J Comp Physiol A (1994) 174:103-110

,dkoum~ e f hint, (p~llttp~,~ljh~ W ""='' 9 Springer-Verlag 1994

Middle-ear development IV. Umbo motion in neonatal mice* D.E. Doan I, Y.E. Cohen 2, J.C. Saunders 3 1 Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA

2 Department of Neurobiology, Stanford School of Medicine, Stanford, CA 94305, USA 3 Department of Otorhinolaryngology:Head and Neck Surgery,University of Pennsylvania,PA 19104, USA Accepted: 29 July 1993

Abstract. Laser interferometry was used to measure umbo velocity in the developing BALB/c mouse middle ear at 133 pure-tone frequencies between 2.0kHz and 40.0 kHz, all at a constant 100 dB sound pressure level. Umbo velocities increased with age across the entire frequency range, and reached adult-like levels by about 19 days between 2.0 and 22.0 kHz. Velocities at 28.0 and 34.0 kHz took 27 and 52 days respectively to reach adultlike levels. A simple middle-ear model utilizing compliance, resistance, and inertia elements matched the general trends of our velocity results and provided an indication of the anatomical basis for the growth in umbo velocity. The model suggested that velocity development at the lowest frequencies may be attributed to increases in tympanic membrane compliance. The model also indicated that both the frictional resistance of the middle ear and the inertia of the tympanic membrane and ossicles decreased during the growth period. At frequencies below 20.0 kHz, age-related increases in umbo velocity coincided with improvements in N~ thresholds recorded from the round window and evoked potential thresholds obtained from the cochlear nucleus. These results indicated that the functional development of the middle-ear plays a major role in the development of hearing in the mouse. Key words: Middle ear - Auditory development - Mouse - Laser interferometry - Umbo velocity

Introduction Several studies have focused on the developmental aspects of the mouse inner ear and central auditory pathways. For example, recordings of sound-evoked electrophysiological activity have been made during development at the round window membrane (Mikaelian 1979; * Portions of this work were presented at the Fifteenth Meeting of the Association for Research in Otolaryngology

Correspondence to: D.E. Doan

Shnerson and Pujol 1982), the cochlear nucleus (Mikaelian 1979; Saunders et al. 1980), and the inferior colliculus (Shnerson and Willott 1979). The physiological responses measured in these studies were produced by acoustic stimuli transmitted through an intact middle ear. The structural features of the middle ear undergo developmental expansion in size until about 20 days of age in the mouse (Huangfu and Saunders 1983). Changes occurring in the conductive structures of the middle ear during this growth period presumably alter the overall characteristics of sound transmission through the conductive apparatus. Indeed, functional changes in the tympanic membrane (TM) response have been found to coincide with the structural maturation of various middle-ear components in several species (Cohen et al. 1992a, b, c, 1993; Relkin and Saunders 1980; Relkin et al. 1979). The developmental changes in the structure and function of the middle ear will alter the transmission of sound vibrations to the fluid filled spaces of the cochlea. As a consequence, the physiological responses of the cochlea and the neural activity in the auditory central nervous system should also be influenced by middle-ear development. A full understanding of hearing development, therefore, requires investigation of the maturation of sound transmission through the middle ear. To date, the authors are unaware of any research describing the functional ontogeny of sound conduction in the mouse middle-ear system. The present investigation used laser interferometry to examine TM velocity in response to acoustic stimuli. These responses were measured at the umbo (the tip of the long process of the malleus) and the measured velocity was expressed as a function of frequency for a constant sound pressure level (SPL) at the TM. Mice at various neonatal ages were used for these measurements. The observations of umbo velocity reported here were then compared to a simple middle-ear model. This model allowed us to predict those anatomical structures that influence middle-ear development to the greatest degree. Additionally, the umbo velocities were compared to the results of other authors describing the development of electrophysiological thresholds at the cochlear nucleus and round window.

104

From this comparison we hope to further elucidate the role of the conductive apparatus in the overall development of hearing.

D.E. Doan et al.: U m b o motion in neonatal mice immobilization and vent tube modifications, the preparations for the 5 and 10 day old pups remained the same as those for the older animals.

