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1 A novel mechanism of cochlear excitation during simultaneous stimulation and 2 pressure relief through the round window 3 Thomas D. Weddell1, Yury M. Yarin2, Markus Drexl3, Ian J. Russell1, Stephen J. 4 Elliott4 and Andrei N. Lukashkin1 5 6 1 7 BN2 4GJ, UK 8 2 9 Dresden, Fetscherstr. 74, D-01307 Dresden, Germany School of Pharmacy and Biomolecular Sciences, University of Brighton, Brighton, Clinic of Otorhinolaryngology, Department of Medicine, Universitätsklinikum 10 3 11 15, 81377 Munich, Germany 12 4 13 Southampton, SO17 1BJ, UK 14 Short title: round window stimulation of the cochlea 15 Authors for correspondence: 16 Andrei N. Lukashkin 17 e-mail: [email protected] 18 Stephen J. Elliott 19 e-mail: [email protected] 20 21 22 23 24 25 26 German Vertigo Center, Ludwig-Maximilians University Munich, Marchioninistr. Institute of Sound and Vibration Research, University of Southampton, 27 Summary 28 The round window membrane (RW) provides pressure relief when the cochlea is 29 excited by sound. Here we report measurements of cochlear function from guinea pigs 30 when the cochlea was stimulated at acoustic frequencies by movements of a miniature 31 magnet which partially occluded the RW. Maximum cochlear sensitivity, 32 corresponding to subnanometer magnet displacements at neural thresholds, was 33 observed for frequencies around 20 kHz, which is similar to that for acoustic 34 stimulation. Neural response latencies to acoustic and RW stimulation were similar 35 and taken to indicate that both means of stimulation resulted in the generation of 36 conventional travelling waves along the cochlear partition. It was concluded that the 37 relatively high impedance of the ossicles, as seen from the cochlea, enabled the region 38 of the RW not occluded by the magnet, to act as a pressure shunt during RW 39 stimulation. We propose that travelling waves, similar to those due to acoustic far- 40 field pressure changes, are driven by a jet-like, near-field component of a complex 41 fluid-pressure field, which is generated by the magnetically vibrated RW. Outcomes 42 of research described here are theoretical and practical design principles for the 43 development of new types of hearing aids, which utilise near-field, RW excitation of 44 the cochlea. 45 Key words: cochlear round window; guinea pig cochlea; cochlear excitation; active 46 middle ear prosthesis; implantable hearing aid, near-field excitation. 47 48 49 50 51 52 53 54 55 1. Introduction 56 The round window membrane (RW) acts as a pressure relief valve for the almost 57 incompressible fluids of the cochlea, making possible movement of the stapes and, 58 hence, movement of the inner ear structures. It has long been known (e.g. see Culler et 59 al [1]) that cochlear function is impaired when the RW membrane is immobilised, 60 thickened, congenitally malformed or absent [2-4]. These observations signify the 61 physiological importance of the RW membrane for audition, and the necessity to 62 retain it, which has been revealed during surgery of the middle and inner ear [5]. 63 Traumatic damage or rupture of the RW membrane can cause hearing loss and 64 deafness due to perilymph aspiration or loss of the normal pressure-releasing function 65 of a compliant RW [6-9]. 66 It has been established, however, that while normal function of the RW is important 67 for effective stimulation of the cochlea through the conventional, oval window, route, 68 the cochlea can be stimulated successfully in non-conventional ways (e.g. through 69 bone conduction, through the RW, and through perforations in the cochlea’s apical 70 turn). All of these techniques produce similar patterns of cochlear sensitivity and 71 excitation [10-12]. In recent years significant recovery of hearing thresholds has been 72 achieved in human patients through the use of active middle ear implants (vibrating 73 electro-mechanical devices) to stimulate the cochlea through the RW at the 74 frequencies of the incoming sound [13-17]. The RW approach could be an effective 75 and preferable alternative to conventional hearing aids for hearing rehabilitation in 76 patients with, for example, chronic inflammatory middle ear diseases, recurrent 77 cholesteatoma, when the anatomy of the middle ear is highly distorted [14], and for 78 patients with congenital malformations of the outer and middle ear, i.e. in cases of 79 conductive hearing loss. In the latter situation dysplasia and immobilization of the 80 ossicles, often in combination with malformations of the oval window, can make 81 hearing reconstruction through the oval window impossible. The feasibility of the RW 82 approach for the above disorders, and for conditions when the oval window is 83 inaccessible, has been demonstrated in successful attempts to combine outer and 84 middle ear reconstruction with implantation of active middle ear prostheses on the 85 RW [13, 15, 16]. An understanding of the mechanisms of the cochlear excitation 86 through the RW is essential to ensure that the technique is to be predictable and 87 effective in the clinic. 