INTRODUCTION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS DISCUSSION OF PLUGGED CANAL... APPENDIX REFERENCES

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.

View larger version (24K): [in this window] [in a new window]   Fig. 1. Experimental set up. Schematic shows the location of the glass rod used to plug the membranous duct, the location of the horizontal canal (HC) mechanical stimulator and the location of the utricular stimulator (gray ellipse). Apparatus was secured to a rate table with the plane horizontal canal oriented perpendicular to the axis of rotation for controlled delivery of sinusoidal angular motion.

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

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS DISCUSSION OF PLUGGED CANAL... APPENDIX REFERENCES

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.

View larger version (37K): [in this window] [in a new window]   Fig. 2. Afferent responses during (A) and after (C and D) HC duct occlusion. Two separate afferents are shown (A, C, and D). Small arrows (A) indicate times when the glass rod was manually lowered to partially compress (plug) the membranous duct. Rapid increase in HC afferent firing rate always accompanied canal compression until complete blockage was attained. Response of a 2nd afferent to angular whole-body rotation is shown after the canal was completely plugged in the bottom series of panels (C and D) for 4 different frequencies as indicated in the columns. B: angular velocity (°/s); upward movement of the trace corresponds to the right-hand-rule about an axis perpendicular to the HC running in the ventral, excitatory, direction. C: firing rate of the afferent (spikes/s). D: phase histogram showing the cycle averaged afferent firing rate (solid, cityscape histograms), the 1st-harmonic fit (solid sinusoidal curve), and the angular stimulus velocity (dashed sinusoidal curves). For this afferent, the phase of the peak response aligns closely with angular jerk and shows marked increases in gain (spikes/s per °/s) with increasing frequency (from left to right).

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.

View larger version (21K): [in this window] [in a new window]   Fig. 3. Individual afferent responses in the control and occluded conditions. The gain (A; spikes/s per °/s) and phase with respect to head velocity (B; °) of 2 representative afferents from the same fish are shown; one before plugging (+, - - -), and a second in the plugged condition (o, ). Polynomial fits provided to illustrate trends in the data. Note the highly advanced phase and large gain exponent (slope) in the plugged condition (). Such responses () are not present in the control afferent population.

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).

View larger version (27K): [in this window] [in a new window]   Fig. 4. Summary of afferent responses in the control and occluded conditions. Number of afferent records (A), the average gain (B; spikes/s per °/s) and average phase (C; °) are shown before plugging in the control condition (thin solid curves) and after plugging in the occluded condition (thick solid curves) in the same animals. Vertical bars indicate 1 SD resulting from interafferent variability in response dynamics. Application of the elastohydrodynamic model to the unoccluded data (thin curves) shows how the control population would be predicted to respond if recorded after occlusion of the endolymphatic duct (dashed curves in B and C).

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 deflectionthe 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.

View larger version (23K): [in this window] [in a new window]   Fig. 5. Afferent responses to 1-Hz mechanical indentation of the horizontal canal (A; spikes/s) and the utricle (B; spikes/s) in the plugged condition. Solid curves represent indentation stimuli; · · ·, firing rate. Locations of the mechanical stimulators are indicated in Fig. 1. It is significant to note that afferents continue to respond, and robustly for particularly sensitive afferents, to indentation of the utricle (B) even after the HC duct has been completely blocked.

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.

View larger version (23K): [in this window] [in a new window]   Fig. 6. Predicted attenuation caused by canal plugging. Mechanical attenuation (A; nondimensional) and phase shift (B; ° re: control condition) predicted to be caused by plugging was determined by dividing the cupular displacement in the plugged condition by that predicted in the control condition. Model results are in the form of Bode plots. Phase >0 corresponds to a lead caused by plugging, and attenuation factor <1 corresponds to a loss in sensitivity. Model predictions are shown for the toadfish (solid curves), human (thick long dashed curves), and squirrel monkey (thick short dashed curves) for the acute conditions employed in the present study (I, plugged endolymphatic duct and surgically opened perilymphatic space). All 3 species were predicted to respond similarly in the surgically opened acute condition. Thin curves for the primates are for a hypothetical condition (II) where the osseous canal was completely plugged and the perilymphatic space was sealed completely.