Acoustic instrumentation and calibration. Pure tone stimuli were

Materials and methods Subjects and groups. The BALB/c mouse strain was used because of an available breeding colony within the division of Laboratory Animal Resources at the University of Pennsylvania. The colony was checked twice daily for new births, and mice were organized into 8 age groups, each denoted by the number of days postpartum: 5, 10, 12, 15, 20, 30, 45, and 60 days or older (adult). U m b o velocity was measured from at least 5 mice per age group. Surgical preparation. Each mouse was anesthetized with a 25% ethyl carbamate (Urethane) solution injected intramuscularly (approximately 0.009 ml/g of body weight). When fully anesthetized the mouse was tracheotomized, a small area of skin was retracted from the right side of the skull, and the underlying bone of the skull was scraped clean of connective tissue. The animal was then immobilized in a head holder that securely clamped the snout and upper jaw. The head was further secured by cementing the exposed portion of the skull directly to the head holder with cyanoacrylate and dental cement. The left pinna and external auditory meatus were then retracted to expose the TM. As the retraction progressed great care was taken to avoid contact between the T M and either surgical instruments or blood. A small hole was made in the temporal bone encasing the bulla, and a polyethylene tube (0.28 mm I.D., 30 mm length) was inserted into the hole to vent the bulla. This procedure prevented the accumulation of negative pressure in the bulla cavity (Guinan and Peake 1967). Fleischer (1978) predicted two separate axes of ossicle rotation in the micro-type middle ear of the mouse, and the work of Saunders and Summers (1982) has supported this hypothesis. In the mouse, the predicted low frequency rotation was about an axis that extended from the gonial through the malleus-incus joint to the posterior ligament of the incus. The second, or high frequency, axis extended from the gonial through the head of the malleus. The orientation and position of these axes indicate that the umbo is situated at the point of maximal displacement for either axis of rotation, thus making this position the most sensitive to sound stimulation. Hence the umbo was chosen as the optimal location for velocity recording. A glass bead (30~50 gm in diameter) was placed on the TM at the tip of the umbo. The bead facilitated alignment of the laser beam, and has been shown to increase substantially the signal-tonoise ratio of the laser signal (Cohen et al. 1992a; Decraemer et al. 1989). The T M response was measured with and without the bead in order to determine if the bead was tightly coupled to the membrane. The difference in T M velocity for the 2 conditions was _+ 3 dB between 2.0 kHz and 40.0 kHz. The youngest animals required special care in their surgical preparation. Immobilizing the head was quite difficult for 5 day old mice because of the small size and delicacy of these pups. An alternative method for securing the head was developed in which the trachea and the tissue on the right side of the skull were left intact. A small piece of clay was attached to the head holder, and the right side of the head was coated with cyanoacrylate and pressed into the clay. This successfully immobilized the skull and permitted umbo velocity measurements. Additionally, animals in both the 5 and 10 day groups had a great deal of fluid in the middle-ear cavity. Middle-ear fluid is frequently a sign of abnormal (or in this case, immature) eustachian tube function (Magnuson and Falk 1988). Thus, the ears in 5 and 10 day old animals were probably unvented. Insertion of a venting tube would unjustifiably vent the middle ear and could also drain some fluid from the ear. For this reason the bulla wall was left intact and a vent tube was not used at these ages. Other than the head

generated by a frequency synthesizer (Audio Precision, Inc., System One) and presented to the animal under free-field conditions. Due to the extensive hearing range of the mouse, two speakers were needed to deliver the full frequency range of stimuli. This required that each animal be tested once with a low frequency speaker and once with a high frequency speaker. Pure tones at frequencies between 2.0 kHz and 20.0 kHz were produced by a 14.0 cm mid-range speaker (Altec Co., model 405-8H), while tones between 4.0 kHz and 40.0 kHz were generated by a 10.0 cm tweeter (Realistic, model 40-1377). The frequency overlap of the two speakers allowed us to check both the accuracy of the sound delivery system and the stability of the T M response. If the umbo velocities elicited by the two speakers were not within 2 dB of each other in the overlap region, then the data from that animal were discarded (in only one case did this occur). The spectral response of each speaker was tested periodically with a spectrum analyzer to ensure that all harmonic distortion and noise remained at least 40 dB below the fundamental signal at all test frequencies. The SPL (in dB referenced to 20 laPa) of the stimuli were measured using a calibrated probe tube (0.5 mm diameter, 50 mm long) connected to a 12.5 mm condenser microphone (Briiel & Kjaer, Inc., model 4134). The probe tube was positioned such that the tip protruded slightly over the outer rim of the TM. The probe-tube response to the acoustic signal was measured by the band-limited voltmeter portion of System One. On the basis of this probe-tube response, System One was programmed to automatically adjust its frequency synthesizer output to produce a constant 100 dB SPL stimulus at the TM across all frequencies (Cohen et al. 1992a, 1993).

