1Department of Bioengineering, University of Utah, Salt Lake City, Utah 84112; 2Department of Otolaryngology/Head-Neck Surgery and Department of Physiology and Pharmacology, Oregon Health Sciences University, Portland, Oregon 97201; 3Departments of Otolaryngology and Neurobiology, Washington University, St. Louis, Missouri 63110; and 4Marine Biological Laboratory, Woods Hole, Massachusetts 02543
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Rabbitt, R. D., R. Boyle, and S. M. Highstein. Influence of Surgical Plugging on Horizontal Semicircular Canal Mechanics and Afferent Response Dynamics. J. Neurophysiol. 82: 1033-1053, 1999. Mechanical occlusion of one or more of the semicircular canals is a surgical procedure performed clinically to treat certain vestibular disorders and used experimentally to assess individual contributions of separate canals and/or otoliths to vestibular neural pathways. The present experiments were designed to determine if semicircular canal afferent nerve modulation to angular head acceleration is blocked by occlusion of the endolymphatic duct, and if not, what mechanism(s) might account for a persistent afferent response. The perilymphatic space was opened to gain acute access to the horizontal canal (HC) in the oyster toadfish, Opsanus tau. Firing rate responses of HC afferents to sinusoidal whole-body rotation were recorded in the unoccluded control condition, during the process of duct occlusion, and in the plugged condition. The results show that complete occlusion of the duct did not block horizontal canal sensitivity; individual afferents often exhibited a robust firing rate modulation in response to whole-body rotation in the plugged condition. At high stimulus frequencies (about >8 Hz) the average sensitivity (afferent gain; spikes/s per °/s of head velocity) in the plugged condition was nearly equal to that observed for unoccluded controls in the same animals. At low stimulus frequencies (about <0.1 Hz), the average sensitivity in the plugged condition was attenuated by more than two orders of magnitude relative to unoccluded controls. The peak afferent firing rate for sinusoidal stimuli was phase advanced ~90° in plugged canals relative to their control counterparts for stimulus frequencies ~0.1-2 Hz. Data indicate that afferents normally sensitive to angular velocity in the control condition became sensitive to angular acceleration in the plugged condition, whereas afferents sensitive to angular acceleration in the control condition became sensitive to the derivative of acceleration or angular jerk in the plugged condition. At higher frequencies (>8 Hz), the phase of afferents in the plugged condition became nearly equal, on average, to that observed in controls. A three-dimensional biomechanical model of the HC was developed to interpret the residual response in the plugged condition. Labyrinthine fluids were modeled as incompressible and Newtonian; the membranous duct, osseous canal and temporal bone were modeled as visco-elastic materials. The predicted attenuation and phase shift in cupular responses were in close agreement with the observed changes in afferent response dynamics after canal plugging. The model attributes the response of plugged canals to labyrinthine fluid pressure gradients that lead to membranous duct deformation, a spatial redistribution of labyrinthine fluids and cupular displacement. Validity of the model was established through its ability to predict: the relationship between plugged canal responses and unoccluded controls (present study), the relationship between afferent responses recorded during mechanical indentation of the membranous duct and physiological head rotation, the magnitude and phase of endolymphatic pressure generated during HC duct indentation, and previous model results for cupular gain and phase in the rigid-duct case. The same model was adjusted to conform to the morphology of the squirrel monkey and of the human to investigate the possible influence of canal plugging in primates. Membranous duct stiffness and perilymphatic cavity stiffness were identified as the most salient model parameters. Simulations indicate that canal plugging may be the most effective in relatively small species having small labyrinths, stiff round windows, and stiff bony perilymphatic enclosures.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The role of the vestibular end organs in providing inputs to
motion-control neural systems such as the vestibuloocular reflex (VOR)
first was demonstrated by Mach, Crum-Brown, and Ewald in the late 1800s
(Camis 1930; Crum-Brown, 1894
;
Ewald, 1892
). Ewald was among the first to use surgical
modifications of the labyrinth to manipulate semicircular canal
afferent inputs to the brain stem (Camis 1930
;
Ewald, 1892
). He pioneered the approach termed "canal
plugging," where the slender duct of a semicircular canal is occluded
surgically in an attempt to block sensitivity to angular head
accelerations. Since the reintroduction of canal plugging by
Money and Scott (1962)
, the approach has been employed
for the treatment of certain vestibular disorders (Minor et al.
1998
; Parnes 1992
; Parnes and McClure
1990
), to improve the exposure of the internal auditory canal
fundus (Antonelli et al. 1995
), and to study the
influence of individual canals as well as otolithic inputs to
vestibular reflex systems (e.g., Aw et al. 1996
;
Baker et al. 1982
; Böhmer et al.
1985
; Correia and Money 1970
; Minor and
Goldberg 1990
; Money 1967
; Paige 1983
,
1985
; Parnes and McClure 1990
; Schor and
Miller 1982
; Watt 1976
). Results of these
investigations are consistent with the hypothesis that the procedure
selectively blocks the sensory capability of the occluded semicircular
canal, at least under the conditions tested. It is unclear to what
extent efficacy of the procedure might extend to other experimental
conditions and/or motion stimuli.
Recent evidence indicates that the angular VOR recovers a
high-frequency component even after the semicircular canals have been
plugged completely (Angelaki and Hess 1996;
Angelaki et al. 1996
; Broussard and Bhatia
1996
; Cohen et al. 1996
; Davis et al. 1997
; Lasker et al. 1997
; Yakushin et al.
1997
). If plugged canals indeed are rendered nonfunctional by
the surgical manipulation, then one might conclude that the recovered
responses reflect a form of neural adaptation that may use inputs from
the otolith organs to sense angular movements. Another possibility is
that canal plugging may not completely inactivate semicircular canal afferent responses and that the recovered VOR may draw, at least in
part, from residual inputs originating from the plugged canals. Present
results support the second hypothesis. Data recorded from single
afferent nerves in the toadfish, Opsanus tau, show that the
semicircular canals continue to respond, with modified dynamics, to
angular accelerations after complete surgical occlusion of the
endolymphatic duct. Pressure-induced deformation of the membranous labyrinth appears to be the key mechanism underlying the residual response. This is supported by the fact that a biomechanical model, accounting for membranous duct elasticity and labyrinthine fluid flows,
quantitatively accounts for the observed changes in semicircular canal
afferent responses in the toadfish after duct occlusion. When the same
model was applied to the morphology of the human and of the squirrel
monkey, it predicted a residual plugged-canal response in these species
as well. Results may have important implications regarding the
contributions of individual end organs to vestibular mediated neural
systems in plugged-canal preparations.
Experimental methods
Preparation of toadfish and neural recording methods follow that
previously described by Boyle and Highstein (1990) and
Rabbitt et al. (1995)
. Briefly, fish of either sex and
weighing ~500 g were provided by the Marine Biological Laboratory,
Marine Resources facility (Woods Hole, MA). Anesthesia was induced by
immersion in MS222 (25 mg/l sea water, 3-aminobenzoic acid ethyl ester, Sigma). Fish were immobilized partially by an intramuscular injection of pancuronium bromide (0.05 mg/kg); pancuronium bromide does not block
opercular motion and allows for natural respiration by "gilling."
Each fish was placed in a plastic tank filled with fresh sea water
covering all but the dorsal surface of the animal. The eyes and
remainder of the body were kept covered with moist tissues.