88 One uncertainty relates to the mechanisms of basilar membrane (BM) excitation 89 using probes that cover only a part of the RW membrane, whereby the area of the RW 90 not covered by the probe provides an effective pressure shunt (Békésy [11], page 91 197). This might make excitation of the cochlea problematic through shunting 92 pressure changes that would otherwise excite the BM. Mobility of the stapes is 93 probably not essential for successful cochlear excitation through the RW if most of 94 the pressure relief is provided by the non-occluded area of the RW. The paper 95 presented here deals with the mechanisms of cochlear excitation, using a miniature 96 magnet that only partially occludes the RW. With the stapes mobility decreased, a 97 novel form of cochlear excitation is achieved with a sensitivity that matches that of 98 conventional acoustic stimulation. 99 2. Material and methods 100 Pigmented guinea pigs (280-390 g) were anaesthetised with the neurolept anaesthetic 101 technique (0.06 mg/kg body weight atropine sulphate s.c., 30 mg/kg pentobarbitone 102 i.p., 500 l/kg Hypnorm i.m.). Additional injections of Hypnorm were given every 40 103 minutes. Additional doses of pentobarbitone were administered as needed to maintain 104 a non-reflexive state. The heart rate was monitored with a pair of skin electrodes 105 placed on both sides of the thorax. The animals were tracheotomized and artificially 106 respired, and their core temperature was maintained at 38C with a heating blanket 107 and a heated head holder. The middle ear cavity of the ear used for the measurements 108 was opened to reveal the RW. Compound action potentials (CAPs) of the auditory 109 nerve were measured from the cochlear bony ridge in the proximity of the RW 110 membrane using Teflon-coated silver wire (S in figure 1). Thresholds of the N1 peak 111 of the CAP were estimated visually using 10 ms tone stimuli at a repetition rate of 10 112 Hz. Latencies of the N1 peak for acoustic and RW stimulation were estimated off-line 113 using recording of the CAP using 50 averages. 114 For acoustic stimulation sound was delivered to the tympanic membrane by a closed 115 acoustic system comprising two Bruel and Kjaer 4134 ½” microphones for delivering 116 tones and a single Bruel and Kjaer 4133 ½” microphone for monitoring sound 117 pressure at the tympanum. The microphones were coupled to the ear canal via 1 cm 118 long, 4 mm diameter tubes to a conical speculum, the 1 mm diameter opening of 119 which was placed about 1 mm from the tympanum. The closed sound system was 120 calibrated in situ for frequencies between 1 and 50 kHz. Known sound pressure levels 121 were expressed in dB SPL re 210-5 Pa. 122 A neodymium iron boron disk magnet (M in figure 1) (diameter 0.6 mm, thickness 0.2 123 mm), was placed on the RW to stimulate the cochlea through the RW. The magnet 124 covered about one fourth of the RW surface of total area of 1.18 mm2 [18]. A 125 miniature coil (C in figure 1) made of two turns of copper wire (0.15 mm in diameter) 126 was placed above the magnet. The magnet was driven with a magnetic field created 127 by AC current through the coil. Stimulating current through the coil was generated by 128 a Data Translation 3010 board, attenuated and fed to the coil through a current buffer. 129 Maximum voltage applied to the coil in this study was 10 V which corresponded to 0 130 dB attenuation. High-frequency cut-off of the system for electrical stimulation in situ 131 was above 100 kHz. No signals associated with the coil current were recorded in the 132 absence of the magnet which confirms an absence of electrical interference between 133 the coil and the CAP electrode. The efficacy of the floating magnet RW stimulation 134 varies between preparations (see below). The floating magnet does not, however, 135 impose a variable DC load on the RW, which undergoes large, slow, periodic, 136 movements caused by middle ear muscle contraction in anaesthetised animals. This 137 would not be the case for probes that employ a rigid lever in contact with the RW, 138 which would provide a variable DC load depending on the phase of the large RW 139 movement, with the possibility of causing damage to the RW. 140 Displacements of the magnet and the stapes were measured using a displacement- 141 sensitive laser diode interferometer without the need for reflective beads [19]. The 142 beam of the interferometer was focused centrally on the exposed surface of the 143 magnet or the head of the stapes. The output signal of the interferometer was 144 processed using a signal conditioning amplifier, digitised at 250 kHz with Data 145 Translation 3010 board and instantaneous amplitude and phase of the wave were 146 recorded and averaged 10 times using a digital phase-locking algorithm. 