Laser interferometry. A heterodyne laser interferometer (Polytec, Inc., Model OFV-100 Laser Doppler Vibrometer) was used to make non-invasive measurements of TM motion. The laser was connected to an optical head which focused the outgoing signal beam and detected the reflected light from the glass bead on the TM. The interference pattern between the reflected beam and an internal reference beam were processed by the interferometer, which then produced an output signal that was proportional to the peak-topeak velocity of the vibrating glass bead. The accuracy of the interferometer velocity measures was verified with the use of an accelerometer (Briiel & Kjaer, Inc., model 8000) attached to a piezoelectric crystal driver (Cohen et al. 1992a). The piezoelectric driver was set into motion with a sinusoidal input, and the resulting motion was measured by both the interferometer and the accelerometer. The velocity of the piezoelectric driver as detected by the laser and accelerometer were found to be in agreement, and thus we concluded that the interferometer could be used to provide an accurate and reliable indication of umbo velocity.

Testing procedure. The mouse was positioned in the sound field on a table that could be moved in micron increments in the XY plane. This table was in turn mounted on a heavy granite slab inside a sound-attenuating booth. The slab and booth were both supported by vibration dampers which further reduced low frequency substrate noise at the TM. A heating pad was placed under the animal and rectal temperature was maintained at 37~ The head of the mouse was then positioned so that the TM was orthogonal to the laser beam, and the laser was focused on the glass bead and adjusted for maximum signal-to-noise conditions. After calibrating the stimulus to 100 dB SPL at the TM, System One was programmed to sweep the frequency range of the first speaker in 120 discrete frequency steps, while simultaneously measuring the magnitude and phase of the interferometer velocity signal. Frequently, second and sometimes third runs were made to test the reliability of the velocity measures. Reliability of the data was dependent on the signal-to-noise ratio of the interferometer output, and multiple runs with a high signal-to-noise laser signal typically

D.E. Doan et al.: Umbo motion in neonatal mice produced velocity plots that were identical to each other. If the second or third runs produced results that were different than the first, then the laser beam alignment and focus was readjusted until a strong, reliable signal was received from the interferometer. After obtaining a reliable response during stimulation with the first speaker, the second speaker was positioned above the mouse, the stimulus was calibrated, and System One swept the frequency range of that speaker, again in 120 discrete frequency steps. Additional frequency sweeps were made to test the reliability of the velocity measures. A total of 133 non-redundant frequencies were tested by both speakers. The mid-range and tweeter speakers were alternated in testing sequence from one animal to the next to eliminate any sequence bias, and collection of velocity and phase data took approximately 2 rain for each speaker. Animals with exceptionally strong interferometer signals were tested for linearity of the velocity response. In these mice two additional frequency sweeps were made, one at 80 dB SPL and another at 90 dB SPL, and the velocity responses of the TM were recorded at each sound pressure.

Noise floor. The laser beam was focused on the head holder apparatus, and the velocity response from 2.0 to 40.0 kHz was recorded without an acoustic stimulus. This measure gave an indication of the noise floor of our laser interferometer. The noise floor defined the smallest velocities that the interferometer could record across all frequencies. Velocity responses from mice of three different ages are compared to the noise floor results in Fig. 1. The velocity measures from the mice were taken at the umbo during a 100 dB SPL stimulus. Except at the lowest frequencies, the 10 day umbo velocities were almost identical to the noise floor. Therefore, the velocity measures at this age actually may have been smaller than our equipment could record, and the true characteristics of the umbo response to sound cannot be ascertained. For this reason much of the data presented in this paper focuses on results from animals older than 10 days. Specifically, phase and linearity data were used only after 12 days of age. However, the umbo velocities at 10 days of age

0.3 0'11

-

Umb~ vel~

]

o

j

0.01

. . . ' ' " i " . ' ." . . . . .

o

'~or

were used in some developmental comparisons because the measures provided a conservative estimate of the lower limit of TM velocity development.

