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Mechanics of a single-ossicle ear: I. The extra-stapedius of the pigeon
Hearing Research, 39 (1989) 1-14 Elsevier
HRR
01191
Mechanics of a single-ossicle ear: I. The extra-stapedius
of the pigeon
Anthony W. Gummer ‘, Jean W.Th. Smolders 2 and Rainer Klinke 2 ’ Developmental Neurobiology Group, Research School of Biological Sciences, Australian National University, Canberra, A.C. T., Australia and ’ Klinikum der J. W. Goethe UniversitSit, Zentrum der Physiologic, Frankfurt am Main, E R.G. (Received
5 July 1988; accepted
27 November
1988)
The motion of the conical peak of the tympanic membrane (TM) at the tip of the extra-stapedius (ES) and of the columella footplate (CFP) were measured in the pigeon using the Mijssbauer technique. The dimensions of middle-ear structures were measured in some of the experimental animals. The averaged velocity response at the ES for frequencies of 0.25-2.378 kHz was that of a second order, mass and stiffness controlled, resonant system with resonant frequency of 1.2 kHz and Q, dB of 1.2. The mean velocity amplitude at resonance was 3.7 mms-’ at 100 dB SPL, which is approximately equal to the theoretical value of 3.5 mms-’ required for maximum energy transfer from a uniform plane acoustic wavefront in air. For the frequency regions 0.125-0.25 kHz and 2.378-5.657 kHz, the mean amplitude slopes for the velocity at the ES were 2 dB oc-’ and - 3 dB act-‘, respectively. Above 5.657 kHz there was considerable inter-animal variation in the ES velocity responses. The direction of motion at the ES was frequency dependent above 1 kHz. For frequencies up to 1 kHz the ratio of CFP to ES velocity was independent of frequency; the mechanical lever ratio was 2.7, which was attributed to the geometry of the middle ear. At these frequencies the total transformer ratio for the middle ear, expressing the ratio of fluid pressure at the CFP to sound pressure at the ES, was estimated to be 35 dB. Pigeon;
Bird; Single-ossicle;
Extra-stapedius;
Tympanic
membrane;
Introduction The efficiency of the avian middle ear in transforming air-borne sound to ossicular motion has received little attention. Despite its apparently simple structure, having only a single ossicle, the neglect is rather surprising given that the avian model has provided a wealth of information about the ontogenesis (Rubel, 1984) and the temporal coding properties (Konishi, 1986) of the auditory system. Two reports on the ‘function’ of the avian middle ear based on vibration measurements are to be found in the literature (Saunders and Johnstone, 1972; Saunders, 1985). However, neither of these reports contain phase data essential for a description of ‘function’. Saunders and Johnstone
Correspondence to: A.W. Gummer, Developmental ology Group, Research School of Biological Australian National University, GPO Box 475, A.C.T. 2601, Australia. 0378-5955/89/$03.50
NeurobiSciences, Canberra,
0 1989 Elsevier Science Publishers
Columella
footplate;
Middle
ear; Miissbauer
technique
(1972) give the amplitude of the middle-ear transfer function in the Barbary Dove and Saunders (1985) gives the amplitude response of the tympanic membrane (TM) in chick and parakeet. The latter report also contains a quantitative description of the anatomy of the middle ear as viewed with the electron microscope. Pohlman (1921) provides a most comprehensive anatomical and functional description of the middle ear of Gallus. An extensive bibliography on avian middle ear is given by Gaudin (1968). A model for a structurally comparable single-ossicle ear does exist; namely, that proposed by Rosowski et al. (1985) for the alligator lizard. Although that model provides a basis for understanding the physics of the single-ossicle case, it is not completely applicable to the avian situation, principally because the loading conditions at the output of the middle ear are different: basilar-membrane (BM) motion in the alligator lizard is determined primarily by the middle ear, whereas the BM of the bird supports a travelling wave (Gummer et al., 1987). Moreover,
B.V. (Biomedical
Division)
2
the frequency response of the columella footplate (CFP) exhibits anti-resonance at high frequencies (Gummer et al., 1986). This paper reports on the motion of the middle ear of the pigeon, concentrating on the motion of the conical peak of the tympanic membrane (TM) at the tip of the extra-stapedius (ES), the middleear input stage. Although low-frequency data for the output stage, the CFP, is also included, the high-frequency motion of this structure is the subject of the companion paper (Gummer et al., 1989). Vibration measurements were made with the Mijssbauer technique. Materials and Methods
The experimental procedures were identical to those which were described extensively by the authors in a previous report (Gummer et al., 1987). Briefly, recordings were made from Nembutal(36 mg kg- ‘) anaesthetized pigeons ~C~~~~a liuia) of age OS-5 years (mode: 1.5) and weighing 390-500 g (450 * 50). Supplementary l/4-doses of anaesthetic were administered as required. Animals were artificially respired with a humidified gas mixture of 4% CO, and 96% 0, at 0.5 1 mm-‘. Body temperature was controlled (41 f 0.5 o C under the left wing) and the el~tr~~~o~~ was recorded. Animals were paralyzed with alcuronium chloride (10 mg kg-r), approximately 0.5 h before beginning the mechanical measurements. Sound was presented closed field from a Bri.iel and Kjaer 4134 12.7~mm condenser microphone. The level and the phase of the sound pressure at a distance of about 1.5 mm from the TM, about 0.5 mm dorsal to its conical peak, were measured with a calibrated l-mm probe tube mounted in the tip of the sound delivery cone. Sound pressure level (SPL) is re. 20 PPa and phase is negative for a lag. Sound pressure was measured at each stage of the experiment. The physiological condition of the ear was ascertained with a compound action potential (CAP) frequency threshold curve (FTC) recorded from a silver electrode placed on the co&ear wall at the ventral border of the round window, and referenced to a neck-muscle electrode. The hole made in the dorsal lateral side of the skull to place
the CAP electrode was not closed, thus enabling the condition of the round window membrane, the electrode tip, the CFP and the annular ligament to be clearly visualized; the diameter of the hole was about 4 mm. A CAP FTC was recorded at each stage of the experiment. The Mbssbauer source used for middle-ear measurements was a 200 X 2OO X 6 pm3 foil cut from a 57Co doped rhodium matrix with an initial total activity of 1.85 GBq mm-* and estimated weight of 3.3 pg. The absorber was a 4% 57Fe enriched vanadium foil. The combination had an isomer shift (Vi> of -0.27 mm-r and a full line-width at half ma~mum (F) of 0.79 mm-‘, calibrated in air with an acceptance angle of 30 *. This angle was typical of the acceptance angles used for recordings from middle-ear structures. The non-zero isomer shift gave phase ambiguity of integral cycles only. The amplitude and phase of the source velocity were estimated from period histograms of the transmitted 14.4keV y-radiation, using a non-tinear, least mean square algorithm (Wolberg, 1967), with constant parameters Vi and I’. For recordings of TM motion the Mossbauer source was placed on the conical peak of the TM opposite the tip of the ES (Fig. 1). The sound delivery cone was repositioned and sealed for closed field conditions. Good counting statistics were obtained without the need to fabricate a viewing window in the external auditory meatus. For recordings of CFP motion the Mossbauer source was placed on the CFP near its posterior extremity, about mid-way between the annular ligament and the base of the columellar stalk. A light smear of Vaseline on the contact surface of the source ensured adhesion to the moving surfaces. Anatomical constraints, together with the inherent uncertainty in the direction of the velocity vector of the moving surface, means that a component of the velocity vector was measured. Recordings were made with the Mijssbauer absorber positioned so as to obtain the maximum fractional Mtjssbauer effect. This fraction for the TM measurement configuration (0.20-0.28; 0.25 f 0.03) tended to be slightly larger than that for the CFP measurement configuration (0.17-0.27; 0.23 + 0.03), because of larger radiation scatter in the latter configuration.
3
Firm adhesion to the moving surface, maintained during the entire experiment, was indicated in two ways. Firstly, the source was always found firmly attached, precisely where it had been placed. Secondly, for all frequencies the cycle histograms did not deviate from the shapes expected for rigid coupling to a sinusoidally moving surface. The effects of insufficient coupling were examined through experiments in which the velocity of a source on the diaphram of a 12.7~mm condenser microphone (Brtiel and Kjaer, 4134) was used. If an adhesive was not used, or if the temperature at the diaphram became sufficiently high to cause the Vaseline to become less viscous, then the cycle histograms deviated from their normal appearance. Typically, under such conditions, a histogram would be skewed during half-cycles be-
tween zero velocities, or saturation of the count rate would be indicated during one half-cycle, but the count rate in the other half-cycle would be non-saturated with peak rate greater than the apparent saturation rate in the other half-cycle. Data were collected at source velocities of about 0.5 mms-r for frequencies above 0.7 kHz and 0.3 mill.5 -I for lower frequencies, where the former velocity produced optimal phase accuracy without overstimulation and the latter velocity resulted from limitations imposed by the sound system, particularly when making CFP recordings. On the average, the required SPL above 0.7 kHz was 88 dB for the TM and 100 dB for the CFP, and at lower frequencies was 90 dB for the TM and 95 dB for the CFP. Measurements started at 2 kHz, then usually went sequentially to higher frequen-
Pig. 1. Simplified fine drawing of the right middle ear of an adult pigeon; (a) three-dimensional medial view and (b) two-dimensional view identifying the angles used for calculating the geometric lever ratio. The extra-columella is composed of three cartilaginous structures: extra-stapedius (ES), ~fra-strap~us (IS) and supra-status (SS), which have approximately mutely orthogonat orientation. Cal: columelk CFP: columella footplate, TM: tympanic membrane; PL: Platner’s ligament: S: synchondrosis. The drum tubal ligaments and the intra-aural muscle are not shown. The dimensions of the different structures and the angles a,b,c and d are given in Table I. The broken line in (a) is the line representation of the axis of rotation of the extra-columella; (b) is drawn in a plane approximately orthogonal to this axis. The direction of the (mechanical) velocity vectors vus at the ES and cCFp at the CFP are defined, respectively, by rotation of the extra-columella about the axis passing through the point 0, and by translation of the CFP orthogonal to its medial surface. Components of Tim and fccFp were measured with the Mbssbauer technique.