The experimental set-up is illustrated in Fig. 1. A small craniotomy was made lateral to the dorsal course of the anterior canal, allowing direct access to the horizontal canal (HC) nerve, anterior canal (AC) ampulla, common crus (CC), and the utricle. The posterior canal (PC) and caudal section of the HC were not exposed. The craniotomy was elongated to expose the horizontal semicircular canal for a distance of ~0.8-1.3 cm posterior to the ampulla measured along the curved centerline of the horizontal canal. A bolus of fluorocarbon (FC75, 3M Corp.) was injected into the cranial opening to partially fill the dorsal region of the perilymphatic vestibule. The fluorocarbon improved optical access to the labyrinth and prevented evaporation of perilymph and dehydration of tissue. Fluorocarbon is not soluble in water or perilymph such that the bolus remained isolated to a constrained region of the surgical opening. A layer of normal perilymph remained on the surface of the labyrinth and a pool of perilymph continued to bathe the HC nerve. Glass microelectrodes filled with 2 M NaCl or LiCl2 were used for extracellular or intraaxonal afferent recordings from the right horizontal canal nerve ~1 mm from the HC ampulla. Conventional amplification and spike discrimination were employed.
|
The HC of each fish was occluded mechanically by compressing the membranous endolymphatic duct firmly against the cartilaginous bone using a ~1.2-mm-diam glass rod tipped with a malleable substance (Takiwax; Cenco) that conforms to any surface irregularities. The location of the plug was measured in each fish using a pointer secured to a three-axis micromanipulator. Plugs were located 1 ± 0.2 cm from the crista as measured along the curved centerline of the canal. To ensure that the plugging procedure did not damage the transduction apparatus, afferent responses to sinusoidal stimulation (angular rotation and/or mechanical canal indentation) were monitored continuously while compressing the canal. After each experiment, a saturated solution of alcine green in artificial endolymph was injected into the HC ampulla to allow visual confirmation of the canal blockage. In several fish, the dye moved through the position of the blockage, indicating that only a partial plug was achieved. Data from partially plugged canals were excluded from the study.
In five experiments, the fish tank was secured to a velocity
servo-controlled rate table (10 ft-lb DC servo motor, Contraves) and
oriented to provide maximal angular stimulation to the horizontal canal
(Boyle and Highstein 1990). Micromanipulators (Fig. 1)
were secured rigidly to the rate table and rotated with the animal. Control afferent responses to sinusoidal rotation were collected before
canal plugging in each fish. The firing rate response of individual
afferents to sinusoidal rotation of the animal (whole body = head
velocity) were collected at angular velocities of ~0.1-20°/s over
the frequency range ~0.1-20 Hz in the unoccluded and occluded conditions.
In five separate animals, horizontal canal afferent responses to
micromechanical indentation of the slender duct and utricle were
recorded in the unoccluded control condition and in the occluded condition. In these experiments, the fish tank was placed on a vibration-isolation table. The micromechanical stimuli used
microindenters fashioned from flat-end, ~0.12-cm diam glass rods,
with one positioned perpendicular to the long-and-slender portion of
the HC and a second glass rod over the utricle; the HC and utricular
stimulators were lowered to static preload indentations of ~12.5 and
~25 µm, respectively (Boyle and Highstein 1991;
Dickman and Correia 1989
; Rabbitt et al.
1995
). The HC indenter was located ~0.3 cm from the cupula,
as measured along the curved centerline of the canal, between the canal
block and the ampulla. The utricular indenter was located ~0.5 cm
from the HC cupula as measured along the curved centerline coordinate.
Each rod was secured to a piezoelectric microactuator (Burleigh PZL
060-11) mounted in-line with a linear variable differential transducer
(LVDT; Schaevitz DEC-050) to obtain an analog measurement of
instantaneous position of the glass rod stimulator.
Digital data acquisition (Cambridge Electronic Design 1401Plus, Apple Macintosh interface) was used to record externally discriminated spike times, angular velocity of the rate table, and the displacement of the indenters (LVDTs). The tachometer and LVDT signals were amplified externally to span the 12-bit range of the A/D. This places the A/D digital round off two orders of magnitude below the noise thus providing resolution of ~0.25°/s table velocity and <0.5 µm indentation displacement. These analog signals were filtered at 250 Hz and digitized at 500 samples per second. Stimulus trigger signals and externally discriminated spikes were recorded to a resolution of 0.08 ms.
Analysis was done off-line using a custom interactive analysis
procedure (IgorPro, Wave Metrics). The constrained first-harmonic gain
and phase of afferent modulation were determined using the data
analysis described by Rabbitt et al. (1995, 1996
).
Briefly, afferent gain and phase were computed for five or more
consecutive stimulus cycles by manually selecting portions of the
record and averaging the results by cycle. Afferent spike times were
averaged relative to the stimulus trigger using 100 bins per cycle
phase histograms. Results were subsequently inverted to yield the
firing rate (spikes/second) as a function of phase in the cycle. A
discrete Fourier analysis was applied to the stimulus waveform and to
the phase histogram neural response to compute the first-harmonic amplitude and phase of the stimulus and the afferent response. Empty
bins were ignored in the afferent fitting procedure and the average
rate was constrained to be
0 (Rabbitt et al. 1996
). The complex-valued first harmonic afferent response then was divided by
the complex-valued first harmonic of the stimulus to determine the
afferent response dynamics. Results are reported in Bode form: afferent
gain (spikes/s per °/s) and phase (° re: peak angular velocity). As
the stimulus level is increased some semicircular canal afferents in
O. tau exhibit a saturating nonlinearity that causes the
first-harmonic gain and phase to be functions of stimulus level (see
Boyle and Highstein 1990
). In the present study,
rotational stimuli were maintained at relatively low levels where the
constrained first-harmonic afferent response is approximately linear
and the gain and phase are insensitive to amplitude (Boyle and
Highstein 1990
; Rabbitt et al. 1996
). For
plugged canals, this required the stimulus velocity to be decreased
with increasing frequency.
Modeling methods
To understand how canal plugging might alter cupula deflections,
we derived a three-dimensional mathematical model based on the
morphology of the HC, membranous duct deformability, and labyrinthine fluid mechanics. The model includes cupular visco-elasticity, fluid
viscosity, membranous duct visco-elasticity, osseous canal/temporal bone visco-elasticity, and, in primates, the connection to the middle
ear via the cochlea. A detailed derivation of the model is provided in
the APPENDIX. Plugging enters into the model by reducing the cross-sectional areas of the membranous duct and/or osseous canal
to zero along a short segment of the canal (modeled as 0.13 cm in
length). This occludes the flow of labyrinthine fluids at the location
of the plug. The model was applied to the HC morphology of the fish,
human, and squirrel monkey. The squirrel monkey model was based on
morphological data from Igarashi and colleagues (Igarashi 1966; Igarashi et al. 1981
), the infant human
model was based on Curthoys and colleagues (Curthoys and Oman
1987
; Curthoys et al. 1977
), and the fish model
was based on work by Ghanem et al. (1998)
. Measures of
squirrel monkey membranous duct thickness were provided by C. Fernández (unpublished data). The curved centerlines of the
primate HC models were assumed to fall within a single plane. The local
cross-sectional area was simplified to a circular endolymphatic duct
enveloped by an annular perilymphatic canal. For the fish and human
models, the plug was located along the slender portion of the HC at a
distance of 1 cm from the crista as measured along the curved
centerline of the duct; for the squirrel monkey, this distance was
reduced to 0.5 cm to account for the smaller size.
Short cylindrical fluid elements (100) were used to model the endolymph and 100 short annular fluid elements to model the perilymph. The elements were of equal length and oriented concentricity along the curved centerline of the HC. The geometry enters into the model by specification of a unique spatial position and cross-sectional area for each of the cylindrical and annular fluid elements. Continuity of fluid pressure and mass flow rate were enforced at the boundaries between adjacent fluid elements. Endolymph flow within the each cylindrical element was modeled as unsteady axisymmetric Stoke's flow. Perilymphatic flow also was modeled as unsteady axisymmetric Stoke's flow but was confined to an annular space rather than a cylindrical space.
Angular acceleration of the head induces inertial forces in both the perilymph and the endolymph; this lead to fluid flows and associated pressure gradients. The resulting transmembrane pressure gradients (local endolymph minus perilymph pressures) are counteracted in the model by the distentional stiffness of the membranous duct. The elastic modulus and thickness of the membrane was assumed to be homogeneous in the present simulations. The volume compliance of each cylindrical segment of the membranous duct was therefore dependent only on position and local duct size. Larger cross-sections are more compliant due to Laplace's law and Hooke's law (Eq. A14). Proportional damping was used to model viscous properties of the membrane. The bone enclosing the perilymphatic space also was modeled as a visco-elastic using the same equations as for the membranous duct but adjusting the thickness and stiffness to that of the bone.
