodynamic model of the hair cell it is pos-
sible to fill in the missing hairs in the W to make it a V and measure the change in
forces acting upon the sterocilia.
EXPERIMENTAL MODEL
To measure the forces and the force directions of each hair un, a hair cell, a model was
built. In the model the force and the force direction were measured by using hydrostatic
manometers. Each hair was connected to four manometers and there were lU2 hairs in the
model, giving a total of 408 manometers. The geometry of the manometer connections can be
seen in Figs. 1 and 2.
Figure 2 also shows the locations of the hairs relative to each other and the channel sys-
tem going from the hairs and to the manometers. To make it possible to manufacture the
channel system, the model had to be very much larger than the real hair cell, so the model
was built in the scale 10 000:1. This means that the hairs became 5U-lUO nun:s long and
10 mm in diameter, and the total size of the model was about half a meter in diameter.
See Fig. 3.
To get the same flow pattern in the model as in a real ear the fluid had to be about
10 000 times more viscous than the perilymph, if the density was the same. As model fl id
a heavy lubricating oil was c hosen with the viscosity at room temperature about 10 Ns /ft
and with the density 900 kg/m .
The working principle for the model is, that a variator motor drives a wing-pump (Figs. 4
and 5). This gives a flow of oil through the hair cell hairs (see Fig. 4). The direction
of the flow velocity can be changed to any direction from 0 0 to 3600 by rotating the oil
tank relative to the table and the hair cell, shown in Figs. 5 and 6. The flow gives a
force on each hair. This force makes the hair tilt in the direction of the force.
Through the bottom of each hair, see Fig. 1, oil canes into channel A from a hydrostatic
oil pressure source. The same pressure source is connected to all the hairs with equally
long tubes, so the pressure in channel A is the same for all hairs. The oil then flows
through the 4 channels B and out to the manometers through the 4 channels C for each hair.
The level of the liquid in the manometers will then rise to different heights depending on
the force and force direction on the hair. The hairs are not fitting exactly into the
holes in the "hair cell", but have a radial clearance of 0,1 mm. This means that when the
hydrodynamic flow force has tilted the hair over, so that the channel B is tightly con-
nected with channel C, for instance at the left side of the hair in Fig. 1, the oil will
flow into this manometer. The oil wil; also flow into the manometer at the opposite side
of the hair through that channel B, but there a lot of the oil will leak away through the
0,2 mm clearance between hair and the hole in the hair cell. The oil level in the mano-
meters will rise until the pres-. •e at the connection point between channel B and channel
C is such, that the hydrostatic forces acting upon the hair will balance the hydrodynamic
forces from the outer flow. Then the hair will tilt back so that the leakage at the
connection between the channels B and C will be exactly the same as the flow through the
channel B. This means that the oil level in the manometer will be stationary.
The time, for the oil levels in the manometers to become stationary, was about 5 hours.
MEASURING TECHNIQUE
It was not possible to just start the apparatus, wait 5 hours and then make a set of
measurements.
As the hairs were not standing on a ooint, but a circular ring, see Fig. 1, it was not
possible to guarantee that zero force on the hair gave equally high pressures in all four
manometers connected to the hair. To overcome this difficulty, all measurements were made
as differential measurements. First the pressure was put on in the pressurizing system
for 5 hours. The ding purip was riot driven during that time. At the end of the pres-
surizing time the manometer readings were registered. Then the wing pump was put on,
circulating the oil with a velocity which could be varied between zero and a maximum
speed. The maximum speed was much higher than the speed in a real ear. (It was given by
the maximum slope of the free oil surface). After 5 hours, pressure readings were made.
The force components on the hair, caused by the flow, were proportional to the second dif-
ference of the pressure. The flow force in the x-direction, see Fig. 7, was then
F x = A[(P 2 - PI ) flow - ( P2 - Pl)no flow]
and in the y-direction
F  = A [ ( P4 - P3)flow - (P4 - P3 ) no flow]
where A is a constant.