147 Voltage signals to the coil were sinusoidal stimuli of 40 ms in duration (with 110 ms 148 between stimuli) shaped with raised cosines of 0.5 ms duration at the beginning and at 149 the end of each sinusoidal pip. All acoustic stimuli in this work were shaped with 150 raised cosines of 0.5 ms duration at the beginning and at the end of stimulation. White 151 noise for acoustical calibration and tone sequences for auditory and mechanical 152 stimulation were synthesised by a Data Translation 3010 board at 250 kHz and 153 delivered to the microphones or to the coil through low-pass filters (100 kHz cut-off 154 frequency). Signals from the acoustic measuring amplifier were digitised at 250 kHz 155 using the same board and averaged in the time domain. Experimental control, data 156 acquisition and data analysis were performed using a PC with programmes written in 157 TestPoint (CEC, MA, USA). All procedures involving animals were performed in 158 accordance with UK Home Office regulations with approval from the local ethics 159 committee. 160 3. Results 161 3.1 Pressure distribution in a model of cochlear stimulation through partially 162 occluded RW 163 The RW is assumed to be driven by a piston (magnet) over a part of its area and the 164 remaining part of the RW is flexible and generates an equal and opposite volume 165 velocity, since the fluid is assumed to be incompressible and the cochlear wall is rigid. 166 The internal pressure in the cochlea is then made up of two components. 167 The first component is an average alternating pressure, 𝑃𝑀 , which is the same 168 throughout the cochlea. The magnitude of this will depend on the stiffness, 𝑆, of the 169 freely moving area of the RW. 𝑃𝑀 is required to be large enough to force this area to 170 have a volume velocity equal and opposite to that of the driving piston. The force on 171 the freely moving part is thus 𝑆𝑥, where 𝑥 is its mean displacement. Its volume 172 velocity, 𝑞, is thus 𝑖𝜔𝐴𝑥, where 𝐴 is the freely moving area and 𝜔 is the stimulation 173 frequency. Because the force on the freely moving part is equal to 𝑃𝑀 𝐴, we can define 𝑃𝑀 = 𝑆𝑞 2 𝑖𝜔𝐴 . (1) 174 Since the average pressure is uniform throughout the volume, it does not cause any 175 excitation of an incompressible cochlear partition. It is worth noting that if the 176 stiffness, 𝑆, of the freely moving area of the RW is small then the mean pressure 177 generated within the fluid volume is also small. 178 Even if the volume velocity of the freely moving part of the RW is equal and opposite 179 to that of the piston, the second pressure component, a near-field pressure, is 180 generated close to the RW. This is due to the pressure required to accelerate the fluid 181 from below the piston into the freely moving part of the RW and is thus dependent on 182 the fluid inertia. The spatial distribution of this near-field pressure will depend on the 183 details of the geometry, but its magnitude will be proportional to the fluid density, 𝜌, 184 and to the acceleration of the piston, 𝑖𝜔𝑞. An indicative overall magnitude of 𝑃𝑁 can 185 then be defined as 𝑃𝑁 ∝ 𝑖𝜔𝜌𝑞. (2) 186 For a given piston volume velocity, the average pressure (Eq. 1) decreases with 187 increasing the stimulation frequency, whereas the average near-field pressure (Eq. 2) 188 increases with the frequency. 189 It is worth noting that if the cochlear wall is not perfectly rigid, for example if the 190 stapes is not completely fixed, the internal pressure also generates a volume velocity 191 on the oval window, as illustrated in figure 2A. This would generate a pressure 192 component due to the flow of fluid across the cochlea that would depend on the fluid 193 inertia rather than the stiffness of the window. A near-field pressure would then be 194 generated in the vicinity of both the oval window and the RW. 195 The on-axis near-field pressure, 𝑃𝑁 , due to RW stimulation can be estimated using a 196 simple model of cancelling piston sources. The assumed geometry is shown in figure 197 2B in which an inner piston with a radius of 𝑎1 has a velocity of 𝑣1 and an annular 198 piston with an inner radius of 𝑎1 and an outer radius of 𝑎2 has a velocity of 𝑣2 . 199 The volume velocity of the inner piston thus is 200 𝑞1 = 𝜋𝑎21 𝑣1 , (3) 𝑞2 = 𝜋(𝑎22 − 𝑎21 )𝑣2 . (4) and that of the outer piston is 201 If the cochlea is sealed, the volume velocities are equal and opposite so that 𝑞2 = 202 −𝑞1, and the ratio of the two linear velocities must be 𝑣2 𝑎21 = , 𝑣1 𝑎22 − 𝑎21 (5) 203 which is plotted in figure 3. 204 Assuming free field conditions, the complex on-axis pressure a distance of 𝑟 from a 205 single piston of radius 𝑎 vibrating with velocity 𝑣 is given (e.g. see Kinsler et al [20]) 206 as 𝑝(𝑟) = −𝜌𝑐𝑣 (𝑒−𝑖𝑘√𝑟 2 +𝑎2 − 𝑒−𝑖𝑘𝑟 ), (6) 207 where 𝑘 = 2𝜋/𝜆 is the wavenumber, 𝜆 is the acoustic wavelength and 𝑐 is the speed 208 of sound in the fluid. Distance between the RW and the BM, which is <1 mm in both 209 guinea pigs and humans [21], is much smaller than the wavelength, which is equal to 210 about 1.5m at 1 kHz assuming a speed of sound of 1500 ms-1 in the cochlear fluid. 211 Hence, we can assume 𝜆 ≫ 𝑟, and 𝑘𝑟 = 2𝜋𝑟 ≪ 1. 𝜆 (7) 212 In this case we can take the first order series approximation to the exponentials in 213 equation (6) to give the pressure due to the inner piston as 𝑝1 (𝑟) ≈ 𝑖𝜌𝜔𝑣1 (√𝑟2 + 𝑎21 − 𝑟). (8) 214 The pressure due to the annular piston is equal to that due to a piston of radius 𝑎2 and 215 velocity 𝑣2 minus that due to a piston of radius 𝑎1 and velocity 𝑣1 𝑝2 (𝑟) ≈ 𝑖𝜌𝜔𝑣2 (√𝑟2 + 𝑎22 − √𝑟2 + 𝑎21 ). (9) 216 The total near-field pressure 𝑃𝑁 (𝑟) is the superposition of those due to the inner and 217 outer pistons in equations (8) and (9) with 𝑣2 /𝑣1 given by equation (5) 𝑃𝑁 (𝑟) = 𝑖𝜌𝜔𝑣1 [(√𝑟2 + 𝑎21 − 𝑟) − 𝑎21 (√𝑟2 + 𝑎22 − √𝑟2 + 𝑎21 )]. 