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Imaging Electrically Evoked Micromechanical Motion within the Organ of Corti of the Excised Gerbil Cochlea

K. Domenica Karavitaki ^*  and David C. Mountain   

^* Harvard-Massachusetts Institute of Technology, Division of Health Sciences and Technology, Speech and Hearing Bioscience and Technology Program, Massachusetts Institute of Technology, Cambridge, Massachusetts; and Hearing Research Center, Department of Biomedical Engineering, and Department of Otolaryngology, Boston University, Boston, Massachusetts

Correspondence: Address reprint requests to K. Domenica Karavitaki, Harvard Medical School, Department of Neurobiology, 220 Longwood Ave., Goldenson 443, Boston, MA 02115. Tel.: 617-432 2479; Fax: 617-432-2508; E-mail: domenica{at}alum.mit.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX A: THE EFFECT... APPENDIX B: COCHLEAR... SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
The outer hair cell (OHC) of the mammalian inner ear exhibits an unusual form of somatic motility that can follow membrane-potential changes at acoustic frequencies. The cellular forces that produce this motility are believed to amplify the motion of the cochlear partition, thereby playing a key role in increasing hearing sensitivity. To better understand the role of OHC somatic motility in cochlear micromechanics, we developed an excised cochlea preparation to visualize simultaneously the electrically-evoked motion of hundreds of cells within the organ of Corti (OC). The motion was captured using stroboscopic video microscopy and quantified using cross-correlation techniques. The OC motion at 2–6 octaves below the characteristic frequency of the region was complex: OHC, Deiter's cell, and Hensen's cell motion were hundreds of times larger than the tectorial membrane, reticular lamina (RL), and pillar cell motion; the inner rows of OHCs moved antiphasic to the outer row; OHCs pivoted about the RL; and Hensen's cells followed the motion of the outer row of OHCs. Our results suggest that the effective stimulus to the inner hair cell hair bundles results not from a simple OC lever action, as assumed by classical models, but by a complex internal motion coupled to the RL.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX A: THE EFFECT... APPENDIX B: COCHLEAR... SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Gold, in 1948 (1), was the first to hypothesize that cochlear tuning and sensitivity were the result of a feedback system. In this system, in-phase correspondence between the feedback force and the basilar membrane (BM) velocity would lead to an enhancement of the cochlear tuning by canceling the viscous forces acting on the BM. It is currently hypothesized that voltage-dependent OHC length changes function as a key component of this feedback system.

OHCs are one of the major types of cochlear sensory cells located in the organ of Corti (OC) of the inner ear. Evidence for direct involvement of OHCs in cochlear function came with the observation that eliminating the OHCs and leaving the rest of the OC intact leads to a significant loss of sensitivity (2–4). Stimulation of cochlear efferents, which terminate mostly on OHCs, altered the production of distortion-product emissions (5) and tuning of inner hair cells (IHCs) (6). The discovery of electrically-evoked otoacoustic emissions (7) and of voltage-dependent length changes in isolated OHCs (8,9) provided more evidence for the active role of OHCs in cochlear function. Recently, OHC electromotility has been attributed to the voltage-sensitive motor protein prestin (10). Prestin-mutant mice have a 40- to 60-dB hearing loss and lack OHC somatic motility in vitro (11), further supporting the idea of OHCs as key players in cochlear amplification.

There is currently little understanding on how OHC length changes affect the vibration characteristics of the cochlear partition and contribute to cochlear tuning. The intricate anatomy of the OC and the diverse mechanical properties of the cellular components (see, e.g., Olson and Mountain (12,13), Naidu and Mountain (14), and Scherer and Gummer (15)) suggest that the OC vibration pattern can be complex. Moreover, both the anatomy and the mechanical properties of individual cells in the OC change along the length of the cochlea. Therefore, to understand the micromechanical motion of the OC in response to OHC length changes, measurements have to be made at multiple positions within the organ and along the cochlea for multiple stimulus conditions.

To investigate OC mechanics, most researchers have made measurements across the BM (16–22), or the reticular lamina (RL) and/or the tectorial membrane (TM) (17,22–30). Some of this work is reviewed by Ulfendahl (31) and Robles and Ruggero (32). Little information is available on the internal micromechanical motion of the OC due to OHC contractions. Measurement of this internal motion is important to our understanding of the mechanical role of OHC somatic motility but has been a challenge because the internal structure of the OC is not optically accessible. Few attempts have been made to make such internal OC measurements. Richter et al. (33), Hu et al. (25), and Cai et al. (34) used a hemicochlea preparation which allowed visualization of the radial profile of the OC, and reported that the vibration pattern is complex. Fridberger et al. (35) used an excised cochlea preparation combined with confocal microscopy to reconstruct the radial deformation of the OC. In response to static pressure changes, the authors reported a complex deformation pattern in the apical turn of the guinea pig cochlea. These studies, however, did not isolate the effect of OHC somatic motility on OC motion, and the data were limited to one radial location.