Results

Velocity The velocity response curves for three groups of mice are shown in Fig. 2. The animals were grouped into "young", "middle", and "old" ages to show the trends in the data more clearly. The young group was comprised of 10 day old mice; middle was the average of 12 and 15 day old mice; and old was the average of 20, 30, 45 day, and adult mice. The TM transfer functions, in general, had an inverted "V" shape, much like those seen in other mammalian middle ears (e.g., Cohen et al. 1993; Manley et al. 1972; Relkin and Saunders 1980). Moreover, with increasing age, the magnitude of umbo velocity increased systematically across the entire frequency range. The middle curve in Fig. 2 was, on average, about 5 dB greater than the young group, and the old mice had a velocity response that was about 6 dB larger than the middle aged animals. The reader is reminded that the young group, since it consisted of 10 day old mice, was near the noise floor of our velocity recording apparatus (see Fig. 1). The velocities in the young group may have been smaller than the interferometer could detect, and, therefore, the difference between the young and middle groups could be larger than the 5 dB that we measured. When the response curves were replotted as a function of age at selected frequencies (Fig. 3), it became apparent that umbo velocity developed rapidly, reaching asymptotic velocity levels by about 20 days at frequencies up to 22.0 kHz. In the 28.0 kHz and 34.0 kHz panels the development is slightly slower, and the growth of velocity appears almost linear when compared to frequencies below 20.0 kHz. A 90% "mature" criterion was established in

15 Day

0.3 ,~o

"'.

105

0.1

0.010"03

,..':":",",'i',',',

.

.""

.

.

> 1 I. . . . . . . .

O

O O ~

0.3i ~ / ] 0.1

0.1

o

9

0.03

0.030.01.."~"i","," 2.0

".','~"".... , " " i " ' ,

4.0 10.0 20.0 40.0 Frequency (kHz)

Fig. 1. Comparison of umbo velocities and the noise floor of the laser. The noise floor of the laser was estimated by measuring the vibrational velocity of the head holder without a sound stimulus. Umbo velocities for 10 day (n= 1), 15 day (n= 1), and adult (n= 1) mice were measured in response to a 100 dB SPL stimulus. All velocities are peak-to-peak

2.0

..9

- ---......

Old (n=21) Middle (n=ll) Young (n=5)

'4:o.... ;o'0 20o Frequency

,o0

(kHz)

Fig. 2. Averaged peak-to-peak umbo velocities for three age groups plotted as a function of frequency. Young is the average of the lO day group; middle the average of 12 and 15 day groups; old the average of 20, 30, 45 day, and adult mice

106

D.E. Doan et al.: U m b o motion in neonatal mice 9 F 9 ,

9 ,

velocities were all similar in that they reached the 90% mature criterion by approximately 19 days. The velocities at 28.0 and 34.0 kHz, however, took 27 and 52 days respectively to reach the 90% level.

0.3

~J

0.1 . . . . . 4.0 kHz 0.03

Linearity of the umbo response .~ o ,~ ~;~ 0

0.3 0.1 0.03

0.3

g.1 0.03 20

40

80

20

40

80

Age ( d a y s ) Fig. 3. Peak-to-peak umbo velocity responses plotted as a function of age at selected frequencies. Error bars represent one standard deviation from the mean. The dotted line represents 90% of the average from 30 day, 45 day, and adult mice (see text for full explanation). Each age group consisted of 5 animals, except 15 and 20 days which had 6 mice apiece

1

10 k H z

The umbo responses at 80, 90, and 100 dB SPL for the middle and old groups (as defined for Fig. 2) are shown in Fig. 4. Each panel represents a different frequency. The responses for the oldest group are, for the most part, linear at 10.0, 16.0, and 20.0 kHz, indicating that for every dB of added sound pressure the umbo vibrates by one additional dB. Saunders and Summers (1982) showed that the linearity in adult mice extended to about 130 dB SPL. Comparing the results between ages, the middle group showed a smaller velocity response with a shallower slope than the old group. The shallower slope may be an indication of a non-linear middle-ear system and/or a velocity measure confounded by the noise floor (which is also shown in Fig. 4). It is unclear what mechanisms may be responsible for non-linearity (if it exists) in the middle ears of the younger mice.

Phase angle

0.3 O.I 0.03

I

1

o

i

i

i

I

16 k H z

0.3

.,,.~ o o

0.1 0.03 i

o 1

20 k

~

Phase of the umbo velocity response was recorded relative to the phase angle of the pure-tone stimulus at the TM. The phase results for two groups of animals are shown in Fig. 5. The old and middle groups are defined as they were in Figs. 2 and 4. The voltmeter was unable to obtain a stable phase measurement at frequencies above 25.0 kHz. Therefore, only phase angles below 25.0 kHz are reported here. All phase plots were referenced to an origin within + 180~ at 2.0 kHz. The old group demonstrated a decreasing phase angle at progressively higher frequencies, falling from 105 ~ to 398 ~ over the frequency range examined. In contrast to

0.3

o.1 ~ 0.03

i 00

Stimulus

....