In the present experiments, a small volume of perilymph within
the surgical opening was replaced with fluorocarbon. To account for
this, the density of the fluid for the annular elements located in this
region was set to that of fluorocarbonnormal perilymph density was
used elsewhere. The same portion of the perilymphatic cavity was opened
surgically to air. To account for this in the model simulations, the
stiffness of the bony enclosure was set to zero in this region. For the
squirrel monkey and the human, a short region of the perilymphatic
vestibule was modeled as connected to the cochlea rather than lined by
bone. A single lumped compliance was used to model the net volumetric
stiffness of the cochlea and the middle ear.
The local streamwise endolymph volume displacement, streamwise
perilymph volume displacement, endolymph pressure, perilymph pressure,
membranous duct deformation, and bony enclosure deformation were
allowed to vary as a function of position and were used in computations
as the dependent variables. The model equations were cast in
finite-difference form and solved using LU decomposition for sinusoidal
forcing (Press et al. 1986) using custom software programmed in Igor Pro (Wave Metrics, Lake Oswego, OR).
Simulations were carried out independently for both the control and the
plugged conditions. The response attenuation predicted to be caused by
plugging was determined by dividing the complex-valued cupular volume
displacement in the plugged condition by the cupular volume
displacement in the control condition. Attenuation results are reported
in Bode form (magnitude: cupular displacement in the plugged condition
divided by the displacement in the control condition; and phase:
cupular phase in the plugged condition minus the phase in the control
condition). The model is linear, so the predicted attenuation did not
change with stimulus amplitude. The global cupular attenuation and
phase shift was predicted to extend to individual spatial locations and
hair cells almost uniformly across the sensory epithelium (see
DISCUSSION). An attenuation of 0.1, for example, would
therefore imply that the mechanical stimuli exciting each hair cell
would be 10 times smaller in the occluded condition than in the control
condition. For stimuli restricted to the range where hair cells and
afferents respond linearly (Boyle and Highstein 1990;
Highstein et al. 1996
; Rabbitt et al.
1996
), a 10-times reduction in the mechanical activation of
hair cells would further predict a 10-times reduction in afferent gain.
![]() |
EXPERIMENTAL RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Afferent response to rotation after canal occlusion
Afferent responses to sinusoidal rotation (0.1-20 Hz) were
collected before canal plugging in each fish to ensure that the organ
was responding normally in the control condition. The HC duct then was
plugged slowly, and a second set of afferent responses was recorded in
the occluded condition. Control afferent nerves were typed into three
groups, "low gain, velocity sensitive" (LG), "high gain, velocity
sensitive" (HG), and "acceleration sensitive" (A) based on
responses to sinusoidal whole-body rotation using the scheme developed
by Boyle and Highstein (1990). The control population
consisted of 261 records from 18 afferents (5 LG, n = 47; 4 HG, n = 46; 9 A, n = 168). An
average of 15 (min 5, max 41) records were obtained for each control
afferent at single frequencies over the range from 0.1-20 Hz. After
occlusion, 440 records were obtained from 25 afferents in the same five
fish. An average of 18 (min 5, max 50) records were obtained at
discrete frequencies for each afferent in the plugged condition.
Because the plugging procedure alters afferent response dynamics, it
was not possible to use previously established methods to directly determine LG, HG, and A types in the plugged condition. It was possible, however, to estimate afferent types on the basis of data
collected in the plugged condition using the model. This estimate is
provided in the following text along with model results.
In each experiment, the firing rate of an individual afferent was
monitored while slowly compressing the membranous duct against the
cartilaginous substrate. Occlusion by compression of the duct is in
itself a type of mechanical stimulus that induced large magnitude
increases in afferent firing rate (Rabbitt et al. 1995). Figure 2A shows the response
of an afferent recorded during compression of the duct; the afferent
was LG type (0.28 spikes/s per °/s head velocity with a 2° phase
lag before plugging at 2 Hz). The sharp increases in firing rate
(indicated in A by arrows) correspond to the periods of duct
compression made by manually lowering a glass rod using a fine
micromanipulator drive. The afferent was allowed to recover to a firing
rate near its resting value before continuing compression. Brief
disturbances in the recovery, most evident from 700 to 930 s in
this record, are fish movement artifacts that were unavoidable in some
specimens. After the period of compression, recovery to the background
firing rate was slowest for low-gain afferents, presumably due to the
near absence of adaptation and rate sensitivity (Boyle and
Highstein 1990
; Fernández and Goldberg 1971
; Goldberg and Fernández 1971a
,b
).
Afferents always maintained a firing rate during plugging. However, the
modulation of the firing rate to rotation was maintained only when the
compression of the canal proceeded at an average rate of
4-5 µm/s.
Rapid compression of the membranous duct always damaged the end organ and eliminated any detectable afferent modulation to rotational stimuli, followed up to ~6 h after compression. Injection of alcine dye into the labyrinth provided evidence of partial or complete detachment of the cupula at its apex after rapid compression of the
canal; data from these damaged canals were excluded from this report.
|
After duct occlusion, individual afferents routinely were observed to
exhibit robust firing rate modulations in response to angular head
accelerations. On the whole, however, the population averages showed
consistent differences in the plugged and control conditions. The
firing rate behavior of one example afferent to sinusoidal rotation
recorded after complete plugging is shown in Fig. 2, C and
D, at four stimulus frequencies as indicated (0.5, 1, 2, and
5 Hz). The sinusoidal angular velocity of the rate table is given in
B, the corresponding afferent firing rate in C,
and phase histograms averaged over multiple cycles in D. To
avoid firing rate nonlinearities (see Boyle and Highstein
1990) and improve recording stability, the peak angular
velocity of the stimulus was reduced (in this case from 8.3 to 1°/s)
as the frequency of rotation was raised (in this case from 0.5 to 5 Hz). Examine the middle two panels in B-D. At
the same stimulus amplitude of 4.5°/s, a dramatic increase in the
magnitude of firing rate modulation was observed when the stimulus
frequency was increased from 1 to 2 Hz. To quantify the modulation, the
response gain was defined as the constrained first harmonic of the
afferent phase histogram (output; D, solid line) divided by
the first harmonic of the stimulus (input; D, dashed line).
For this particular afferent, the gain increased by two orders of
magnitude as the frequency was increased from 0.5 to 5 Hz. This large
increase in gain over this frequency range was not observed in control
canals. Although the frequency response of this afferent is quite
distinct from individual controls, it is notable that the response
magnitude at any given frequency falls well within the physiological
range observed for present control population and previously studied afferents in this species (Boyle and Highstein 1990
;
Rabbitt et al. 1995
).