In this study, we wanted to quantify the internal micromechanical motion of the OC due to OHC contractions in a semi-intact cochlea preparation. We developed an excised cochlea preparation that allowed us to image, in the same cochlear preparation, the responses of hundreds of cells located at many radial locations and multiple focal levels, starting at the TM level and moving down to the BM level, at 2-µm intervals. We present data from the apical and middle turns for low-stimulus frequencies, because at these frequencies the observed motions were larger and easier to quantify. Using our system, we have been able to collect data (not included here) up to 9 kHz for selected cells within the OC (36,37). For the work presented here, the term "low frequency" refers to frequencies 2–6 octaves below the characteristic frequency (CF) of the measurement location. Stimulus frequency and CF are indicated in the figures as needed. The CF of our measurement locations was estimated using the place-frequency map of the gerbil cochlea (38) and ranged from 0.4 to 4 kHz. We show that in response to electrically-evoked OHC contractions, the motion of the OC at low frequencies is complex, and is qualitatively similar in both the apical and middle turns of the gerbil cochlea. We also show, using a simple electroanatomical model of the cochlea, that the magnitude of OHC length change in this study is similar to that observed in isolated OHC studies.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX A: THE EFFECT... APPENDIX B: COCHLEAR... SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Surgical preparation of gerbil cochleae
Young female Mongolian gerbils were decapitated after being anesthetized (no paw-withdrawal reflex and no corneal reflex) with an intraperitoneal injection of sodium pentobarbital (60 mg/kg, Steris Laboratories, Phoenix, AZ) or using a mixture of ketamine (160 mg/kg, Fort Dodge Animal Health, Fort Dodge, IA) and xylazine (8 mg/kg, Bayer, Shawnee Mission, KS). The procedures followed an institutionally approved protocol with guidelines provided by the Laboratory Animal Care Facility at Boston University. All chemicals were purchased from Sigma Chemicals (St. Louis, MO) unless noted otherwise. Both temporal bones were excised, and muscular and brain tissue was removed. After opening the bulla, the bones were immersed in oxygenated culture medium (Leibovitz L-15) supplemented with 5 mM D-glucose. The pH of the solution was adjusted to 7.3 at the beginning of each experiment using NaHCO₃ (J.T. Baker Chemical Company, Phillipsburg, NJ). In later experiments, the medium was a Cl^–-modified perilymph-like solution composed of 140 mM D-gluconic acid, 6.6 mM NaCl, 100 µM CaCl₂, 3 mM KCl, 5 mM NaH₂PO₄, 100 µM MgCl₂, 5 mM D-glucose, and 5 mM HEPES (298 mOsm, pH 7.3, adjusted using 1 M NaOH). Both solutions were at room temperature (18°C) during the experiment. The later solution was formulated to improve the condition of the preparation and the viability of the cells. Using this solution, we were able to reliably collect data for a maximum of 9 h after decapitation.

The next step in the surgical procedure was to transfer the immersed bone under a dissecting scope (AO570, American Optical, Buffalo, NY) and remove the tympanic membrane, the malleus, the incus, and part of the semicircular canals. Most of the temporal bone was left intact and was used to hold the cochlea. We then exposed the turn of interest without damaging Reissner's membrane, and removed as much of the bone surrounding the scala tympani of the lower turn as necessary to establish a better optical path.

For experiments in the apical (low-frequency) turn, the round window membrane was removed along with most of the bone surrounding the basal (high-frequency) turn. This allowed access to the modiolus between the basal and middle turns. The modiolus was then cut with a pair of forceps and the basal turn was removed along with the bone of the scala tympani and sometimes the scala media (SM) of the middle turn. Next, a hole was made with a sharp pick at the very tip of the apical turn. Using the band of stria vascularis as a guide, the bone covering the scala vestibuli (SV) was removed using a thin pair of forceps, and the apical turn was exposed. This procedure ensured that the SM remained intact.

For experiments in the middle turn, the basal turn of the cochlea was removed and a hole was made in the apical turn as before. Using a thin pair of forceps, the apical turn was completely removed and the bone covering the SV of the middle turn was carefully peeled away. As mentioned previously, this procedure ensured that the SM was anatomically preserved (Fig. 1). The average time for the surgical procedure after decapitation was 20 min.

View larger version (40K): [in this window] [in a new window]   FIGURE 1  Midmodiolar cross section of a gerbil cochlea (slide provided by J. C. Adams, Harvard Medical School, 2000) to illustrate our middle-turn preparation. The apical and basal turns have been removed and a small opening has been made in the SV above the region of interest. Note that Reissner's membrane is intact and therefore the anatomical architecture of the entire turn is preserved. Also shown is the relative electrode placement for the electrical stimulation paradigm.

View larger version (64K): [in this window] [in a new window]   FIGURE 2  Low-magnification surface view of our excised cochlea preparation. This is a middle turn preparation of a left cochlea and it spirals clockwise toward the apex. Notice that the entire turn of interest is present. The arrow points to the opening of the SV above the region of interest. The opening is outlined for clarity.

View larger version (80K): [in this window] [in a new window]   FIGURE 3  High-magnification surface views of our excised cochlea preparation. All views are from the same cochlea location and were acquired by focusing the objective at different depths of the OC. (A) Tectorial membrane (TM) level. Arrows point to the TM radial fibers and the edge of the TM (TM_edge). (B) Cuticular plate level. Arrows point to the IHC (IHC_s) and OHC1 (OHC1_s) hair bundles. (C) OHC-basal-end level. Arrows point to the outer pillar cells (OPC), first through third rows of OHCs (OHC1, OHC2, and OHC3, respectively), and Hensen's cells (HC). (D) Basilar membrane level. Arrows point to the arcuate zone of the BM (BM_AZ), the radial fibers of the pectinate zone of the BM (BM_PZ), and the edge of the HC (HC_edge).

The stimuli were sine waves with frequencies from 30 to 120 Hz. Movements synchronized to the stimulus frequency were captured using stroboscopic illumination. A custom-made current source was used to deliver current pulses of 200-mA peak to a light-emitting diode (AND190AYP, Purdy Electronics, Sunnyvale, CA) emitting more than 50 Cd at a 4° viewing angle. The light-emitting diode was mounted on a holder designed to replace the light source of the microscope. The input pulses to the strobe system were generated using the Tucker-Davis Technologies system. The pulses occurred at fixed phases within the period of the stimulus, with duration equal to 10% of the stimulus period.

