Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.

1.
Biot
M. A.
,
1941
, “
General theory of three-dimensional consolidation
,”
J. Appl. Phys.
, Vol.
12
, pp.
155
164
.
2.
Bowen, R. M., 1976, “Theory of mixtures,” in: Continuum Physics, A. C. Eringen, ed., Academic Press, New York, Vol. III, pp. 1–127.
3.
Boyle
R.
, and
Highstein
S. M.
,
1990
, “
Resting discharge and response dynamics of horizontal semicircular canal afferents of the toadfish, Opsanus tau
,”
J. Neurosci.
, Vol.
10
, pp.
1557
1569
.
4.
Corey
D. P.
, and
Hudspeth
A. J.
,
1979
, “
Ionic basis of the receptor potential in a vertebrate hair cell
,”
Nature
, Vol.
281
, pp.
675
677
.
5.
Corey
D. P.
, and
Hudspeth
A. J.
,
1983
, “
Kinetics of the receptor current in bullfrog saccular hair cells
,”
J. Neurosci.
, Vol.
3
, pp.
962
976
.
6.
Damiano
E. R.
,
Duling
B. R.
,
Ley
K.
, and
Skalak
T. C.
,
1996
, “
Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer
,”
J. Fluid Mech.
, Vol.
314
, pp.
163
189
.
7.
Damiano
E. R.
, and
Rabbitt
R. D.
,
1996
, “
A singular perturbation model of fluid dynamics in the vestibular semicircular canal and ampulla
,”
J. Fluid Mech.
, Vol.
307
, pp.
333
372
.
8.
Dohlman
G. F.
,
1971
, “
The attachment of the cupulae, otolith and tectorial membranes to the sensory cell areas
,”
Proc. Natl. Acad. Sci.
, Vol.
90
, pp.
8347
8351
.
9.
Ferna´ndez
C.
, and
Goldberg
J. M.
,
1971
, “
Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. II Response to sinusoidal stimulation and dynamics of peripheral vestibular system
,”
J. Neurophysiol.
, Vol.
34
, pp.
661
675
.
10.
Goldberg
J. M.
, and
Ferna´ndez
C.
,
1971
, “
Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. III Variations among units in their discharge properties
,”
J. Neurophysiol.
, Vol.
34
, pp.
676
684
.
11.
Highstein
S. M.
,
Rabbitt
R. D.
, and
Boyle
R.
,
1996
, “
Determinants of semicircular canal afferent response dynamics in the toadfish, Opsanus tau
,”
J. Neurophysiol.
, Vol.
75
, pp.
575
596
.
12.
Hillman
D. E.
,
1974
, “
Cupular structure and its receptor relationship
,”
Brain Behav. Evol.
, Vol.
10
, pp.
52
68
.
13.
Hou
J. S.
,
Holmes
M. H.
,
Lai
W. M.
, and
Mow
V. C.
,
1989
, “
Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
111
, pp.
78
87
.
14.
Hou, J. S., Holmes, M. H., Lai, W. M., and Mow, V. C., 1990, “Squeeze film lubrication for articular cartilage with synovial fluid,” in: Biomechanics of Diarthrodial Joints, V. C. Mow, A. Ratcliffe, and S. L-Y. Woo, eds., Springer-Verlag, Berlin, pp. 347–367.
15.
Hudspeth
A. J.
,
1983
, “
Mechanoelectrical transduction by hair cells in the acousticolateralis sensory system
,”
Ann. Rev. Neurosci.
, Vol.
6
, pp.
187
215
.
16.
Hudspeth
A. J.
, and
Jacobs
R.
,
1979
, “
Stereocilia mediate transduction in vertebrate hair cells
,”
Proc. Natl. Acad. Sci.
, Vol.
76
, pp.
1506
1509
.
17.
Igarashi
M.
, and
Alford
B. R.
,
1969
, “
Cupula, cupular zone of otolythic membrane, and tectorial membrane in the squirrel monkey
,”
Acta Otolaryngol.
, Vol.
68
, pp.
420
426
.
18.
Lai
W. M.
,
Hou
J. S.
, and
Mow
V. C.
,
1991
, “
A triphasic theory for the swelling and deformation behaviors of articular cartilage
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
113
, pp.
245
258
.
19.
Lai
W. M.
, and
Mow
V. C.
,
1980
, “
Drag-induced compression of articular cartilage during a permeation experiment
,”
Biorheology
, Vol.