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).

View larger version (23K): [in this window] [in a new window]   Fig. 7. Predicted transmembrane pressure distribution at 5.7 Hz for the fish. Model results are shown for the control condition (left) and for the acute plugged condition (right). Location of the plug is indicated by the green circle. For sinusoidal stimuli, the pressure varies sinusoidally about an average of 0. Colors denote the magnitude of pressure ranging from white (peak negative pressure) and orange (0) to black (peak positive pressure). Five instants in time are shown covering one-half of the rotational stimulus cycle (A, time of peak angular head acceleration; C, peak velocity; E, peak displacement). Time increases from top to bottom. Streamwise endolymphatic displacement profiles at 6 different locations in the duct are indicated by the red solid curves surrounding the outline of each canal. Fluid displacement amplitudes are highly exaggerated and normalized relative to peak cupular displacement for the purpose of illustration. Note that the endolymph displacement is predicted to be 0 at the position of the plug but relatively large in the ampulla. Results shown are for rotation about the center of the HC.

View larger version (24K): [in this window] [in a new window]   Fig. 8. Pressure distributions at 5.7 Hz for the fish (A and B) and the human (C and D). Endolymphatic pressure (thin solid curves), perilymphatic pressure (thin short dashed curves), and transmembrane (endolymphatic minus perilymphatic pressure, thick solid curves) are shown in the plugged condition as functions of distance from the crista along the curved centerline. Location of the plug is indicated by an arrow. Transmembrane pressures (thick dashed curve) are shown in the control condition. Curves are in the form of amplitude (A and C) and phase (B and D) as functions of distance from the sensory epithelium along the curved centerline of the canal. At each spatial location, pressures were predicted to vary sinusoidally with the indicated amplitude and phase (re: angular velocity).

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.

DEGREE 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.

View larger version (23K): [in this window] [in a new window]   Fig. 9. Influence of the extent of endolymphatic duct blockage. Model predicts that the effectiveness of canal plugging is highly sensitive to the fraction of the endolymphatic duct blocked. Figure shows the cupular attenuation (A) and phase shift (B) predicted to be caused reducing the membranous duct cross-sectional area in the fish HC model by 50-100% as indicated.

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.

View larger version (21K): [in this window] [in a new window]   Fig. 10. Influence of membranous duct stiffness. Predicted changes in attenuation (A) and phase (B) caused by altering the stiffness of the fish membranous labyrinth by 1 order of magnitude up (long dashed curves) and 1 order of magnitude down (dotted curves). Two intermediate levels also are shown. Labyrinthine stiffness may show significant intersubject and interspecies variations and hence the influence of plugging on canal afferent responses may be quite variable. Stiffness used to obtain the thick solid line was optimized to fit the present average data (Fig. 4).

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 10⁸ 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/cm²a 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.

View larger version (22K): [in this window] [in a new window]   Fig. 11. Influence of cochlea/middle-ear stiffness. Primate model predictions were sensitive to the overall stiffness of the vestibule as influenced by the connection to the middle ear and/or any compromise of the temporal bone associated with the surgical procedure. Predicted changes in the cupular attenuation (A) and phase (B) caused by altering the stiffness by 2 orders of magnitude up (thin solid curves) and 2 orders of magnitude down (dotted curves) are shown for the human model. Note that plugging was predicted to become much less effective in attenuating canal responses if the stiffness of the bony cavity is compromised.

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 spacea 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.

View larger version (20K): [in this window] [in a new window]   Fig. 12. Sensitivity to eccentricity of rotation. The cupular attenuation (A) and phase shift (B) caused by canal plugging were predicted to depend on the axis of rotation owing to linear acceleration sensitivity. Predictions are shown for rotations about the neck (thick solid curves), ipsilateral canal (thin solid curves), nasal offset (dotted curves), occipital offset (dashed curves), and contralateral canal (dot-dashed curves) in the human model.

	DISCUSSION OF PLUGGED CANAL AFFERENT RESPONSES

TOP ABSTRACT INTRODUCTION EXPERIMENTAL RESULTS DISCUSSION OF PLUGGED CANAL... APPENDIX REFERENCES

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 pressurein 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