Data were collected for eight equally spaced, randomized phases and for two conditions: 1), with the stimulating current present, and 2), with the stimulating current turned off, referred to as the "no-stimulus condition". The no-stimulus condition gave us an estimate of the magnitude of the minimum resolvable motion of our system and also verified that the motions observed were due to the current being present. For each stimulus period, pulses occurred only at one particular phase. Thus, to collect data from eight phases, the same frequency was played eight times. For each frequency-phase combination the stimulus was on for 1 s to provide enough images for subsequent averaging. Typically, we used a 16-frame average. The video frames of interest were subsequently digitized and animations of the observed motion were created by playing the images from each phase in succession.

Voltage measurements
To quantify the voltage drop in the fluid between our stimulating electrodes, we performed voltage measurements using glass pipettes filled with 3 M NaCl, which had the same inner diameter as the current electrodes (300 µm). The ground-voltage electrode was placed next to the return-current electrode. The active-voltage electrode was placed first next to the input-current electrode and then was sequentially moved to locations away from the input-current electrode. The voltage electrodes were connected to a direct current-coupled differential amplifier (Tektronix, Richardson, TX). The output of the amplifier was connected to an analog to digital interface (AD2, Tucker-Davis Technologies) used to store the resulting waveforms.

The voltage measurements were performed using a current stimulus of 1 mA at five frequencies: 60 Hz, 120 Hz, 450 Hz, 810 Hz, and 1200 Hz. Measurements at higher frequencies (>1200 Hz) were not practical due to contamination from capacitive coupling between the electrodes.

Image processing and motion estimation
Electrically evoked motion was estimated using two-dimensional (2D) cross-correlation. In traditional signal processing, cross-correlation is performed to obtain a measure of similarity between two signals f₁(t) and f₂(t) as a function of a scanning parameter . This parameter is usually the time shift of one signal with respect to the other. An important application of cross-correlation in image processing is in the area of template matching, where the goal is to find the closest match between an unknown image and a set of known images (39). The scanning parameter in this case is the spatial shift of one image with respect to the other. Since we are interested in 2D discrete images, the spatial shift applies for any combination of x (radial dimension) and y (longitudinal dimension) on the image plane. For the discrete 2D case the cross correlation of two images f(x,y) and g(x,y) is given by

(1)

for x = 0,1,2,..., M – 1 and y = 0,1,2,..., N – 1. The symbols M, N refer to the image's radial and longitudinal dimensions, respectively. The following cross correlation theorem,

(2)

holds for u=0,1,2,..., M – 1 and v = 0,1,2,..., N – 1. The functions F, G are the frequency domain representations of f, g. The theorem states that the cross-correlation of two images in the spatial frequency domain is the result of a simple multiplication of their spatial Fourier transforms. The asterisk indicates that the complex conjugate of the function is taken. Cross-correlation functions computed with fast Fourier transforms (FFTs) are often referred to as circular cross-correlation functions, since the FFT treats the image as though it represents a periodic pattern. As a result, the computed cross-correlation is periodic. Since the motions in our experiments were small compared to the extraction size, the largest peak near the origin was chosen for the displacement estimate. If the displacement was larger than half the image size, then the peak was wrapped around to the origin and the phase adjusted accordingly.

Cross-correlation was used to estimate radial and longitudinal displacements, and it is demonstrated in Fig. 4 for the one-dimensional case. In this method, two images taken under different conditions are considered at a time. In our case, one of those images is the one taken at the no-stimulus condition of a particular phase and is considered as the reference image. The other image is the one taken at the phase corresponding to the no-stimulus condition. Cross-correlation between the two images was performed by first extracting a portion of the image containing a feature of interest like the edge of a hair cell (Fig. 4 A). The same portion was extracted from an image taken at a different stimulus phase. (Fig. 4, B–D).

View larger version (41K): [in this window] [in a new window]   FIGURE 4  (A) High-magnification surface view of the OC captured with our video stroboscopy system at one particular phase of the stimulus (exp. 131). Several structures of interest are shown: the basal end of IHCs, the head of the pillar cells (PC), the three rows of OHCs, and the area of the HC. In all our images, the radial dimension is from spiral lamina to spiral ligament and the longitudinal dimension from base to apex. Radial motions toward the spiral ligament and longitudinal motions toward the base are positive by convention. To estimate these motions, a portion of the image containing a feature of interest like the edge of a hair cell was extracted from each of the eight phases and the corresponding no-stimulus conditions. For simplicity, we present the analysis for three time points. (B–D) Shown are three time frames of the edge of an OHC. Each panel is a matrix of 16 x 16 pixels (432-nm resolution). For illustration purposes, the analysis is shown for one row of pixels (illustrated in each time frame), but during motion estimation the analysis is done for the entire extracted image. (E–G) The intensity of each pixel across one row is plotted as a function of radial position (solid squares). Note that the shape of the intensity profile could be similar (but not identical) from one time frame to the next but shifted with respect to the radial position. The next step was to quantify this shift. Because the motion of interest was usually less than a pixel, interpolation was used (solid circles between squares). The resulting images had a resolution of 27 nm/pixel. (H and I) Cross-correlation computed with fast Fourier transforms was used to quantify the shift that yields the best fit between two images. For the curves shown in E and F, the best fit was at a shift of 320 nm toward the left and for the curves in E and G, the best fit was at a shift of 260 nm toward the right. (J) Cross-correlation was repeated for all the stimulus phases to derive the time waveform of the displacement shown by the squares. Fourier analysis was then performed on the time waveform and from the fundamental component we estimated the peak amplitude and phase of motion for each stimulus frequency.