4
ties and then to lower frequencies; in some experiments the measurements went sequentially from the highest to the lowest frequency. Repeat measurements were made at 2 kHz; the sequence always terminated with a 2-kHz measurement. The results were independent of the me~urement sequence. A cycle histogram containing 64 X lo3 counts required 42-98 s (64 f 13) to collate. Upon completion of an experiment, the animal was perfused systemically with buffered Ringer solution at 40” C followed by a fixative of 2.5% paraformaldehyde and 0.75% glutaraldehyde in 0.07M phosphate buffer at 4O C. The dimensions of middle-ear structures were measured in the manner similar to that used by Saunders (1985), the main difference being that light microscopic observations were made; the head was mounted in the experimental head-holder. Results In order to emphasize that vibration measurements were made at the conical peak of the TM opposite the tip of the ES, these responses will be referred to as ES responses. According to the morphological observations of Saunders (1985), the TM is firmly attached to the ES along its entire length. Responses of the ES and of CFP are presented as velocity relative to sound pressure at the TM; the SPL is 100 dB. Velocity amplitude at 100 dB SPL was calculated from the stimulus SPL and measured velocity amplitude assuming linearity: no evidence of non-linear motion of either structure was found in the experimental range 77-117 dB SPL. Phases (relative to sound pressure phase) are plotted using a logarithmic frequency axis in order that amplitude and phase curves may be
compared directly, particularly in the region of amplitude irregularities. Velocities rather than displacements are chosen because when expressed relative to sound pressure the latter yield functions which are proportional to acoustic admittances, transfer functions or tr~s~ssion functions. Thus, the so-called ES response is proportional to the transfer function of the TM at the tip of the ES, where the constant of proportionality is fi because velocity amplitudes are given here as peak values and SPL is an rms quantity. The so-called CFP response is proportional to the middle-ear transmission function where for piston-like motion the constant of proportion~ty is G/A,, where A, is the effective area of the CFP, which converts (mechanical) velocity to volume velocity. The reader is well referred to Rosowski et al. (1985) for terminology. Data are from ears (N = 6) in good physiological condition as judged by the CAP FTC. At the best frequency of the CAP FTC, namely at 1.414 kHz, the mean threshold was 42 f 7 dB SPL for the first CAP recordings and 41 i 5 dB SPL just before beginning the ES vibration measurements. These values compare with the mean of 39 f 5 dB SPL reported for the pigeon (Gummer et al., 1987). There was no significant difference between CAP FTCs recorded before and after the ES response me~urements (40 + 10 dB SPL at 1.414 kHz). Experiments are identified with an animal number prefixed by the acronym PGN. All recordings, except one (PGN 87), are from the right ear.
The amplitude and phase of the velocity of the ES at 100 dB SPL is shown in Fig. 2 for four
Fie. 2. Amnhtude (a.c.e.rr) ~ ,_, and .chase (b.d.f.h) . , of ES velocity and CFP velocity at 100 dB SPL as a function of frequency, for 4 . pigeons, identified as PGNs 87, 95, 96, 99. The unity subs&ipts on ES for PGN 99 and on CFP for PGN 96 indicate that the associated reponses were the first in a group of responses measured at that structure. The cochlea was intact for PGN 87,%, 99. For PGN 95 the responses of the BM, abneural limbus and CFP were measured in that order, before measuring the ES response; the Mossbatter source used for the former m~urements was left on the abneural limbus; the cochlea was full of fhrid and there was a hole in the co&ear wall. Data points are at frequency intervals of 0.25 act for frequencies up to 6.727 kHz and at 0.125 or 0.25 act for higher frequencies; (for PGN 99 there are data points at two additional frequencies, 5.339 and 6.169 kkiz). Arrows indicate the expected amplitude of the velocity (3.5 mms-‘) of the ES at 100 dB SPL if the specific impedance at the ES is half that of a uniform plane acoustic wavefront in air and, as such, represent a theoretical optimum velocity for the ES (Wilson and Bruns, 1983). In this and all subsequent Figures the amplitude plotting scale is 12 dB oc-r,
Velocity
Velocity ,
! I II!,
i0t
0 I
PGN 95
PGN 96
IOOdB SPL
IOOdB SPL
PGN 99 lOOd6
;;i
SPL
0 25
0)
iI _$
-0.25
e, zi AZ -0.75 a_ 0.1
L
0.2
0.5
1.0
Frequency
2
5
(kliz)
IO
20
0.1
0.2
I
*
srt*2tl 0.5
1.0
Frequency
,,,,,A 5
2
(kHzf
IO
20
6
animals, together with their CFP responses. Data from individual animals are displayed in separate panels in order that the salient features of each be discerned. Results from the ES are sup~~mposed in Fig. 3 to facilitate inter-animal comparisons and the mean ES response (six animals) is displayed in Fig. 4. The ES response exhibited a resonance with maximum between 1 and 1.414 kI-Iz dependent on the animal. The maximum velocity amplitude was approximately equal to the theoretical optimum amplitude of 3.5 rn.m~-~ at 100 dB SPLI given by the requirement that the specific impedance at the ES be equal to half the specific impedance of a u~fo~ plane acoustic wavefront in air (half the ch~acte~stic impedance of air, pc/Z), in order that maximum energy be transferred (Wilson and Bruns, 1983). In the remainder of this section the mean ES response in Fig. 4 is referred to because, despite some scatter in the absolute velocity amplitudes at low frequencies, it was an accurate representa~on of the ES response. The frequency
-2 22 -0.25
K
Y $
-0.75
W if -I
.25 0.l
0.2
0.5
1.0
Frequency
2
5
IO
20
fkHzi
Fig. 3. Superposition of the ES responses which have been displayed individually in Fig. 2. Arrows indicate the optimum ES velocity amplitude (3.5 mms-‘).
IOOdBSPL
0.25 ‘;i
2%
2, o
-0.25
g 6z -0.75 tl.i
0.2
05
1.0
Frequency
2
5
IO
20
(ktfzl
Fig 4. (a) Amplitude and (b) phase of the mean ES velocity from 6 animals at 100 dB SPL as a function of frequency. Points are at frequency intervals of 0.25 act up to 6.727 kHz, and at 0.125 act above 6.727 kHz. For the frequency regions 0.125-0.25, 0.297-L 1.189-2.378, 2.828-5.6.57, 6.727-11.314 kHz, respectively, the mean amplitude error was -9, -6, -13, - 14, - I1 dB; and the mean phase error was 0.025, 0.033, 0.053, 0.039, 0.12 cycles. Arrows indicate the optimum ES velocity amplitude (3.5 mms-‘f.
at which the phase was zero, called the resommt frequency, was 1.236 kHz (calculated by interpolation on a linear frequency axis). For frequencies of 0.25-2.378 kHz the ~p~tude slopes on either side of resonance were i6 dB act-‘, implying a second order resonant system. The Q3 dBwas 1.2, giving for a second order system, a damping constant of 0.64 and a group delay at the resonant frequency of 0.50 periods or 0.40 ms. The velocity amplitude at resonance was 3.7 mm-i, which would have been sufficiently close to the optimum of 3.5 mms-i to be almost equal to it. For frequencies of 0X25-0.25 kHz and 2.378-5.657 kHz the amplitude slopes were 2 dB act - ” and - 3 dB act-1, respectively. Above 5.6’75 kHz the amplitude slope was -6 dB act-I; the inter-anal variations were considerable. The amplitude response exhibited an end-slope varying from -38 dB act-’ in FGN 95 to 5 dB act-t in PGN 96. There was a phase difference of 0.5 cycles for 6-11.314 kIIz in PGNs 95 and 99, whereas the phase change above 5.657 kHz was small for PGNs 87 and 96.
Direction of motion of the extra-stapedius response
In order to ascertain the direction of motion of the ES and its possible frequency dependence, the motion of the ES was measured with the Mossbatter absorber in different orientations. The convention for spatial co-ordinates is given in Fig. 5. The results of an extensive experiment on PGN 99 are illustrated in Figs. 6 and 7. The first ES response was determined in that orientation which yielded the maximum Mossbauer fraction (/3 = 21 O, y = - 50 o in Fig. 7~). Having completed this set of recordings the absorber was rotated ventrally in the same vertical plane to y = - Sl“, and following the second set of recordings again ventrally in the same vertical plane to y = - 113”) where a third set of recordings was made. The differences of 31’ and 32” between subsequent recording configurations were chosen to be approximately equal to .the solid angle subtended by the Mijssbauer absorber at the source (28’); that is, the regions through which the radiation was absorbed were adjacent, with little overlap. The results are shown in Fig. 6. This series of measurements was followed by one in which measurements were made at five frequencies for 10 positions in the plane fl= 21’ (Fig. 7). The frequency
y (dorsal) 4
x (rostral)
Fig. 5. Convention for spatial co-ordinates. The line segment OP is the position repre~~tion of the rne~~ern~t axis, defined as the line from the Mossbauer source located at the origin 0, normal to the surface of the Mossbauer absorber at its centre, P. Notice that y is negative when the absorber is located ventrally as, in fact, it was for all experiments. The dashed line is the position representation of the surface normal of the CFP.
E
c3 a
5
99,-
0. I
-50’
-81' 99,--- - -113 99,-
p=210 lco_iBSPL
0.25
I
I
I111111
I
I111111
~
‘;; 9 -0.25 0” aI ; -0.79 -
99,99,-
a’
99,- -.- -113’
-1.251 0.1
I
02
-50’ -81’
I
I
p=21* I
IllIll
0.5
1.0
Frequency
2
5
10
20
(kHz)
Fig. 6. (a) Amplitude and (b) phase of ES velocity at 100 dB SPL as a function of frequency for 3 recording configurations for PGN 99. B and y are defined in Fig. 5. The solid angle subtended by the Mossbauer absorber at the source at the ES was 28O. Arrows indicate the optimum ES velocity amplitude (3.5 mms-1).
sequence was 2.378, 4.757, 6.727, 3.364, 8 kHz; and the angle sequence began at the most ventral position and increased monotonically. The change of measurement axis had insignificant effect on the recorded amplitudes below 1 kHz (Fig. 6a), indicating that the angle y for the ES velocity vector was close to the value of y for the measurement axis at the ~d-r#r~g location (y = - 81” >_However, at higher frequencies the measured velocity amplitudes were dependent on the recording angle. The consistent differences of about 3 dB in Fig. 6a could not be attributed to experimental errors because: (i) measured velocity amplitudes were reproducible to within 1 dB; (ii) the statistical error * for amplitude estimates was no more than + 0.6 dB; and (iii) the physiolo~c~ * These statistical errors are the mean values of the standard deviations of the amplitude estimates produced by the non-linear, least mean square fitting algorithm at all frequencies in a given amplitude response curve.
angle can, according to data in Fig. 7a, be attributed to the cosine effect. Moreover, and most importantly, the spatial invariance of the measured phase responses excludes the possibility of interference from other vibration modes. It is therefore concluded that the direction of motion of the ES simply changed for frequencies above 1 kHz. Columella footplate stapedius response
response
relative
to extra-
Conditions prevailing at the CFP are more complicated than might be expected from such an apparently simple structure. The CFP responses relative to the ES responses for three of the animals from Fig. 2 are presented in Fig. 8. The measurement axis for the CFP was typically /3 = 90 O, y = - 25 ‘. For frequencies up to about 1 kHz the CFP and ES moved in phase with CFP motion attenuated relative to ES motion by a constant
20
-160
-90
1
I I,/,,11
CFP re ES /
/ I I , , ,I,
a.