𝑎22 − 𝑎21 (10) 218 Although this expression is not strictly valid in the present case unless the near-field 219 pressure has died away over the width of the cochlea, the modulus of equation (10) is 220 plotted in figure 4 as a function of distance from the centre of the source distribution, 221 𝑟, for various values of 𝑎1 /𝑎2 and with a constant value of 𝑣1 . The pressure drops 222 quickly with the distance from the piston, especially for small 𝑎1 /𝑎2, but the shortest 223 distance between the RW and the BM is also only 0.2 mm in guinea pigs [21]. Hence, 224 excitation of the cochlea with a probe which covers just a part of the RW is possible 225 by the near-field pressure in vicinity of the RW. A natural consequence of the simple 226 model of cancelling piston sources is higher near-field pressure for larger 𝑎1 /𝑎2 ratios 227 for constant piston velocity. In the real cochlea, however, the RW piston velocity is 228 likely to drop for larger 𝑎1 /𝑎2 ratios as a consequence of an increase in cochlear 229 impedance as seen by the piston. A model is needed, which takes into account this 230 effect and measurements of the RW impedance for different proportions of the RW 231 covered by the magnet, in order to find an optimum 𝑎1 /𝑎2 ratio which provides the 232 most efficient stimulation of the cochlea through the RW. It also should be noted that 233 within the validity of equation (10), the total near-field pressure 𝑃𝑁 (𝑟) is proportional 234 to the acceleration of the inner piston. The BM is a pressure detector [22], it should, 235 therefore, be expected that BM stimulation is proportional to piston acceleration. 236 3.2 Placement of magnet on the RW does not alter the sensitivity of the cochlea to 237 acoustic stimulation 238 The cochlear neural threshold to acoustic stimulation, measured as a threshold for the 239 N1 peak of the CAP, did not change after placement of the magnet on the RW and 240 during the entire experiment (up to 3 hours after the placement) (figure 5). It is well 241 established that increases in the impedance of the RW leads to elevation of the 242 hearing threshold (e.g. see Culler et al [1]), thus the observed stability of the CAP 243 thresholds after placement of the magnet revealed that the RW impedance did not 244 increase and the area of the RW not covered by the magnet could provide effective 245 pressure relief at acoustic frequencies when the cochlea is stimulated conventionally. 246 The RW impedance is much lower than any other leakage impedance in the cochlea 247 (e.g. see Stieger et al [23]). Thus, in view of the stability of the N1 thresholds 248 following placement of the magnet, we can conclude that the RW impedance 249 remained the smallest impedance in the system, even after this manipulation. 250 3.3 Frequency dependence of neural thresholds in response to subnanometer RW 251 and acoustic stimulation are similar 252 The coil voltage - magnet displacement relationship was linear in all six preparations 253 where this characteristic was studied (an example is given in figure 6). In all 254 preparations, the frequency dependence of the magnet displacement resembled that of 255 a low-pass filter with the high-frequency slope being between 12 - 18 dB/octave 256 (figure 7A). A slope of 12 dB/octave is to be expected if the magnet is behaving as a 257 mass subject to a constant force caused by the magnetic field due to the voltage. In 258 this case, the magnet acceleration should not depend on frequency, which is indeed 259 observed for most of the frequency range used in this study (figure 7B). Because the 260 high-frequency cut-off of the system for electrical stimulation was above 100 kHz, the 261 relatively steep high-frequency slope of the coil voltage - magnet displacement 262 relationship for frequencies below 10 kHz (figure 7A) most likely reflects the multiple 263 degrees of freedom of the mechanical system formed by the inductively coupled coil 264 and the magnet inertia, together with the RW and the cochlear fluid. 265 There were no major differences between CAP threshold curves for acoustic 266 stimulation between all preparations used in this study (figure 7C). However, in the 267 same preparations, CAP threshold curves expressed as a function of the coil voltage 268 required to generate threshold CAP for magnetically driven RW stimulation varied by 269 ~10 dB over the 8 – 20 kHz range (figure 7D). Likely bases for these CAP threshold 270 variations could include differences, between preparations, in the relative position of 271 the magnet and the coil and to slightly different locations of the magnet on the RW. 272 The smallest coil voltages required to generate the threshold CAP was observed for 273 frequencies between 10-11 kHz. Taking into account the linearity of the magnet 274 displacement (figure 6), the corresponding magnet displacements for the threshold 275 coil voltage could be readily derived from the iso-voltage response curves at 10 V 276 (figure 7A) and the CAP threshold curves (figure 7D) using the following equation: 277 displacement at threshold = displacement at 10 V / 10^(attenuation at threshold/20). 