(3)

(4)

where S_x refers to the kernel applied in the radial direction, and S_y to the kernel applied in the longitudinal direction. These kernels are also known as Sobel operators (39) and were chosen over other gradient operators because they can detect edges while also having a smoothing effect, therefore reducing additional noise introduced by high-pass filtering the images. Both kernels operated on a pixel-by-pixel basis.

Because the motion of interest was usually less than our pixel size, the next step was to interpolate the extracted images. For simplicity, we outline our methodology for the one-dimensional case (for example, the radial dimension). A detailed analysis of this procedure is given in Oppenheim and Schafer (40). Our objective was to up-sample the image I[m] to I_i[m] as given by

(5)

where I_i[m] is the interpolated version of I[m], L is the interpolation factor, and M is the radial length of the image. One way to derive I_i[m] is by first using an expander on I[m] such that

(6)

where I_e[m] is the expanded version of I[m] and is the unit impulse function. I_i[m] is then obtained by low-pass filtering I_e[m] with a cutoff frequency of /L and gain equal to L. We implemented this procedure in the spatial-frequency domain. Notice that the Fourier transform of I[m] and I_e[m] is given by

(7)

From Eq. 7, we see that is a frequency-scaled version of .We therefore expanded the Fourier transform of our extracted image in the spatial-frequency domain by appending zeros to expand it to the desired interpolation size. We then calculated the inverse Fourier transform of the image to obtain the interpolated version of our original image. Notice that in our analysis our images are band limited; therefore, the form of the low-pass filter is rectangular. Such a filter is ideal, since the amount of distortion in the added samples is zero. We used a 16x interpolation factor and with that, our final pixel resolution was 27 nm. The resulting interpolated intensity profiles for the images shown in Fig. 4, B–D, are shown in Fig. 4, E–G (solid circles between squares) (here, the interpolation factor is limited to 4x for visualization purposes).

Once the extracted images were interpolated, the cross-correlation between two images was computed using FFTs. The location of the cross-correlation peak, with respect to the origin, gave us an estimate of the magnitude and direction of motion between the original images (Fig. 4, H and I). This procedure was then repeated for all the stimulus phases to derive the time waveform of the motion (Fig. 4 J).

Fourier analysis was then performed on the time series to estimate the peak magnitude and the phase of motion for each frequency. Specifically we used the complex exponential Fourier series (41) to reconstruct the time waveform, as given by

(8)

where N is the number of samples per period, n is the harmonic number, k is the discrete increment of time, i.e., t = kT, where T is the sampling interval, and finally

(9)

We then computed the magnitude and the phase of motion of the fundament (n = 1) by

(10)

Conventional Fourier analysis references phase to a cosine; we therefore added 90° to our motion-phase data to reference them to our sine wave stimuli. From this 2D analysis, we were able to estimate motion in two directions. The first was the radial direction (referring to the axis running from spiral lamina to spiral ligament) and the second was the longitudinal direction (referring to the axis running along the OC from base to apex). By convention, positive displacements are toward the spiral ligament in the radial direction, and toward the base in the longitudinal direction (Fig. 4 A).

There are several implicit assumptions in our method for motion estimation: 1), the motion is much smaller than the analysis window; 2), the motion is periodic, with frequency equal to the stimulus frequency; and 3), changes in the shape of the region of interest (ROI) are smaller than the displacement of that region.

Estimation of noise
Several factors contributed to variability in our measurements. One was functional differences between the cells related to the physiological state of each cell. Functional differences might show up as differences in the amplitude and phase of motion between individual cells. Another factor was low-frequency vibration and drift in the cochlear holder. Finally, another source of variability was noise within the images.

To estimate the noise in our measurements, we assumed that the measured response was the vectorial sum of a sinusoidal signal with fixed amplitude and phase plus a noise with fixed amplitude but random phase (Fig. 5 A). The presence of noise will affect both the magnitude and the phase of the measured response. In our experiments, the magnitude of the response across cells exhibited more variability than the phase. We believe that this is due to the cells differing in their absolute sensitivity (i.e., being frequency-independent), which would affect the magnitude but not the phase. We therefore decided to consider the effect of noise on just the phase of the measured response.

View larger version (10K): [in this window] [in a new window]   FIGURE 5  Estimation of the SNR from the standard deviation of the phase of our measured response. (A) The measured response is the vectorial sum of the signal (S) and a randomly varying noise (N). The magnitude and the phase () of the measured response depend on the phase of the noise (). (B) Standard deviation of (s) as a function of SNR.

(11)

where is the phase of the noise and SNR is defined as the signal²/noise². We solved Eq. 11 numerically for uniformly distributed from – to + and for the SNR ranging from 1 to 10 and estimated the standard deviation of as a function of the SNR. The results of this calculation are plotted in Fig. 5 B. Note that when the SNR is <1, the measured responses are below the noise level and the standard deviation of the phase is >52°.

Therefore, to estimate the noise in our experiments, we calculated the standard deviation of the phase of the displacements across multiple cells as a function of stimulus level or frequency. We then recorded the corresponding magnitude of the displacements where the standard deviation of the phase was >52° and set the noise level to be equal to that displacement. In general, the noise level ranged from 10 to 100 nm peak-to-peak. In our motion measurements, the noise level was different across experiments and cell structures. It is important to note that the conclusions of this work do not rely on measurements near the noise level.