7
0
3 ventral --I Fig. 7. (a) Amplitude and (b) phase of ES velocity at 100 dB SPL as a function n&recording angle for 5 frequencies for PGN 99. The angle y was varied for constant j3 = 21’. Frequency code: o 2.378 kHz, v 3.364 kHz, 0 4.757 kHz, A 6.727 kHz, 0 8 kHz. The curve in (a) shows a hypothetical cosine variation of velocity amplitude with recording an&e: the chosen velocity amplitude is 5 mm-’ at y = -90°. Arrows indicate the opium ES velocity amplitude (3.5 mms-“). (c) Mossbauer fraction - notice that it is smaller at the more ventral locations. Repeat measurements were made at y = - 81 o (constant /3 = 21 o ).
condition of the auditory periphery was stable, as judged by the CAP thresholds (34 f 2 dB SPL at 1.414 lcHz). Moreover, the phase responses in Fig. 6b are virtually superimposable and the phase plots in Fig. 7b form near horizontal lines, which would not have been expected had experimental conditions changed. However, the dependence of the measured velocity amplitudes on recording
Frequency Fig. 8. (a) Amplitude ES velocity
(kHz)
and (b) phase of CFP velocity relative from 3 of the animals of Fig. 2.
to
9
amount of 9.2 * 2.4 dB. That is, in this frequency range there was a simple frequency independent transformation from ES velocity to CFP velocity. At higher frequencies, however, the transformation was frequency dependent. An anti-resonance at 4-8 kHz was evident in some responses and was due to an anti-resonance measured at the CFP. This high-frequency effect is associated with the coupling between the CFP and cochlea and is the subject of the companion paper, (Gummer et al., 1989). Discussion
Resonance in the ES response According to behavioural auditory threshold data (Harrison and Furumoto, 1971; Hienz et al., 1977; Wit et al., 1985), the relevant frequency range for auditory function in the pigeon is 0.25-4 kHz. For frequencies of 0.25-2.378 kHz the ES response was that of a second order, mass and stiffness controlled, resonant system with resonant frequency of 1.2 kHz and Q3 dB of 1.2, where resonance is defined as the frequency at which the phase response is zero. The velocity amplitude at resonance was 3.7 mms-’ at 100 dB SPL, which is approximately equal to the theoretical value of 3.5 required for optimal detection of a uniIllIll-’ form plane acoustic wavefront in air. The situation would appear to be somewhat different from the three other avian species for which the amplitude of the ES response has been published. From the reports of Saunders and Johnstone (1972) and Saunders (1985) one calculates for Barbary Dove, 6-9 day old chicks and parakeet, respectively, Q3 dB of 1.1, 0.7, 0.6, and maximum velocity amplitude at 100 dB SPL of 1.3, 2, 5 rmn~-~. Since phase data are not available for these species the resonant frequency required for calculation of Qj dB was approximated by the frequency at maximum velocity amplitude in Barbary Dove (2 kHz) and the octave centre of the frequency range of maximum velocity response in chick and parakeet (3 and 2.1 kHz, respectively). In these species however the resonance is not of second order because although the low-frequency amplitude slope was 6 dB act-‘, the high-frequency slope was - 16 dB act- ’ in chick and parakeet (Saunders, 1985) and - 12 dB
act-’ in Barbary Dove (between 8-10 kHz in Fig. 6 of Saunders and Johnstone, 1972). The resonance in the ES response for the alligator lizard is similar to that for the pigeon, although it is over-damped (Q3 dB = 0.5); the velocity amplitude at the resonant frequency of 1.6 kHz is 4.7 rnms-’ at 100 dB SPL (calculated from Rosowski et al., 1985, Fig. 3). The high-frequency amplitude slope of - 7 dB act- ‘, which is close to - 6 dB act -l for second order resonant condiover the entire hightions, was maintained frequency range of 1.8 to 9 kHz (Peake and Ling, 1980; Rosowski et al., 1985). Comparisons with published data for three-ossicle ears indicate that the resonance in the ES response for the pigeon is most akin to that for two species of bat ( Rhinolophus ferrumequinum and Eptesicus pumilis), except of course, that their resonant frequencies are far greater (55 and 25 kHz, respectively) - the resonance is of second order with Q3 dB of 1 and near-optimum velocity amplitude at resonance (Wilson and Bruns, 1983).
Low- and high-frequency ES responses For frequencies of 0.125-0.25 kHz and 2.378-5.657 kHz the slopes of the mean amplitude curve were not f 6 dB act- ‘, as required of a second order resonant system, but rather 2 dB act -’ in the lower frequency range and - 3 dB act-’ in the upper frequency range (Fig. 4a). Moreover, the low-frequency phase asymptote was 0.15 cycles (Fig. 4b), instead of the 0.25 cycles required of a second order resonant system. The low-frequency phase values cannot be accounted for by the acoustic delay (= 4 ps) incurred by the separation (= 1.5 mm) between the tip of the probe tube coupler, where sound pressure was recorded, and the MSssbauer source at the tip of the ES. For frequencies of 6-11.314 kHz the interanimal variation in the ES responses was considerable. The largest amplitude slope was -38 dB act t1 (PGN 95) and the slope of the mean amplitude curve was - 6 dB act- ‘. This value is smaller than values of - 12 dB act- ’ for Barbary Dove (Saunders and Johnstone, 1972) and - 16 dB act- ’ for chick and parakeet (Saunders, 1985). Similar intra-species variations are found in the mean high-frequency slope of the velocity amplitudes
for reptiles (Manley, 1972a,b; Saunders and Johnstone, 1972; Peake and Ling, 1980; Rosowski et al., 1985), and anurans (Saunders and Johnstone, 1972; Moffat and Capranica, 1978; Pinder and Palmer, 1983; VIaming et al., 1984). ES responses recorded along different measurement axes produced no evidence for other vibration modes acting at the ES which could have interfered with the normal vibration mode at high frequencies. Instead the direction of motion of the ES simply appeared to change for high-frequency stim~ation, as has been reported for geckos (Manley, 1972a,b). Given the morphological observations of Saunders (1985) that the columella
TABLE
and extra-columella are tightly joined by a synchondrosis, it would appear that this joint cannot be directly responsible for the high-frequency responses. The results of cochIear ma~pulation experiments (Gummer et al., 1989) show that the cochiea acts as a frequency dependent load. For frequencies of 0.125-0.25 kHz the helilcotrema and Ductus brevis, both of which have been described in the pigeon by De Burlet (1929), Schwartzkopff and Winter (1960), and Kohlliiffel (1984), may provide inertial pathways for fluid flow, as has been proposed for the mammal (Dallas, 1970; Lynch et al., 1982; Rosowski et al., 1985) and
I
DIMENSIONS
a OF THE PIGEON
Structure
MIDDLE
EAR h
Measure
Tympanic
membrane
Columella
footplate
Oval window
Extra-stapedius Columella
Extra-stapedius to columella Columella to columella footplate Columella to tympanic membrane
maximum diameter ’ minimum diameter planar area d half cone angle (d) over extra-stapedius maximum diameter ~~rnurn diameter amae maximum diameter minimum diameter area e length ’ length g lateral angle ( fi) h elevation angle ( - u) angle (b) i angle (c) J angle (a) ’
Mean 5.6 4.1 18.0 66 1.90 0.92 1.23 2.08 0.97 1.63 1.73 2.08 56 12 162 95 104
Range 5.433.6816.27-
5.70 4.40 19.35
59 - 71 1.801.95 0.851.00 l.OO1.4s 2.052.10 0.881.08 1.4% 1.75 1.531.91 1.902.23 52 - 60 8 -15 160 -164 91 -100 102 -105
a Units: mm, mm2, degrees. b From the right ear of five pigeons (PGN 88, 89, 95, 96, 99). ’ The margin is located at the transition from the translucent, smooth tympanic membrane into the opaque grey-white tissue outlining the external auditory meatus. pushing gently on the tip of the extra-stapedius, thus moving the tympanic membrane, aided definition of the margin. d Caiculated from maximum and minimum diameters assuming an ellipse. e Measured from phot~aphs. f From the synchondrosis (between columella and extra-columella) to the tip of the extra-stapedius. s From the synchondrosis to the point of insertion of the columella stalk in the columellar footplate. Since the columellar stalk is slightly bowed, this line is used to define its long axis. h Angles /3 and y defined in Fig. 5 with the head mounted in the experimental head-holder. i Obtuse angle between the lines defined in f and g. J Obtuse angle between the columellar stalk and the columella footplate. The orientation of the columella footplate is such that the surface normal to the columella footplate is defined approximately by B = 61 O, y = - 12 O. k Obtuse angle between the columellar stalk and the piane formed by the margin of the tympanic membrane.
11
which has also been proposed for the bird by Kohllbffel(l984). The impedance of this pathway can account for the observed deviation of the ES response from that of a second order resonant system below 0.25 kHz. Above 2,378 kHz there is evidence for a second vibration mode at the CFP, which interferes with the presumed piston-like mode, causing a sharp anti-resonance tuned to about 6 kHz (Gu~er et al., 1989). That is, the middle ear is confronted by a near infinite impedance in the 6kHz region, which would cause the middle-ear complex to bend or flex, the exact site of which is unknown. This mechanism can account for the observed deviation of the ES response from that of a second order resonant system above 2.378 kHz. Moreover, the age-dependent ossification of the extra-columellar stalk (Gaudin, 1968; Saunders, 1985) can explain the observed interanimal variations above 5657 kHz.
To aid further discussion the dimensions of middle-ear structures of five of the pigeons used in this study are summarized in Table I. Although some dimensions, such as the diameters, are not referred to in the text, they are included for completeness and to allow ~mp~son with the values reported by Saunders (1985). The most significant differences between the two sets of data, believed to be inter-animal differences, are in the size of the CFP and its orientation to the columella: in the present group of animals the area of the CFP is larger and the long axis of the columellar stalk is tilted from the surface normal of the CFP by 5 o rather than by the 17.8” reported by Saunders (1985). Leuer ratios
The frequency independent attenuation of CFP velocity relative to ES velocity of 9.2 dB for frequencies up to 1 kHz, together with the zero phase difference, imply a measured mechanical lever ratio of 2.9 at these frequencies. This value corresponds to the measured value of 3.2 for Barbary Dove using the Mossbauer technique (Saunders and Johnstone, 1972) and to the geometric value of 3 for alligator lizard using anatomical data (Rosowski et al., 1985). The value of the true mechanical lever ratio is
different from the measured value because anatomical constraints meant that only components of the ES and CFP velocity vectors Gould be measured; these vectors are denoted by _uEsand gcrP in Fig. lb. Estimation of the angle between the ES velocity vector and the ES measurement axis requires a knowledge of the location of the axis of rotation of the ES. Careful surgical exposure of the middle ear and s~ulatian of the CFP and of the ES with a glass micropipette indicated that at low frequencies the axis of rotation passed through two points on the margin of the TM; namely, at the insertion of the infrastapedius and at the insertion of a line projected along the tympanic surface of the ES (Fig. la). The direction of the ES velocity vector is then described by the angles /3 = 48 a) y = - 63O, which for the usual ES measurement axis with p = 21*, means that the ES recordings were y= -50°, made at an angle of 20° to the ES velocity vector *, which corresponds to an attenuation of 0.5 dB. The surface normal of the CFP is defined by the angles B = 61°, y = -12”, which for the usual CFP m~surement axis with /3 = 90 O, y = - 25 O, and for a presumed piston-like motion of the CFP, means that the CFP recordings were made at an angle of 30” to the CFP velocity vector, which corresponds to an attenuation of 1.3 dB. Thus, the true mechanical lever ratio is estimated to be 2.7 (2.9 cos 3O/cos 20) for frequencies up to 1 kHz. This mechanical lever ratio may be compared with the theoretical geometric lever ratio derived for rigid bodies. As a first approbation let the relative motion between the columellar stalk and the extra-columella at or near the synchondrasis be approximated by motion about a pin connection located at the synchondrosis. If the ES rotates about the axis described in the foregoing paragraph and the CFP is constrained by the annular ligament to piston-like motion, then the geometric lever ratio, la, may be appro~mat~ by I,=
cos 8 sin(d-8)
sin e sina
* If the angles f&, yt) and (&, y2) define the directiom of two vectors, then the angle, 8, between them is defined by cosB=cosy,cnsy,cos{S,-_P,)+sinytsiny,.