The constant A is the same for all hairs, as it is assumed that the nerve signals in a
real ear will be caused by bending of the hairs and not so much by shearing of the hairs
(the bending strains and stre , ,;-s are 50-100 times higher than the ones caused by
shearing).
The totai hydrodynamic force on a hair was
F= F 2
+ F 2
x	 y
2
and the d irection of the farce was given by the angle
a s arctan (r-ylFx)
MEASUREMENTS
The size and d^'on of the force on each hair is shown in Figs. 9 and 10 for the nor-
mal geometry. In Fig. 9 the flow is coming from the top of the figure, that is hitting
the W from the outside. In Fig. 10, the flow cones from the bottom of the figure,
that is hitting the W from the inside.
The forces acting on the hairs were very symmetrical relative to the center line of the
hair group (t10 percent), why in the Figs. 9 and 10 the the force distribution was
made completely symmetrical by adding, hair by hair, a force on a hair on the left side
to the force on a hair on the right side and divide by two.
The sizes and directions of the forces acting on the hairs when they are placed in a
V-form are shown in Figs. 11 and 12. This geometry of the outer hair cell hairs is not
found in animals or humans. As can be seen from Figs. 11 and 12, the forces are not
synmetrical around the center line of the model, why the measured forces in this case
could not be made symmetrical. A possible explanation of the unsymmetrical force dis-
tribution can be a slight inclination (til°) of the mean flow velocity to the geometri-
cal center line of the hair pattern. Figures 11 and 12 show that the force distribution
on the hairs is very irregular, both when the flow goes into the V and when it comes
from the outside of the V.
DISCUSSION OF THE RESULTS
The forces acting on the hairs, placed in W-form, (Figs. 9 and 10), are not at all equal
for all hairs. When the flow comes from the outside of the W, the direction of the
forces is fairly constant and perpendicular to the legs of the W. This is true except
for the center of the W and the outer most parts of the W, see Fig. 9. When the flow
comes from the inside of the W, the forces on the hairs are much more irregular, see
Fig. 10. Both the sizes and the directions of the forces are changing from hair to
hair. The maximum force, acting on a hair in Fig. 10 is about 6U percent bigger than
the maximum force on any hair in Fig. 9. There is one thing in common with the Figs. 9
and 10. That is the variation of the force from hair to hair.
Over big areas of the sterocilia pattern, the size of the force on the hair is changing
almost sinusodial from hair to hair or with a longer wavelength. A very strange be-
havior is shown by the sterocilia nr 73 and 97 in the inner row of hairs. The forces on
these sterocilia change the direction with 90° and the size with a factor 5 when the
flow direction is reversed.
The forces, acting on the hairs placed in V-form (Figs. 11 and 12), are irregular for
both the flow directions tested. It seems as if the missing hair in the W-form has a
strong stabilizing effect on the forces, when the flow comes from the outside of the
W. The measurements also show that the sensitivity for misalignment is much less for
the W-form than for the V-form. The misalignment was the same for the :wo geometries
within 0.05°.
CONCLUSION
When the f oow across a hair cell is reversed, the forces on the hairs are not reversed.
This can explain the rectification effect of the cochlea when it transforms mechanical
signals to nerve signals. Depending on the structure of the sensory cells, they can
either fire a signal when the forces on the hairs are all in the same direction or when
the difference between the hairs is as big as possible. In both cases, the result will
be a rectification of the signals when it transforms from a mechanical signal to a nerve
signal.
Wher the hairs are placed in a V-form, the force distribution is irregular even when the
flow comes from the outside of the V. The force distribution for the V-form is much
more sensitive to misalignment of the flow velocity than the W-form.
ACKNOWLEDGEMENT
The author si grate u
	 or the help of P. 0. Jacobson with preparing the hair cell model
for the experiments and for the supply of model "perilymph" from AB Nynas Petroleum.
REFERENCES
1. Allaire,77.77, "Two Dimensional Fluid Waves and Cochlear Partition Stiffness in the
Cochlear," Ph.D. Dissertation, Northwestern University, 1971.