Alternative methods of estimating the SNR would have been to compare the stimulus-frequency response to "sidebands" or to collect matching data sets with the stimulus turned off. Since our technique only sampled one period of the response, all Fourier components (other than direct current) are harmonics of the stimulus and are potentially nonlinear responses to the stimulus. In other words, we have no sidebands in the Fourier transform. We did not use the approach of using matching data sets with the stimulus turned off, because this would have doubled our data collection time and we felt that it was important to collect the data from multiple focal planes as quickly as possible to prevent artifacts due to drift in the position of the preparation or in the condition of the cells.

Control experiments
Electrical stimulation
At the beginning of each experiment, after positioning the electrodes, a test stimulus was presented at a frequency of 120 Hz with the strobe flashing at 126 Hz. If the electrodes were positioned correctly and the preparation was in good condition, we observed a 6-Hz motion. If no response was observed within the 0.5–4 mA stimulus range, then the electrodes were repositioned and the test stimulus repeated. The level of the stimulus was kept to a minimum (i.e., displacements were just visually detectable) to avoid overstimulation of the tissue.

Motion artifacts
During data collection, low-frequency building vibrations and drift in the cochlear holder introduced mechanical noise in our measurements. The impact of drift was minimized by collecting a no-stimulus condition before each stimulus phase. Cross-correlation was then performed between the image at a particular phase and the image at the corresponding no-stimulus condition. This control also verified that the motions observed were due to the applied current. In addition, cross correlation was performed among the no-stimulus-condition images to quantify any mechanical drift.

Frame grabber and image processing algorithm
The following experiment was designed to test whether the frame grabber captured the correct frames and whether the motion estimation algorithm gave accurate results. A piezoelectric probe (12) was used to produce a known sinusoidal displacement magnitude for frequencies ranging from 30 Hz to 3 kHz. Images of the force probe were collected using our stroboscopic system. The displacement of the probe was then estimated from these images using our cross-correlation technique. The displacement of the probe was also measured using a motion transducer system (Angstrom Resolver Model 201, Opto Acoustic Sensors, Raleigh, NC), and the results were compared with the displacements obtained using our motion estimation algorithm. The magnitude results were within 1.5 dB and the phase results were within 15° for frequencies between 30 and 2 kHz. Above this frequency range, the response of the force probe was not reliable due to its own resonance.

Anatomical orientation
Typically, at the end of each experiment, images were collected at multiple focal levels to establish the anatomical orientation of our excised cochlea preparation with respect to our imaging plane (I_p). To interpret our motion estimation results, it was important to know the anatomical orientation of our preparation for each experiment. In Fig. 6, we show cartoons of the radial and longitudinal view of the OC and identify the angles of interest that will be used in the analysis of our results. The long axis of the OHCs is oriented at an oblique angle with respect to the RL in both the radial direction (_R) and the longitudinal direction (_L). Because the I_p is not always parallel to the RL, an additional angle is introduced between the I_p and the RL (ß_R for the radial direction, ß_L for the longitudinal direction) and between the I_p and the long axis of the OHC (_R for the radial direction, _L for the longitudinal direction). By convention, when (in the radial direction) the spiral ligament or (in the longitudinal direction) the apical end of the I_p is below the RL (as shown in Fig. 6), then the angle ß is negative. The relationship between the angles is

(12)

View larger version (26K): [in this window] [in a new window]   FIGURE 6  Anatomical cartoons showing the radial and longitudinal views of the OC. Also, shown are possible orientations of our imaging plane (Ip) to illustrate the different angles that are important for understanding the motion estimation results from our surface views. In the radial and longitudinal directions, respectively, R and L indicate the angle between the long axis of the OHCs and the RL; ßR and ßL the angle between the Ip and RL; and R and L the angle between the Ip and the long axis of the OHCs.

(13)

and

(14)

A histogram of all the angles was plotted and the mode of the histograms was chosen as our estimate of _R, _L.

To estimate ß_R, ß_L, we used our multiple focal level images and identified those focal depths where key structures such as the hair bundles of the IHCs and OHCs first came into focus. We assumed that when the I_p is parallel to the RL in the radial dimension, we would see the IHC and OHC hair bundles in focus at the same time. Similarly, when the I_p is parallel to the RL in the longitudinal dimension, we would see the entire row of a given structure in our field of view (e.g., the entire row of IHC hair bundles) in focus at the same time. For example, in Fig. 4 A, notice that the three rows of OHCs are all in focus at the same time for both the radial and longitudinal directions. In addition, for this experiment, when we focused at the level of the stereocilia they were all in focus at the same time. This means that the I_p is parallel to the RL in both the radial and longitudinal dimensions. The next step in estimating ß_R, ß_L was to measure the vertical distance (H) between the focal levels at which the identified structures came into focus and the radial (R) or longitudinal (L) distance between those structures. Using these distances, ß_R, ß_L were calculated by

(15)

and

(16)

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX A: THE EFFECT... APPENDIX B: COCHLEAR... SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Voltage measurements in SV
Fig. 7 shows the voltage in the fluid as a function of longitudinal distance from the input-current electrode, for an apical-turn experiment. The input current was 1 mA. We were not able to measure the voltage closer than 300 µm from the input-current electrode due to the large tip diameter of the electrodes. Therefore, in Fig. 7, although the input-current electrode was at 0 µm, the first voltage measurement was 300 µm away. For any given frequency, the voltage decreased as we moved away from the input-current electrode. The decrease was similar for all frequencies tested (i.e., 60, 120, 450, 810, and 1200 Hz). In Fig. 7, we plot the average voltage and corresponding standard deviation for all frequencies. As the distance from the input-current electrode increased, the standard deviation of the voltage at that location also increased.

View larger version (8K): [in this window] [in a new window]   FIGURE 7  Voltage in the fluid between the input- and ground-current electrode as a function of longitudinal distance from the input-current electrode, for an apical turn experiment. Each point represents the average voltage of the frequencies tested (i.e., 60, 120, 450, 810, and 1200 Hz) using a 1-mA current stimulus. The vertical lines above and below each point are the average value ± 1 SD. The line is the resulting exponential fit using Eq. 17.