12
where e=9O-(b
-a)
(2)
and a, b, c, d are defined in Fig. lb and Table I. The first ratio in Eq. (1) is the lever ratio for the tip of the ES and the synchondrosis, while the second ratio is the lever ratio for the synchondrosis and the CFP; the first ratio dominates 1,. For the angles a, b, c, d listed in Table I, 1, 1s 1.6, which is somewhat smaller than the mechanical lever ratio. However, 1, is critically dependent on the difference angle (d-B), which is specified by three angle measurements. If (d - 8) is reduced by only 15 “, from 34” to 19’, then the ratio of 2.7 is obtained. That is, given the inherent inaccuracies in the angle measurements, together with inaccuracies incurred by approximating the geometry of a three ~~ension~ structure by straight lines in a plane, it appears that the low-frequency mechanical lever ratio can be accounted for by the geometric lever ratio. It may be emphasized that the foregoing calcultions have presumed CFP motion to be piston-like at low frequencies, as do also, for example, Pohlman (1921) and Saunders (1985). However, others such as ~hw~t~opff (1954) and Gaudin (1968) have argued that the CFP must rotate about the posterior margin of the oval window; the annular ligament is narrower in that region. Gaudin (1968) made double-exposure photographs of the middle ear in ‘fresh preparations’ (presumably post mortem), in response to unspecified applied pressure on the TM. A rotational motion of the mammalian stapes, based on post mortem observations, had been proposed many times prior to the report of Guinan and Peake (1967), which demonstrated piston-like motion of the stapes in cats with ears in apparently good physiological condition (click N, threshold no more than 10 dB above the median). Examination of Gaudin’s kinematic drawing (Gaudin, 1968; Fig. 10) and extrapolation of our mean ES velocity data in Fig. 4a to very low frequencies, where his observations are expected to have been made, and use of our measured mechanical lever ratio of 2.7, would suggest that at a frequency of, say, 1 Hz, a SPL of at least 118 dB would be required to produce the displacement amplitude depicted in Fig. 10 by Gaudin
(1968) at the centre of the posterior region of the CFP, where the Mijssbauer source was placed in our experiments. Although our vibration measurements at a single point on the CFP can not resolve the question directly, the size of the lever ratios reported here implies that translational motion is dominant, at least at low frequencies: the lever ratios would be expected to be about a factor of 2 smaller for rotation of the CFP about the posterior margin of the oval window. In summary, the low-frequency mechanical lever ratio can be accounted for solely by the geometric lever ratio of a rigid body, where the axis of rotation of the ES passes through the points of insertion in the tympanic margin of the infra-stapedius and of the projection of the tympanic surface of the ES, and where CFP motion is piston-like. Told ~r~~sfor~er ratio
The total transformer ratio for the middle ear, which expresses the ratio of fluid pressure at the CFP, P,, to sound pressure at the tip of the ES, P-r, is under lossless conditions the product of the mechanical lever ratio, 1, and the ratio of the effective areas of the TM and CFP, Ar/A,, (e.g. Dallas, 1973). The values of A, and A, are not known for the bird. We shall adopt the defi~tions of A, and A, given by Rosowski et al. (1985) for the single-ossicle ear of the alligator lizard; namely, A, is the ratio of the magnitude of the volume velocity of air at the TM to the magnitude of the mechanical velocity of the tip of the ES, and A, is the ratio of the magnitude of the volume and mechanical velocities of the CFP. Also by analogy to the work of Rosowski et al. (1985) we set A-r equal to 1.63 times the geometric planar area of the TM, denoted by A,,, and A, equal to the averaged area of the CFP and oval window. From the averaged anatomical data in Table I, we have A TM= 18.0 mm2, A, = 1.43 rnm2, which together with 1 = 2.7, gives P,/Pr = 55, which is equivalent to a pressure gain of 35 dB. This value is 8 dB smaller than that for alligator lizard (Rosowski et al., 1985); the geometric area ratio for alligator lizard is a factor of 2.4 larger, and the lever ratio is a factor of 1.1 larger. It is consistent with direct measurements for the three-ossicle ears of cat (Nedzelnitsky, 1980) and guinea pig (Dancer and
13
Franke, 1980). It should be emphasized that this low-frequency pressure gain is much larger than the gain of 22 dB calculated from the geometric planar area ratio alone. Firstly, by analogy to alligator lizard, the effective area of the TM has been presumed to be 1.63 times the geometric planar area, giving an additional gain of 4.2 dB. Secondly, and very importantly, despite being a single-ossicle ear, the pigeon middle ear does possess a mechanical lever mechanism which, according to the vibration measurements, contributes 8.6 dB to the gain. Acknowledgements
The experiments were conducted at Zentrum der Physiologie, Frankfurt, and were supported by the Deutsche Forschungsgemeinschaft, SFB 45. References Dallos, P. (1970) Low-frequency auditory characteristics: species dependence. J. Acoust. Sot. Am. 48, 489-499. Dallos, P. (1973) The Auditory Periphery. Academic Press, New York and London. Dancer, A. and Franke, R. (1980) Intracochlear sound pressure measurements in guinea pigs. Hear. Res. 2, 191-205. De Burlet, H.M. (1929) Zur vergleichenden Anatomie und Physiologie des perilymphatischen Raumes. Acta OtoLaryngol. 13, 153-187. Gaudin, E.P. (1968) On the middle ear of birds. Acta Otolaryngol. 65, 316-326. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1986) The mechanics of the basilar membrane and middle ear in the pigeion. In: J.B. Allen, J.L. Hall, A. Hubbard, S.T. Neely and A. Tubis (Eds.), Peripheral Auditory Mechanisms Springer-Verlag, Berlin, pp. 81-88. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1987) Basilar membrane motion in the pigeon measured with the Miissbauer technique. Hear. Res. 29, 63-92. Gummer, A.W., Smolders, J.W.Th. and Khnke, R. (1989) Mechanics of a single-ossicle ear: II. The columella footplate of the pigeon. Hear. Res. 39, 15-26. Harrison, J.B. and Furumoto, L. (1971) Pigeon audiograms: comparison of evoked potential and behavioral thresholds in individual birds. J. Audit. Res. XI, 33-42. Hienz, R.D., Sinnott, J.M. and Sachs, M.B. (1977) Auditory sensitivity of the redwing blackbird (Ageluius phoeniceur) and brown-headed cowbird (Molothrur arer). J. Comp. Physiol. Psych. 91, 1365-1376. Kohlloffel, L.U.E. (1984) Notes on the comparative mechanics of hearing. II. On co&ear shunts in birds. Hear. Res. 13, 77-81.
Konishi, M. (1986) Centrally synthesized maps of sensory space. TINS, April, 163-168. Lynch, T.J., III, Nedzelnitsky, V. and Peake, W.T. (1982) Input impedance of the cochlea in cat. J. Acoust. Sot. Am. 72, 108-130. Manley, G.A. (1972a) The middle ear of the Tokay Gecko, J. Comp. Physiol. 81, 239-250. Manley, G.A. (1972b) Frequency response of the middle ear of geckos. J. Comp. Physiol. 81, 251-258. Moffat, A.J.M. and Capranica, R.R. (1978) Middle ear sensitivity in anurans and reptiles measured by light scattering spectroscopy. J. Comp. Physiol. 127, 97-107. Nedzelmtsky, V. (1980) Sound pressures in the basal turn of the cat cochlea. J. Acoust. Sot. Am. 68, 1676-1689. Peake, W.T., and Ling, A., Jr. (1980) Basilar-membrane motion in the alligator lizard: Its relation to tonotopic organization and frequency selectivity. J. Acoust. Sot. Am. 67, 1736-1745. Pinder, A.C. and Palmer, A.R. (1983) Mechanical properties of the frog ear: vibration measurements under free- and closed-field acoustic conditions. Proc. R. Sot. Lond. B 219, 371-396. Pohlman, A.G. (1921) The position and functional interpretation of the elastic ligaments in the middle-ear region of Gallus. J. Morphol. 35, 229-262. Rosowski, J.J., Peake, W.T., Lynch, T.J., III, Leong, R. and Weiss, T.F. (1985) A model for signal transmission in an ear having hair cells with free-standing stereocilia. II. Macromechanical stage. Hear. Res. 20, 139-155. Rubel, E..W. (1984) Ontogeny of auditory system function. Ann. Rev. Physiol. 46, 213-229. Saunders, J.C. (1985) Auditory structure and function in the bird middle ear: An evaluation by SEM and capacitive probe. Hear. Res. 18, 253-268. Saunders, J.C. and Johnstone, B.M. (1972) A comparative analysis of middle-ear function in non-mammalian vertebrates. Acta Otolaryngol. 73, 353-361. Schwartzkopff, J. (1954) Schallsinnesorgane, ihre Funktion und biologische Bedeutung bei Vtigeln. Int. Ornithological Congress. llth, Basel, Proceedings, 189-208. Schwartzkopff, J. and Winter, P. (1960) Zur Anatomie der Vogel-Cochlea unter nattirlichen Bedingungen. Biol. Zbl. 79, 607-625. Vlaming, M.S.M.G., Aersten, A.M.H.J. and Epping, W.J.M. (1984) Directional hearing in the grass frog (Rana remporaria L.): I. Mechanical vibrations of tympanic membrane. Hear. Res. 14, 191-201. Wilson, J.P. and Bruns, V. (1983) Middle-ear mechanics in the CF-bat Rhinolophus ferrumequinum. Hear. Res. 10, l-13. Wit, H.P., Scheurink, A.J.W. and Bleeker, J.D. (1985) Hearing thresholds of normal and fenestrated deaf pigeons. Acta Otolaryngol. (Stockh.) 100, 36-41. Wolberg, J.R. (1967) Prediction Analysis. D. van Nostrand Co. Inc., New Jersey.
