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Mechanics of a single-ossicle ear: II. The columella footplate of the pigeon
15
Hearing Research, 39 (1989) 15-26 Elsevier
HRR 01192
Mechanics of a single-ossicle ear: II. The columella footplate 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 Universitiit, Zentrum der Physiologic, Frankfurt am Main, F.R G. (Received
5 July 1988; accepted
27 November
1988)
The motion of the columella footplate (CFP) was measured in the pigeon using the Mossbauer technique. At the upper frequency limit of the cochlea the measured CFP response exhibited anti-resonant phenomena. These high-frequency responses were dependent on the orientation of the radiation detector, in a way which could not be explained by the cosine effect. The dependence of the recorded phase response on the measurement axis implies an additional vibration mode, which was out of temporal phase and non-collinear with the presumed translational vibration mode. The anti-resonant phenomena were not observed when the cochlear labyrinth was extirpated, thus excluding an explanation in terms of extraneous vibrations in the experimental apparatus or of loading by the Mijssbauer source. Intra-cochlear reflection is proposed as the origin of the interference mode. Pigeon;
Single-ossicle;
Columella
footplate;
Middle
ear; Basilar
Introduction The mechanical conditions prevailing at the input to the avian cochlea have not been adequately described. For frequencies up to 1 kHz in pigeon the motion of the columella footplate (CFP) is in phase, although attenuated, with the motion of the extra-stapedius (ES); the mechanical lever ratio is 2.7, and can be attributed to the geometry of the middle ear (Gummer et al., 1989). At higher frequencies the mechanical lever ratio is frequency dependent. Although frequency dependence is inevitable, the exact form of the dependence is surprising: under most recording conditions the middle-ear transmission function, which expresses CFP volume velocity relative to sound pressure at the tympanic membrane (TM), displays anti-resonant phenomena for frequencies above 2.828 kHz, (Gummer et al., 1986). If CFP motion is then used as a reference for basilar membrane (BM) motion in the basal region of the basilar papilla (BP), BM
Correspondence to: A.W. Gummer, Developmental Neurobiology Group, Research School of Biological Sciences, Australian National University, GPO Box 475, Canberra A.C.T. 2601, Australia. 0378-5955/89/$03.50
0 1989 Elsevier Science Publishers
membrane;
Mlissbauer
technique
motion appears to lead CFP motion over an extended frequency range (Gumrner et al., 1987). Anti-resonances are not observed in: (i) the response of the ES, (Gummer et al., 1989); (ii) the BM velocity response expressed relative to sound pressure at the TM; and (iii) the compound action potential (CAP) frequency tuning curve (FTC), (Gummer et al., 1987). Anti-resonances have been reported in the motion of the incus in the guinea pig in a similar frequency range (3-8 kHz) by Wilson and Johnstone (1975), where it was attributed to a frequency-dependent transverse motion. Anti-resonance in this frequency range was not particularly troublesome in that report because BM motion was recorded from the basal region of the cochlea, so that when stapes motion was used as a reference, the frequencies of antiresonance appeared on the low-frequency tail of the relative BM response. The highest frequency represented on the BM of guinea pig is 45 kHz, (Wilson and Johnstone, 1975), whereas it is only 6 kHz in pigeon, (Gurmner et al., 1987). The antiresonant phenomena deserve further investigation because their presence begs the question: what is the effective input to the cochlea? To this end, we have recorded the motion of the CFP of the
B.V. (Biomedical
Division)
16
pigeon using the Mossbauer technique, before and after structural manipulations of the cochlea. Methods
The experimental procedures are identical to those which were described extensively by the authors in a previous report, (Gummer et al., 1987) and which were also presented in a condensed form in the companion paper (Gummer et al., 1989). Very briefly, recordings were made from Nembutal (36 mg kg-‘) anaesthetized pigeons (Columba hia) of age 0.5-5 years (mode: 1.5) and weighing 360-550 g (450 t- 60). Supplements l/Cdoses of anaesthetic were administered as required. The physiological condition of the ear was ascertained with a CAP FTC recorded from the ventral border of the round window, and referenced to a neck electrode. Measurements of CFP velocity were made with the cochlea in various states: (i) intact; (ii) fenestrated; (iii) fenestrated, cochlear labyrinth extirpated; and (iv) as for (iii) but fluid drained. It suffices to mention that: (i) a muscle relaxant was used (alcuronium chloride, 10 mg kg-‘); (ii) sound pressure at the TM was measured after each structural manipulation of the cochlea; (iii) the isomer shift of the Mossbauer source-absorber combination was non-zero (-0.27 mm s-l), giving phase ambiguity of integral cycles only; (iv) the minimal detectable velocity was 0.05-0.1 mms-‘. Results
Responses of the 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 the measured velocity amplitude assuming linearity: no evidence of non-linear motion was found in the experimental range 77-117 dB SPL and 0.1-11.314 kHz. Data are from ears (N = 20) in good physiological condition as judged by the CAP FTC. Experiments are identified with an animal number prefixed by the acronym PGN. Most recordings are from the right ear, the exceptions being from PGN 84, 87, 104. At the best frequency of the
CAP FTC (1.414 kHz), the mean threshold was 40 + 5 dB SPL for the first CAP recordings *. This value compares with the mean of 39 i 5 dB SPL reported for the pigeon (Gummer et al., 1987). Data are included from seven animals from earlier experiments (up to PGN 95) from which intra-cochlear vibration recordings had been made. The mean CAP threshold at 1.414 kHz, recorded just before beginning the CFP vibration recordings, was 42 f 5 dB SPL for the intact cochlea group and 67 it: 10 dB SPL for the non-intact group. There was no significant difference between CAP FTCs recorded before and after the CFP response measurements (43 i 7 and 64 f 6 dB SPL, respectively, for the intact and non-intact groups, at 1.414 kHz).
The amplitude and phase of the velocity of the CFP at 100 dB SPL is shown in Fig. 1 for seven animals. Two classes of phase response were evident at high frequencies (Fig. lc); the phase difference between low and high frequencies (0.125 and 11.314 kHz) was either one or two cycles. In order to facilitate comparisons, the amplitude responses have been placed in separate panels (a or b) in Fig. 1 according to the division of the high-frequency phases. For the usual position of the Mbssbauer absorber the number of phase responses in each class was equal (20 experimental animals). A dependence of the recorded responses on the position of the Mijssbauer absorber is described in the next two sections. Seven of the eight responses in Fig. 1 illustrate the three unusual features of the CFP response found at high frequencies: (i) anti-resonance; (ii) exceedingly large phase rotation (two cycles at 11.314 kHz); and (iii) positive phase slope. The eighth response (PGN 92) is an example of one of the five responses which did not exhibit these high-frequency effects. The anti-resonances were found in both classes of phase response. There were nine animals which exhibited anti-resonance which could be described as having been sharp, with Q3 dB greater than or equal to 8. Their mean Q 3 dB was 17 + 8. In the case of these sharp
* Statistical
errors
are siandard
deviations.
Cotumella 10.0
I
footptate
1 1111111
velocity 1
I ,,I1111
I
100
-Q-
106,
Frequency
0.
dg SPL
IOOdB SPL
(kHzz)
Fig. 1. (a), (b) Amplitude and {c) phase of CFP velocity at 100 dl3 SPL as a function of frequency for 8 measurements series in 7 pigeons. The co&lea was intact for pigeon (PGN) 96, 102, 104, 105,. and 106t. BM motion was measured prior to measurement of CFP motion in PGN 92 and 95, as well as abneural limbus motion in PGN 95. For PGN 96 the Mossbauer absorber was shifted by 33* from its initial position (96,), where the fractional Mossbauer effect was greatest, to a position where the measurement axis was more aligned with the surface normal of the CFP (96,). Amplitude responses are grouped according to the ~~-fr~uenc~ phase values. (Gummer et al., 1988)
anti-resonances there existed a frequency (or narrow band of frequencies) in the immediate vicinity of the displayed amplitude minimum where a stimulus did not elicit a measurable velocity. This frequency (or frequencies) is not indicated on the curves; that is, in such cases the displayed amplitude minimum represents the first detectable response above the noise floor of the recording system (0.05-0.1 mms-‘). The mean frequency of the amplitude minima for these sharp anti-resonances was 6.4 + 1.4 kHz. The positive phase slopes were associated with sharp anti-resonances {e.g. PGN 104, 105,). To aid discussion, we called the frequency at which the phase slope reversed from negative to positive values the lower reversal frequency, f,, and similarly the frequency at which the phase slope reversed from positive to negative values, the upper reversal frequency, f,. For example, PGN 104 had f, = 4.757 kHz, and f, = 5.339 kHz; PGN 105, had f, = 4.727 kHz, and f, = 8 kHz. The phase at f, relative to the phase at f, was, with one exception (PGN 103), close to 0.25 cycles (0.26 + 0.05, with range 0.20-0.32, N = 6, excluding the exception of 0.46 cycles). These ~~-frequency effects were found for both the intact cochlea and also for those cochleae in which BM recordings had been made prior to CFP recordings. No evidence of anti-resonance was found in the BM motion when referred to sound pressure at the TM (Gummer et al., 1987). The frequency resolution in Fig. 1 is so high that there can be no likelihood of phase error arising from phase ambiguity. Responses were independent of the frequency sequence of the recordings and were reproducible for any one CFP. At first sight these high-frequency effects may be considered anomalous and unimportant because the highest frequency represented on the BM is 6 kHz (Gummer et al., 1987). However, differences in phase responses from different animals already became evident at 2.828 kHz. If a phase response from the 2-cycle group were to be used as a phase reference for BM motion recorded in the basal region of the BP then BM motion would appear to lead CFP motion at most frequencies (Gummer et al., 1987). In the Discussion a single mechanism will be proposed to account for these three ~~-frequency effects.