(17)

where V is the voltage, C is a constant, y is the longitudinal distance from the input current electrode, and is the space constant describing the rate at which the voltage decreases with longitudinal distance from the input-current electrode. For the fit shown in Fig. 7, C = 2.8 V and = 150 µm. The space constant indicates that the voltage will drop to 37% of its maximum value at 150 µm away from the input source.

Effect of current level on OHC displacement
In Fig. 8, we show the magnitude and phase of radial displacements, as a function of stimulus level, for two OHCs. The magnitude of the second and third harmonics was >40 dB below the primary component at all frequencies and stimulus levels. The response magnitude of OHCs increased as the stimulus current increased. At low stimulus levels (when the motion of the cells could just be detected visually), the responses increased linearly with current. As the stimulus level increased further, the responses saturated and, at very high stimulus levels, decreased. The phase of the responses remained constant for all stimulus levels. The radial motion of the first row of OHCs (OHC1) was 180° out of phase with the motion of the third row (OHC3). This phase difference was observed in all of our experiments and will be further addressed in the following sections.

View larger version (9K): [in this window] [in a new window]   FIGURE 8  Peak-to-peak magnitude and phase of radial displacements as a function of stimulus current. The stimulus frequency was 120 Hz. Dotted line has unity slope. (A and C) Responses from an apical turn OHC1 (OHC1b, exp. 615). (B and D) Responses from a middle-turn OHC3 (OHC3a, exp. 614). Note that the current axis ranges from 1 to 10 mA in A and C, and from 0.1 to 10 mA in B and D. Repeated measurements (25 min later, open circles) were used to evaluate the effect of time on OHC responses.

Finally, note that the current levels used are different for the two cells shown in Fig. 8. In our preparation, the minimum current needed to evoke detectable OHC motion depended on two factors. The first was the exact position of the input-current electrode with respect to the OHCs of the imaging location, and the second was the condition of the preparation. If the input electrode was close to the SV of the imaging location and the preparation was in good condition, the amount of current needed to stimulate the OHCs was small. A preparation was considered to be in good condition when the cells were not swollen and responses of adjacent cells in the same row were in phase. Also note that in all of the preparations used for data collection the TM was intact and extended above the OC as expected in vivo (Fig. 3, A and B; also see Discussion). Typically, the stimulus currents ranged from 0.1 to 4 mA, and for that range of currents, displacements up to 2 µm were in the linear regime.

Anatomical measurements
Figs. 8 and 9 illustrate results from two (one apical- and one middle-turn) of the four (two apical- and two middle-turn) experiments in which we estimated _R, _L, ß_R, and ß_L. The calculation of these angles was described in Methods. Fig. 9, A and B, shows the apparent radial position of individual OHC1, second row of OHC (OHC2), and OHC3 as a function of focal depth. As we focused from the RL toward the BM level, the radial position of all structures shifted toward the spiral ligament. Fig. 9, C and D, shows the histograms of _R, which correspond to the apical- and middle-turn experiment shown in Fig. 9, A and B, respectively. The average _R for each turn was taken to be the mode of the distribution shown in the histograms. For the experiments shown, _R = 83° in the apical turn and 85° in the middle turn. Finally, for these experiments, ß_R = –9° in the apical-turn and +14° in the middle-turn experiment.

View larger version (17K): [in this window] [in a new window]   FIGURE 9  Measurements to estimate R in the apex (exp. 1008, CF 0.4 kHz) and middle turn (exp. 1011, CF 4 kHz). (A and B) Peak radial displacement of individual OHCs from each of the three rows as a function of depth from the RL to the BM. The displacements are positive, indicating that as we focused lower into the organ the cells shifted toward the spiral ligament. Due to the large longitudinal tilt in this experiment, the cells came into focus at different focal levels, and hence the extractions do not all start from the same focal level. In general, extractions from the middle-turn experiments span fewer levels, since the OHCs in this turn are shorter than those from the apical turn. (C and D) Histogram of the angles calculated from A and B (see text).

View larger version (16K): [in this window] [in a new window]   FIGURE 10  Measurements to estimate L in the apex (exp. 1008, CF 0.4 kHz) and middle turn (exp. 1011, CF 3 kHz). (A and B) Peak longitudinal displacement of individual OHCs from each of the three rows as a function of depth from the RL to the BM. The displacements are negative, indicating that as we focused lower into the organ the cells shifted toward the apex. Due to the large longitudinal tilt in this experiment, the cells came into focus at different focal levels, and hence the extractions do not all start from the same focal level. In general, extractions from the middle-turn experiments span fewer levels, since the OHCs in this turn are shorter than those from the apical turn. (C and D) Histogram of the angles calculated from A and B (see text).

Apparent diameter changes
For most of our experiments, we were able to analyze motion for either the spiral-lamina (referring to the side of the cell toward the spiral lamina) or the spiral-ligament (the side toward the spiral ligament) side of a cell. For example, in Fig. 4 A, the structure of interest is the lamina side of the cell. To maximize the SNR, we analyzed the motion of the side of the cell with the greatest contrast. For some experiments, we were able to analyze both sides of the cell for all three rows of OHCs.