HRR
01191
Mechanics of a single-ossicle ear: I. The extra-stapedius
of the pigeon
Anthony W. Gummer ‘, Jean W.Th. Smolders 2 and Rainer Klinke 2 ’ Developmental Neurobiology Group, Research School of Biological Sciences, Australian National University, Canberra, A.C. T., Australia and ’ Klinikum der J. W. Goethe UniversitSit, Zentrum der Physiologic, Frankfurt am Main, E R.G. (Received
5 July 1988; accepted
27 November
1988)
The motion of the conical peak of the tympanic membrane (TM) at the tip of the extra-stapedius (ES) and of the columella footplate (CFP) were measured in the pigeon using the Mijssbauer technique. The dimensions of middle-ear structures were measured in some of the experimental animals. The averaged velocity response at the ES for frequencies of 0.25-2.378 kHz was that of a second order, mass and stiffness controlled, resonant system with resonant frequency of 1.2 kHz and Q, dB of 1.2. The mean velocity amplitude at resonance was 3.7 mms-’ at 100 dB SPL, which is approximately equal to the theoretical value of 3.5 mms-’ required for maximum energy transfer from a uniform plane acoustic wavefront in air. For the frequency regions 0.125-0.25 kHz and 2.378-5.657 kHz, the mean amplitude slopes for the velocity at the ES were 2 dB oc-’ and - 3 dB act-‘, respectively. Above 5.657 kHz there was considerable inter-animal variation in the ES velocity responses. The direction of motion at the ES was frequency dependent above 1 kHz. For frequencies up to 1 kHz the ratio of CFP to ES velocity was independent of frequency; the mechanical lever ratio was 2.7, which was attributed to the geometry of the middle ear. At these frequencies the total transformer ratio for the middle ear, expressing the ratio of fluid pressure at the CFP to sound pressure at the ES, was estimated to be 35 dB. Pigeon;
Bird; Single-ossicle;
Extra-stapedius;
Tympanic
membrane;
Introduction The efficiency of the avian middle ear in transforming air-borne sound to ossicular motion has received little attention. Despite its apparently simple structure, having only a single ossicle, the neglect is rather surprising given that the avian model has provided a wealth of information about the ontogenesis (Rubel, 1984) and the temporal coding properties (Konishi, 1986) of the auditory system. Two reports on the ‘function’ of the avian middle ear based on vibration measurements are to be found in the literature (Saunders and Johnstone, 1972; Saunders, 1985). However, neither of these reports contain phase data essential for a description of ‘function’. Saunders and Johnstone
Correspondence to: A.W. Gummer, Developmental ology Group, Research School of Biological Australian National University, GPO Box 475, A.C.T. 2601, Australia. 0378-5955/89/$03.50
NeurobiSciences, Canberra,
0 1989 Elsevier Science Publishers
Columella
footplate;
Middle
ear; Miissbauer
technique
(1972) give the amplitude of the middle-ear transfer function in the Barbary Dove and Saunders (1985) gives the amplitude response of the tympanic membrane (TM) in chick and parakeet. The latter report also contains a quantitative description of the anatomy of the middle ear as viewed with the electron microscope. Pohlman (1921) provides a most comprehensive anatomical and functional description of the middle ear of Gallus. An extensive bibliography on avian middle ear is given by Gaudin (1968). A model for a structurally comparable single-ossicle ear does exist; namely, that proposed by Rosowski et al. (1985) for the alligator lizard. Although that model provides a basis for understanding the physics of the single-ossicle case, it is not completely applicable to the avian situation, principally because the loading conditions at the output of the middle ear are different: basilar-membrane (BM) motion in the alligator lizard is determined primarily by the middle ear, whereas the BM of the bird supports a travelling wave (Gummer et al., 1987). Moreover,
B.V. (Biomedical
Division)
2
the frequency response of the columella footplate (CFP) exhibits anti-resonance at high frequencies (Gummer et al., 1986). This paper reports on the motion of the middle ear of the pigeon, concentrating on the motion of the conical peak of the tympanic membrane (TM) at the tip of the extra-stapedius (ES), the middleear input stage. Although low-frequency data for the output stage, the CFP, is also included, the high-frequency motion of this structure is the subject of the companion paper (Gummer et al., 1989). Vibration measurements were made with the Mijssbauer technique. Materials and Methods
The experimental procedures were identical to those which were described extensively by the authors in a previous report (Gummer et al., 1987). Briefly, recordings were made from Nembutal(36 mg kg- ‘) anaesthetized pigeons ~C~~~~a liuia) of age OS-5 years (mode: 1.5) and weighing 390-500 g (450 * 50). Supplementary l/4-doses of anaesthetic were administered as required. Animals were artificially respired with a humidified gas mixture of 4% CO, and 96% 0, at 0.5 1 mm-‘. Body temperature was controlled (41 f 0.5 o C under the left wing) and the el~tr~~~o~~ was recorded. Animals were paralyzed with alcuronium chloride (10 mg kg-r), approximately 0.5 h before beginning the mechanical measurements. Sound was presented closed field from a Bri.iel and Kjaer 4134 12.7~mm condenser microphone. The level and the phase of the sound pressure at a distance of about 1.5 mm from the TM, about 0.5 mm dorsal to its conical peak, were measured with a calibrated l-mm probe tube mounted in the tip of the sound delivery cone. Sound pressure level (SPL) is re. 20 PPa and phase is negative for a lag. Sound pressure was measured at each stage of the experiment. The physiological condition of the ear was ascertained with a compound action potential (CAP) frequency threshold curve (FTC) recorded from a silver electrode placed on the co&ear wall at the ventral border of the round window, and referenced to a neck-muscle electrode. The hole made in the dorsal lateral side of the skull to place
the CAP electrode was not closed, thus enabling the condition of the round window membrane, the electrode tip, the CFP and the annular ligament to be clearly visualized; the diameter of the hole was about 4 mm. A CAP FTC was recorded at each stage of the experiment. The Mbssbauer source used for middle-ear measurements was a 200 X 2OO X 6 pm3 foil cut from a 57Co doped rhodium matrix with an initial total activity of 1.85 GBq mm-* and estimated weight of 3.3 pg. The absorber was a 4% 57Fe enriched vanadium foil. The combination had an isomer shift (Vi> of -0.27 mm-r and a full line-width at half ma~mum (F) of 0.79 mm-‘, calibrated in air with an acceptance angle of 30 *. This angle was typical of the acceptance angles used for recordings from middle-ear structures. The non-zero isomer shift gave phase ambiguity of integral cycles only. The amplitude and phase of the source velocity were estimated from period histograms of the transmitted 14.4keV y-radiation, using a non-tinear, least mean square algorithm (Wolberg, 1967), with constant parameters Vi and I’. For recordings of TM motion the Mossbauer source was placed on the conical peak of the TM opposite the tip of the ES (Fig. 1). The sound delivery cone was repositioned and sealed for closed field conditions. Good counting statistics were obtained without the need to fabricate a viewing window in the external auditory meatus. For recordings of CFP motion the Mossbauer source was placed on the CFP near its posterior extremity, about mid-way between the annular ligament and the base of the columellar stalk. A light smear of Vaseline on the contact surface of the source ensured adhesion to the moving surfaces. Anatomical constraints, together with the inherent uncertainty in the direction of the velocity vector of the moving surface, means that a component of the velocity vector was measured. Recordings were made with the Mijssbauer absorber positioned so as to obtain the maximum fractional Mtjssbauer effect. This fraction for the TM measurement configuration (0.20-0.28; 0.25 f 0.03) tended to be slightly larger than that for the CFP measurement configuration (0.17-0.27; 0.23 + 0.03), because of larger radiation scatter in the latter configuration.
3
Firm adhesion to the moving surface, maintained during the entire experiment, was indicated in two ways. Firstly, the source was always found firmly attached, precisely where it had been placed. Secondly, for all frequencies the cycle histograms did not deviate from the shapes expected for rigid coupling to a sinusoidally moving surface. The effects of insufficient coupling were examined through experiments in which the velocity of a source on the diaphram of a 12.7~mm condenser microphone (Brtiel and Kjaer, 4134) was used. If an adhesive was not used, or if the temperature at the diaphram became sufficiently high to cause the Vaseline to become less viscous, then the cycle histograms deviated from their normal appearance. Typically, under such conditions, a histogram would be skewed during half-cycles be-
tween zero velocities, or saturation of the count rate would be indicated during one half-cycle, but the count rate in the other half-cycle would be non-saturated with peak rate greater than the apparent saturation rate in the other half-cycle. Data were collected at source velocities of about 0.5 mms-r for frequencies above 0.7 kHz and 0.3 mill.5 -I for lower frequencies, where the former velocity produced optimal phase accuracy without overstimulation and the latter velocity resulted from limitations imposed by the sound system, particularly when making CFP recordings. On the average, the required SPL above 0.7 kHz was 88 dB for the TM and 100 dB for the CFP, and at lower frequencies was 90 dB for the TM and 95 dB for the CFP. Measurements started at 2 kHz, then usually went sequentially to higher frequen-
Pig. 1. Simplified fine drawing of the right middle ear of an adult pigeon; (a) three-dimensional medial view and (b) two-dimensional view identifying the angles used for calculating the geometric lever ratio. The extra-columella is composed of three cartilaginous structures: extra-stapedius (ES), ~fra-strap~us (IS) and supra-status (SS), which have approximately mutely orthogonat orientation. Cal: columelk CFP: columella footplate, TM: tympanic membrane; PL: Platner’s ligament: S: synchondrosis. The drum tubal ligaments and the intra-aural muscle are not shown. The dimensions of the different structures and the angles a,b,c and d are given in Table I. The broken line in (a) is the line representation of the axis of rotation of the extra-columella; (b) is drawn in a plane approximately orthogonal to this axis. The direction of the (mechanical) velocity vectors vus at the ES and cCFp at the CFP are defined, respectively, by rotation of the extra-columella about the axis passing through the point 0, and by translation of the CFP orthogonal to its medial surface. Components of Tim and fccFp were measured with the Mbssbauer technique.