~

i 90

1000 idl,enil, j

........ i 100

500

- -

01d

(n=21)

.T~I~I

[L,

L e v e l ( d B SPL)

Fig. 4. Linearity of the umbo velocity response measured at 10.0, 16.0, and 20.0 kHz. The dotted line represents the noise floor, the dashed line is the middle group (12 and 15 days; n =2), and the solid line is the old group (20, 30, 45 day, and adult; n=6). Error bars represent one standard deviation from the mean

~'

m

-500

order to quantify the rate of development at these selected frequencies. "Mature" was defined as the velocity average of the 30 day, 45 day, and adult mice. This value was then multiplied by 0.9 to find the 90% velocity criterion at each frequency. The dotted line in each plot represents this criterion. The 4.0, 10.0, 16.0, and 22.0 kHz umbo

'

. . . .

;i.o

o.o

(kHz) Fig. 5. Phase of umbo velocity relative to the phase of the pure-tone stimulus at the TM. The middle group contains 12 and 15 day old mice, and the old group represents mice 20 days and older. Error bars represent the standard error of the mean Frequency

D.E. Doan et al.: Umbo motion in neonatal mice the old group, the phase angle rose steadily in the middle group, progressing from 48 ~ to 935 ~ between 2.0 and 25.0 kHz. The increase in phase above 10 kHz was quite unexpected, as phase angle usually decreases with increasing frequency (e.g., Cohen et al. 1992a; Decraemer et al. 1990; G u m m e r et al. 1989). The anomalous phase data may be the result of interference with the noise floor of the system. In Fig. 1 the signal-to-noise ratio of 15 day old mice was lower than the adult ratio, and this may have influenced the accuracy of phase measurements, especially at higher frequencies. Indeed, at 12 days the signal-to-noise ratio was probably worse than at 15 days. Thus, the phase data above 10 kHz for the 12 and 15 day old mice may have been compromised by the relatively poor signal-to-noise ratio.

107 and capacitive probe for detecting T M motion. The capacitive probe integrated velocity over an area approximately 25 times greater than the "spot" size of the laser, and integration over a larger area would tend to reduce the magnitude of the peaks and valleys in the velocity response (Cohen et al. 1992a). Alternatively, the absence of peaks and valleys in the capacitive probe measures could be the result of poor frequency resolution. The Saunders and Summers (1982) results were described at just 12 frequencies, whereas our data were obtained from 133 data points. Finally, differences in middle-ear behavior among mouse strains could account for some of the dissimilarities seen in Fig. 6.

Anatomical basis of the changing velocity response Discussion

Comparison with previous umbo velocity measures Saunders and Summers (1982) described the umbo response to a 100 dB SPL stimulus in adult C57BL/6J mice with a capacitive probe. Figure 6 compares their results to the T M responses obtained from our adult group. Despite the differences in techniques, the responses have a very similar shape. Nevertheless, the laser estimates of umbo velocity exceeded those detected by the capacitive probe by about 10 dB across frequency. This difference may have arisen because the capacitive probe is a relatively large device positioned close to the umbo (within about 64 gm), and this could have attenuated the acoustic signal that reached that portion of the TM. The laser head, in contrast, was positioned about 10 cm away from both the speaker and the mouse, making its acoustic interference negligible. Both plots in Fig. 6 show a steady increase in velocity up to about 10.0 kHz, where each graph shows a peak. At frequencies above 10.0 kHz the laser data show several peaks and valleys which were not apparent in the capacitive probe measures. This disparity may be due to differences in the sensitivity of the laser

The vibrational properties of the middle ear are derived from the mechanical characteristics of the individual middle-ear components. These mechanical characteristics may be broken down into three categories: compliance, resistance, and inertia. These categories can be used to form a three element, lumped sum, middle-ear model. Such a model was introduced by Relkin (1988). Detailed information was given in that paper and elsewhere (Fletcher 1992) concerning the influence of various middle-ear structures on the parameters of this type of model. We attempted to fit Relkin's model to our data in order to estimate how much the resistance, compliance, and inertia changed with age in mice. From these changes we hope to draw some conclusions about which structures influenced umbo velocity development in mice. Relkin's model has a single peak in the admittance versus frequency curve, and the frequency at which this peak occurs is referred to as the resonant frequency. At frequencies significantly lower than resonance ~low) the effects of inertia and resistance on the middle-ear response are minimal, leaving compliance (C) as the major determinant of middle ear admittance (Y~ow)at the very lowest frequencies: Ytow~ 2rCfowC

(1)

The admittance (Ylow)can be related to the low frequency umbo velocity (Vlow)by the approximation: Adult ....