In Fig. 11, we show results from a middle-turn experiment where we were able to estimate the radial displacements from both the lamina (R_lam) and ligament (R_lig) edges of individual cells from each of the three rows. We plot the absolute difference (apparent diameter change) between motions of the two edges (R) as a function of the mean displacement (R_mean). Each point in the graph corresponds to a different cell. R_mean ranged from 90 to 200 nm and R from 20 to 150 nm. For all cells, the R_lam side of the cell moved in phase with the R_lig side of the cell (not shown in Fig. 11). For OHC1 and OHC2, R_lam > R_lig, whereas for OHC3, R_lig > R_lam. Similar to our previous findings from the apical turn (42), OHC1 and OHC2 moved in phase (toward the spiral lamina) and OHC3 moved 180° out of phase with respect to the other two rows (toward the spiral ligament).

View larger version (7K): [in this window] [in a new window]   FIGURE 11  Absolute difference (diameter change) between the spiral-lamina edge of the cell and the spiral-ligament edge of the cell as a function of the average displacement of the two edges. All data points are from the same middle-turn experiment (exp. 1011, CF4 kHz). The stimulus frequency was 60 Hz.

View larger version (12K): [in this window] [in a new window]   FIGURE 12  Peak-to-peak radial (solid symbols) and longitudinal (open symbols) displacements as a function of depth relative to the RL, for four radial locations. All responses are from the middle-turn region (CF 4 kHz) from the same animal (exp. 1026). The stimulus frequency was 60 Hz. For this experiment R = 91° and L = 90°. Zero-degrees phase indicates motion toward the spiral ligament in the radial direction and toward the base in the longitudinal direction. (A and E) Magnitude and phase of OPC region displacements, with RL defined as the top of the OPC. (B and F) Magnitude and phase of OHC1 region displacements, with RL defined as the top of the OHC1 hair bundles. (C and G) Magnitude and phase of OHC3 region displacement, with RL defined as the top of the OHC3 hair bundles. (D and H) Magnitude and phase of HC region displacement, with RL defined as the top of OHC3 hair bundles.

The phase of the longitudinal component of the OC motion (Fig. 12, E–H, open symbols) was the same for all structures: during the depolarizing phase of our stimulus (OHCs contracting, see Discussion), all the structures were displaced toward the basal end of the cochlea. The phase of the radial component of the OC motion (Fig. 12, E–H, solid symbols) was more complex: during the depolarizing phase of our stimulus, the TM, OPC, OHC1, basal end of the third row of DC, and HC were displaced toward the spiral lamina, whereas the OHC3 and the adjacent HC region (up to 75 µm below the RL) were displaced toward the spiral ligament.

We also measured the responses of the edge of the TM (TM_edge), the inner pillar cell (IPC), and the IHC hair bundles. Motion of all these structures was usually near or below the noise floor of our measurements. We sometimes saw motion in the IHC hair bundles and the TM_edge. During the depolarizing phase of our stimulus, the IHC hair bundles were displaced toward the spiral ligament. The phase of the radial motion of the TM_edge was toward the spiral ligament (i.e., in phase with OHC3 and out of phase with the rest of the TM).

Fig. 13 shows the corresponding data from our one apical-turn experiment (CF 0.4 kHz). Similar to the middle-turn data, the magnitude of motion near the TM level (Fig. 13, focal depth <0 µm) and near the BM level (depth 100–130 µm) was hundreds of times smaller compared to the magnitude of the OC motion near the basal end of the OHCs at their junction with the DCs (depth 40–70 µm). This observation is most obvious for the OHC1 and OHC3 radial locations. Unlike in the middle turn, the magnitude of the radial component of motion in the apical turn was usually around four times larger than and sometimes similar to the magnitude of the longitudinal component. The magnitude of motion observed at all focal depths of the OPC region was generally hundreds of times smaller compared to that near the basal end of the OHCs. We often saw a small increase (100 nm) in the magnitude of the radial OPC motion close to the basal end of the OHCs (Fig. 13 A, focal depth 70 µm).

View larger version (12K): [in this window] [in a new window]   FIGURE 13  Peak-to-peak radial (solid symbols) and longitudinal (open symbols) displacements as a function of depth relative to the RL, for four radial locations. All responses are from the apical turn region (CF 0.4 kHz) from the same animal (exp. 325). The stimulus frequency was 30 Hz. For this experiment, R = 73° and L = 95°. Zero-degrees phase indicates motion toward the spiral ligament in the radial direction and toward the base in the longitudinal direction. (A and E) Magnitude and phase of OPC region displacements, with RL defined as the top of the OPC. (B and F) Magnitude and phase of OHC1 region displacements, with RL defined as the top of the OHC1 hair bundles. (C and G) Magnitude and phase of OHC3 region displacement, with RL defined as the top of the OHC3 hair bundles. (D and H) Magnitude and phase of HC region displacement, with RL defined as the top of OHC3 hair bundles.

The magnitude of motion of the IHC hair bundles and the IPC was hundreds of times smaller (usually near the noise of our measurements) compared to the magnitude of motion near the basal end of the OHCs. When motion was seen in the IHC hair bundles, it was similar in phase with the motion seen in the middle turn, i.e., during the depolarizing phase of our stimulus, the IHC hair bundles were displaced toward the spiral ligament. Unlike in the middle turn, we were not able to image the TM_edge effectively in the apical turn, so no motion measurements were made for this structure.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX A: THE EFFECT... APPENDIX B: COCHLEAR... SUPPLEMENTARY MATERIAL ACKNOWLEDGEMENTS REFERENCES

 
Excised cochlea preparation
The major advantage of the excised cochlea preparation is that video microscopy can be used to observe, in the same experimental preparation, the responses of hundreds of cells in the OC simultaneously. Therefore, the relative motion of these cells in response to OHC electromotility can be investigated directly. This is especially important in vibration analysis, which requires the direct comparison of the relative magnitude and phase of motion of several points along the plane of interest and between different planes.