18
Columella footplote velocity I
!
II/l,,,
I
I1
,111
:’ a.
96, 96,
E
o----a b---.-A
b lOOd9 SPL
:
I 1
O.Ol/ 0.25
2
-0.75
75 u” e,
-i.25
;; E
-I
75
-2 25 0.1
1 02
I11111 0.5
/I 1.0
Frequency
2
5
b IO
] 20
&Hz1
Fig. 2. (a) Amp~tude
and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for 3 recording configurations for PGN 96. The measured angle between configurations 1 and 2 was 33’, and between 1 and 3 was 17 O. A cross check on the accuracy of the angle measurements was afforded by calculation of the latter two angles using the measured values of /? and y; the result was 36’ and 16 O. For PGN 96,. 96, and 96,, respectively: the calculated angle between the surface normal of the CFP and the measurement axis was 30 O, 23O, 14*; the solid angle subtended by the Miissbauer absorber at the source on the CFP was 14O, 16”, 15O; the fractional Miissbauer effect was 0.26, 0.24,0.24.
Spatial variation A possible spatial variation of the recorded CFP response was examined by measuring CFP motion with the Mossbauer absorber in different orientations. The convention for spatial coordinates was given in the companion paper (Fig. 5, Gummer et al., 1989). The results of an extensive experiment on PGN 96 are illustrated in Fig. 2. The first CFP response was determined in that orientation which yielded the maximum fractional Miissbauer effect; namely, at p = 90”, y = - 25”.
Having completed this set of recordings (PGN 96, ), the absorber was shifted 33’ (p = 50 O, y = - 33 o ), in a direction which gave closer alignment of the measurement axis with the surface normal of the CFP (p = 61”, y = -12O). The calculated angles * between the CFP normal and the measurement axes were 30” and 23”, respectively. The angle between the two measurement axes was approximately twice the solid angles subtended by the Mossbauer absorber at the source (14” and 16”); that is, the regions through which the radiation was absorbed were well-separated. The most significant difference between the two recorded responses was the reduced phase lag in the second configuration (PGN 96,) for frequencies above 2.828 kHz, so that at the highest measurement frequency (11.314 kHz) the two phase responses were separated by almost one cycle (0.88). The ~plitude response of PGN 96, exhibited a shallow, but well-defined, anti-resonance with minimum at 5.657 kHz. The phase difference between the two responses at 5.657 kHz was 0.50 cycles. A third set of recordings (PGN 96,) was made at an intermediate position (p = 75 O, y = - 17O). The angle difference between the first and the third measurement axes was 17 O, and the calculated angle relative to the surface normal of the CFP was 14”. The main result was that the phase response was similar to that for the first recording configuration; the phase difference at 5.657 kHz was only 0.09 cycles. There was, however, an unexpected reduction in amplitude below 1 kHz. This reduction was probably associated with a layer of fluid and fibrin found on the CFP after completion of the one-hour recording session for the third configuration; the layer was not present at the beginning of this last recording session when the high-frequency recordings were made. This load would be expected to have influenced mainly the effective stiffness of the annular ligament which, according to impedance data for the annular ligament and stapes in cat (Lynch et al., 1982), would only have affected the low-frequency response.
* If the angles (&, yt) and (&, y2) define the directions two vectors, then the angle, 8, between them is defined cos B = cos y, cos y; cos( & - &) + sin yI sin ys.
of by
19
Columello footplate velocity IO
,
I
I,,,!,
1
1 ,1,,,,,
a.
.Ct
*
-0.25 ;i; ” : 2 $
-0.75
-1.25
p
0
‘d
109, 00 106” 90” -23” -15”
109,
iz
-2.25 1 0.1
0.2
I 4 ,,l,, 0.5
1.0
Frequency
b
2
5
,,,rb IO
I 20
(kHz1
Fig. 3. (a) ~p~tude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for two recording configurations for PGN 109. The angle between the two configurations was 17’. For PGN 109, and 109*, respectively: the calculated angle between the surface normal of the CFP and the measurement axis was 44’, 30’; the solid angle subtended by the Massbauer absorber at the source on the CFP was 18O, 19O; the fractional Miissbauer effect was 0.17.0.20.
In conclusion, the recorded CFP response was dependent on the orientation of the measurement axis in a way which could not be accounted for by the cosine-effect for frequencies above 2.828 kHz. Double anti-resonance In two animals a double
~ti-resonance was found in the CFP response. The frequencies of anti-resonance were not harmonically related. For the first recording in PGN 109 (/? = 106 O, y = - 15 “) the frequencies of minimum amplitude response, called the best frequencies of the antiresonances, were 4.490 and 7.551 kHz (Fig. 3). The phase response exhibited a region of positive
phase slope with lower and upper reversal frequencies of 6.924 kHz and 7.551 kHz, respectively. The phase at 7.551 kHz relative to the phase at 6.924 kHz was 0.29 cycles. The two anti-resonances were dependent on the orientation of the measurement axis. A second set of recordings was made at an angle of 17’ to the first set. The difference of 17” was equal to the solid angle subtended by the Mijssbauer absorber at the source; that is, the regions through which the radiation, was absorbed were adjacent, with little overlap. The calculated angle between the surface normal of the CFP and the first and second measurement axes was 44 o and 30 ‘, respectively. The tuned region of the first anti-resonance was then located 0.21 octaves below that recorded with the initial measurement axis; the best frequency was 3.886 kHz. For 4.238-10.375 kHz the velocity ~plitudes were elevated relative to the initial ones by 4-19 dB (mean: 10 + 4). The best frequency of the second anti-resonance (6.924 kHz) was close to that recorded with the initial measurement axis (7.551 kHz), although this anti-resonance was no longer sharply tuned and the amplitudes were elevated (19 dB at 7.551 kHz). There was a concomitant change in the phase response; the phase difference between 6.924 and 7.551 kHz was then only -0.01 cycles, rather than the 0.29 cycles recorded with the initial measurement axis. Modified cochlea
In order to elucidate the origin of the highfrequency responses the CFP response was recorded after having extirpated the entire cochlear labyrinth, and with the cochlea either full of fluid or drained. The labyrinth was extirpated in one piece. There was some initial bleeding as a result of the extirpation; however, the blood was quickly removed with an absorbent wick so that the cochlea was devoid of blood. The cochlea was allowed to refill with fluid generated from within the cochlea; the fluid appeared to have the texture of perilymph. The fluid level remained constant at the level of the hole in Scala tympani through which the labyrinth had been withdrawn. Since the recorded CFP response depended on the measurement axis, if possible we avoided moving the Mbssbauer absorber after the initial recording of the CFP response with the cochlea intact. The
Columella footplate velocity
animal’s head was not moved. If it was necessary to shift the absorber between manipulations on the cochlea, it was returned to its original position. However, with some forethou~t and use of a 350~mm objective lens on the operating microscope, it was often possible to leave the absorber undisturbed. Data for PGN 106 are displayed in Fig. 4 and data for four pigeons are shown superimposed in Fig. 5. In general the important results at high frequencies were that in the absence of the co&ear lab~th: (i) ~p~tude notches vanished, the double anti-resonance included; (ii> the phase response in the anti-resonant region no longer exhibited positive slopes; and (iii) the phase difference between low and high frequencies was always less than one cycle, and up to 3 kHz it was no more than 0.5 cycles. In the absence of the cochlear labyrinth the effect of fluid in the cochlea ,.
Columella E
’
footplate
velocity I I1 I,,,,,
20ww
IOOdB SPL
b. _ 0
i
a.
“1”“’
-
Intact ---
u_
-201
1 I
PGN 106
0.01
I
I
Illllll
I
I
I
IOOdB
SPL 1
I11111
i
b.
-
ii!
Intact Extirpated
-
\
0.1
1
0.2
i
/
/
1
I!,,,
0.5
IO
Frequency
I
,I,:///
5
2
IO
20
(kHz)
oralned \
(I" -I 25I
t -I 751 01
6 dramed
Fig. 5. (a) Amplitude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for four pigeons: (i) intact cochlea; and (ii) entire cochlear labyrinth extirpated and cochlea drained. The frequency of minimum amplitude of the anti-resonance, called the best frequency of the anti-resonance, was 7.772 kHz for PGN 105,, 5.823 kHz for PGN 106, and 5.657 kHz for PGN 107,. There existed a double anti-resonance for PGN 103, with best frequencies of 4.757 and 6.169 kHz.