278 The derived magnet displacement threshold curves (figure 7E) reveal that the 279 sensitivity of the guinea pig cochlea to RW stimulation is in the sub nanometre range. 280 Maximum sensitivity, which corresponds to the smallest magnet displacements at 281 threshold, was observed for frequencies around 20 kHz, which is similar to the 282 frequency of maximum sensitivity for acoustic stimulation (figures 5, 7C, note 283 different frequency ranges in these figures). The absolute sensitivity of the magnet 284 displacement threshold curves varied between preparations (figure 7E), probably, as 285 pointed out above, because of variations between preparations in the relative locations 286 of the coil, the magnet and the RW membrane. Magnet displacement threshold curves 287 within the range of those shown in figure 7E were obtained for three further 288 preparations but, for clarity, are not shown. 289 Near-field pressure, which is likely to excite the BM responses in our experiments, is 290 proportional to the acceleration of the magnet (figure 7F) which, at threshold, was 291 calculated from the threshold displacement (figure 7E). The threshold acceleration 292 changes only by about 20 dB within the frequency range studied (figure 7F). This 293 change corresponds better to the changes in the threshold SPL for acoustic stimulation 294 within the same frequency range (figure 7C) while threshold displacement changes by 295 more than 40 dB for the same frequencies (figure 7E). This last observation provides 296 an additional confirmation that in our experiments the BM is excited by the near-field 297 pressure which is proportional to the magnet acceleration. 298 3.4 Latencies of neural responses to acoustic and RW stimulation are similar 299 To gain insight into the mechanisms by which the cochlea is excited through RW 300 stimulation, we compared the CAP latencies for suprathreshold stimulation within 10 301 dB above the thresholds for acoustic and RW stimulation of the cochlea (figure 8). 302 The latencies were essentially the same. The CAP latency for low-level acoustic 303 stimulation depends on the traveling wave delay and is inversely related to the 304 characteristic frequency of the fibre (e.g. see Goldstein et al [24]). Hence, we can 305 conclude that the mechanisms of energy propagation to the characteristic frequency 306 place were similar for both acoustic and RW stimulation. 307 3.5 Increase in the stapes impedance does not affect efficiency of cochlear 308 stimulation through the partially occluded RW 309 As suggested previously, the relatively high acoustic impedance of the middle ear 310 ossicles (as seen from the cochlea), combined with a magnet that only partially 311 occluded the RW, may allow the region of the RW not covered by the magnet to act 312 as a pressure shunt during RW stimulation. It may thus be suggested that stapes 313 mobility plays little or no role in the stimulation of the cochlea through the RW. 314 Indeed, when the cochlea was excited through the RW, movements of the stapes at the 315 frequency of stimulation were observed above the noise floor of the interferometer 316 only at low frequencies <7 kHz and high stimulation amplitudes (figures 9A-B). 317 Preparations with the largest and smallest stapes responses are shown in figure 9A-B. 318 Similar results were observed in two further preparations. When the stapes impedance 319 was increased by filling the ear canal with superglue, and stapes displacements could 320 not be detected above the noise floor of the interferometer regardless of the frequency 321 and magnitude of the control voltage to the stimulating coil (figures 9A-B), thresholds 322 of RW elicited CAPs before and after increase in the stapes impedance were largely 323 similar (figure 9C). According to this observation it is suggested that stapes mobility 324 is not required for effective excitation of the cochlea in our experimental 325 configuration, i.e. when relatively large part of the RW was not occluded. 326 4. Discussion 327 On the basis of CAP threshold measurements at stimulus frequencies that span almost 328 its entire auditory range, the guinea pig cochlea is sensitive to sub-nanometre 329 displacements and minute accelerations of the RW (figure 7). The CAP data, set in the 330 context of a model of cochlear stimulation through the partially occluded RW, support 331 the viability of RW stimulation as an effective route for exciting the mammalian 332 cochlea, further building on previous studies of the mechanical properties of the 333 cochlea and recent work concerning the implementation of RW implantable hearing 334 devices [13, 25, 26]. Quantification of the RW transducer displacement/acceleration 335 presented here provides parameters essential for the design of future devices, although 336 these parameters vary within individuals (figures 7 and 9). These factors may include 337 the shape of the transducer and the area of the RW it covers. Most significant is 338 whether the transducer completely covers the RW, as demonstrated by other groups 339 [27-29], or leaves a RW area partially free [26, 30-32]. The outcome of our 340 experiments reveals that partial coverage of the RW may not affect RW impedance 341 sufficiently to affect cochlear stimulation with the exposed portion of the RW 342 membrane acting as a pressure shunt (figure 5). Complete coverage would probably 343 remove this shunt, possibly resulting in a different mechanism of BM stimulation. 