Bode plots were constructed for the response of each afferent using
neural impulses collected during sinusoidal angular rotation at
discrete frequencies (0.1-20 Hz). Figure
3 shows responses, plotted in the form of
gain (spikes/s per °/s; A) and phase (° re: peak head velocity;
B), of two afferents from one fish tested separately, one in
the unoccluded control condition (+) and the other in the occluded
condition (o). Because of the length of time required for initial
afferent characterization and the irreversible nature of the plugging
procedure, we were unsuccessful in obtaining a direct comparison of the
responses of a single afferent in the plugged and unoccluded
conditions. The afferents presented in Fig. 3 were selected for
illustration because their responses fell near the population averages
in the control and occluded conditions. Simple polynomial curve fits
( and - - -) are provided to illustrate the trends. Note the large
phase advance in B of the afferent in the occluded
condition. The peak of the response modulation led peak ipsilaterally
directed head velocity by ~140° at 1 Hz, for example. This large
phase advance was not observed in the present unoccluded controls or in
previous studies (Boyle and Highstein 1990
;
Rabbitt et al. 1995
). Also note the pronounced increase
in the slope of the gain (A) that occurred in the plugged condition; again, a response property not observed in controls.
|
The trends in afferent gain and phase following canal occlusion are
most clearly illustrated by the population results. Figure 4 provides the average gain
(B) and phase (C) of responses obtained in the
control condition (thin solid lines) and in the plugged condition
(thick solid lines). The number of records at each frequency is
provided in A. Boyle and Highstein (1990)
demonstrated previously that afferents in the toadfish define a
continuous distribution with large interafferent variability in gain
and phase. This interafferent variability is responsible for the spread
in the current population averages, indicated by the vertical bars at
each frequency (1 SD).
|
On average, acute canal plugging caused ~100-fold attenuation in gain
at 0.1 Hz, 4-fold attenuation at 1 Hz, but only a factor of ~2 at 10 Hz (Fig. 4B). The average slope of the plugged-canal gain
was considerably steeper than the control population. In controls,
afferent responses fell between angular velocity sensitive and angular
acceleration sensitive (Fig. 4C) (also see Boyle and Highstein 1990). After canal occlusion, afferent responses were advanced an additional ~90° for stimulus frequencies less than ~2-5 Hz and fell between angular acceleration sensitive and angular jerk sensitive. Greater than 2-5 Hz the phase of plugged-canal population dropped and became nearly equal to the average of control afferents greater than ~8 Hz. These data show that canal plugging under the current experimental conditions does not eliminate afferent responses but rather changes their frequency-dependent response dynamics (gain and phase).
Afferent response to mechanical indentation after canal occlusion
The persistence of afferent modulation after HC duct occlusion
indicated that cupular deflections also persisted after plugging. This
led to the hypothesis that acceleration of the head caused transmembrane pressure gradients (local endolymph pressure minus perilymph pressure) sufficiently large to induce local distentions and
contractions of the membranous duct, ampulla, and utricle accompanied
by concomitant redistributions of endolymph and perilymph. Movement of
endolymph in the ampulla during such a redistribution would lead to
afferent modulations. To investigate feasibility of this idea,
transmembrane pressure gradients were generated by mechanical
indentation of the membranous duct in the absence of head acceleration.
Mechanical stimuli were applied to the HC limb and to the utricle as
described by Rabbitt et al. (1994, 1995
). In these
previous studies as well as in present control afferents
(n = 18), indentation of the HC limb elicited an
excitatory response, whereas indentation of the utricle elicited an
inhibitory response of HC afferents. The excitatory response is
associated with movement of endolymph out of the slender duct toward
the utricle; the inhibitory response is associated with movement of endolymph out of the utricle toward the slender duct. To determine if
this behavior persists after canal plugging, responses of individual afferents (n = 12) were recorded during HC and
utricular indentation after complete occlusion of the duct. Mechanical
stimulator locations were as indicated in Fig. 1. All afferents
continued to be excited by HC indentation and continued to be inhibited
by utricular indentation after plugging. Responses of a representative
afferent after complete HC duct occlusion are shown in Fig.
5 for both HC (A) and
utricular (B) indentation. Notice that the phase of the
afferent response is reversed for utricular indentation relative to HC
indentation indicating oppositely directed cupular deflection
the same
type of relationship observed in unoccluded controls. The afferent shown was typed as LG and responded nearly in phase with positive HC
indentation; other afferents, particularly those having characteristics identified as HG or A type had high gains to indentational stimuli exceeding 10-20 times that of the LG afferent shown.
|
Excitatory responses of plugged canals to indentation of the HC duct
were expected because all endolymph flow caused by indentation was
forced to move through the ampulla and displace the cupulathe other
direction of flow was blocked. The more significant observation is that
all afferents continued to show inhibitory responses to mechanical
indentation of the utricle even after the HC was blocked completely.
These responses were recorded in the absence of linear or angular
accelerations and hence cannot be attributed to inertial forces or
movement artifact. Afferent responses to utricular indentation would
not be expected if the membranous duct was completely rigid. The
observed firing rate modulations are consistent with the interpretation that transmembrane pressure gradients generated by utricular
indentation caused distention of the membranous canal wall, thereby
allowing flow into the region located between the ampulla and the canal plug. This flow would lead to afferent firing rate modulations precisely as observed during utricular indentation.
Model results and discussion
The mathematical model derived in the APPENDIX was used to interpret the present data and to address to what extent the results might extrapolate to other species and conditions. Two distinct experimental conditions were simulated: a surgically opened perilymphatic cavity corresponding to the present acute recording conditions in the toadfish (acute condition) and a sealed perilymphatic cavity with a completely ossified HC plug modeling a hypothetical chronic plugged-canal condition (chronic condition). The two conditions are discussed separately in the following text.
Acute condition
For stimuli between ~0.1 and 2 Hz, data indicate that afferents
sensitive to angular velocity in the control condition became sensitive
to angular acceleration in the acute plugged condition, whereas
afferents sensitive to angular acceleration in the control condition
became sensitive to angular jerk. As an example, consider the gains of
two afferents shown in Fig. 2A. The gain of the patent canal
afferent (+) had a slope of m ~ 1/2
[m = log(spikes/°/s)/
log(Hz)]. Because this
slope is on a log-log scale, it provides the exponent of a power law.
The afferent (o) shown after plugging had a gain exponent of
m ~ 2. The exponent determines to what extent the afferent is sensitive to displacement (m =
1),
velocity (m = 0), acceleration (m = 1),
or jerk (m = 2). In previous studies (Boyle and
Highstein 1990
) and in the present population, afferents in the
control condition had gain exponents primarily in the range 0 < m < 1, indicating sensitivity falling between angular
velocity and acceleration. Afferents from plugged canals had gain
exponents primarily in the range 1 < m < 2, indicating sensitivity falling between angular acceleration and jerk.
The increased phases observed in the plugged condition are consistent
with this change in exponent. The same trends are exhibited clearly in
the population average shown in Fig. 3.
Afferent responses to angular movements were present immediately after the plugging procedure. Time was not sufficient for adaptation or remodeling of the end organ, so the increased gain exponent and advanced phase in plugged-canal responses relative to controls must reflect changes in canal mechanics. The model derived in the APPENDIX was applied to investigate if canal macromechanics could account for the observed changes in afferent response dynamics. Care was taken to reproduce the same conditions present during the experiments. To model the surgically opened condition, the pressure on the surface of the perilymph was set equal to atmospheric in the region of the surgical opening (0 gauge pressure). The plug was modeled by reducing the cross-sectional area of the endolymphatic duct to zero along a short segment of the canal. The perilymphatic duct was not occluded in the experiments nor was it occluded in the simulations for the acute condition.
Dashed curves in Fig. 4 show how the present control population (thin
solid curves) would be predicted by the model to respond had it been
possible to record the very same afferents in the plugged condition.
This theoretical result was computed by dividing the model prediction
for the cupular volume displacement in the plugged condition by the
model prediction for the control condition to obtain a transfer
function describing mechanical attenuation. The attenuation then was
multiplied by the average first-harmonic afferent data collected in the
control condition to project the data to the plugged condition (dashed
curves, Fig. 4). There is reasonably good agreement between the gain
and phase predicted by the model (dashed curves) and the average data
collected in the plugged condition (thick solid curves). Both the phase
and gain recorded in the plugged condition, however, are slightly under
predicted by this model projection. Part of the difference may be due
to the fact that data in the control and plugged conditions were
recorded from two distinct afferent populations. By using the model to
project plugged data to the control condition, we estimate that the
plugged population consisted of 13, 138, and 289 records obtained from
2 LG-, 9 HG-, and 14 A-type afferents, respectively. As noted in the
preceding text, the control population consisted of 47, 46, and 168 records obtained from 5 LG-, 4 HG-, and 9 A-type afferents,
respectively. The apparent difference between the control and occluded
populations may indicate a sampling bias toward HG- and A-type
afferents in the plugged conditiona bias that could explain the
relatively small difference between the plugged canal data and the
model projection.