0.25 r
Extrpated
t
I 0.2
I I I Ill// 05
1.0
Frequency
I 2
I
I II/III 5 IO
~
I 20
(kHz1
Fig. 4. (a) Amplitude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for PGN 106: (i) intact cochlea: (ii) entire co&ear labyrinth extirpated, and cochlea filled with fluid (perilymph?); and (ii) as for (ii) but cochlea drained. (Modified from Gummer et al., 1988).
was simply to reduce the resonant frequency (0.17 act for PGN 105; 0.34 act for PGN 106) and to increase the Q3 dB (4% for PGN 105; 16% for PGN 106). The greatest inter-animal differences were found in the range of resonant frequencies (0.77-1.44 kHz) and Q3 dR (1.6-3.9). Thus provided the condition of other structures was not altered by extirpation of the cochlear labyrinth, these results demonstrate that the high-
21
frequency effects were dependent on the presence of the co&ear labyrinth. For frequencies below 0.4 kHz the increased velocity amplitude and reduced phase lag were most likely due to the absence of the two intracochlear, inertial shunt pathways through the helicotrema and Ductus brevis (Kohlloffel, 1984). Discussion
At the upper-frequency limit of the cochlea of the pigeon we have described three unusual features of the CFP response: (i) anti-resonance; (ii) exceedingly large phase rotation; and (iii) positive phase slope. They were observed in 15 of the 20 experimental animals. These features were dependent on the orientation of the radiation detector, in a way which could not be explained by the cosine effect, and on the presence of the cochlear labyrinth. They could therefore not have been due to a Helmholtz resonance in the middle ear or in the intra-cranial cavities, nor to extraneous vibration in the experimental apparatus, nor to loading by the Mossbauer source. The weight of the Miissbauer source (3.3 pg) was small compared with the weight of the columella (550 f 100 I-18, N = 4). A muscle relaxant had also been administered prior to beginning the mechanical measurements to prevent contractions of the intra-aural muscle. There exists only one report on the motion of another avian CFP; namely, the amplitude response for Babary Dove in the classic paper by Saunders and Johnstone (1972). There is no evidence of anti-resonance in that case, presumably because the much lower radioactivity of the Mossbauer sources available at that time precluded recordings with the necessary frequency resolution to detect anti-resonance. Sharp notches have been reported in amplitude responses of middle-ear structures in guinea pig, both in the 3-8 kHz region (Wilson and Johnstone, 1975) and also near their upper-frequency limit (Manley and Johnstone, 1974). In an earlier report (Gummer et al., 1986) attention was drawn to the unusual high-frequency features of the pigeon CFP response and in a following report (Gummer et al., 1987) BM motion was referred to the mean CFP response derived from the five pigeons which did not exhibit these features (PGN
92 in Fig. 1 of this paper is such an example). However, until now, the phenomenon had not been investigated. In interpreting the results of the cochlear manipulation experiments we assume that the middle ear, together with the annular ligament and the round window membrane, were unaffected by the manipulations. Nevertheless, one must keep in mind that opening of Scala tympani may have indirectly influenced the annular ligament impedance below 0.3 kHz because the ensuing (presumed) reduction of static pressure may have caused a decrease in the ligament stiffness, as originally proposed by Lynch et al. (1982) for cat. However, from recordings of CFP response before and after opening the cochlea (from the same animals) we found no evidence for an influence from the presence of a hole in the cochlear wall overlying the tympanic recess. The stiffness of the round window membrane is likely to have increased as a result of the manipulations because of a possible interruption of its vascular supply and loss of its bathing medium. Again, however, these effects are considered, to be relevant, if at all, only at low frequencies. It may be added that in contradistinction to observations of Oeckinghaus (1985) in starling, the round window membrane did not collapse at any stage during the experiment. Spatial variation
The dependence of both the amplitude and the phase of the recorded CFP response above 2.828 kHz on the orientation of the measurement axis implies the existence of a high-frequency vibration mode(s) which destructively interfers with the presumed piston-like mode. Since this finding is a crucial one, the underlying physical principle deserves to be described in some detail. The measured velocity is the component of the velocity vector in the direction of the measurement axis. This vector is composed of velocity vectors arising from different vibration modes, such as translation, rotation, bending of the CFP, or even reflections from within the cochlea. The translational mode appears to be the dominant mode for stapedial motion in the three-ossicle mammalian ear (Guinan and Peake, 1967), and also for CFP motion in the single-ossicle ear of the alligator lizard
22
(Rosowski et al., 1985). Therefore, we will assume, without loss of generality, that the dominant mode is translation; the discussion is equally applicable to other modes. Consider then the simplest situation in which there are only two vibration modes: a translational mode giving an instantaneous velocity vector u_~at a point P and another mode, which we shall call an interference mode, giving an instantaneous velocity vector LIPat P. Then the total (mechanical) velocity vector u_of a point P on the CFP is u=&+U. _I
0)
For sinusoidal motion of radial frequency w this equation may be written as u=V,COS(wt-~,)e,+Vi
COS(wt-_j)ni
(2)
where the translational and interfering velocity vectors, respectively, have ~p~tudes V, and Vi, temporal phases (p, and +i, and unit vectors n_, and IX,describing their spatial directions. Each of these parameters may be frequency-dependent. For a measurement axis with direction defined by the unit vector n, the measured velocity u, is the scalar quantity - -m u, =u-n
(3)
= v, cos e,, cos( ot - (p,) + v, cos l9, cos( wt - +i)
(4)
where S,, and 8, are the spatial angles between the measurement axis and, respectively, the translational velocity vector and the interfe~ng velocity vector. The sum is readily written as a single sinusoid of amplitude V,,, and phase CP,; namely, unl =V,cos(wt-&)
0)
where V,=
IV: COS28,,-tZV;V,COS e,, COS S, COS ~jsi, i-
vi’
cos2B,]“2
(pm=$+- tan-’
1
Vj COS 0, sin ~,it v, cos e,, + vi cos Bfi cos cpi,
I
(7)
and (Pit =
Cpi -
cPt
(8)
Consider the following three cases: (i) If there is no interfering component, then V,,, = V, cos d,t, and $I, = 9,. That is, provided &,,, is independent of frequency, a change of measurement axis simply causes a frequency independent change of the measured amplitude response, without affecting the measured phase response. The measured phase response is identical with the phase response of the translational velocity vector. If S,, is frequency dependent, as would happen if the direction of the translational velocity vector were frequency dependent, then the measured phase response is still identical with the phase response of the translational velocity vector, but the change of measurement axis causes a frequency dependent change of the measured amplitude response. In fact this was the situation for motion at the ES for frequencies above 1 kHz, reported in the companion paper (Gummer et al., 1989). (ii) If the interfering velocity vector is in temporal phase with the tr~slational velocity vector; that is if (Pi= (bt, then V, = V, cos B,, + Vi cos S,, and #, = (p,. If, in addition, the interfering component is frequency dependent, then a change of measurement axis causes a frequency dependent change of the measured amplitude response, but without affecting the measured phase response. Again, the measured phase response is identical with the phase response of the tr~slational velocity vector. (iii) In the more general case where the interfering velocity is not in temporal phase with the translational velocity vector, the measured phase response differs from the phase response of the translational velocity vector, as described by Eq. (7). Moreover, a change of me~urement axis not only affects the measured amplitude response, but also causes a frequency dependent change of the measured phase response, provided that the absolute value of the direction cosines, cos O,, and cos O,,, are unequal (except possibly at the antiresonant frequency). Indeed, a dependence of the measured phase response on measurement axis
23
was observed experimentally 2.828 kHz (Figs 2 and 3).