344 Our experiments demonstrate that middle ear prostheses, which partially cover the 345 RW, can be used effectively for simultaneous cochlear stimulation and pressure relief 346 through the RW. The existence of a “third window” (an additional pressure shunt, 347 𝒁𝟑,𝑺𝑽 , 𝒁𝟑,𝑺𝑻 , figure 10) in the cochlea has been postulated to account for the efficiency 348 of RW stimulation because of the relatively high impedance, as seen from the cochlea, 349 presented by the ossicles [30]. The proposed identity of the third window ranges from 350 the vasculature of the cochlea to the cochlea and vestibular aqueducts [17, 30]. 351 Evidence for the existence of the third window and its ability to shunt pressure is 352 claimed from experiments in which the RW membrane is completely blocked during 353 normal acoustic stimulation or the stapes is immobilized and the cochlea is stimulated 354 through the RW route. Despite blockage or fixation, the air conduction thresholds are 355 raised by between 20-50 dB depending on the study cited [3, 30, 33-35]. However, 356 even the comparatively low experimental value of a 20 dB rise in threshold level is 357 significant when compared with the low thresholds achieved in the current study 358 (figure 9). Additionally, it is unlikely that a hypothetical third window is responsible 359 and, indeed, required for pressure relief in our experiments. The RW impedance 360 (𝒁𝑹𝑾 , figure 10A) is much lower than any other leakage impedance in the cochlea 361 during normal acoustic stimulation (e.g. see Stieger et al [23]), i.e. 𝒁𝑹𝑾 ≪ 𝒁𝟑,𝑺𝑻 and 362 pressure at point 𝑁 is determined mainly by 𝒁𝑹𝑾 . Moreover, the neural thresholds are 363 highly sensitive to increases in RW impedance (e.g. see Culler et al [1]). In our 364 experiments, the neural thresholds during acoustic stimulation did not change after the 365 magnet placement (figure 5). We took this finding to indicate that the RW impedance 366 remained the smallest impedance in the system even after this manipulation (i.e. 367 𝒁𝑹𝑾 ≪ 𝒁𝟑,𝑺𝑻 after the magnet placement) and provided an effective pressure shunt 368 minimising the pressure at point 𝑁 (figure 10B) and the far-field pressure drop across 369 the impedance of the cochlear partition (𝒁𝑩𝑴 , figure 10B). This outcome might also 370 be expected from the direct finding that intracochlear pressure differences between the 371 scala vestibuli and scala tympani remained low during RW stimulation [23]. On the 372 basis of our findings reported here, we propose that the pressure shunting occurred 373 through the area of the RW which remained exposed. This proposal is also supported 374 by the findings of Schraven et al [32] who tested different sized actuator tips and their 375 coupling to the RW. Schraven et al [32] found that stimulation by actuators with tip 376 sizes well below the dimensions of the RW resulted in reduced stapedial movements 377 compared with those tips that covered most of the RW. This result could be accounted 378 for if the free exposed area of the RW acted as a pressure shunt. This does not 379 discount other “windows” contributing to pressure relief but it is clear from results 380 presented here that their contribution appears to be negligible in our experiments. 381 We found that CAP thresholds did not change after stapes impedance (𝒁𝑴𝑬 , figure 382 10B) was increased (figure 9). CAP threshold elevation was, however, observed in 383 earlier studies using RW stimulation through a partially blocked RW [30]. 384 Furthermore, where we found RW stimulation through the partially occluded RW 385 elicited stapes displacements only at high intensities below 7 kHz, under similar 386 stimulus conditions, Lupo et al [30] observed stapes movement in chinchillas across a 387 wider frequency range of 0.25 -16 kHz. We suggest that tighter hydromechanical 388 coupling between the RW transducer and the stapes, and consequent changes in the 389 hydromechanical properties of the cochlea after stapes immobilisation, may account 390 for elevation of the CAP thresholds after stapes fixation observed by Lupo et al [30]. 391 Correspondingly, differences in transducer shape and the proportion of the RW 392 covered, may potentially account for differences in the transducer-stapes 393 hydromechanical coupling reported in this study and by Lupo et al [30]. 