O "-"

(n=5

Saunders laaZ(n

l ands

Vlo w S

......

r, ow 27 p

where p is the sound pressure and S is the surface area of the T M (Fletcher 1992). By combining Eqs. 1 and 2, we can solve for the compliance in terms of parameters that are known:

O.S

o O

'~

0.1

C~

x

/r . 2.0

, 4.0

,

, , ..i 10.0

VlowS

- (3) 4.6 ~fow P At the resonant frequency, admittance (Y~os)is given by the equation:

0 0.03

(2)

20.0

40.0

Frequency (kHz) Fig. 6. Adult velocity measures from the present study compared to those of Saunders and Summers (1982) measured with a capacitive probe

1 Y~es= -

(4)

r

where r is the resistance of the middle ear. Assuming that the approximation in Eq. 2 is still valid at the resonant

D.E. Doan et al.: Umbo motion in neonatal mice

108 Table 1. Parameters for middle-ear admittance modelsa

Age

Vlow b

Sc

0.53 • 10 - 3 0.81 x 10 3 0.90 x 10 3

2.3 M10 6 2.2 • 10 - 6 2.7 x 10 6 2.8x 10 6 2.7 x 10.6 2.7x 10 6

m/s

12 15 20 30 45 Adult

C

m2

1 . 3 x 10 - 3

0.95 x 10 3 1.1 • 10 - 3

d

Vres

rd

I

kHz

m/s

Pa. s / m 3

Pa- s2/m3

25.0 24.4 22.0 19.6 22.6 31.0

2.3 x 10 3 4.5 X 10 - 3 8.4 X 10 - 3 9.2x 10 3 7.8 X 10 - 3 11 x 10 3

2.4 • l09 1.3 • 109 0.58 X 109

8200 5760 5330 4550 4720 2250

fres

m3/pa 4.9 x 10-15 7.4 x 10-15 9.8 x 10-15 1 4 x 10 -15

10 x 10-15 12x 10-15

0 . 5 0 X 109

0.63 x 109 0 . 4 4 x 109

Abbreviations: PlowLow frequency umbo velocity; S Surface area of TM; C Compliance;j~es Resonant frequency; vre~Umbo velocity at the resonant frequency; r Resistance; I Inertia b Average velocity from 2.0 to 4.0 kHz ~ow= 3.0 kHz) Pars tensa area from Huangfu and Saunders (1983). Value at 12

days was interpolated from 10 and 15 day data. Adult value was taken from the oldest mice in their study (45 days) d Value for sound pressure level (p) is 5.66 Pa (100 dB SPL, peak-topeak)

frequency, we can combine Eqs. 2 and 4 to solve for the resistance of the middle ear in terms of the sound pressure level (p), the surface area of the TM (S), and the umbo velocity at the resonant frequency (Vres):

model parameters give a reasonable estimate of the real values of resistance, compliance, and inertia in the mouse middle ear. The parameters in Table 1 can be used to plot the model umbo velocities (Vmod~l)versus frequency (]) for each age group by means of the following formula (from Relkin 1988 and Eq. 2):

a

2.3p

r~--

(5)

/)r~sS

The inertia (I) of the middle ear can be derived from the compliance (C) and the resonant frequency (fres):

/)model =

2"/r+.2+/ S

2

(2

2

(7)

1

I - 4rtzfl~csC

(6)

We can now approximate the compliance, resistance, and inertia for the middle ears of any age group. The numerical values for the parameters in Eqs. 1 through 6 are presented in Table 1 for mice 12 days and older. The parameters from Table 1 may be used to create theoretical umbo velocity plots based on Relkin's three element model. By comparing these model velocities against our empirically measured umbo velocities, we can verify that Relkin's model reproduces the general trends of our empirical data. The close fit of the model to the empirical data is the basis for our assumption that the