for the CFP above
The frequency of anti-resonance is that frequency at which the measured amplitude is zero. This occurs when the measured components of the translational and interfering velocities are of equal amplitude and 180” out of temporal phase; that is, when V, cos &,, = Vi cos 13~ and sbir= 180 O, or when V, COS B,, = -Vi COS e,i, a.nd #it=OO. Near the anti-resonant frequency the measured phase tends to +, = s#++ (n + 4) 180 *, where n=O, 1, 2 ,.... That is, near the anti-resonant frequency the measured phase differs from the temporal phase of the translational velocity vector by odd multiples of 90 “. This principle accounts for the near quarter-cycle phase reversals observed for sharp anti-resonances (e.g. PGN 104 and 105, in Fig. l(c); PGN 109, in Fig. 3(b)). In some cases the meas~ement axis was such that the recorded anti-resonance was broadly tuned, which indicates partial cancellation of the translational component by an interfering component; that is, the recorded amplitude response displays a minimum rather than a zero. At a minimum the translational and interfering components are still 180” out of temporal phase, but the measured amplitude is V,,, = V, cos 8,, Vi cos &, and the measured phase is +,,, = & f n180 O, where n = 0, 1, 2,. . . . That is, at the frequency of amplitude minimum the measured phase differs from the temporal phase of the translational velocity vector by multiples of 180”. This principle accounts for the spatial dependence of recordings such as those of PGN 96 in Fig. 2(b)+ Thus, the high-frequency characteristics of the measured CFP response can be accounted for by a single mechanism in which a second vibration mode destructively interfers with the presumed piston-like vibration mode. The interference mode is evident above 2.828 kHz and is most pronounced near 6.4 kHz, the mean anti-resonant frequency for the set of recordings. The exact form of the measured CFP response depends on the relative amplitudes and temporal phases of the two vibration modes, arid on their directions. Although it is not possible to derive a complete description from our experiments, several im-
portant pieces of information have emerged. The two modes are 180° out of temporal phase near the (mean) anti-resonant frequency of 6.4 kHz, and for sharp ~ti-reson~ce have near equal component amplitudes at this frequency. Moreover, the absolute value of the direction cosines relative to the measurement axis are unequal, except possibly at the anti-resonant frequency. This latter property means, amongst other things, that for frequencies not equal to the anti-resonant frequency the two vibration modes are not directed along the same straight line. In those animals (5 of 20) for which the recorded CFP responses did not exhibit these highfrequency features, the interference velocity was small compared with the translational velocity and/or the measurement axis was approximately orthogonal to the direction of the interference velocity vector at all frequencies. In either case, such responses (e.g. PGN 92 in Fig. 1) and their mean (Fig. 15, Gummer et al., 1987) approximately represent the translational velocity response. At frequencies above about 5.657 kHz, the mean amplitude response was noisy (+ 3 dB maximum deviation from the mean in Fig. 15, Gummer et al., 1987), probably due to the presence of a relatively small, interference component and to the associated inter-animal and measurement-axis differences. Interference modes There are four main contenders for producing interference: (i) transverse motion of the extra-colbelly-columell~ complex; (ii) rotation of the CFP; (iii) bending of the CFP; and (iv) reflection from within the cochlea. Clearly, from measurements at a single point on the CFP it is not possible to decide which of these modes was responsible for destructive interference. However, these possibilities deserve discussion. Wilson and Johnstone (1975) reported a series of one to three sharp notches between 3 and 8 kHz in the amplitude response of the long process of the incus in the guinea pig, which could not be attributed to a Helmholtz resonator. They proposed ‘that the incus and stapes have a lightly damped side to side resonant mode’ or ‘that the motion of the incus changes from rotation around an axis of suspension at low frequencies to a
24
different axis with minimum moment of inertia at high frequencies’. Both of these proposals imply a single mode operating at any one frequency. This however cannot be the case for the pigeon middle ear because, as discussed in the last section, the spatial dependence of the measured phase response of the CFP requires the presence of two modes, which are not in temporal phase and which are acting in directions such that the absolute value of their direction cosines relative to the measurement axis are unequal. For a simple change of the columella motion from a ~~slational to a transverse mode the recorded response would be independent of the measurement axis, except for a frequency independent cosine attenuation. The model calculations of Geisler and Hubbard (1972) predicted a sharp resonance in the input impedance of the human cochlea near 10 kHz, which was due to the fact that the length of the human cochlea is equal to a quarter length of the average fluid pressure wave at that frequency. This condition is not applicable to the pigeon because the BM length of 4 mm (Takasaka and Smith, 1971) yields a quarter-wave frequency of 91 kHz. Rotation of the CFP should be considered because of eccentricities in the columefla and in the insertion of the CFP in the oval window. The centre of the base of the columellar stalk is located about one third of the distance along the major diameter from the posterior margin of the CFP (Saunders, 1985, Fig, 5 and personal observation). The posterior margin of the annular ligament is narrower than the anterior margin (Schwartzkopff, 1954; Gaudin, 1968; Saunders, 1985), by a factor 3-4 (Saunders, 1985, Fig. 5 and personal observation). Therefore, provided the fibres of the annular ligament are evenly distributed and of similar elasticity, as they would appear to be (Pohlman, 1921), rotation of the CFP about the posterior margin of the oval window would be indicated. In fact, Schw~opff (1954) and Gaudin (X968) have proposed rotation, rather than translation, as the dominant vibration mode. Gaudin (1968) has photographed rotational motion of the middle ear at an unspecified applied pressure (presumably at SPLs in excess of 118 dB) in ‘fresh preparations’. However, as discussed in the companion paper (Gummer et al., 1989), we found no evidence for
rotational motion of the middle ear at moderate SPLs and frequencies up to 1 kHz for cochleae in apparently good physiological condition. Moreover it is unlikely that rotation about the posterior margin would have provided a significant interference mode because the amplitude of the displacement vector of the rotational component would have been so small compared with the radius of rotation that the translational and rotational components would effectively have had the same direction, thus precluding the existence of the observed interference effects. From those recordings which showed no evidence of anti-resonance the amplitude of the translational velocity vector near 6 kHz was about 0.2 mms-’ at 100 dB SPL. Thus, the displacement amplitude of the interference mode is estimated to have been about 5 nm at an anti-resonant frequency of 6.4 kHz and 100 dB SPL, which is almost 5 orders of magnitude smaller than the distance from the posterior margin of the oval window to the recording site on the CFP. Rotation about other axes, resulting from motion in the system of ligaments suspending the columella, would also seem unlikely because this interference mode would be expected to be still evident, or perhaps more evident, after emptying the cochlea. This does not appear to have been the case. Bending of the CFP should be considered because the pigeon columella lacks the (two) crurae of the mammalian stapes, so that force applied to the columella would have acted more centrally on the CFP, rather than at its circumference {Fleischer, 1978). However, it would be expected that the bending mode would be stih operative after removal of the cochlear labyrinth and with the cochlea full of fluid. This does not appear to have been the case. Therefore it is unlikely that bending of the CFP would have provided a significant interference mode. Reflected waves must be produced from within the cochlea because of the different impedances of the various structures, notably the c~t~a~nous limbus and the basilar membrane (BM). The question is whether the reflected wave reaching the CFP would have sufficient amplitude and the correct spatial and temporal phases to cause interference with the incident translational mode of the CFP at high frequencies. Several points deserve to
25
be mentioned. Firstly, the results of the cochlear manipulation experiments do indicate that interference requires the presence of the cochlear labyrinth. Secondly, the frequency of maximum interference (6.4 + 1.4 kHz) coincides with the maximum frequency represented on the BM (6.0 * 0.7 kHz, Gummer et al., 1987). As frequency is increased from low values to this maximum value the relative amplitude of the reflected wave may be expected to increase as the peak of the travelling wave envelope is positioned closer to the interface between the limbus and the BM at the basal end. At higher frequencies the relative amplitude of the reflected wave would be expected to diminish as the entire BM undergoes low-amplitude, evanescent wave motion and compressional wave motion in the fluid becomes significant. It must be emphasized however that if the measured phase response of the CFP is to be dependent on the location of the measurement axis, then the incident and reflected modes at the CFP must be out of temporal phase and the absolute value of their direction cosines relative to the measurement axis must be unequal. Moreover, at the frequency of minimum amplitude the two modes must be 180 o out of temporal phase. It is unknown whether these phase conditions are fulfilled. Finally, the occurrence of an auxillary anti-resonance at a lower frequency (two cases) can be accounted for by reflection from a local, animal specific, irregularity at the position on the BM corresponding to that anti-resonant frequency. Although the proposal of an intra-cochlear reflection mechanism is very speculative, and we have not attempted to present a quantitative hydrodynamical model, we believe that this mechanism provides the most likely explanation for the observed high-frequency effects. Acknowledgements The experiments were conducted at Zentrum der Physiologie, Frankfurt, and were supported by the Deutsche Forschungsgemeinschaft, SFB 45. References Fleischer, G. (1978) Evolutionary Middle Ear. Springer-Verlag,
Principles of the Mammalian Berlin, Heidelberg, New York.
Gaudin, E.P. (1968) On the middle ear of birds. Acta Otolaryngol. 65, 316-326. Geisler, C.D. and Hubbard, A.E. (1972) New boundary conditions and results for the Peterson-Bogert model of the cochlea. J. Acoust. See. Am. 52, 1629-1634. Guinan, J.J., Jr. and Peake, W.T. (1967) Middle-ear characteristics of anesthetized cats. J. Acoust. Sot. Am. 41, 1237-1261. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1986) The mechanics of the basilar membrane and middle ear in the pigeon. 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 Khnke, R. (1987) Basilar membrane motion in the pigeon measured with the Mossbauer technique. Hear. Res. 29, 63-92. Gummer, A.W., Smolders, J.W.Th. and Klinke, R. (1988) Determinants of high-frequency sensitivity in the bird. In: J.P. Wilson and D.T. Kemp (Eds.), Co&ear Mechanisms Structure, Function and Models, Plenum Press, New York, pp. 377-386. Gummer, A.W., Smolders, J.W.Th. and Klinke, R. (1989) Mechanics of a single-ossicle ear: I. The extra-stapedius of the pigeon. Hear. Res. 39, 1-14. Kohlliiffel, L.U.E. (1984) Notes on the comparative mechanics of hearing. II. On cochlear shunts in birds. Hear. Res. 13, 77-81. Lynch, T.J., III, Nedzelmtsky, V. and Peake, W.T. (1982) Input impedance of the cochlea in cat. J. Acoust. Sot. Am. 72, 108-130. Manley, G.A. and Johnstone, B.M. (1974) Middle-ear function in the guinea pig. J. Acoust. Sot. Am. 56, 571-576. Oeckinghaus, H. (1985) Modulation of activity in starling co&ear ganglion units by middle-ear muscle contractions, perilymph movements and lagena stimuli. J. Comp. Physiol. A 157, 643-655. Pohlman, A.G. (1921) The position and functional interpretation of the elastic ligaments in the middle-ear region of Gallus. J. Morphology 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. Macro-mechanical stage. Hear. Res. 20, 139-155. 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) Schallsimresorgane, ihre Fur&ion und biologische Bedeutung bei Mgeln. Proceedings 11th Int. Ornithological Congress, Basel, pp. 189-208. Takasaka, T. and Smith, C.A. (1971) The structure and innervation of the pigeon’s basilar papilla. J. Ultrastruct. Res 35,20-65. Wilson, J.P. and Johnstone, J.R. (1975) Basilar membrane and middle-ear vibration in guinea pig measured by capacitive probe. J. Awust. Sot. Am. 57, 705-723.