394 Pre-tension of the RW, which can potentially increase stiffness of the exposed area of 395 the RW, and hence the average pressure within the cochlear (Eq. 1), can enhance 396 stapedial movement during RW stimulation [31, 36]. It is apparent that differences in 397 the outcomes of different studies, including ours presented here, depend on a number 398 of factors including the choice of both the size and shape of the transducer and pre- 399 tension of the RW. The finding by Stieger et al [23] that the stapes velocity is not a 400 good measure of the effectiveness of reverse stimulation of the cochlea, might reflect 401 sensitivity of the stapedial responses to variations in the parameters of RW 402 stimulation mentioned above. Control of these parameters is important to ensure that 403 mobility of the ossicular chain is reduced to levels that negate the need for additional 404 intrusive procedures that might cause sensorineural hearing loss. 405 In our experiments the RW provided an effective common pathway for both cochlear 406 stimulation and pressure relief. Therefore, we conclude that the mode of cochlear 407 excitation through the RW in this case is different from that observed during 408 conventional, acoustical cochlear stimulation or RW stimulation, which does not 409 allow pressure relief through the RW [28, 29]. Our results together with direct 410 measurements of the pressure in the cochlea during RW stimulation [23] using a 411 transducer that leaves the RW partially exposed, indicate that under this condition the 412 transducer displacement probably is not able to cause a far-field pressure difference 413 between the cochlear scalae, which is the normal stimulus for the cochlea [12]. Far- 414 field pressure differences between the scalae are unlikely to be caused by the type of 415 RW stimulation we employed because of the high impedance of the ossicular chain, 416 as seen from the cochlea [27, 28], and pressure backflow around the transducer [11]. 417 We propose, instead, that during RW stimulation through the partially occluded RW, 418 the BM is stimulated via the near-field complex pressure generated in the vicinity of 419 the RW (figure 4), i.e. a fluid-jet flow, which, however, results in the generation of 420 conventional travelling waves along the cochlear partition. In this sense, the cochlear 421 excitation due to the RW stimulation in our experiments is similar to excitation due to 422 rocking movement of the stapes, which creates only local pressure gradients/fluid 423 motion in the cochlea [37, 38] resulting, nevertheless, in generation of the travelling 424 waves and neural excitation [39, 40]. In our experiments, the near-field pressure is 425 proportional to the acceleration of the transducer which allows effective cochlear 426 stimulation even at extremely small RW displacements at high frequencies. This 427 conclusion should be taken into account during the design of hearing-aid devices 428 which stimulate the cochlea through the partially occluded RW. The near-field 429 pressure variations will be limited to the vicinity of the RW membrane (figure 4), but 430 the close spatial relationship between the RW and the BM [21] make excitation of the 431 BM by these localised near-field pressure variations possible. Once the BM is 432 stimulated in the vicinity of the RW, a conventional travelling wave is generated 433 along the cochlear partition, which is supported by our CAP recordings. This 434 conclusion is based on our finding that the 12-25 kHz region of the cochlea, which is 435 most sensitive to RW magnet stimulation (figure 7E,F), is located in the middle of the 436 basal turn of the cochlea and this region is not adjacent to, or cannot be observed 437 through the RW. Indeed, the CAP latency for low-level acoustic stimulation, which 438 depends on the travelling wave delay (e.g. see Goldstein et al [24]), is similar for both 439 acoustic and RW stimulation (figure 8). Furthermore, CAP threshold tuning curves 440 derived through acoustic (figures 5 and 7C) and RW magnet (figure 7E,F) 441 stimulations have similar maxima in sensitivity between 12-25 kHz. 442 It should be noted that it is not essential for the excitation that the motion of the 443 magnet is strictly piston-like. It is likely that the magnet underwent some rocking 444 motion in our experiments. This possibility, however, does not affect our conclusion 445 about the mode of cochlear excitation and, in terms of the model (figure 2B), simply 446 corresponds to a different ratio 𝑎1 /𝑎2 which should still provide effective stimulation. 447 Our investigation of the mechanisms underlying cochlea stimulation through the RW 448 using a transducer that partially covers the RW membrane has important significance 449 for future clinical use of such devices. RW stimulation does not even require mobility 450 of the ossicular chain, as demonstrated in this study, to provide input to the cochlea 451 that is similar to that obtained acoustically in a ‘normal’ ear. RW stimulation does, 452 however, involve a novel mechanism of generating travelling waves along the 453 cochlear partition, which we believe has not previously been considered. 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Eiber A, Huber AM, Lauxmann M, Chatzimichalis M, Sequeira D, Sim JH. 2012 Contribution of complex stapes motion to cochlea activation. Hear. Res. 284, 82-92. 571 FIGURE LEGENDS 572 Figure 1. Schematic view of the cochlea (CH) through a lateral opening in the 573 temporal bone. M indicates a neodymium iron boron disk magnet (diameter 0.6mm, 574 thickness 0.2mm) placed on the surface of the round window (RW). C labels a 575 miniature coil situated above the magnet. S denotes a Teflon-coated silver wire used 576 for recording of activity of the auditory nerve. IS indicates incudostapedial joint. 