4
ties and then to lower frequencies; in some experiments the measurements went sequentially from the highest to the lowest frequency. Repeat measurements were made at 2 kHz; the sequence always terminated with a 2-kHz measurement. The results were independent of the me~urement sequence. A cycle histogram containing 64 X lo3 counts required 42-98 s (64 f 13) to collate. Upon completion of an experiment, the animal was perfused systemically with buffered Ringer solution at 40” C followed by a fixative of 2.5% paraformaldehyde and 0.75% glutaraldehyde in 0.07M phosphate buffer at 4O C. The dimensions of middle-ear structures were measured in the manner similar to that used by Saunders (1985), the main difference being that light microscopic observations were made; the head was mounted in the experimental head-holder. Results In order to emphasize that vibration measurements were made at the conical peak of the TM opposite the tip of the ES, these responses will be referred to as ES responses. According to the morphological observations of Saunders (1985), the TM is firmly attached to the ES along its entire length. Responses of the ES and of CFP are presented as velocity relative to sound pressure at the TM; the SPL is 100 dB. Velocity amplitude at 100 dB SPL was calculated from the stimulus SPL and measured velocity amplitude assuming linearity: no evidence of non-linear motion of either structure was found in the experimental range 77-117 dB SPL. Phases (relative to sound pressure phase) are plotted using a logarithmic frequency axis in order that amplitude and phase curves may be
compared directly, particularly in the region of amplitude irregularities. Velocities rather than displacements are chosen because when expressed relative to sound pressure the latter yield functions which are proportional to acoustic admittances, transfer functions or tr~s~ssion functions. Thus, the so-called ES response is proportional to the transfer function of the TM at the tip of the ES, where the constant of proportionality is fi because velocity amplitudes are given here as peak values and SPL is an rms quantity. The so-called CFP response is proportional to the middle-ear transmission function where for piston-like motion the constant of proportion~ty is G/A,, where A, is the effective area of the CFP, which converts (mechanical) velocity to volume velocity. The reader is well referred to Rosowski et al. (1985) for terminology. Data are from ears (N = 6) in good physiological condition as judged by the CAP FTC. At the best frequency of the CAP FTC, namely at 1.414 kHz, the mean threshold was 42 f 7 dB SPL for the first CAP recordings and 41 i 5 dB SPL just before beginning the ES vibration measurements. These values compare with the mean of 39 f 5 dB SPL reported for the pigeon (Gummer et al., 1987). There was no significant difference between CAP FTCs recorded before and after the ES response me~urements (40 + 10 dB SPL at 1.414 kHz). Experiments are identified with an animal number prefixed by the acronym PGN. All recordings, except one (PGN 87), are from the right ear.
The amplitude and phase of the velocity of the ES at 100 dB SPL is shown in Fig. 2 for four
Fie. 2. Amnhtude (a.c.e.rr) ~ ,_, and .chase (b.d.f.h) . , of ES velocity and CFP velocity at 100 dB SPL as a function of frequency, for 4 . pigeons, identified as PGNs 87, 95, 96, 99. The unity subs&ipts on ES for PGN 99 and on CFP for PGN 96 indicate that the associated reponses were the first in a group of responses measured at that structure. The cochlea was intact for PGN 87,%, 99. For PGN 95 the responses of the BM, abneural limbus and CFP were measured in that order, before measuring the ES response; the Mossbatter source used for the former m~urements was left on the abneural limbus; the cochlea was full of fhrid and there was a hole in the co&ear wall. Data points are at frequency intervals of 0.25 act for frequencies up to 6.727 kHz and at 0.125 or 0.25 act for higher frequencies; (for PGN 99 there are data points at two additional frequencies, 5.339 and 6.169 kkiz). Arrows indicate the expected amplitude of the velocity (3.5 mms-‘) of the ES at 100 dB SPL if the specific impedance at the ES is half that of a uniform plane acoustic wavefront in air and, as such, represent a theoretical optimum velocity for the ES (Wilson and Bruns, 1983). In this and all subsequent Figures the amplitude plotting scale is 12 dB oc-r,
Velocity
Velocity ,
! I II!,
i0t
0 I
PGN 95
PGN 96
IOOdB SPL
IOOdB SPL
PGN 99 lOOd6
;;i
SPL
0 25
0)
iI _$
-0.25
e, zi AZ -0.75 a_ 0.1
L
0.2
0.5
1.0
Frequency
2
5
(kliz)
IO
20
0.1
0.2
I
*
srt*2tl 0.5
1.0
Frequency
,,,,,A 5
2
(kHzf
IO
20
6
animals, together with their CFP responses. Data from individual animals are displayed in separate panels in order that the salient features of each be discerned. Results from the ES are sup~~mposed in Fig. 3 to facilitate inter-animal comparisons and the mean ES response (six animals) is displayed in Fig. 4. The ES response exhibited a resonance with maximum between 1 and 1.414 kI-Iz dependent on the animal. The maximum velocity amplitude was approximately equal to the theoretical optimum amplitude of 3.5 rn.m~-~ at 100 dB SPLI given by the requirement that the specific impedance at the ES be equal to half the specific impedance of a u~fo~ plane acoustic wavefront in air (half the ch~acte~stic impedance of air, pc/Z), in order that maximum energy be transferred (Wilson and Bruns, 1983). In the remainder of this section the mean ES response in Fig. 4 is referred to because, despite some scatter in the absolute velocity amplitudes at low frequencies, it was an accurate representa~on of the ES response. The frequency
-2 22 -0.25
K
Y $
-0.75
W if -I
.25 0.l
0.2
0.5
1.0
Frequency
2
5
IO
20
fkHzi
Fig. 3. Superposition of the ES responses which have been displayed individually in Fig. 2. Arrows indicate the optimum ES velocity amplitude (3.5 mms-‘).
IOOdBSPL
0.25 ‘;i
2%
2, o
-0.25
g 6z -0.75 tl.i
0.2
05
1.0
Frequency
2
5
IO
20
(ktfzl
Fig 4. (a) Amplitude and (b) phase of the mean ES velocity from 6 animals at 100 dB SPL as a function of frequency. Points are at frequency intervals of 0.25 act up to 6.727 kHz, and at 0.125 act above 6.727 kHz. For the frequency regions 0.125-0.25, 0.297-L 1.189-2.378, 2.828-5.6.57, 6.727-11.314 kHz, respectively, the mean amplitude error was -9, -6, -13, - 14, - I1 dB; and the mean phase error was 0.025, 0.033, 0.053, 0.039, 0.12 cycles. Arrows indicate the optimum ES velocity amplitude (3.5 mms-‘f.
at which the phase was zero, called the resommt frequency, was 1.236 kHz (calculated by interpolation on a linear frequency axis). For frequencies of 0.25-2.378 kHz the ~p~tude slopes on either side of resonance were i6 dB act-‘, implying a second order resonant system. The Q3 dBwas 1.2, giving for a second order system, a damping constant of 0.64 and a group delay at the resonant frequency of 0.50 periods or 0.40 ms. The velocity amplitude at resonance was 3.7 mm-i, which would have been sufficiently close to the optimum of 3.5 mms-i to be almost equal to it. For frequencies of 0X25-0.25 kHz and 2.378-5.657 kHz the amplitude slopes were 2 dB act - ” and - 3 dB act-1, respectively. Above 5.6’75 kHz the amplitude slope was -6 dB act-I; the inter-anal variations were considerable. The amplitude response exhibited an end-slope varying from -38 dB act-’ in FGN 95 to 5 dB act-t in PGN 96. There was a phase difference of 0.5 cycles for 6-11.314 kIIz in PGNs 95 and 99, whereas the phase change above 5.657 kHz was small for PGNs 87 and 96.
Direction of motion of the extra-stapedius response
In order to ascertain the direction of motion of the ES and its possible frequency dependence, the motion of the ES was measured with the Mossbatter absorber in different orientations. The convention for spatial co-ordinates is given in Fig. 5. The results of an extensive experiment on PGN 99 are illustrated in Figs. 6 and 7. The first ES response was determined in that orientation which yielded the maximum Mossbauer fraction (/3 = 21 O, y = - 50 o in Fig. 7~). Having completed this set of recordings the absorber was rotated ventrally in the same vertical plane to y = - Sl“, and following the second set of recordings again ventrally in the same vertical plane to y = - 113”) where a third set of recordings was made. The differences of 31’ and 32” between subsequent recording configurations were chosen to be approximately equal to .the solid angle subtended by the Mijssbauer absorber at the source (28’); that is, the regions through which the radiation was absorbed were adjacent, with little overlap. The results are shown in Fig. 6. This series of measurements was followed by one in which measurements were made at five frequencies for 10 positions in the plane fl= 21’ (Fig. 7). The frequency
y (dorsal) 4
x (rostral)
Fig. 5. Convention for spatial co-ordinates. The line segment OP is the position repre~~tion of the rne~~ern~t axis, defined as the line from the Mossbauer source located at the origin 0, normal to the surface of the Mossbauer absorber at its centre, P. Notice that y is negative when the absorber is located ventrally as, in fact, it was for all experiments. The dashed line is the position representation of the surface normal of the CFP.
E
c3 a
5
99,-
0. I
-50’
-81' 99,--- - -113 99,-
p=210 lco_iBSPL
0.25
I
I
I111111
I
I111111
~
‘;; 9 -0.25 0” aI ; -0.79 -
99,99,-
a’
99,- -.- -113’
-1.251 0.1
I
02
-50’ -81’
I
I
p=21* I
IllIll
0.5
1.0
Frequency
2
5
10
20
(kHz)
Fig. 6. (a) Amplitude and (b) phase of ES velocity at 100 dB SPL as a function of frequency for 3 recording configurations for PGN 99. B and y are defined in Fig. 5. The solid angle subtended by the Mossbauer absorber at the source at the ES was 28O. Arrows indicate the optimum ES velocity amplitude (3.5 mms-1).
sequence was 2.378, 4.757, 6.727, 3.364, 8 kHz; and the angle sequence began at the most ventral position and increased monotonically. The change of measurement axis had insignificant effect on the recorded amplitudes below 1 kHz (Fig. 6a), indicating that the angle y for the ES velocity vector was close to the value of y for the measurement axis at the ~d-r#r~g location (y = - 81” >_However, at higher frequencies the measured velocity amplitudes were dependent on the recording angle. The consistent differences of about 3 dB in Fig. 6a could not be attributed to experimental errors because: (i) measured velocity amplitudes were reproducible to within 1 dB; (ii) the statistical error * for amplitude estimates was no more than + 0.6 dB; and (iii) the physiolo~c~ * These statistical errors are the mean values of the standard deviations of the amplitude estimates produced by the non-linear, least mean square fitting algorithm at all frequencies in a given amplitude response curve.
angle can, according to data in Fig. 7a, be attributed to the cosine effect. Moreover, and most importantly, the spatial invariance of the measured phase responses excludes the possibility of interference from other vibration modes. It is therefore concluded that the direction of motion of the ES simply changed for frequencies above 1 kHz. Columella footplate stapedius response
response
relative
to extra-
Conditions prevailing at the CFP are more complicated than might be expected from such an apparently simple structure. The CFP responses relative to the ES responses for three of the animals from Fig. 2 are presented in Fig. 8. The measurement axis for the CFP was typically /3 = 90 O, y = - 25 ‘. For frequencies up to about 1 kHz the CFP and ES moved in phase with CFP motion attenuated relative to ES motion by a constant
20
-160
-90
1
I I,/,,11
CFP re ES /
/ I I , , ,I,
a.