2. Allaire, P., Raynor, S., and Billone, M., "Human Cochlear Partition Stiffness,"
Journal of the Acoustical Society of America, vol. 52, 1972, No. 1, Pt. 1, p. 14U
(Abstract).
3. von 86kdsy, G. V., "Zur Theori des Horens; Die Schwingungsform der Basilar-membran,"
Ph sikalische Zeitschrifte, Vol. 29, 1928, pp. 793-810.
4. von bekesy, 6. V.77Th—e -Fariation of Phase along the Basilar Membrane with Sinuso;-
dal Vibrations," Journal of the Acoustical Society of America, Vol. 19, No. 3, May
1947, pp. 452-460.
5. von Bdkfsy, G. V., "The Vibration of the Cochlear Partition in Anatomical Prepara-
tions and in Models of the Inner Ear," Journal of the Acoustical Society of America,
Vol. 21, No. 3, May, 1949, pp. 233-245.
6. von 86kdsy, G. V., "Microphonics Produced by Touching the Cochlear Partition with a
Vibrating Electrode," Journal of the Acoust i :al Society of America. Vol. 23, No. 1,
Jan. 1951, pp. 29-35.
7, vcn 86kdsy, G. V., "Description of Some Mechanical Properties of the Organ of
Corti," Journal of the AcOLStiral S,7.^^ty of America. Vol. 25, No. 4, July 1953, pp.
770-785.
8. von 86k6sy, G. V., "Shearing Micr ,..onics Produced by Vibrations Near the Inner and
Outer Hair Cells," Journal of the Acoustical Society of America, Vol. 25, No. 4,
July 1953, pp. 786-790.
9. von Bdkdsy, G., Experiments in Hearing. McGraw-Hill, New York, 1960.
10. Billone, M. C., *MeChanical Stimulation of Co hlear Hair Cells," Ph.D. Uissertation,
Northwestern University, 1972.
11. Bilione, M. C., and Raynor, S., "Transmission of Radial Shear Forces to Cochl-ar
Hair Cells," Journal of the Acoustical Society of America, Vol. 54, No. 5, 1973,
pp. 1143-1156.
12. Engstrom, H., Ades, H. W., and Hawkins, J. E., Jr., "Structure and Functions of the
Senosry Hairs of the Inner Ear," Journal of the Acoustical Socieiy of America, Vol.
34, No. 8, Pt. 2, Sept. 1962, pp..
13. Flock, A., "Physiological Properties of Sensory Hairs in the Ear," Ps cho h sits and
Ph^Z^;iolo	 of Hearing, E. F. Evans and J. P. Wiison, eds., Academic, London,
14. HeT e, R., " e ectivitats-Steigerung in Einem Hydromechanischen Innerohrmodell mit
Basilar-und Ueckmembran," (English title is "Increase in Selectivity in a Hydro-
mechanical Cochlea Model with Basilar Membrane and Tectorial Membrane"), Acoustica,
Vol. 3n , No. 6, June 1974, pp. 301-312.
15. Zwicker, E., "Ein Hydromechanischen Ausschnittmodell des Innerohres zur Erforschung
des adaquaten Reizes der Sinneszellen," (English title is "A Hydromechanical Sec-
tional Model of the Inner Ear for Investigatiny the Necessary Stimulus of the Sen-
sory Cells"), Acoustica, Vol. 30, No. 6, June 1974, pp. 313-319.
Figure 1. - Hair and manometer 	 Is
connectimns.
Figure 2. - The hair locations and i hannel
systems.
Figure 3. - Hair cell model.
ORIGINAL PAGE
BLACK AND WHITE PHOTOGP.APH
PUMP-\
Figure 4. - Drawinq of the apparatus.
—OIL TANK
Inv
7
Figure 5. - Photo of the apparatus and the manometers.
ORIGINAL PAGE
,J-ACK AND WHITE PHOTOGRAPH
F	 - IR
Figure 6. - Photo of the hair cell model and the
manometer connections.
P1
— X
P2
Fx
^Y
P4
P3
Figure 7. - Pressures acting on the
hair.
Figure 3. - Force components.
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A hydrodynamic model of an outer hair cell

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