Hearing Research, 39 (1989) 15-26 Elsevier
HRR 01192
Mechanics of a single-ossicle ear: II. The columella footplate 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 Universitiit, Zentrum der Physiologic, Frankfurt am Main, F.R G. (Received
5 July 1988; accepted
27 November
1988)
The motion of the columella footplate (CFP) was measured in the pigeon using the Mossbauer technique. At the upper frequency limit of the cochlea the measured CFP response exhibited anti-resonant phenomena. These high-frequency responses were dependent on the orientation of the radiation detector, in a way which could not be explained by the cosine effect. The dependence of the recorded phase response on the measurement axis implies an additional vibration mode, which was out of temporal phase and non-collinear with the presumed translational vibration mode. The anti-resonant phenomena were not observed when the cochlear labyrinth was extirpated, thus excluding an explanation in terms of extraneous vibrations in the experimental apparatus or of loading by the Mijssbauer source. Intra-cochlear reflection is proposed as the origin of the interference mode. Pigeon;
Single-ossicle;
Columella
footplate;
Middle
ear; Basilar
Introduction The mechanical conditions prevailing at the input to the avian cochlea have not been adequately described. For frequencies up to 1 kHz in pigeon the motion of the columella footplate (CFP) is in phase, although attenuated, with the motion of the extra-stapedius (ES); the mechanical lever ratio is 2.7, and can be attributed to the geometry of the middle ear (Gummer et al., 1989). At higher frequencies the mechanical lever ratio is frequency dependent. Although frequency dependence is inevitable, the exact form of the dependence is surprising: under most recording conditions the middle-ear transmission function, which expresses CFP volume velocity relative to sound pressure at the tympanic membrane (TM), displays anti-resonant phenomena for frequencies above 2.828 kHz, (Gummer et al., 1986). If CFP motion is then used as a reference for basilar membrane (BM) motion in the basal region of the basilar papilla (BP), BM
Correspondence to: A.W. Gummer, Developmental Neurobiology Group, Research School of Biological Sciences, Australian National University, GPO Box 475, Canberra A.C.T. 2601, Australia. 0378-5955/89/$03.50
0 1989 Elsevier Science Publishers
membrane;
Mlissbauer
technique
motion appears to lead CFP motion over an extended frequency range (Gumrner et al., 1987). Anti-resonances are not observed in: (i) the response of the ES, (Gummer et al., 1989); (ii) the BM velocity response expressed relative to sound pressure at the TM; and (iii) the compound action potential (CAP) frequency tuning curve (FTC), (Gummer et al., 1987). Anti-resonances have been reported in the motion of the incus in the guinea pig in a similar frequency range (3-8 kHz) by Wilson and Johnstone (1975), where it was attributed to a frequency-dependent transverse motion. Anti-resonance in this frequency range was not particularly troublesome in that report because BM motion was recorded from the basal region of the cochlea, so that when stapes motion was used as a reference, the frequencies of antiresonance appeared on the low-frequency tail of the relative BM response. The highest frequency represented on the BM of guinea pig is 45 kHz, (Wilson and Johnstone, 1975), whereas it is only 6 kHz in pigeon, (Gurmner et al., 1987). The antiresonant phenomena deserve further investigation because their presence begs the question: what is the effective input to the cochlea? To this end, we have recorded the motion of the CFP of the
B.V. (Biomedical
Division)
16
pigeon using the Mossbauer technique, before and after structural manipulations of the cochlea. Methods
The experimental procedures are identical to those which were described extensively by the authors in a previous report, (Gummer et al., 1987) and which were also presented in a condensed form in the companion paper (Gummer et al., 1989). Very briefly, recordings were made from Nembutal (36 mg kg-‘) anaesthetized pigeons (Columba hia) of age 0.5-5 years (mode: 1.5) and weighing 360-550 g (450 t- 60). Supplements l/Cdoses of anaesthetic were administered as required. The physiological condition of the ear was ascertained with a CAP FTC recorded from the ventral border of the round window, and referenced to a neck electrode. Measurements of CFP velocity were made with the cochlea in various states: (i) intact; (ii) fenestrated; (iii) fenestrated, cochlear labyrinth extirpated; and (iv) as for (iii) but fluid drained. It suffices to mention that: (i) a muscle relaxant was used (alcuronium chloride, 10 mg kg-‘); (ii) sound pressure at the TM was measured after each structural manipulation of the cochlea; (iii) the isomer shift of the Mossbauer source-absorber combination was non-zero (-0.27 mm s-l), giving phase ambiguity of integral cycles only; (iv) the minimal detectable velocity was 0.05-0.1 mms-‘. Results
Responses of the 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 the measured velocity amplitude assuming linearity: no evidence of non-linear motion was found in the experimental range 77-117 dB SPL and 0.1-11.314 kHz. Data are from ears (N = 20) in good physiological condition as judged by the CAP FTC. Experiments are identified with an animal number prefixed by the acronym PGN. Most recordings are from the right ear, the exceptions being from PGN 84, 87, 104. At the best frequency of the
CAP FTC (1.414 kHz), the mean threshold was 40 + 5 dB SPL for the first CAP recordings *. This value compares with the mean of 39 i 5 dB SPL reported for the pigeon (Gummer et al., 1987). Data are included from seven animals from earlier experiments (up to PGN 95) from which intra-cochlear vibration recordings had been made. The mean CAP threshold at 1.414 kHz, recorded just before beginning the CFP vibration recordings, was 42 f 5 dB SPL for the intact cochlea group and 67 it: 10 dB SPL for the non-intact group. There was no significant difference between CAP FTCs recorded before and after the CFP response measurements (43 i 7 and 64 f 6 dB SPL, respectively, for the intact and non-intact groups, at 1.414 kHz).
The amplitude and phase of the velocity of the CFP at 100 dB SPL is shown in Fig. 1 for seven animals. Two classes of phase response were evident at high frequencies (Fig. lc); the phase difference between low and high frequencies (0.125 and 11.314 kHz) was either one or two cycles. In order to facilitate comparisons, the amplitude responses have been placed in separate panels (a or b) in Fig. 1 according to the division of the high-frequency phases. For the usual position of the Mbssbauer absorber the number of phase responses in each class was equal (20 experimental animals). A dependence of the recorded responses on the position of the Mijssbauer absorber is described in the next two sections. Seven of the eight responses in Fig. 1 illustrate the three unusual features of the CFP response found at high frequencies: (i) anti-resonance; (ii) exceedingly large phase rotation (two cycles at 11.314 kHz); and (iii) positive phase slope. The eighth response (PGN 92) is an example of one of the five responses which did not exhibit these high-frequency effects. The anti-resonances were found in both classes of phase response. There were nine animals which exhibited anti-resonance which could be described as having been sharp, with Q3 dB greater than or equal to 8. Their mean Q 3 dB was 17 + 8. In the case of these sharp
* Statistical
errors
are siandard
deviations.
Cotumella 10.0
I
footptate
1 1111111
velocity 1
I ,,I1111
I
100
-Q-
106,
Frequency
0.
dg SPL
IOOdB SPL
(kHzz)
Fig. 1. (a), (b) Amplitude and {c) phase of CFP velocity at 100 dl3 SPL as a function of frequency for 8 measurements series in 7 pigeons. The co&lea was intact for pigeon (PGN) 96, 102, 104, 105,. and 106t. BM motion was measured prior to measurement of CFP motion in PGN 92 and 95, as well as abneural limbus motion in PGN 95. For PGN 96 the Mossbauer absorber was shifted by 33* from its initial position (96,), where the fractional Mossbauer effect was greatest, to a position where the measurement axis was more aligned with the surface normal of the CFP (96,). Amplitude responses are grouped according to the ~~-fr~uenc~ phase values. (Gummer et al., 1988)
anti-resonances there existed a frequency (or narrow band of frequencies) in the immediate vicinity of the displayed amplitude minimum where a stimulus did not elicit a measurable velocity. This frequency (or frequencies) is not indicated on the curves; that is, in such cases the displayed amplitude minimum represents the first detectable response above the noise floor of the recording system (0.05-0.1 mms-‘). The mean frequency of the amplitude minima for these sharp anti-resonances was 6.4 + 1.4 kHz. The positive phase slopes were associated with sharp anti-resonances {e.g. PGN 104, 105,). To aid discussion, we called the frequency at which the phase slope reversed from negative to positive values the lower reversal frequency, f,, and similarly the frequency at which the phase slope reversed from positive to negative values, the upper reversal frequency, f,. For example, PGN 104 had f, = 4.757 kHz, and f, = 5.339 kHz; PGN 105, had f, = 4.727 kHz, and f, = 8 kHz. The phase at f, relative to the phase at f, was, with one exception (PGN 103), close to 0.25 cycles (0.26 + 0.05, with range 0.20-0.32, N = 6, excluding the exception of 0.46 cycles). These ~~-frequency effects were found for both the intact cochlea and also for those cochleae in which BM recordings had been made prior to CFP recordings. No evidence of anti-resonance was found in the BM motion when referred to sound pressure at the TM (Gummer et al., 1987). The frequency resolution in Fig. 1 is so high that there can be no likelihood of phase error arising from phase ambiguity. Responses were independent of the frequency sequence of the recordings and were reproducible for any one CFP. At first sight these high-frequency effects may be considered anomalous and unimportant because the highest frequency represented on the BM is 6 kHz (Gummer et al., 1987). However, differences in phase responses from different animals already became evident at 2.828 kHz. If a phase response from the 2-cycle group were to be used as a phase reference for BM motion recorded in the basal region of the BP then BM motion would appear to lead CFP motion at most frequencies (Gummer et al., 1987). In the Discussion a single mechanism will be proposed to account for these three ~~-frequency effects.