7
0
3 ventral --I Fig. 7. (a) Amplitude and (b) phase of ES velocity at 100 dB SPL as a function n&recording angle for 5 frequencies for PGN 99. The angle y was varied for constant j3 = 21’. Frequency code: o 2.378 kHz, v 3.364 kHz, 0 4.757 kHz, A 6.727 kHz, 0 8 kHz. The curve in (a) shows a hypothetical cosine variation of velocity amplitude with recording an&e: the chosen velocity amplitude is 5 mm-’ at y = -90°. Arrows indicate the opium ES velocity amplitude (3.5 mms-“). (c) Mossbauer fraction - notice that it is smaller at the more ventral locations. Repeat measurements were made at y = - 81 o (constant /3 = 21 o ).
condition of the auditory periphery was stable, as judged by the CAP thresholds (34 f 2 dB SPL at 1.414 lcHz). Moreover, the phase responses in Fig. 6b are virtually superimposable and the phase plots in Fig. 7b form near horizontal lines, which would not have been expected had experimental conditions changed. However, the dependence of the measured velocity amplitudes on recording
Frequency Fig. 8. (a) Amplitude ES velocity
(kHz)
and (b) phase of CFP velocity relative from 3 of the animals of Fig. 2.
to
9
amount of 9.2 * 2.4 dB. That is, in this frequency range there was a simple frequency independent transformation from ES velocity to CFP velocity. At higher frequencies, however, the transformation was frequency dependent. An anti-resonance at 4-8 kHz was evident in some responses and was due to an anti-resonance measured at the CFP. This high-frequency effect is associated with the coupling between the CFP and cochlea and is the subject of the companion paper, (Gummer et al., 1989). Discussion
Resonance in the ES response According to behavioural auditory threshold data (Harrison and Furumoto, 1971; Hienz et al., 1977; Wit et al., 1985), the relevant frequency range for auditory function in the pigeon is 0.25-4 kHz. For frequencies of 0.25-2.378 kHz the ES response was that of a second order, mass and stiffness controlled, resonant system with resonant frequency of 1.2 kHz and Q3 dB of 1.2, where resonance is defined as the frequency at which the phase response is zero. The velocity amplitude at resonance was 3.7 mms-’ at 100 dB SPL, which is approximately equal to the theoretical value of 3.5 required for optimal detection of a uniIllIll-’ form plane acoustic wavefront in air. The situation would appear to be somewhat different from the three other avian species for which the amplitude of the ES response has been published. From the reports of Saunders and Johnstone (1972) and Saunders (1985) one calculates for Barbary Dove, 6-9 day old chicks and parakeet, respectively, Q3 dB of 1.1, 0.7, 0.6, and maximum velocity amplitude at 100 dB SPL of 1.3, 2, 5 rmn~-~. Since phase data are not available for these species the resonant frequency required for calculation of Qj dB was approximated by the frequency at maximum velocity amplitude in Barbary Dove (2 kHz) and the octave centre of the frequency range of maximum velocity response in chick and parakeet (3 and 2.1 kHz, respectively). In these species however the resonance is not of second order because although the low-frequency amplitude slope was 6 dB act-‘, the high-frequency slope was - 16 dB act- ’ in chick and parakeet (Saunders, 1985) and - 12 dB
act-’ in Barbary Dove (between 8-10 kHz in Fig. 6 of Saunders and Johnstone, 1972). The resonance in the ES response for the alligator lizard is similar to that for the pigeon, although it is over-damped (Q3 dB = 0.5); the velocity amplitude at the resonant frequency of 1.6 kHz is 4.7 rnms-’ at 100 dB SPL (calculated from Rosowski et al., 1985, Fig. 3). The high-frequency amplitude slope of - 7 dB act- ‘, which is close to - 6 dB act -l for second order resonant condiover the entire hightions, was maintained frequency range of 1.8 to 9 kHz (Peake and Ling, 1980; Rosowski et al., 1985). Comparisons with published data for three-ossicle ears indicate that the resonance in the ES response for the pigeon is most akin to that for two species of bat ( Rhinolophus ferrumequinum and Eptesicus pumilis), except of course, that their resonant frequencies are far greater (55 and 25 kHz, respectively) - the resonance is of second order with Q3 dB of 1 and near-optimum velocity amplitude at resonance (Wilson and Bruns, 1983).
Low- and high-frequency ES responses For frequencies of 0.125-0.25 kHz and 2.378-5.657 kHz the slopes of the mean amplitude curve were not f 6 dB act- ‘, as required of a second order resonant system, but rather 2 dB act -’ in the lower frequency range and - 3 dB act-’ in the upper frequency range (Fig. 4a). Moreover, the low-frequency phase asymptote was 0.15 cycles (Fig. 4b), instead of the 0.25 cycles required of a second order resonant system. The low-frequency phase values cannot be accounted for by the acoustic delay (= 4 ps) incurred by the separation (= 1.5 mm) between the tip of the probe tube coupler, where sound pressure was recorded, and the MSssbauer source at the tip of the ES. For frequencies of 6-11.314 kHz the interanimal variation in the ES responses was considerable. The largest amplitude slope was -38 dB act t1 (PGN 95) and the slope of the mean amplitude curve was - 6 dB act- ‘. This value is smaller than values of - 12 dB act- ’ for Barbary Dove (Saunders and Johnstone, 1972) and - 16 dB act- ’ for chick and parakeet (Saunders, 1985). Similar intra-species variations are found in the mean high-frequency slope of the velocity amplitudes
for reptiles (Manley, 1972a,b; Saunders and Johnstone, 1972; Peake and Ling, 1980; Rosowski et al., 1985), and anurans (Saunders and Johnstone, 1972; Moffat and Capranica, 1978; Pinder and Palmer, 1983; VIaming et al., 1984). ES responses recorded along different measurement axes produced no evidence for other vibration modes acting at the ES which could have interfered with the normal vibration mode at high frequencies. Instead the direction of motion of the ES simply appeared to change for high-frequency stim~ation, as has been reported for geckos (Manley, 1972a,b). Given the morphological observations of Saunders (1985) that the columella
TABLE
and extra-columella are tightly joined by a synchondrosis, it would appear that this joint cannot be directly responsible for the high-frequency responses. The results of cochIear ma~pulation experiments (Gummer et al., 1989) show that the cochiea acts as a frequency dependent load. For frequencies of 0.125-0.25 kHz the helilcotrema and Ductus brevis, both of which have been described in the pigeon by De Burlet (1929), Schwartzkopff and Winter (1960), and Kohlliiffel (1984), may provide inertial pathways for fluid flow, as has been proposed for the mammal (Dallas, 1970; Lynch et al., 1982; Rosowski et al., 1985) and
I
DIMENSIONS
a OF THE PIGEON
Structure
MIDDLE
EAR h
Measure
Tympanic
membrane
Columella
footplate
Oval window
Extra-stapedius Columella
Extra-stapedius to columella Columella to columella footplate Columella to tympanic membrane
maximum diameter ’ minimum diameter planar area d half cone angle (d) over extra-stapedius maximum diameter ~~rnurn diameter amae maximum diameter minimum diameter area e length ’ length g lateral angle ( fi) h elevation angle ( - u) angle (b) i angle (c) J angle (a) ’
Mean 5.6 4.1 18.0 66 1.90 0.92 1.23 2.08 0.97 1.63 1.73 2.08 56 12 162 95 104
Range 5.433.6816.27-
5.70 4.40 19.35
59 - 71 1.801.95 0.851.00 l.OO1.4s 2.052.10 0.881.08 1.4% 1.75 1.531.91 1.902.23 52 - 60 8 -15 160 -164 91 -100 102 -105
a Units: mm, mm2, degrees. b From the right ear of five pigeons (PGN 88, 89, 95, 96, 99). ’ The margin is located at the transition from the translucent, smooth tympanic membrane into the opaque grey-white tissue outlining the external auditory meatus. pushing gently on the tip of the extra-stapedius, thus moving the tympanic membrane, aided definition of the margin. d Caiculated from maximum and minimum diameters assuming an ellipse. e Measured from phot~aphs. f From the synchondrosis (between columella and extra-columella) to the tip of the extra-stapedius. s From the synchondrosis to the point of insertion of the columella stalk in the columellar footplate. Since the columellar stalk is slightly bowed, this line is used to define its long axis. h Angles /3 and y defined in Fig. 5 with the head mounted in the experimental head-holder. i Obtuse angle between the lines defined in f and g. J Obtuse angle between the columellar stalk and the columella footplate. The orientation of the columella footplate is such that the surface normal to the columella footplate is defined approximately by B = 61 O, y = - 12 O. k Obtuse angle between the columellar stalk and the piane formed by the margin of the tympanic membrane.
11
which has also been proposed for the bird by Kohllbffel(l984). The impedance of this pathway can account for the observed deviation of the ES response from that of a second order resonant system below 0.25 kHz. Above 2,378 kHz there is evidence for a second vibration mode at the CFP, which interferes with the presumed piston-like mode, causing a sharp anti-resonance tuned to about 6 kHz (Gu~er et al., 1989). That is, the middle ear is confronted by a near infinite impedance in the 6kHz region, which would cause the middle-ear complex to bend or flex, the exact site of which is unknown. This mechanism can account for the observed deviation of the ES response from that of a second order resonant system above 2.378 kHz. Moreover, the age-dependent ossification of the extra-columellar stalk (Gaudin, 1968; Saunders, 1985) can explain the observed interanimal variations above 5657 kHz.
To aid further discussion the dimensions of middle-ear structures of five of the pigeons used in this study are summarized in Table I. Although some dimensions, such as the diameters, are not referred to in the text, they are included for completeness and to allow ~mp~son with the values reported by Saunders (1985). The most significant differences between the two sets of data, believed to be inter-animal differences, are in the size of the CFP and its orientation to the columella: in the present group of animals the area of the CFP is larger and the long axis of the columellar stalk is tilted from the surface normal of the CFP by 5 o rather than by the 17.8” reported by Saunders (1985). Leuer ratios
The frequency independent attenuation of CFP velocity relative to ES velocity of 9.2 dB for frequencies up to 1 kHz, together with the zero phase difference, imply a measured mechanical lever ratio of 2.9 at these frequencies. This value corresponds to the measured value of 3.2 for Barbary Dove using the Mossbauer technique (Saunders and Johnstone, 1972) and to the geometric value of 3 for alligator lizard using anatomical data (Rosowski et al., 1985). The value of the true mechanical lever ratio is
different from the measured value because anatomical constraints meant that only components of the ES and CFP velocity vectors Gould be measured; these vectors are denoted by _uEsand gcrP in Fig. lb. Estimation of the angle between the ES velocity vector and the ES measurement axis requires a knowledge of the location of the axis of rotation of the ES. Careful surgical exposure of the middle ear and s~ulatian of the CFP and of the ES with a glass micropipette indicated that at low frequencies the axis of rotation passed through two points on the margin of the TM; namely, at the insertion of the infrastapedius and at the insertion of a line projected along the tympanic surface of the ES (Fig. la). The direction of the ES velocity vector is then described by the angles /3 = 48 a) y = - 63O, which for the usual ES measurement axis with p = 21*, means that the ES recordings were y= -50°, made at an angle of 20° to the ES velocity vector *, which corresponds to an attenuation of 0.5 dB. The surface normal of the CFP is defined by the angles B = 61°, y = -12”, which for the usual CFP m~surement axis with /3 = 90 O, y = - 25 O, and for a presumed piston-like motion of the CFP, means that the CFP recordings were made at an angle of 30” to the CFP velocity vector, which corresponds to an attenuation of 1.3 dB. Thus, the true mechanical lever ratio is estimated to be 2.7 (2.9 cos 3O/cos 20) for frequencies up to 1 kHz. This mechanical lever ratio may be compared with the theoretical geometric lever ratio derived for rigid bodies. As a first approbation let the relative motion between the columellar stalk and the extra-columella at or near the synchondrasis be approximated by motion about a pin connection located at the synchondrosis. If the ES rotates about the axis described in the foregoing paragraph and the CFP is constrained by the annular ligament to piston-like motion, then the geometric lever ratio, la, may be appro~mat~ by I,=
cos 8 sin(d-8)
sin e sina
* If the angles f&, yt) and (&, y2) define the directiom of two vectors, then the angle, 8, between them is defined by cosB=cosy,cnsy,cos{S,-_P,)+sinytsiny,.