ATTENUATION IN THE ACUTE CONDITION. Figure 6 shows the frequency dependent attenuation (A, nondimensional) and phase shift (B, ° re: control condition) predicted to be caused by canal plugging in the surgically opened acute condition for the toadfish (solid curves), squirrel monkey (thick short dashed curves) and the human (thick long dashed curves). Simulations for the chronic condition with a sealed perilymphatic cavity are discussed in the following text. Attenuation predictions for primates in the acute recording condition are remarkably similar to data for the fish even though there are relatively large interspecies differences in labyrinthine morphology and absolute cupular volume displacements. This similarity occurs because the differences in cupular volume displacement between the species are present in both the control and plugged conditions and hence cancel out to a large extent in computing the attenuation. Attenuation curves in the surgically opened acute condition depend primarily on the morphology and mechanical properties of the membranous duct; in the chronic condition discussed in the following text, the stiffness of the perilymphatic cavity, osseous canal, and connection to the middle ear are also important model parameters.
|
PRESSURE DISTRIBUTIONS. The model predicts that endolymph movement and cupular displacements arise in plugged canals owing to distention of some regions of the endolymphatic duct accompanied by concomitant contractions of other regions. Understanding the response of plugged canals therefore requires an understanding of transmembrane pressure gradients underlying the membranous duct deformation. Predicted transmembrane pressure gradients for the fish are shown in Fig. 7 for canal-centered rotation at five instants in time spanning one-half of the 5.7-Hz stimulus cycle (color scale gradients within each canal, see Fig. 8A for quantitative results). Time increases from top to bottom. Plugged-canal simulations are shown on the right and control simulations on the left. The top panels show the instant in time corresponding to peak clockwise (CW, ipsilateral) acceleration (A), the middle panels peak clockwise velocity (C), and the bottom panels peak counterclockwise (CCW) acceleration (or peak CW displacement, E).
|
|
ENDOLYMPH DISPLACEMENT. For a perfectly rigid membranous duct, the position dependent magnitude of the endolymph displacement would be inversely proportional to the local duct cross-sectional area owing to conservation of mass. This was approximately true for simulations in the control condition where membranous duct distention was relatively small but was not the case for plugged canals where the endolymph flow was entirely dependent on duct distention. In control canal simulations, endolymph displacement was large in the slender duct relative to the ampulla. The opposite was predicted in plugged canals. The phase of peak endolymph displacement also was predicted to change between the two conditions. At 0.1 Hz, for example, the endolymph displacement in the control condition was predicted to be maximum at the time corresponding to peak head velocity, but in the plugged canal, the displacement was predicted to be maximum at the time corresponding to peak head acceleration. Hence consistent with the data, the integrating effect of fluid viscosity was lost in plugged canals.
Greater than ~2 Hz, endolymph flow was predicted to become unsteady resulting in more complex fluid displacement profiles. A balance between unsteady inertia and viscous shear stress was responsible for the complex flow patterns predicted in the large cross-sectional regions of the canal. Profiles in the slender region of the membranous duct were predicted to remain nearly Poiseuille at 5.7 Hz; but this did not extend greater than ~15 Hz, where the unsteady effect was predicted to extend to the slender duct as well. The unsteady effect depends on the local cross-sectional area and is identified most easily by the "M"-shape endolymph displacement patterns in Fig. 7, B-D. Similar unsteady profiles have been shown previously in simple one-dimensional flows by Stokes in the late 1800s (see Fung, 1990DEGREE OF BLOCKAGE. One of the most important model parameters influencing the effectiveness of canal plugging was the extent to which the lumen of the endolymphatic duct was blocked. Quantitative predictions are provided in Fig. 9 for the toadfish in the acute condition at seven levels of blockage ranging from 100% (thick solid curve) to 50% (thin solid curve). Complete endolymphatic plugs were predicted to cause large attenuations at low frequencies, whereas leaky plugs were predicted to be much less effective. For example, reducing the membranous duct area by 50% over a length of 1.3 mm was predicted to have little effect on the mechanical response (attenuation in Fig. 9 is ~1 and the phase shift is ~0). At high frequencies (more than ~8 Hz), canal plugging in the acute recording condition was predicted to be ineffective in attenuating the cupular gain regardless of the extent of endolymphatic duct occlusion.
|
PLUG LOCATION. Plugs positioned close to the ampulla were predicted by the model to be more effective than plugs located further from the ampulla. This was due to the increase in total volumetric compliance of the section of the duct located between the ampulla and the plug that accompanies the increased length. At 1 Hz in the fish, a plug located 1.2 cm from the crista, measured along the curved center line of the duct, was predicted to attenuate the cupular displacement by a factor of 0.27, whereas a plug located 0.4 cm from the crista was predicted to attenuate the cupular displacement by a factor of 0.17. The shift in phase was insensitive to the position of the plug and was predicted to vary by only 1° when the plug was located at 1.2 versus 0.4 cm from the crista. In the experiments, the plug was located 1 ± 0.2 cm from the crista. According to the model, the ±0.2 cm variation in the position of the plug may have introduced ~15% interanimal variation in the attenuation data and ~0.5% variation in the phase.
MEMBRANOUS DUCT STIFFNESS.
The model also predicted that increasing the membrane stiffness would
make canal plugging more effective in attenuating cupular responses,
whereas reducing the stiffness would cause the opposite. Quantitative
predictions for the fish are provided in Fig.
10 for the acute recording conditions.
The phase predicted at high frequencies was particularly sensitive to
membranous duct stiffness. Stiff labyrinths were predicted to show a
phase advance of ~90° at 10 Hz after plugging, whereas compliant
labyrinths were predicted to respond with a phase similar to controls.
It is not uncommon to have interanimal variations in soft tissue
stiffness spanning more than an order of magnitude (Fung 1981,
1990
). Soft-tissue stiffness also is known to vary
systematically with age and sex. Hence some of the variability in
high-frequency results between individual animals, between species, and
between different laboratories may simply reflect natural variations in
labyrinthine membrane stiffness. In the present simulations, we
optimized the stiffness to fit the average data reported in Fig. 4 (see
Table 1). The stiffness ascertained by
this method fell within the range reported by Yamauchi et al.
(1998)
for the toadfish labyrinth based on pressure-volume
data. It should be noted, however, that these pressure data span more
than an order of magnitude, indicating large interanimal variability in
membrane stiffness. This is consistent with the interanimal variability
seen in the phase of plugged canal afferent responses in the present
population at high frequencies of rotation. Results for the human and
squirrel monkey discussed in the following text were computed using the
same stiffness as for the fish. Predictions for these species therefore
may change as experimental data become available.
|
|
MECHANICAL INDENTATION. As described earlier, Fig. 5 shows the response of a single LG afferent to mechanical indentation of the HC duct (A) and the utricle (B) in the plugged condition. It is important to note that positive utricular indentation continues to cause inhibitory responses even after complete occlusion of the HC, thus indicating endolymph movement through the ampulla and a concomitant distention of the membranous duct. The ratio of the afferent gain during HC indentation to that recorded from the same afferent fibers during utricular indentation was 6.7 ± 2.6 (range 3.2-13.4; 0.5-5 Hz, n = 13) in the control unoccluded condition and increased to 20.6 ± 9.2) (range 8.2-34.6; 0.5-5 Hz; n = 12) in the occluded condition. The present model predicted a ratio of 9.4 for the control condition and 15.4 for the plugged condition; values well within the observed range. These model predictions are sensitive to the morphology of the duct, position of the plug, positions of the stimulators, and preload of the stimulators, factors that varied between individual animals used in the experiments. Hence the relatively small differences between the model predictions and the average data are not surprising. What is most important to note is that a single model including membranous duct distensibility is sufficient to account for the observed changes in afferent responses after semicircular canal plugging for both physiological head rotation and for mechanical indentation stimuli.
MODEL VALIDATION IN THE ACUTE CONDITION.