18
Columella footplote velocity I
!
II/l,,,
I
I1
,111
:’ a.
96, 96,
E
o----a b---.-A
b lOOd9 SPL
:
I 1
O.Ol/ 0.25
2
-0.75
75 u” e,
-i.25
;; E
-I
75
-2 25 0.1
1 02
I11111 0.5
/I 1.0
Frequency
2
5
b IO
] 20
&Hz1
Fig. 2. (a) Amp~tude
and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for 3 recording configurations for PGN 96. The measured angle between configurations 1 and 2 was 33’, and between 1 and 3 was 17 O. A cross check on the accuracy of the angle measurements was afforded by calculation of the latter two angles using the measured values of /? and y; the result was 36’ and 16 O. For PGN 96,. 96, and 96,, respectively: the calculated angle between the surface normal of the CFP and the measurement axis was 30 O, 23O, 14*; the solid angle subtended by the Miissbauer absorber at the source on the CFP was 14O, 16”, 15O; the fractional Miissbauer effect was 0.26, 0.24,0.24.
Spatial variation A possible spatial variation of the recorded CFP response was examined by measuring CFP motion with the Mossbauer absorber in different orientations. The convention for spatial coordinates was given in the companion paper (Fig. 5, Gummer et al., 1989). The results of an extensive experiment on PGN 96 are illustrated in Fig. 2. The first CFP response was determined in that orientation which yielded the maximum fractional Miissbauer effect; namely, at p = 90”, y = - 25”.
Having completed this set of recordings (PGN 96, ), the absorber was shifted 33’ (p = 50 O, y = - 33 o ), in a direction which gave closer alignment of the measurement axis with the surface normal of the CFP (p = 61”, y = -12O). The calculated angles * between the CFP normal and the measurement axes were 30” and 23”, respectively. The angle between the two measurement axes was approximately twice the solid angles subtended by the Mossbauer absorber at the source (14” and 16”); that is, the regions through which the radiation was absorbed were well-separated. The most significant difference between the two recorded responses was the reduced phase lag in the second configuration (PGN 96,) for frequencies above 2.828 kHz, so that at the highest measurement frequency (11.314 kHz) the two phase responses were separated by almost one cycle (0.88). The ~plitude response of PGN 96, exhibited a shallow, but well-defined, anti-resonance with minimum at 5.657 kHz. The phase difference between the two responses at 5.657 kHz was 0.50 cycles. A third set of recordings (PGN 96,) was made at an intermediate position (p = 75 O, y = - 17O). The angle difference between the first and the third measurement axes was 17 O, and the calculated angle relative to the surface normal of the CFP was 14”. The main result was that the phase response was similar to that for the first recording configuration; the phase difference at 5.657 kHz was only 0.09 cycles. There was, however, an unexpected reduction in amplitude below 1 kHz. This reduction was probably associated with a layer of fluid and fibrin found on the CFP after completion of the one-hour recording session for the third configuration; the layer was not present at the beginning of this last recording session when the high-frequency recordings were made. This load would be expected to have influenced mainly the effective stiffness of the annular ligament which, according to impedance data for the annular ligament and stapes in cat (Lynch et al., 1982), would only have affected the low-frequency response.
* If the angles (&, yt) and (&, y2) define the directions two vectors, then the angle, 8, between them is defined cos B = cos y, cos y; cos( & - &) + sin yI sin ys.
of by
19
Columello footplate velocity IO
,
I
I,,,!,
1
1 ,1,,,,,
a.
.Ct
*
-0.25 ;i; ” : 2 $
-0.75
-1.25
p
0
‘d
109, 00 106” 90” -23” -15”
109,
iz
-2.25 1 0.1
0.2
I 4 ,,l,, 0.5
1.0
Frequency
b
2
5
,,,rb IO
I 20
(kHz1
Fig. 3. (a) ~p~tude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for two recording configurations for PGN 109. The angle between the two configurations was 17’. For PGN 109, and 109*, respectively: the calculated angle between the surface normal of the CFP and the measurement axis was 44’, 30’; the solid angle subtended by the Massbauer absorber at the source on the CFP was 18O, 19O; the fractional Miissbauer effect was 0.17.0.20.
In conclusion, the recorded CFP response was dependent on the orientation of the measurement axis in a way which could not be accounted for by the cosine-effect for frequencies above 2.828 kHz. Double anti-resonance In two animals a double
~ti-resonance was found in the CFP response. The frequencies of anti-resonance were not harmonically related. For the first recording in PGN 109 (/? = 106 O, y = - 15 “) the frequencies of minimum amplitude response, called the best frequencies of the antiresonances, were 4.490 and 7.551 kHz (Fig. 3). The phase response exhibited a region of positive
phase slope with lower and upper reversal frequencies of 6.924 kHz and 7.551 kHz, respectively. The phase at 7.551 kHz relative to the phase at 6.924 kHz was 0.29 cycles. The two anti-resonances were dependent on the orientation of the measurement axis. A second set of recordings was made at an angle of 17’ to the first set. The difference of 17” was equal to the solid angle subtended by the Mijssbauer absorber at the source; that is, the regions through which the radiation, was absorbed were adjacent, with little overlap. The calculated angle between the surface normal of the CFP and the first and second measurement axes was 44 o and 30 ‘, respectively. The tuned region of the first anti-resonance was then located 0.21 octaves below that recorded with the initial measurement axis; the best frequency was 3.886 kHz. For 4.238-10.375 kHz the velocity ~plitudes were elevated relative to the initial ones by 4-19 dB (mean: 10 + 4). The best frequency of the second anti-resonance (6.924 kHz) was close to that recorded with the initial measurement axis (7.551 kHz), although this anti-resonance was no longer sharply tuned and the amplitudes were elevated (19 dB at 7.551 kHz). There was a concomitant change in the phase response; the phase difference between 6.924 and 7.551 kHz was then only -0.01 cycles, rather than the 0.29 cycles recorded with the initial measurement axis. Modified cochlea
In order to elucidate the origin of the highfrequency responses the CFP response was recorded after having extirpated the entire cochlear labyrinth, and with the cochlea either full of fluid or drained. The labyrinth was extirpated in one piece. There was some initial bleeding as a result of the extirpation; however, the blood was quickly removed with an absorbent wick so that the cochlea was devoid of blood. The cochlea was allowed to refill with fluid generated from within the cochlea; the fluid appeared to have the texture of perilymph. The fluid level remained constant at the level of the hole in Scala tympani through which the labyrinth had been withdrawn. Since the recorded CFP response depended on the measurement axis, if possible we avoided moving the Mbssbauer absorber after the initial recording of the CFP response with the cochlea intact. The
Columella footplate velocity
animal’s head was not moved. If it was necessary to shift the absorber between manipulations on the cochlea, it was returned to its original position. However, with some forethou~t and use of a 350~mm objective lens on the operating microscope, it was often possible to leave the absorber undisturbed. Data for PGN 106 are displayed in Fig. 4 and data for four pigeons are shown superimposed in Fig. 5. In general the important results at high frequencies were that in the absence of the co&ear lab~th: (i) ~p~tude notches vanished, the double anti-resonance included; (ii> the phase response in the anti-resonant region no longer exhibited positive slopes; and (iii) the phase difference between low and high frequencies was always less than one cycle, and up to 3 kHz it was no more than 0.5 cycles. In the absence of the cochlear labyrinth the effect of fluid in the cochlea ,.
Columella E
’
footplate
velocity I I1 I,,,,,
20ww
IOOdB SPL
b. _ 0
i
a.
“1”“’
-
Intact ---
u_
-201
1 I
PGN 106
0.01
I
I
Illllll
I
I
I
IOOdB
SPL 1
I11111
i
b.
-
ii!
Intact Extirpated
-
\
0.1
1
0.2
i
/
/
1
I!,,,
0.5
IO
Frequency
I
,I,:///
5
2
IO
20
(kHz)
oralned \
(I" -I 25I
t -I 751 01
6 dramed
Fig. 5. (a) Amplitude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for four pigeons: (i) intact cochlea; and (ii) entire cochlear labyrinth extirpated and cochlea drained. The frequency of minimum amplitude of the anti-resonance, called the best frequency of the anti-resonance, was 7.772 kHz for PGN 105,, 5.823 kHz for PGN 106, and 5.657 kHz for PGN 107,. There existed a double anti-resonance for PGN 103, with best frequencies of 4.757 and 6.169 kHz.