12
where e=9O-(b
-a)
(2)
and a, b, c, d are defined in Fig. lb and Table I. The first ratio in Eq. (1) is the lever ratio for the tip of the ES and the synchondrosis, while the second ratio is the lever ratio for the synchondrosis and the CFP; the first ratio dominates 1,. For the angles a, b, c, d listed in Table I, 1, 1s 1.6, which is somewhat smaller than the mechanical lever ratio. However, 1, is critically dependent on the difference angle (d-B), which is specified by three angle measurements. If (d - 8) is reduced by only 15 “, from 34” to 19’, then the ratio of 2.7 is obtained. That is, given the inherent inaccuracies in the angle measurements, together with inaccuracies incurred by approximating the geometry of a three ~~ension~ structure by straight lines in a plane, it appears that the low-frequency mechanical lever ratio can be accounted for by the geometric lever ratio. It may be emphasized that the foregoing calcultions have presumed CFP motion to be piston-like at low frequencies, as do also, for example, Pohlman (1921) and Saunders (1985). However, others such as ~hw~t~opff (1954) and Gaudin (1968) have argued that the CFP must rotate about the posterior margin of the oval window; the annular ligament is narrower in that region. Gaudin (1968) made double-exposure photographs of the middle ear in ‘fresh preparations’ (presumably post mortem), in response to unspecified applied pressure on the TM. A rotational motion of the mammalian stapes, based on post mortem observations, had been proposed many times prior to the report of Guinan and Peake (1967), which demonstrated piston-like motion of the stapes in cats with ears in apparently good physiological condition (click N, threshold no more than 10 dB above the median). Examination of Gaudin’s kinematic drawing (Gaudin, 1968; Fig. 10) and extrapolation of our mean ES velocity data in Fig. 4a to very low frequencies, where his observations are expected to have been made, and use of our measured mechanical lever ratio of 2.7, would suggest that at a frequency of, say, 1 Hz, a SPL of at least 118 dB would be required to produce the displacement amplitude depicted in Fig. 10 by Gaudin
(1968) at the centre of the posterior region of the CFP, where the Mijssbauer source was placed in our experiments. Although our vibration measurements at a single point on the CFP can not resolve the question directly, the size of the lever ratios reported here implies that translational motion is dominant, at least at low frequencies: the lever ratios would be expected to be about a factor of 2 smaller for rotation of the CFP about the posterior margin of the oval window. In summary, the low-frequency mechanical lever ratio can be accounted for solely by the geometric lever ratio of a rigid body, where the axis of rotation of the ES passes through the points of insertion in the tympanic margin of the infra-stapedius and of the projection of the tympanic surface of the ES, and where CFP motion is piston-like. Told ~r~~sfor~er ratio
The total transformer ratio for the middle ear, which expresses the ratio of fluid pressure at the CFP, P,, to sound pressure at the tip of the ES, P-r, is under lossless conditions the product of the mechanical lever ratio, 1, and the ratio of the effective areas of the TM and CFP, Ar/A,, (e.g. Dallas, 1973). The values of A, and A, are not known for the bird. We shall adopt the defi~tions of A, and A, given by Rosowski et al. (1985) for the single-ossicle ear of the alligator lizard; namely, A, is the ratio of the magnitude of the volume velocity of air at the TM to the magnitude of the mechanical velocity of the tip of the ES, and A, is the ratio of the magnitude of the volume and mechanical velocities of the CFP. Also by analogy to the work of Rosowski et al. (1985) we set A-r equal to 1.63 times the geometric planar area of the TM, denoted by A,,, and A, equal to the averaged area of the CFP and oval window. From the averaged anatomical data in Table I, we have A TM= 18.0 mm2, A, = 1.43 rnm2, which together with 1 = 2.7, gives P,/Pr = 55, which is equivalent to a pressure gain of 35 dB. This value is 8 dB smaller than that for alligator lizard (Rosowski et al., 1985); the geometric area ratio for alligator lizard is a factor of 2.4 larger, and the lever ratio is a factor of 1.1 larger. It is consistent with direct measurements for the three-ossicle ears of cat (Nedzelnitsky, 1980) and guinea pig (Dancer and
13
Franke, 1980). It should be emphasized that this low-frequency pressure gain is much larger than the gain of 22 dB calculated from the geometric planar area ratio alone. Firstly, by analogy to alligator lizard, the effective area of the TM has been presumed to be 1.63 times the geometric planar area, giving an additional gain of 4.2 dB. Secondly, and very importantly, despite being a single-ossicle ear, the pigeon middle ear does possess a mechanical lever mechanism which, according to the vibration measurements, contributes 8.6 dB to the gain. Acknowledgements
The experiments were conducted at Zentrum der Physiologie, Frankfurt, and were supported by the Deutsche Forschungsgemeinschaft, SFB 45. References Dallos, P. (1970) Low-frequency auditory characteristics: species dependence. J. Acoust. Sot. Am. 48, 489-499. Dallos, P. (1973) The Auditory Periphery. Academic Press, New York and London. Dancer, A. and Franke, R. (1980) Intracochlear sound pressure measurements in guinea pigs. Hear. Res. 2, 191-205. De Burlet, H.M. (1929) Zur vergleichenden Anatomie und Physiologie des perilymphatischen Raumes. Acta OtoLaryngol. 13, 153-187. Gaudin, E.P. (1968) On the middle ear of birds. Acta Otolaryngol. 65, 316-326. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1986) The mechanics of the basilar membrane and middle ear in the pigeion. In: J.B. Allen, J.L. Hall, A. Hubbard, S.T. Neely and A. Tubis (Eds.), Peripheral Auditory Mechanisms Springer-Verlag, Berlin, pp. 81-88. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1987) Basilar membrane motion in the pigeon measured with the Miissbauer technique. Hear. Res. 29, 63-92. Gummer, A.W., Smolders, J.W.Th. and Khnke, R. (1989) Mechanics of a single-ossicle ear: II. The columella footplate of the pigeon. Hear. Res. 39, 15-26. Harrison, J.B. and Furumoto, L. (1971) Pigeon audiograms: comparison of evoked potential and behavioral thresholds in individual birds. J. Audit. Res. XI, 33-42. Hienz, R.D., Sinnott, J.M. and Sachs, M.B. (1977) Auditory sensitivity of the redwing blackbird (Ageluius phoeniceur) and brown-headed cowbird (Molothrur arer). J. Comp. Physiol. Psych. 91, 1365-1376. Kohlloffel, L.U.E. (1984) Notes on the comparative mechanics of hearing. II. On co&ear shunts in birds. Hear. Res. 13, 77-81.
Konishi, M. (1986) Centrally synthesized maps of sensory space. TINS, April, 163-168. Lynch, T.J., III, Nedzelnitsky, V. and Peake, W.T. (1982) Input impedance of the cochlea in cat. J. Acoust. Sot. Am. 72, 108-130. Manley, G.A. (1972a) The middle ear of the Tokay Gecko, J. Comp. Physiol. 81, 239-250. Manley, G.A. (1972b) Frequency response of the middle ear of geckos. J. Comp. Physiol. 81, 251-258. Moffat, A.J.M. and Capranica, R.R. (1978) Middle ear sensitivity in anurans and reptiles measured by light scattering spectroscopy. J. Comp. Physiol. 127, 97-107. Nedzelmtsky, V. (1980) Sound pressures in the basal turn of the cat cochlea. J. Acoust. Sot. Am. 68, 1676-1689. Peake, W.T., and Ling, A., Jr. (1980) Basilar-membrane motion in the alligator lizard: Its relation to tonotopic organization and frequency selectivity. J. Acoust. Sot. Am. 67, 1736-1745. Pinder, A.C. and Palmer, A.R. (1983) Mechanical properties of the frog ear: vibration measurements under free- and closed-field acoustic conditions. Proc. R. Sot. Lond. B 219, 371-396. Pohlman, A.G. (1921) The position and functional interpretation of the elastic ligaments in the middle-ear region of Gallus. J. Morphol. 35, 229-262. Rosowski, J.J., Peake, W.T., Lynch, T.J., III, Leong, R. and Weiss, T.F. (1985) A model for signal transmission in an ear having hair cells with free-standing stereocilia. II. Macromechanical stage. Hear. Res. 20, 139-155. Rubel, E..W. (1984) Ontogeny of auditory system function. Ann. Rev. Physiol. 46, 213-229. Saunders, J.C. (1985) Auditory structure and function in the bird middle ear: An evaluation by SEM and capacitive probe. Hear. Res. 18, 253-268. Saunders, J.C. and Johnstone, B.M. (1972) A comparative analysis of middle-ear function in non-mammalian vertebrates. Acta Otolaryngol. 73, 353-361. Schwartzkopff, J. (1954) Schallsinnesorgane, ihre Funktion und biologische Bedeutung bei Vtigeln. Int. Ornithological Congress. llth, Basel, Proceedings, 189-208. Schwartzkopff, J. and Winter, P. (1960) Zur Anatomie der Vogel-Cochlea unter nattirlichen Bedingungen. Biol. Zbl. 79, 607-625. Vlaming, M.S.M.G., Aersten, A.M.H.J. and Epping, W.J.M. (1984) Directional hearing in the grass frog (Rana remporaria L.): I. Mechanical vibrations of tympanic membrane. Hear. Res. 14, 191-201. Wilson, J.P. and Bruns, V. (1983) Middle-ear mechanics in the CF-bat Rhinolophus ferrumequinum. Hear. Res. 10, l-13. Wit, H.P., Scheurink, A.J.W. and Bleeker, J.D. (1985) Hearing thresholds of normal and fenestrated deaf pigeons. Acta Otolaryngol. (Stockh.) 100, 36-41. Wolberg, J.R. (1967) Prediction Analysis. D. van Nostrand Co. Inc., New Jersey.