17
, pp.
111
123
.
20.
Levick
J. R.
,
1987
, “
Flow through interstitium and other fibrous matrices
,”
Q. J. Exp. Physiol.
, Vol.
72
, pp.
409
438
.
21.
Lim
D. J.
,
1971
, “
Vestibular sensory organs. A scanning electron microscopic investigation
,”
Arch. Otolaryngol.
, Vol.
94
, pp.
69
76
.
22.
Lowenstein, O. E., 1974, “Comparative morphology and physiology,” in: Handbook of Sensory Physiology. VI/1: Vestibular System, H. H. Kornhuber, ed., Springer-Verlag, New York, pp. 75–120.
23.
McLaren
J. W.
, and
Hillman
D. E.
,
1979
, “
Displacement of the semicircular cupula during sinusoidal rotation
,”
Neuroscience
, Vol.
4
, pp.
2001
2008
.
24.
Mow
V. C.
,
Holmes
M. H.
, and
Lai
W. M.
,
1984
, “
Fluid transport and mechanical properties of articular cartilage
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
17
, pp.
377
394
.
25.
Mow
V. C.
,
Kuei
S. C.
,
Lai
W. M.
, and
Armstrong
C. G.
,
1980
, “
Biphasic creep and stress relaxation of articular cartilage in compression: Theory and experiments
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
102
, pp.
73
84
.
26.
Mow, V. C., Kwan, M. K., Lai, W. M., and Holmes, M. H., 1986, “A finite deformation theory for nonlinear permeable soft hydrated tissues,” in: Frontiers in Biomechanics, G. Schmid-Schonbein, S. L-Y. Woo, and B. Zweifach, eds., Springer-Verlag, New York, pp. 153–179.
27.
Oman
C. M.
,
Marcus
E. N.
, and
Curthoys
I. S.
,
1987
, “
The influence of semicircular canal morphology on endolymph flow dynamics
,”
Acta Otolaryngol. (Stockh.)
, Vol.
103
, pp.
1
13
.
28.
Rabbitt
R. D.
,
Boyle
R.
, and
Highstein
S. M.
,
1994
, “
Sensory transduction of head velocity and acceleration in the toadfish horizontal semicircular canal
,”
J. Neurophysiol.
, Vol.
72
, pp.
1041
1048
.
29.
Rabbitt
R. D.
,
Boyle
R.
, and
Highstein
S. M.
,
1999
, “
The influence of surgical plugging on horizontal semicircular canal mechanics and afferent response dynamics
,”
J. Neurophysiol.
, Vol.
82
, pp.
1033
1052
.
30.
Silver
R. B.
,
Reeves
A. P.
,
Steinacker
A.
, and
Highstein
S. M.
,
1998
, “
Examination of the cupula and stereocilia of the horizontal semicircular canal in the toadfish Opsanus tau
,”
J. Comp. Neurol.
, Vol.
402
, pp.
48
61
.
31.
Steer, R. W., Li, Y. T., Young, L. R., and Meiry, J. L., 1967, “Physical properties of the labyrinthine fluids and quantification of the phenomenon of caloric stimulation,” Third Symposium on the Role of Vestibular Organs in Space Exploration, NASA SP-152, pp. 409–420.
32.
Steinhausen
W.
,
1933
, “
U¨ber die beobachtungen der cupula in den bognega¨ng-sampullen des labyrinthes des libenden hecths
,”
Pflu¨gers Arch. Ges. Physiol.
, Vol.
232
, pp.
500
512
.
33.
Truesdell, C., and Toupin, R., 1960, “The classical field theories,” in: Handbuch der Physik, S. Flu¨gge, ed., Springer-Verlag, Berlin, pp. 226–793.
34.
Van Buskirk
W. C.
,
Watts
R. G.
, and
Liu
Y. K.
,
1976
, “
The fluid mechanics of the semicircular canals
,”
J. Fluid Mech.
, Vol.
78
, pp.
87
98
.
35.
Wersa¨ll, J., and Bagger-Sjo¨ba¨ck, G. M., 1974, “Morphology of the vestibular sense organ,” in: Handbook of Sensory Physiology, VI/1: Vestibular System, H. H. Kornhuber, ed., Springer-Verlag, New York, pp. 123–170.
This content is only available via PDF.
You do not currently have access to this content.