0.25 r
Extrpated
t
I 0.2
I I I Ill// 05
1.0
Frequency
I 2
I
I II/III 5 IO
~
I 20
(kHz1
Fig. 4. (a) Amplitude and (b) phase of CFP velocity at 100 dB SPL as a function of frequency for PGN 106: (i) intact cochlea: (ii) entire co&ear labyrinth extirpated, and cochlea filled with fluid (perilymph?); and (ii) as for (ii) but cochlea drained. (Modified from Gummer et al., 1988).
was simply to reduce the resonant frequency (0.17 act for PGN 105; 0.34 act for PGN 106) and to increase the Q3 dB (4% for PGN 105; 16% for PGN 106). The greatest inter-animal differences were found in the range of resonant frequencies (0.77-1.44 kHz) and Q3 dR (1.6-3.9). Thus provided the condition of other structures was not altered by extirpation of the cochlear labyrinth, these results demonstrate that the high-
21
frequency effects were dependent on the presence of the co&ear labyrinth. For frequencies below 0.4 kHz the increased velocity amplitude and reduced phase lag were most likely due to the absence of the two intracochlear, inertial shunt pathways through the helicotrema and Ductus brevis (Kohlloffel, 1984). Discussion
At the upper-frequency limit of the cochlea of the pigeon we have described three unusual features of the CFP response: (i) anti-resonance; (ii) exceedingly large phase rotation; and (iii) positive phase slope. They were observed in 15 of the 20 experimental animals. These features were dependent on the orientation of the radiation detector, in a way which could not be explained by the cosine effect, and on the presence of the cochlear labyrinth. They could therefore not have been due to a Helmholtz resonance in the middle ear or in the intra-cranial cavities, nor to extraneous vibration in the experimental apparatus, nor to loading by the Mossbauer source. The weight of the Miissbauer source (3.3 pg) was small compared with the weight of the columella (550 f 100 I-18, N = 4). A muscle relaxant had also been administered prior to beginning the mechanical measurements to prevent contractions of the intra-aural muscle. There exists only one report on the motion of another avian CFP; namely, the amplitude response for Babary Dove in the classic paper by Saunders and Johnstone (1972). There is no evidence of anti-resonance in that case, presumably because the much lower radioactivity of the Mossbauer sources available at that time precluded recordings with the necessary frequency resolution to detect anti-resonance. Sharp notches have been reported in amplitude responses of middle-ear structures in guinea pig, both in the 3-8 kHz region (Wilson and Johnstone, 1975) and also near their upper-frequency limit (Manley and Johnstone, 1974). In an earlier report (Gummer et al., 1986) attention was drawn to the unusual high-frequency features of the pigeon CFP response and in a following report (Gummer et al., 1987) BM motion was referred to the mean CFP response derived from the five pigeons which did not exhibit these features (PGN
92 in Fig. 1 of this paper is such an example). However, until now, the phenomenon had not been investigated. In interpreting the results of the cochlear manipulation experiments we assume that the middle ear, together with the annular ligament and the round window membrane, were unaffected by the manipulations. Nevertheless, one must keep in mind that opening of Scala tympani may have indirectly influenced the annular ligament impedance below 0.3 kHz because the ensuing (presumed) reduction of static pressure may have caused a decrease in the ligament stiffness, as originally proposed by Lynch et al. (1982) for cat. However, from recordings of CFP response before and after opening the cochlea (from the same animals) we found no evidence for an influence from the presence of a hole in the cochlear wall overlying the tympanic recess. The stiffness of the round window membrane is likely to have increased as a result of the manipulations because of a possible interruption of its vascular supply and loss of its bathing medium. Again, however, these effects are considered, to be relevant, if at all, only at low frequencies. It may be added that in contradistinction to observations of Oeckinghaus (1985) in starling, the round window membrane did not collapse at any stage during the experiment. Spatial variation
The dependence of both the amplitude and the phase of the recorded CFP response above 2.828 kHz on the orientation of the measurement axis implies the existence of a high-frequency vibration mode(s) which destructively interfers with the presumed piston-like mode. Since this finding is a crucial one, the underlying physical principle deserves to be described in some detail. The measured velocity is the component of the velocity vector in the direction of the measurement axis. This vector is composed of velocity vectors arising from different vibration modes, such as translation, rotation, bending of the CFP, or even reflections from within the cochlea. The translational mode appears to be the dominant mode for stapedial motion in the three-ossicle mammalian ear (Guinan and Peake, 1967), and also for CFP motion in the single-ossicle ear of the alligator lizard
22
(Rosowski et al., 1985). Therefore, we will assume, without loss of generality, that the dominant mode is translation; the discussion is equally applicable to other modes. Consider then the simplest situation in which there are only two vibration modes: a translational mode giving an instantaneous velocity vector u_~at a point P and another mode, which we shall call an interference mode, giving an instantaneous velocity vector LIPat P. Then the total (mechanical) velocity vector u_of a point P on the CFP is u=&+U. _I
0)
For sinusoidal motion of radial frequency w this equation may be written as u=V,COS(wt-~,)e,+Vi
COS(wt-_j)ni
(2)
where the translational and interfering velocity vectors, respectively, have ~p~tudes V, and Vi, temporal phases (p, and +i, and unit vectors n_, and IX,describing their spatial directions. Each of these parameters may be frequency-dependent. For a measurement axis with direction defined by the unit vector n, the measured velocity u, is the scalar quantity - -m u, =u-n
(3)
= v, cos e,, cos( ot - (p,) + v, cos l9, cos( wt - +i)
(4)
where S,, and 8, are the spatial angles between the measurement axis and, respectively, the translational velocity vector and the interfe~ng velocity vector. The sum is readily written as a single sinusoid of amplitude V,,, and phase CP,; namely, unl =V,cos(wt-&)
0)
where V,=
IV: COS28,,-tZV;V,COS e,, COS S, COS ~jsi, i-
vi’
cos2B,]“2
(pm=$+- tan-’
1
Vj COS 0, sin ~,it v, cos e,, + vi cos Bfi cos cpi,
I
(7)
and (Pit =
Cpi -
cPt
(8)
Consider the following three cases: (i) If there is no interfering component, then V,,, = V, cos d,t, and $I, = 9,. That is, provided &,,, is independent of frequency, a change of measurement axis simply causes a frequency independent change of the measured amplitude response, without affecting the measured phase response. The measured phase response is identical with the phase response of the translational velocity vector. If S,, is frequency dependent, as would happen if the direction of the translational velocity vector were frequency dependent, then the measured phase response is still identical with the phase response of the translational velocity vector, but the change of measurement axis causes a frequency dependent change of the measured amplitude response. In fact this was the situation for motion at the ES for frequencies above 1 kHz, reported in the companion paper (Gummer et al., 1989). (ii) If the interfering velocity vector is in temporal phase with the tr~slational velocity vector; that is if (Pi= (bt, then V, = V, cos B,, + Vi cos S,, and #, = (p,. If, in addition, the interfering component is frequency dependent, then a change of measurement axis causes a frequency dependent change of the measured amplitude response, but without affecting the measured phase response. Again, the measured phase response is identical with the phase response of the tr~slational velocity vector. (iii) In the more general case where the interfering velocity is not in temporal phase with the translational velocity vector, the measured phase response differs from the phase response of the translational velocity vector, as described by Eq. (7). Moreover, a change of me~urement axis not only affects the measured amplitude response, but also causes a frequency dependent change of the measured phase response, provided that the absolute value of the direction cosines, cos O,, and cos O,,, are unequal (except possibly at the antiresonant frequency). Indeed, a dependence of the measured phase response on measurement axis
23
was observed experimentally 2.828 kHz (Figs 2 and 3).