Both the attenuation and phase shift predicted for the toadfish in the
acute, surgically opened, condition are in quantitative agreement with
the present afferent data (see Figs. 4 and 6). It is important to note
that the very same model (and same parameter set) predicts the
endolymphatic pressure modulations recorded in the ampulla during
mechanical indentation (Yamauchi et al. 1998). The
present model also predicts the experimentally established relationship
between afferent responses during mechanical duct indentation of the HC
and during rotation stimuli in O. tau (Rabbitt et al.
1995
). The same model also reproduces previous theoretical results when the stiffness is increased to simulate the rigid-duct case
(Damiano and Rabbitt 1996
; Oman et al.
1987
). These validations suggest that the model may be
sufficiently general to address questions outside the range of
currently available experimental data.
Chronic condition
PREDICTED ATTENUATION IN CHRONIC CONDITIONS.
To address how the present results might extrapolate to chronic canal
plugs in primates, model parameters were adjusted to account for a
completely sealed perilymphatic space and a stiff ossification
completely precluding flow of endolymph and perilymph at the location
of the plug. The connection to the middle ear, absent in the fish, was
included as a lumped parameter volumetric stiffness located at the
surface of the perilymphatic vestibule. Quantitative predictions for
the chronic condition (II) are shown in Fig. 6 for the squirrel monkey
(thin dotted lines) and the human (thin dashed lines). Canal plugging
was predicted, on average (0.01-20 Hz), to generate ~10 times more
cupular attenuation in the chronic condition (thin dotted and dashed
curves) beyond that present in the surgically opened acute condition
(thick dotted and dashed curves). In all simulations chronic canal
plugging was predicted to attenuate cupular volume displacements by
>100 × less than ~1 Hz and hence is expected to be highly
effective at low frequencies. As the stimulus frequency was increased
sufficiently high, canal plugging was predicted to become ineffective
in attenuating cupular displacements even in the chronic, sealed,
condition. The specific frequency at which plugging was predicted to
become ineffective depended on the specific morphological structure and physical parameters. Parameters for the toadfish are relatively well
known (Rabbitt et al. 1995; Yamauchi et al.
1998
), but parameters for the human and the squirrel monkey are
not as well established. Obtaining afferent recordings without
compromising the perilymphatic space also has proven problematic, such
that direct experimental testing of model predictions for the chronic
condition, has not yet been possible. VOR data for the squirrel monkey
appears to be consistent with the present model (Davis et al.
1997
; Lasker et al. 1997
), but such comparisons
are indirect. Predictions for the chronic condition therefore should be
viewed in light of sensitivities to model parameters discussed in the
following text.
PRESSURE DISTRIBUTIONS. In contrast to the surgically opened acute condition, the endolymphatic and perilymphatic pressures in the sealed chronic condition were predicted to become nearly identical to each other (Fig. 8, C and D; thin dashed and solid curves). This pressure balance leads to relatively small transmembrane pressure gradients in both the patent (thick dashed curves) and plugged (thick solid curves) canals. This difference in the transmembrane pressure distributions between the acute condition (fish; Fig. 8, A and B) and the chronic condition (human; Fig. 8, C and D) underlies the reduced effectiveness of canal plugging predicted for surgically opened preparations (also see Fig. 6).
CONNECTION TO THE MIDDLE EAR.
Computations for the human and the squirrel monkey used a stiff osseous
canal that effectively eliminated any deformation of the bony
perilymphatic space. Compliance of the vestibule therefore was
dominated by the connection to the cochlea and the middle ear. This
compliance has not been measured in primates. Lynch et al.
(1987) report a round-window volumetric compliance in cat on
the order of 10
8
cm5/dyne. It is not appropriate, however, to
directly use this value in the present model due to the difference in
size of the ears and the magnitudes of pressures involved. Treating the
round window as an elastic plate would predict the compliance to be
inversely proportional to the fourth power of the radius. On the basis
of this, the compliance of the human round window may be nearly two orders of magnitude less than that of the cat. It is also important to
note that the cat round window compliance was measured using sinusoidal
stimuli generating pressures on the order of 100 dyn/cm2
a pressure two orders of magnitude
higher than predicted during volitional angular head rotations. It is
well known that, in the absence of pretension, soft tissues become more
compliant for small strains (Fung 1981
). On the basis of
these considerations, volumetric stiffnesses of 5 × 105 and 7.5 × 106
dyn/cm5 were selected as baseline values for the
human and squirrel monkey, respectively (see Table 1). The influence of
changing the middle ear stiffness on the attenuation predicted for the
human is shown in Fig. 11. Results for
the baseline stiffness of 5 × 105
dyn/cm5 are shown as thick solid curves. When the
stiffness was reduced by a factor of 100 (dotted curves), plugging was
predicted to be ineffective in reducing cupular deflections at
frequencies greater than ~1 Hz. In contrast when the stiffness was
increased by a factor of 10 (dashed curves), plugging was predicted to
be highly effective reducing cupular deflections even at frequencies
10 Hz. Increasing the stiffness by a factor of 100 (thin solid curves) produced very little additional attenuation. Therefore the thin
solid curves provide an estimate of the largest attenuation that
reasonably could be expected. VOR data in humans appears to be
consistent with the baseline (thick solid) curves in Fig. 11 (Aw
et al. 1996
), but once again this comparison is indirect. Irrespective of uncertainties in model parameters, it seems clear that
the effective stiffness and structural integrity of the perilymphatic space are important factors. At 1 Hz, for example, decreasing the
compliance changed the attenuation factor nearly two orders of
magnitude from ~0.01 to 1. A bone dehiscence or a surgical procedure,
which increases the compliance of the perilymphatic cavity or middle
ear, would be expected to decrease the effectiveness of canal plugging.
|
ROLE OF LINEAR ACCELERATION.
Model results also indicate that the degree of cupular attenuation
caused by canal plugging may be sensitive to linear accelerations of
the head and/or eccentricity of the axis of rotation. Sensitivity of
the semicircular canals to linear accelerations is a long standing question that has not yet been resolved (Benson 1974;
Estes et al. 1975
; Goldberg and Fernández
1975
; Ledoux 1949
; Lowenstein 1970
; Ross 1936
). Part of the difficulty in
experimentally testing linear sensitivity of semicircular canal
afferents is due to the influence of opening the perilymphatic space
a
significant factor in the present model predictions. To estimate the
possible influence of linear accelerations on chronic plugged-canal
responses, we applied the model for various axes of rotation located
eccentric to the center of the canal in the human. Model results are
shown in Fig. 12 for the right HC in
response to sinusoidal rotations about five different axes (0-4). At 2 Hz, for example, plugged canal cupular responses were predicted to
differ significantly depending on the location of the axis of rotation.
Results indicate that linear acceleration may be an important parameter
to be controlled in the measurement of plugged-canal responses.
|
![]() |
DISCUSSION OF PLUGGED CANAL AFFERENT RESPONSES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Acute damage to the sensory apparatus can be caused by occlusion
Another factor contributing to differences between afferent
responses in acute versus chronic plugged-canal preparations may be the
condition of the cupula. In the present study, individual afferents
were monitored while slowly compressing the duct against the
cartilaginous substrate using a series of discrete indentation steps.
Afferent modulation was maintained only if compression of the canal
proceeded slowly over the course of ~3-5 min (see Fig.
2A). Plugging at faster rates always resulted in loss of canal sensitivity to rotational stimuli. Following the approach of
Hillman (1974), injection of alcine dye into the
endolymph revealed a detachment of the cupula at the apex in
unresponsive canals. As Hillman suggested, cupular detachment appears
to serve as a "relief valve" to accommodate excess transcupular
pressure
in this case, relief for pressure generated by compression of
the duct during the mechanical plugging procedure.
Compression of the endolymphatic duct is a stimulus that produces
controllable semicircular canal afferent responses and has been used to
mimic angular motion of the head (Dickman and Corriea 1989; Rabbitt et al. 1995
). For sinusoidal
stimuli at 1 Hz, a ±1-µm indentation mimics about ±4°/s head
velocity in the toadfish (Rabbitt et al. 1995
). The
stimulus is nearly linear, such that doubling the magnitude of
indentation doubles the magnitude of afferent responses. On the basis
of this experimentally established relationship, rapid compression of
the duct during a short time course, several seconds for example, would
generate pressures and cupular displacements several orders of
magnitude larger than those generated by natural physiological head
movements. Consider, for example, the rapid increases in firing rate
appearing at times 450 and 650 s in the record of Fig.