O 1

r O

--

Adult Umbo Velocity A d u l t Adzzzittance M o d e ~

The umbo velocity plots for Relkin's model are shown for 12 day old mice and adult mice in Fig. 7. Our empirically measured umbo velocities for 12 day and adult mice are also shown in Fig. 7 to give an indication of how the models fit our experimentally measured velocities. Figure 7 demonstrates that a simple three element admittance model is a good predictor of umbo velocity below the resonant frequency in mice. The fit of the model to our data becomes poorer at high frequencies in large part because Eq. 2 is a somewhat inadequate approximation of the complicated relation between velocity and admittance at high frequencies (Fletcher 1992). Nevertheless, this model still assists us in analyzing the changes in compliance, resistance, and inertia because the model does follow the general trends of the experimentally measured umbo velocity plots. First we will examine the changes in compliance (C), and how these changes relate to the structures of the middle ear. Middle-ear compliance depends on the individual compliances of the bulla and the TM. The bulla compliance (Cbulla) in mice can be calculated directly from the bulla volume (Vbulla) , the density of air (9), and the speed of sound in air (c) (Relkin 1988):

0.1 Cbulla --/)bulla

o~

pC 2

~

0.03 .

2.0

.

.

.

v

12

---

12

.

.

4.0

.

Day U m b o Velocity Day Admittance Model

.

i

10.0

Frequency

,

Z0.0

,

,

40.0

(kHz)

Fig. 7. Umbo velocity frequency response at 12 days and adult, compared to Relkin's (1988) models. See text and Table 1 for full explanation of model equations and parameters

(8)

The TM compliance can be calculated from the area, thickness, and material properties of the membrane (Fletcher 1992), but, unfortunately, an examination of the thickness and internal structure of the mouse T M has yet to appear in the literature. A more suitable, although indirect, method of calculating the TM compliance may be through the use of an equation relating the TM c o r n -

D.E. Doan et al.: Umbo motion in neonatal mice

3.0

109

[]

/ V

I

o~

1.0

O 0,3

i 10

~ 20

~ 30

~ 40

~ 50

60

Age (days) Fig. 8. Growth of bulla compliance (V]), TM compliance (V), and total middle-ear compliance (0) with age. Bulla volumes from Huangfu and Saunders (1983), density of air (p = 1.19 kg/m3), and the speed of sound in air (c = 343 m/s) for calculation of Cbunafrom Eq. 8. Total middle-ear compliance (C) from Table 1 and TM compliance (CTM)from Eq. 9 ( C T M ) to the bulla compliance ( C b u l l a ) and total middle-ear compliance (C) (Relkin 1988): pliance

Cbull a ' C CTM

(9)

-- Cbull a -- C

Figure 8 shows the calculated compliances of the bulla and TM, compared to the total middle-ear compliance, all plotted as a function of age. Bulla and T M compliances interact in such a way that the smaller of the two compliances usually dictates the total compliance of the middle ear (Relkin 1988). Figure 8 indicates that the calculated T M compliance is smaller than the bulla compliance, and the patterns of growth for the compliances of the T M and the total middle ear are very similar. These observations lead us to believe that the T M may have had a stronger influence than the bulla on the total compliance of the middle ear. Thus, low frequency umbo velocity development in mice may have been strongly tied to the development of the T M compliance (C ~ CTM see Eq. 3). Figure 8 indicates that T M compliance increased by about 8 dB between 12 days and adult. Only about 1 dB of this change could have been due to change in T M area (S, from Table 1) during this period. Therefore, significant changes in T M thickness and/or material properties must have occurred to achieve the additional 7 dB of T M compliance improvement. Of course, more direct measurements of the T M compliance are needed to verify the value of this parameter and its role in determining the low frequency umbo response in mice. Resistance in the middle-ear system is caused by friction between the moving parts of the middle ear (Relkin 1988). Table 1 indicates that between 12 days and adult the model predicts a reduction in resistance (r) in the mouse middle ear. This is reflected in the increase, with age, of the velocity response near resonance (Fig. 2). The chief contributor to middle-ear resistance is the input to the inner ear (Relkin 1988), and a reduction in middle ear resistance may reflect maturational processes within the