for the CFP above
The frequency of anti-resonance is that frequency at which the measured amplitude is zero. This occurs when the measured components of the translational and interfering velocities are of equal amplitude and 180” out of temporal phase; that is, when V, cos &,, = Vi cos 13~ and sbir= 180 O, or when V, COS B,, = -Vi COS e,i, a.nd #it=OO. Near the anti-resonant frequency the measured phase tends to +, = s#++ (n + 4) 180 *, where n=O, 1, 2 ,.... That is, near the anti-resonant frequency the measured phase differs from the temporal phase of the translational velocity vector by odd multiples of 90 “. This principle accounts for the near quarter-cycle phase reversals observed for sharp anti-resonances (e.g. PGN 104 and 105, in Fig. l(c); PGN 109, in Fig. 3(b)). In some cases the meas~ement axis was such that the recorded anti-resonance was broadly tuned, which indicates partial cancellation of the translational component by an interfering component; that is, the recorded amplitude response displays a minimum rather than a zero. At a minimum the translational and interfering components are still 180” out of temporal phase, but the measured amplitude is V,,, = V, cos 8,, Vi cos &, and the measured phase is +,,, = & f n180 O, where n = 0, 1, 2,. . . . That is, at the frequency of amplitude minimum the measured phase differs from the temporal phase of the translational velocity vector by multiples of 180”. This principle accounts for the spatial dependence of recordings such as those of PGN 96 in Fig. 2(b)+ Thus, the high-frequency characteristics of the measured CFP response can be accounted for by a single mechanism in which a second vibration mode destructively interfers with the presumed piston-like vibration mode. The interference mode is evident above 2.828 kHz and is most pronounced near 6.4 kHz, the mean anti-resonant frequency for the set of recordings. The exact form of the measured CFP response depends on the relative amplitudes and temporal phases of the two vibration modes, arid on their directions. Although it is not possible to derive a complete description from our experiments, several im-
portant pieces of information have emerged. The two modes are 180° out of temporal phase near the (mean) anti-resonant frequency of 6.4 kHz, and for sharp ~ti-reson~ce have near equal component amplitudes at this frequency. Moreover, the absolute value of the direction cosines relative to the measurement axis are unequal, except possibly at the anti-resonant frequency. This latter property means, amongst other things, that for frequencies not equal to the anti-resonant frequency the two vibration modes are not directed along the same straight line. In those animals (5 of 20) for which the recorded CFP responses did not exhibit these highfrequency features, the interference velocity was small compared with the translational velocity and/or the measurement axis was approximately orthogonal to the direction of the interference velocity vector at all frequencies. In either case, such responses (e.g. PGN 92 in Fig. 1) and their mean (Fig. 15, Gummer et al., 1987) approximately represent the translational velocity response. At frequencies above about 5.657 kHz, the mean amplitude response was noisy (+ 3 dB maximum deviation from the mean in Fig. 15, Gummer et al., 1987), probably due to the presence of a relatively small, interference component and to the associated inter-animal and measurement-axis differences. Interference modes There are four main contenders for producing interference: (i) transverse motion of the extra-colbelly-columell~ complex; (ii) rotation of the CFP; (iii) bending of the CFP; and (iv) reflection from within the cochlea. Clearly, from measurements at a single point on the CFP it is not possible to decide which of these modes was responsible for destructive interference. However, these possibilities deserve discussion. Wilson and Johnstone (1975) reported a series of one to three sharp notches between 3 and 8 kHz in the amplitude response of the long process of the incus in the guinea pig, which could not be attributed to a Helmholtz resonator. They proposed ‘that the incus and stapes have a lightly damped side to side resonant mode’ or ‘that the motion of the incus changes from rotation around an axis of suspension at low frequencies to a
24
different axis with minimum moment of inertia at high frequencies’. Both of these proposals imply a single mode operating at any one frequency. This however cannot be the case for the pigeon middle ear because, as discussed in the last section, the spatial dependence of the measured phase response of the CFP requires the presence of two modes, which are not in temporal phase and which are acting in directions such that the absolute value of their direction cosines relative to the measurement axis are unequal. For a simple change of the columella motion from a ~~slational to a transverse mode the recorded response would be independent of the measurement axis, except for a frequency independent cosine attenuation. The model calculations of Geisler and Hubbard (1972) predicted a sharp resonance in the input impedance of the human cochlea near 10 kHz, which was due to the fact that the length of the human cochlea is equal to a quarter length of the average fluid pressure wave at that frequency. This condition is not applicable to the pigeon because the BM length of 4 mm (Takasaka and Smith, 1971) yields a quarter-wave frequency of 91 kHz. Rotation of the CFP should be considered because of eccentricities in the columefla and in the insertion of the CFP in the oval window. The centre of the base of the columellar stalk is located about one third of the distance along the major diameter from the posterior margin of the CFP (Saunders, 1985, Fig, 5 and personal observation). The posterior margin of the annular ligament is narrower than the anterior margin (Schwartzkopff, 1954; Gaudin, 1968; Saunders, 1985), by a factor 3-4 (Saunders, 1985, Fig. 5 and personal observation). Therefore, provided the fibres of the annular ligament are evenly distributed and of similar elasticity, as they would appear to be (Pohlman, 1921), rotation of the CFP about the posterior margin of the oval window would be indicated. In fact, Schw~opff (1954) and Gaudin (X968) have proposed rotation, rather than translation, as the dominant vibration mode. Gaudin (1968) has photographed rotational motion of the middle ear at an unspecified applied pressure (presumably at SPLs in excess of 118 dB) in ‘fresh preparations’. However, as discussed in the companion paper (Gummer et al., 1989), we found no evidence for
rotational motion of the middle ear at moderate SPLs and frequencies up to 1 kHz for cochleae in apparently good physiological condition. Moreover it is unlikely that rotation about the posterior margin would have provided a significant interference mode because the amplitude of the displacement vector of the rotational component would have been so small compared with the radius of rotation that the translational and rotational components would effectively have had the same direction, thus precluding the existence of the observed interference effects. From those recordings which showed no evidence of anti-resonance the amplitude of the translational velocity vector near 6 kHz was about 0.2 mms-’ at 100 dB SPL. Thus, the displacement amplitude of the interference mode is estimated to have been about 5 nm at an anti-resonant frequency of 6.4 kHz and 100 dB SPL, which is almost 5 orders of magnitude smaller than the distance from the posterior margin of the oval window to the recording site on the CFP. Rotation about other axes, resulting from motion in the system of ligaments suspending the columella, would also seem unlikely because this interference mode would be expected to be still evident, or perhaps more evident, after emptying the cochlea. This does not appear to have been the case. Bending of the CFP should be considered because the pigeon columella lacks the (two) crurae of the mammalian stapes, so that force applied to the columella would have acted more centrally on the CFP, rather than at its circumference {Fleischer, 1978). However, it would be expected that the bending mode would be stih operative after removal of the cochlear labyrinth and with the cochlea full of fluid. This does not appear to have been the case. Therefore it is unlikely that bending of the CFP would have provided a significant interference mode. Reflected waves must be produced from within the cochlea because of the different impedances of the various structures, notably the c~t~a~nous limbus and the basilar membrane (BM). The question is whether the reflected wave reaching the CFP would have sufficient amplitude and the correct spatial and temporal phases to cause interference with the incident translational mode of the CFP at high frequencies. Several points deserve to
25
be mentioned. Firstly, the results of the cochlear manipulation experiments do indicate that interference requires the presence of the cochlear labyrinth. Secondly, the frequency of maximum interference (6.4 + 1.4 kHz) coincides with the maximum frequency represented on the BM (6.0 * 0.7 kHz, Gummer et al., 1987). As frequency is increased from low values to this maximum value the relative amplitude of the reflected wave may be expected to increase as the peak of the travelling wave envelope is positioned closer to the interface between the limbus and the BM at the basal end. At higher frequencies the relative amplitude of the reflected wave would be expected to diminish as the entire BM undergoes low-amplitude, evanescent wave motion and compressional wave motion in the fluid becomes significant. It must be emphasized however that if the measured phase response of the CFP is to be dependent on the location of the measurement axis, then the incident and reflected modes at the CFP must be out of temporal phase and the absolute value of their direction cosines relative to the measurement axis must be unequal. Moreover, at the frequency of minimum amplitude the two modes must be 180 o out of temporal phase. It is unknown whether these phase conditions are fulfilled. Finally, the occurrence of an auxillary anti-resonance at a lower frequency (two cases) can be accounted for by reflection from a local, animal specific, irregularity at the position on the BM corresponding to that anti-resonant frequency. Although the proposal of an intra-cochlear reflection mechanism is very speculative, and we have not attempted to present a quantitative hydrodynamical model, we believe that this mechanism provides the most likely explanation for the observed high-frequency effects. Acknowledgements The experiments were conducted at Zentrum der Physiologie, Frankfurt, and were supported by the Deutsche Forschungsgemeinschaft, SFB 45. References Fleischer, G. (1978) Evolutionary Middle Ear. Springer-Verlag,
Principles of the Mammalian Berlin, Heidelberg, New York.
Gaudin, E.P. (1968) On the middle ear of birds. Acta Otolaryngol. 65, 316-326. Geisler, C.D. and Hubbard, A.E. (1972) New boundary conditions and results for the Peterson-Bogert model of the cochlea. J. Acoust. See. Am. 52, 1629-1634. Guinan, J.J., Jr. and Peake, W.T. (1967) Middle-ear characteristics of anesthetized cats. J. Acoust. Sot. Am. 41, 1237-1261. Gummer, A.W., Smolders, J.W.T. and Klinke, R. (1986) The mechanics of the basilar membrane and middle ear in the pigeon. 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 Khnke, R. (1987) Basilar membrane motion in the pigeon measured with the Mossbauer technique. Hear. Res. 29, 63-92. Gummer, A.W., Smolders, J.W.Th. and Klinke, R. (1988) Determinants of high-frequency sensitivity in the bird. In: J.P. Wilson and D.T. Kemp (Eds.), Co&ear Mechanisms Structure, Function and Models, Plenum Press, New York, pp. 377-386. Gummer, A.W., Smolders, J.W.Th. and Klinke, R. (1989) Mechanics of a single-ossicle ear: I. The extra-stapedius of the pigeon. Hear. Res. 39, 1-14. Kohlliiffel, L.U.E. (1984) Notes on the comparative mechanics of hearing. II. On cochlear shunts in birds. Hear. Res. 13, 77-81. Lynch, T.J., III, Nedzelmtsky, V. and Peake, W.T. (1982) Input impedance of the cochlea in cat. J. Acoust. Sot. Am. 72, 108-130. Manley, G.A. and Johnstone, B.M. (1974) Middle-ear function in the guinea pig. J. Acoust. Sot. Am. 56, 571-576. Oeckinghaus, H. (1985) Modulation of activity in starling co&ear ganglion units by middle-ear muscle contractions, perilymph movements and lagena stimuli. J. Comp. Physiol. A 157, 643-655. Pohlman, A.G. (1921) The position and functional interpretation of the elastic ligaments in the middle-ear region of Gallus. J. Morphology 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. Macro-mechanical stage. Hear. Res. 20, 139-155. 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) Schallsimresorgane, ihre Fur&ion und biologische Bedeutung bei Mgeln. Proceedings 11th Int. Ornithological Congress, Basel, pp. 189-208. Takasaka, T. and Smith, C.A. (1971) The structure and innervation of the pigeon’s basilar papilla. J. Ultrastruct. Res 35,20-65. Wilson, J.P. and Johnstone, J.R. (1975) Basilar membrane and middle-ear vibration in guinea pig measured by capacitive probe. J. Awust. Sot. Am. 57, 705-723.