On the other hand, the use of an excised cochlea preparation poses some questions as to how the results can be related back to an intact cochlea. Some of the concerns associated with the excised cochlea preparation are that 1), the endocochlear potential decreases (43) as soon as the animal is decapitated; 2), when the cochlea is opened, the fluid mass acting on the cochlear partition can present a significant load and reduce the amplitude of the vibrations at low frequencies (44–46); 3), during the experiment, the mechanical properties of the cells can change.

When the endocochlear potential decreases, the forward transduction process is compromised. As a result, the gain of the feedback loop in which the OHCs are involved is reduced. This can be used to our advantage if we are interested in investigating the effect of OHC electromotility in the vibration pattern of the OC. By opening the feedback loop, we can directly stimulate the reverse transduction process and understand its contribution to cochlear micromechanics (16).

The vibration pattern of any complex structure depends on the mechanical properties of its individual components, on the anatomical architecture of the structure, and on the type and level of excitation (47). To relate our findings to intact cochlea preparations, we need to address how each of these factors in our excised cochlea preparation relates to intact cochleae.

Naidu and Mountain (14) have measured the stiffness of the excised gerbil OC and found it to agree with in vivo measurements performed on the same species by Olson and Mountain (12,13). Naidu and Mountain (14) also reported that the stiffness measurements were stable over 3 h after decapitation. It was concluded that the mechanical properties of the organ must also remain constant for this time period. Although we were not able to assess the structure of the organ at the subcellular level, we are confident that at the cellular level, the anatomical architecture of the OC was very close to in vivo conditions. This was accomplished by keeping Reissner's membrane intact, thus preserving the anatomy of SM for the entire turn of interest. In addition, using the Cl^–-modified gluconate-based culture medium, we inhibited cell swelling for the duration of the data collection, thus further preserving the anatomy of the OC.

How is in vitro cochlear electrical excitation relevant to in vivo cochlear excitation? The input to the intact cochlea is the pressure difference between the scala tympani and SV. This differential pressure, in combination with the mechanical properties of the cochlea, sets up a traveling wave on the BM. Thus, the BM vibrates and causes bending of the IHC and OHC stereocilia. The bending of the stereocilia changes the ionic conductance at the surface of the cells, allowing positive ions to flow into the cells, depolarizing their membrane and causing them to contract. The precise phase and magnitude of this contraction is currently thought to shape the vibration pattern of the OC. We will refer to the OHC-driven OC vibration as the "OHC-driven component" and to the pressure-driven OC vibration as the "pressure-driven component". The relative contribution of these two components to the total vibration of the OC depends on the type and level of excitation (48). We argue that with our electrical stimulation paradigm we emphasize the OHC-driven component. In the intact cochlea, the contribution of the OHCs appears to dominate at low sound levels; therefore, we expect that the OHC-driven component would be a dominant contributor (albeit not the only one) to the total vibration pattern at low sound levels.

Our data suggest that during the depolarizing phase (positive current into SV) of our stimulus, the OHCs contract. From our multiple plane surface views, we have been able to create low-resolution radial cross sections of the OC; from these new sets of images, we observed that during the depolarizing phase of the stimulus, the OHC3 increased in diameter and moved toward the spiral ligament. During the depolarizing phase of the stimulus, the cells were displaced toward the base; this type of longitudinal displacement could only occur if the cells were contracting (see our discussion of the longitudinal motion). Other studies using electrical stimulation, with similar electrode configurations, showed that during the depolarizing phase of the stimulus, the BM moves toward SV; this phase of motion occurred due to the OHCs contracting and pulling on the BM (16,18).

Although the current path in these experiments is unknown, the most likely path for the current is to go into the cell through the apical channels and out through the basolateral membrane channels. This path agrees with our observation that the OHCs contract during the depolarizing phase of the stimulus. Another possible route for the current would be through the RL, into the hair cell via the lateral membrane, and exiting either via the opposite lateral membrane or the basal portion of the membrane. This latter route appears to be less likely due to the high resistance of the tight junctions that exist between the cells (for a review, see Slepecky (49); also, see Mountain and Hubbard (50)).

Effect of tissue condition on responses
In our early experiments, the excised cochlea was immersed in oxygenated culture medium (Leibovitz L-15) that resembled perilymph. Using this medium, OHC swelling was observed in all of our preparations. The swelling process was accelerated when electrical current was applied, leading to complete loss of motility within a few minutes. Zeddies et al. (51) reported that cell swelling in excised mammalian preparations can be inhibited for up to 3 h if the Cl^– in the culture medium is replaced with a less permeable, larger anion, like lactobionate or gluconate. Gluconate was also found to be effective with lizard cochlea preparations (52,53). When we used gluconate as a Cl^– substitute, we were able to inhibit cell swelling for up to 9 h postmortem.

Cell swelling can affect both the motility of the cell and the response characteristics. In most preparations with swollen cells, OHC motility was completely lost. In a few of these preparations, motion could still be evoked (for a few minutes) if sufficiently high currents were used. It is difficult to know the exact physiological condition of these cells. Swollen cells might have leaky membranes, and therefore larger currents would be needed to stimulate the cells. In addition, cell swelling alters membrane tension, which can lead to a shift in the voltage dependence of the OHC motor complex (54). Similar dependence between membrane tension and voltage shift has been measured for the OHC motor protein prestin (55,56).

Swollen cells from the same row, when motile, moved out of phase with each other. Probably, in these cases, some cells that still exhibited motility displaced the cells that did not respond and those nonresponsive cells passively moved around in random directions. Similar responses have been reported in organ cultures of guinea pig cochleae in response to electric stimulation (57). Although the authors did not comm