cochlea. Resistance may also be reduced at any of several other locations within the middle ear. Among these are the joints of the ossicles, the fibers within the TM, and the middle-ear ligaments. The model also predicts that the inertia (I) of the moving middle-ear components must decrease between 12 days of age and adult (Table 1). The pattern of predicted inertia loss appears to occur in two stages. The first stage was a slow period of inertia reduction from 12 days to 30 days, followed by a second, sharp drop in inertia between 45 days and adult. This pattern of growth was reflected at the highest frequency umbo velocities (28.0 and 34.0 kHz, Fig. 3), and this correspondence between improved high frequency response and reduced inertia is exactly what is expected (Relkin 1988). The reduction in middle-ear inertia may have been due to a decrease in ossicular or T M mass. Alternatively the inertia could have changed if the rotational axis of the ossicles changed with age. At least two axes are present in the adult mouse (Saunders and Summers 1982), but the relation between these axes and age remains to be identified. Comparison with central auditory measures The increase in umbo velocity response after 12 days of age was compared to the development of N 1 thresholds at the round window of the cochlea (Shnerson and Pujol 1982) and evoked potentials from the cochlear nucleus (Saunders et al. 1980) in C57BL/6J mice (Fig. 9). All measures were converted to dB referenced to the best sensitivity for each study. Age-related growth of the electrophysiological recordings coincided with increases in umbo velocity, except at 30.0 and 35.0 kHz. The poor correspondence between umbo velocity and round window thresholds at these frequencies was probably due in part

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110 to the natural degeneration of high frequency hearing in C57BL/6J mice (Shnerson and Pujol 1982). In Fig. 9, an initial sharp rise in response began at 12 days for all electrophysiological and velocity data below 20.0 kHz, and these recordings reached adult-like values at approximately 20 days. The umbo velocities shown in Fig. 9 improved by an average of 12 dB during development. The cochlear nucleus thresholds improved by an average of 47 dB and the round window results showed an improvement of 64 dB. The disparity between the cochlear nucleus and round window developmental ranges were most likely due to procedural differences. Shnerson and Pujol (1982) kept the ear canals of the youngest mice intact for their round window recordings, while Saunders et al. (1980) excised the ear canals in their youngest mice when testing for cochlear nucleus thresholds. The ear canal is normally closed in mice up to 12 days of age. Excising the ear canal would have artificially improved the sensitivity in these mice, and this may explain the enhanced thresholds reported by Saunders and his colleagues in the youngest animals tested. We also removed the ear canals of the youngest mice. Consequently, the cochlear nucleus data from Saunders et al. (1980) may offer a better comparison against the umbo velocity data than do the round window thresholds. Given the serial nature of the auditory periphery, it is clear that immaturity in any of the peripheral structures will be reflected both in the performance of that structure itself, and in the performance of any components more central to it. The hearing thresholds measured by Saunders et al. (1980) and Shnerson and Pujol (1982) reflect the minimal vibrations at the oval window which elicit a neural response. If the cochlea and more central structures are responsive to vibration at the oval window (as they are in 12 day old mice), then any process that improves sound transmission through the middle ear will improve the sensitivity of the auditory system as a whole. Thus it appears that the cochlea, the eighth nerve, and the cochlear nucleus are partially functional by 12 days in the mouse, and about 25% (12 dB out of 47 dB) of the improvement in thresholds after 12 days could be due to improved umbo velocity sensitivity. The improvement in umbo velocity can only indirectly indicate how energy is transferred from the umbo to the inner ear. There may be middle-ear developmental events that not only improve umbo velocity, but also improve the efficiency with which umbo velocity is translated into stapes motion at the oval window of the inner ear. For example the ratio of the TM area to the oval window area increases by 1.5 dB between 15 and 20 days (Huangfu and Saunders 1983). This developmental change improves the transfer of energy from the umbo to the oval window and could enhance threshold sensitivity. Other factors that could improve the transmission of energy through the middle-ear are the ossification of the ossicles and the maturation and strengthening of the joints between them. Improvement in the efficiency of vibrational transmission from the umbo to the inner ear would increase the contribution of the middle ear to the overall development of hearing in mice.

D.E. Doan et al.: Umbo motion in neonatal mice

Acknowledgements. The authors greatly appreciate the thorough journal review provided by Dr. William Peake. The authors also thank Dr. Abraham Noordergraaf for his help with the model, and Ms. Yvonne M. Szymko, Mr. Henry J. Adler, and Ms. Kim A. Fisher for their comments and proofreading of the manuscript. This work was supported by a grant from the NIDCD-NIH (R01DC00531) to JCS, and by an Ashton Fellowship to DED.

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