2A. This low-gain afferent had a measured gain of 0.3 spikes/s per °/s to rotation; therefore an increase of ~50 spikes/s
corresponds to an equivalent angular velocity ~180°/s. Each step in
the compression was carried out during an ~10-s period, which
provides an equivalent angular acceleration of
~18°/s2 and a compression rate of ~4-5
µm/s. Had the same partial compression of the canal been completed in
1 s, the equivalent angular acceleration would approach
~8000°/s2. Complete compression of the canal
in 1 s would increase this value by more than an order of
magnitude. Angular head accelerations and velocities of this magnitude
generally result in trauma (Klinich et al. 1996
). This
is probably why rapid plugging caused cupular detachment.
The present data indicate that cupular damage probably occurs in most
conventional plugging procedures and is inevitable during rapid
compression of the canal. Therefore the question of cupular regeneration/repair becomes important in tracking recovery and adaptation after plugging procedures. Although the present study does
not address the cupular regeneration process, on several occasions, we
noted an absence of rotational response in the canal nerve 6 h after
mechanical labyrinthine trauma. On the basis of the
extracellular-mucopolysaccharide structure of the cupula and variable
extent of damage, complete regeneration may be on the order of several
days to weeks (Bérlanger 1961
; Dohlman
1960
; Hillman 1974
; Silver et al.
1998
). The slow compression approach used here to occlude the
canal maintains integrity of the cupula and thereby allowed for acute
study of afferent response dynamics without a functional recovery of
the cupula being an issue. When using a more conventional, rapid
surgical approach, a reasonable expectation would be for afferents to
reproduce the present data after cupular recovery.
Afferent response dynamics in the occluded condition
Present experimental results show that HC afferents recorded in
the acute condition continue to modulate their firing rate in response
to sinusoidal head rotations even after the endolymphatic duct has been
blocked completely. Because of the isolation of the HC nerve at the
location of axon recordings, there is no doubt that the reported
afferents supply the hair cells of the HC crista (Boyle et al.
1991). Injection of alcine dye into the HC ampulla after the
experiment left no doubt that the endolymphatic duct was completely
plugged. Firm compression of the duct against the cartilaginous
substrate by the glass rod, and the use of rigid fixtures, served to
minimize any possible stimulus due to mechanical movement of the rod
relative to the fish. Plugged-canal responses also were observed for
mechanical indentation of the utricle in the complete absence of
rotational stimuli. As a separate control, at the end of several
experiments an individual afferent was recorded while the glass rod
plugging the canal was raised, thus removing the contact between the
rod and the canal, and no detectable difference in the response was
observed for the examined 5-10 cycles of rotation; the canal was
inspected quickly and a 1.3-mm segment of the limb was observed to
remain completely occluded. Therefore the possibility of artifact is remote.
Afferent responses observed in the toadfish HC after plugging raise the
question concerning why the procedure appears to have reasonable
efficacy in humans and in some experimental studies of the VOR. At
least four factors may contribute to this. The first and most obvious
factor is the condition of the preparation. In the present experiments,
a portion of the perilymphatic space was opened surgically to allow for
access to the HC nerve and endolymphatic duct. This contrasts the
chronic plugged-canal case where, presumably, the perilymphatic space
is sealed in rigid bone the entire plugged region becomes ossified. The
model indicates that this difference could account for about a 10-fold
reduction in cupular displacements in the chronic condition over and
above the reduction present in the acute condition, at least in the low- to midfrequency range (see Fig. 6). A second contributing factor
may be the power spectrum of the stimulus. Occlusion of the duct was
shown here to be highly effective for low-frequency stimuli even after
opening the perilymphatic spaceit is predicted to become even more
effective for an uncompromised perilymphatic space. This does not
extend to high frequencies where the model predicts robust canal
afferent responses in both acute and chronic conditions. Therefore
plugged-canal responses to stimuli containing high-frequency components
should not a priori be attributed to the emergence of an otolith
afferent input or central adaptive mechanism. When comparing results
from different species or attempting to predict afferent response after
the plugging procedure, it is important to note that canal plugging was
predicted by the model to be more effective in species having short
interlabyrinth distances, stiff membranous ducts, and relatively stiff
perilymphatic space and/or connection to the middle ear (such as the
squirrel monkey). A third contributing factor may be differences in
sensitivity of various afferent types to angular motion
stimuli
high-threshold units may be the most susceptible to
attenuation caused by plugging. For the toadfish, they are the LG
afferents, and their counterparts are present in other vertebrates,
e.g., the regularly discharging canal afferents in monkeys
(Goldberg and Fernández 1971b
). This may cause a
change in the population of responding afferents participating in a
particular vestibular reflex favoring the more sensitive high-gain
units after plugging. Given differential projections of various classes
of afferents, plugging may not act uniformly across all systems. Also
plugged-canal responses become phase advanced by ~90° in the
midband relative to controls. The additional phase advance and the
skewing of the entire population toward low-threshold units would both
serve to reduce the angular velocity-sensitive inputs to the brain stem
in favor of angular acceleration and jerk-sensitive inputs. It is
unclear what influence this might have on the central processing and
performance of vestibular reflex systems. In the squirrel monkey, for
example, adaptation of the VOR after plugging apparently would require
an additional central integration of canal inputs and/or the use of
inputs from other organs to be effective. Without central adaptation, a
significant phase lead and frequency sensitivity in the slow-phase VOR
would be expected, at least at low frequencies (see Figs. 3 and 6). There is some experimental evidence supporting these possibilities, in
that phase leads and high-frequency recovery have been observed in
animals with plugged canals (Angelaki et al. 1996
;
Baker et al. 1982
; Broussard and Bhatia
1996
; Lasker et al. 1997
; Yakushin et al.
1997
). Two additional factors may contribute to the long-term dynamics of afferent responses in plugged canals. First, it is not
known to what extent adaptation of the end organ itself might remodel
and further modify afferent responses in chronic preparations. Second,
because most plugging procedures damage/dislodge the cupula, recovery
also must include the influence and time course of cupular regeneration.
It is important to reiterate that the residual afferent responses
observed in plugged semicircular canals are significant only at high
stimulus frequencies. The specific frequency above which canal plugging
becomes ineffective depends on several factors specific to the
particular species and experimental/surgical approach. To provide some
general guidelinespresent results indicate that endolymphatic duct
plugging reduces cupular displacement by
100-fold in the surgically
opened acute perpetration only at stimulus frequencies less than ~0.2
Hz. Results further indicate that complete canal plugging reduces
cupular displacement by
100-fold in the ossified and sealed chronic
preparation only at stimulus frequencies less than ~1 Hz. Given
sensitivities to species-dependent morphological structure, surgical
approach, and experimental design (see Figs. 6 and 9-12), it would not
be surprising to see relatively large variability in the efficacy of
canal plugging particularly for high stimulus frequencies.
![]() |
APPENDIX: ELASTO-HYDRODYNAMIC MODEL |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
A finite difference approach was employed by dividing the
membranous canal and perilymphatic space into N short
discrete segments. Each segment n was assigned a different
cross-sectional area and three-dimensional spatial location. Schematics
of the perilymphatic and endolymphatic segments are illustrated in Fig.
A1
along with model notation. The momentum equation providing the
relationship between the endolymphatic volume displacement
Qnp (cm3) at
cross-section n to the streamwise endolymph pressure
gradient can be written (Damiano and Rabbitt
1996)
![]() |
(A1) |
![]() |
(A2) |
|
|
The coefficient n accounts for the
frequency-dependent shape of the velocity profile across the
cross-section. For Poiseuille flow in the endolymphatic duct, which is
valid for low-stimulus frequencies,
n ~8
,
which is the exact value for steady flow in a circular tube. The
functional dependence of
n on the local
Stokes (St) number is provided in the
following text, and its dependence canal ellipticity by Oman et
al. (1987)
. In the present model, the parameter is
n computed as a function of local diameter,
excitation frequency, and material properties. Circular cross-sections
are assumed.