577 Figure 2. Pressure distribution during cochlear stimulation through partially occluded 578 RW. A Pressure distribution in presence of a mobile stapes. The effect of the mean 579 internal pressure on an imperfectly fixed stapes is to generate a small volume velocity, 580 −𝛼𝑞 , where 𝛼 < 1. In this case, the freely moving area of the RW generates a 581 volume velocity of −(1 − 𝛼)𝑞 and these two components cancel the volume velocity, 582 𝑞, of the driving piston on the RW. Then the internal pressure is the sum of that due to 583 a fixed oval window and that due to two pistons with volume velocities +𝛼𝑞 and −𝛼𝑞 584 on either side of the volume. B Sketch of cancelling piston sources. 585 Figure 3. Dependence of the ratio of the two linear velocities, 𝑣1 /𝑣2 , on the ratio of 586 inner piston to outer piston radii, 𝑎1 /𝑎2. 587 Figure 4. The modulus of the total near-field pressure, |𝑃𝑁 |, as a function of the 588 distance from the piston for different ratio of inner piston to outer piston radii, 𝑎1 /𝑎2. 589 The inner piston velocity, 𝑣1 , is 1 mm/s, the fluid density is 103 kg/m3, the frequency 590 of stimulation is 15 kHz. Cartoons along the 𝑎1 /𝑎2 axis show position of the magnet 591 (grey area) on the RW for different relative probe sizes. 592 Figure 5. Thresholds of acoustic stimulation (dB SPL) vs frequency (kHz) for N1 593 peak of the CAP of the auditory nerve measured before (open symbols) and 2.5 hours 594 after (solid symbols) placement of the magnet on the RW. 595 Figure 6. Displacement of the RW magnet as a function of voltage applied to the coil 596 for three different stimulus frequencies (5, 10 and 20 kHz) measured in situ on the 597 RW of a single preparation. The data at each frequency are pooled and normalized 598 from measurements at different gains of the signal conditioning amplifier. 599 Figure 7. Magnet displacement and neural thresholds as a function of the stimulation 600 frequency in three representative preparations. A Frequency dependence of the 601 magnet displacement at constant voltage (10 V) applied to the coil. B Frequency 602 dependence of the magnet acceleration at constant voltage (10 V) applied to the coil 603 calculated from data at panel A. C CAP thresholds during acoustic stimulation. Note a 604 shorter frequency range than in figure 2. D Dependence of the coil voltage to generate 605 threshold CAP during the RW stimulation. E Corresponding magnet displacement at 606 the CAP threshold. F Corresponding magnet acceleration at the CAP threshold 607 calculated from data at panel E. 608 Figure 8. CAP latency for suprathreshold stimulation within 10 dB of the threshold 609 for the acoustic and RW stimulation of the cochlea (mean SD, N=3 for each 610 condition of stimulation). 611 Figure 9. Effect of stapes fixation on the CAP thresholds during the RW stimulation. 612 A, B Stapes displacements for different attenuation of voltage (re 10V) applied to the 613 coil. Average of three measurements. Error bars are omitted for clarity. Noise floor of 614 the interferometer is indicated by a dashed line. C Corresponding CAP thresholds 615 measured before (solid symbols) and after (open symbols) stapes fixation. 616 Figure 10. Schematics of impedances of the cochlea during acoustic (A) and RW (B) 617 stimulation. 𝒁𝑩𝑴 and 𝒁𝑹𝑾 are impedances of the cochlear partition and the open area 618 of the RW respectively. 𝒁𝑴𝑬 is the stapes impedance as seen from the cochlea. 𝒁𝟑,𝑺𝑽 619 and 𝒁𝟑,𝑺𝑻 are impedances of “third windows” in the scala vestibuli and scala tympani, 620 respectively. 𝒒 indicates a volume velocity generated by stimulation. 21 Figure 1 IS C M RW S CH 22 Figure 2 A B 23 Figure 3 1 -v2/v1 10 -1 10 -3 10 0.0 0.2 0.4 0.6 a1/a2 0.8 1.0 24 Figure 4 25 CAP threshold (dB SPL) Figure 5 30 before magnet placement 2.5 hours after 20 10 0 -10 rw2 -20 1 10 Tone frequency (kHz) 26 Displacement amplitude (AU) Figure 6 10 1dB/dB 1 5kHz 0.1 10kHz 0.01 20kHz rw3 50 40 30 20 10 Attenuation (dB re 10V) 0 27 Magnet displacement (nm) 100 A 10V input 12dB/oct 10 18dB/oct 1 rw2 rw6 rw17 10 Sound pressure (dB SPL) 20 30 Frequency (kHz) C 10 0 -10 rw2 rw6 rw17 -20 5 1 Magnet displacement (nm) 20 10 15 20 25 30 Frequency (kHz) E 0.1 0.01 rw2 rw6 rw17 1E-3 5 10 15 Frequency (kHz) 20 25 30 Magnet acceleration (m/sec^2) Threshold voltage (-dB re 10 V) Magnet acceleration (m/sec^2) Figure 7 120 B 80 40 rw2 rw6 rw17 0 10 30 D 20 30 20 25 30 20 25 30 Frequency (kHz) 40 50 60 rw2 rw6 rw17 70 5 10 15 Frequency (kHz) F 1 0.1 rw2 rw6 rw17 0.01 5 10 15 Frequency (kHz) 28 Figure 8 CAP latency (ms) 2.5 2.0 1.5 magnet stimulation air stimulation 1.0 1 10 Frequency (kHz) 29 Figure 9 Displacement (nm) 10 A noise attenuation 30att 20att 10att 0att 1 0.1 1 10 Frequency (kHz) 10 Displacement (nm) B noise attenuation 30att 20att 10att 0att 1 0.1 Threshold voltage (-dB re 10 V) 1 30 10 Frequency (kHz) C stapes mobile stapes fixed stapes mobile stapes fixed 40 50 60 70 5 10 15 Frequency (kHz) 20 25 30 30 Figure 10 A q Z3,SV ZBM ZRW N Z3,ST B Z3,SV ZME ZBM ZRW N Z3,ST q