Equation A2 describes the volume displacement of a
Kelvin-Voigt viscoelastic material, which reduces to the linearized
Newtonian fluid for the case of zero stiffness and to a simple
linear-elastic solid when the viscosity is set to zero (Fung
1990, 1981
). We take this model to apply to both the endolymph
and the cupula and adjust the modulus of rigidity and the viscosity
appropriately to account for the differing properties of the materials
(see Table 1).
The inertial forcing term, fne in
Eq. A2, is due to angular head acceleration and is computed
for each element using
![]() |
(A3) |
Replacing the superscript "e" with "p" in Eqs.
A1-A3 provides the corresponding equations for the
perilymphatic duct. The inertial forcing for the perilymph must account
for the moving osseous canal as well as the membranous labyrinth.
Accounting for the acceleration distribution between the membranous and
osseous canals provides the inertial forcing for the perilymph in the
form
![]() |
(A4) |
The motion of the membranous duct is determined by perilymphatic
viscous coupling to the osseous canal and by elastic connective filaments spanning the perilymphatic space. In the present model, we
allow the duct to move in two ways. The first is a global rigid-body rotation that allows the membranous duct to move relative to the skull,
and the second is a local distention of the duct. The rigid body
rotation is determined by the global rotation, d
and the distention by local dependent variables described in the
following text. For rigid body rotation of the duct, we apply a simple
base-support model where rotation is determined by the inertial and
viscous drag forces acting on the membrane itself. Summing forces
around the duct provides the angular momentum governing
d as
![]() |
(A5) |
![]() |
(A6) |
![]() |
(A7) |
The fine filaments (trabeculae) connecting the membranous duct to the
osseous canal are modeled as an array of elastic fibers through which
the perilymph is allowed to flow. Stiffness of the filaments is lumped
into an effective shear modulus fil occupying the
perilymphatic space. This shear modulus is distinct from that of the
perilymph in that it does not restrict perilymph movement
it only
restricts movement of the membranous duct relative to the head. The
effective stiffness is obtained by integrating the filament-derived
elastic shear stress around the surface of the membranous duct. The
result is
![]() |
(A8) |
![]() |
(A9) |
![]() |
(A10) |
![]() |
(A11) |
![]() |
(A12) |
The incompressible Navier-Stokes equations were used to estimate the
effect of fluid entrainment by the moving membrane normal to its
surface. This was done by assuming each segment acts as a point source
generating a pure radial flow and integrating the linearized fluid
equations in the direction normal to the membranous duct surface. The
resulting effective mass is
![]() |
(A13) |
![]() |
(A14) |
![]() |
(A15) |
Using a similar approach as applied for the membranous duct, the
osseous perilymphatic canal was modeled using the Fourier operator
![]() |
(A16) |
Conservation of mass requires the total volume of endolymph to
remain constant and the total volume of perilymph to remain constant.
Because of this, the model equations describe a dynamic redistribution
of the perilymphatic and endolymphatic volumesnot a change in their
volumes. The equations are equally valid for application to the normal
case for a closed temporal bone or application to the case of a
surgically opened perilymphatic space. The only difference is the
pressure relief boundary condition or the additional pressure stimulus
that may act at the point of the opening due to fluctuations in
atmospheric pressure or mechanical contact. Conservation of mass is
enforced through a control volume analysis. For the endolymph, the
streamwise volume displacement Qne at
cross-section n is related to the volume displacement of the cupula Qoe and the effective volume
displacement caused by distention of the membranous duct
qne to give
![]() |
(A17) |
For the perilymph, conservation of mass provides
![]() |
(A18) |
![]() |
(A19) |
![]() |
(A20) |
In the limiting case when the membranous canal is infinitely stiff, the
preceding equations become singular and the hydrostatic pressure cannot
be determined. Through a fortuitous selection of dependent variables,
we were able to avoid numerical difficulties arising in the nearly
singular case. This was done by recasting the equations in the
following matrix form
![]() |
(A21) |
![]() |
(A22) |
![]() |
![]() |
Elements of the matrix M and forcing vector were
determined for each segment using the physical parameters provided in
Table 1. The matrix system then was solved using LU decomposition at 40 discrete frequencies equally spaced on a log scale from 0.003 to 30 Hz.
The endolymphatic and perilymphatic pressures are included implicitly
as functions of the centerline coordinate "s" in these
equations. Once results were computed by inversion of Eq. A21, the spatial distribution of pressure then was computed.
Most of the parameters appearing in the model are relatively well
known in terms of the morphology of the different labyrinths and the
physical properties of the fluids (see Table 1). The density and
viscosity of the endolymph and perilymph are nearly equal to water
(Steer et al. 1967). Because the cupula has neutral buoyancy when suspended in endolymph, its effective density was set
equal to the density of the endolymph. The modulus of elasticity for
the cupula was estimated by matching the mechanical lower-corner frequency reported previously for the toadfish (Highstein et al. 1996
; Rabbitt et al. 1996
), which yields a
stiffness on the same order as other mucopolysaccharides (Fung
1981
; Lutz et al. 1973
; Philipoff
1966
). Cupular viscosity was estimated from Yamauchi et
al. (1998)
.
The physical properties of the membranous duct were estimated by
measuring the pressure in the HC ampulla during mechanical indentation
of the canal limb (Yamauchi et al. 1998). The present model assumes circular cross-sections and hence does not include bending stiffness. The magnitude of structural damping within the
membranous duct has not been measured to date. Proportional damping
coefficients have been estimated for similar biological structures, and
the present estimates are based on these data (eardrum: Funnell
et al. 1987
; skin: Wilkes et al. 1973
). Present results are relatively insensitive to changes in these structural damping parameters.
The stiffness of the osseous canal was estimated using the elastic
modulus of bone, which is very high relative to the stiffness of the
membranous duct (Fung 1981). Because of this, the
perilymphatic duct was essentially rigid in the present model and
prevented any flow of perilymph through the surface. In such, model
predictions are insensitive to variations in the perilymphatic duct
wall properties.
Cross-sectional velocity profiles
Following Damiano and Rabbitt (1996), the local
particle displacement of the fluid u(s, r,
)
is governed by
![]() |
(A24) |
Viscous drag and inertial effects in the endolymph are approximated
using circular cross-sections. In this case, the dependence of the
velocity on the local radial cross-sectional coordinate r is
easily found by a Fourier-Bessel expansion to be
![]() |
(A25) |
The same approach is applied for the perilymph but modified to account
for the annular space. Viscous drag and inertial effects in the
perilymph are approximated by replacing J0n in
Eq. A25 with J0n = nY0n, where
Y0n are zero-order Bessel functions of
the second kind. The eigenparameter,
n, is
determined to meet the no-slip boundary condition on the outside
surface of the membranous duct and on the inside surface of the osseous canal.
Once fluid velocity distribution is known, the flow rate
Qn at cross-section n is
![]() |
(A26) |
![]() |
(A27) |
M matrix
![]() |
Pressure distribution
Once the matrix equations are inverted, the pressure
distribution around the endolymphatic duct is computed using
![]() |
(A29) |
![]() |
(A30) |
![]() |
ACKNOWLEDGMENTS |
---|
We thank C. Fernández for providing morphological data used in the squirrel monkey model.
This work was supported by National Institute of Deafness and Other Communications Disorders Grant DC-01837.
![]() |
FOOTNOTES |
---|
Address for reprint requests: R. D. Rabbitt, Dept. of Bioengineering, 2480 Merrill Engineering Bldg., University of Utah, 50 S. Central Campus Dr., Salt Lake City, UT 84112.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 30 April 1997; accepted in final form 9 April 1999.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|