Effects of middle-ear static pressure on pars tensa and pars flaccida of gerbil ears

Hearing Research 153 (2001) 146^163 www.elsevier.com/locate/heares

E¡ects of middle-ear static pressure on pars tensa and pars £accida of gerbil ears Chung-Yi Lee b

a;b;c

, John J. Rosowski

b;c;d;

*

a Department of Otorhinolaryngology, National Taiwan University Hospital, Taipei, Taiwan Department of Otolaryngology and Eaton-Peabody Laboratory, Massachusetts Eye and Ear In¢rmary, 243 Charles Street, Boston, MA 02114, USA c Department of Otology and Laryngology, Harvard University Medical School, Boston, MA, USA d Speech and Hearing Sciences Program, Harvard-MIT Division of Health Sciences and Technology, MIT, Cambridge, MA, USA

Received 10 July 2000; accepted 27 November 2000

Abstract It has long been known that static pressure affects middle-ear function and conventional tympanometry uses variations in static pressure for clinical assessment of the middle ear. However, conventional tympanometry treats the entire tympanic membrane as a uniform interface between the external and middle ear and does not differentiate the behavior of the two components of the tympanic membrane, pars tensa and pars flaccida. To analyze separately the different acoustic behavior of these two tympanic membrane components, laser Doppler velocimetry is used to determine the motion of each of these two structures. The velocities of points near the center of p. tensa and p. flaccida in response to the external-ear sound pressure at different middle-ear static pressures were measured in nine gerbil ears. The effect of middle-ear static pressure on the acoustic response of both structures is similar in that non-zero middle-ear static pressures generally reduce the velocity magnitude of the two membrane components in response to sound stimuli. Middle-ear under-pressures tend to reduce the velocity magnitude more than do middle-ear over-pressures. The acoustic stiffness and inertance of both p. tensa and p. flaccida are altered by static pressure, as shown in our results as changes of transferfunction phase angle. Compared to p. tensa, p. flaccida showed larger reductions in the velocity magnitude to small over- and underpressures near the ambient middle-ear pressure. This higher pressure sensitivity of p. flaccida has been found in all ears and may link the previously proposed middle-ear pressure regulating and the acoustic shunting functions of p. flaccida. We also describe, in both p. tensa and p. flaccida, a frequency dependence of the velocity measurements, hysteresis of velocity magnitude between different directions of pressure sweep and asymmetrical effects of over- and under-pressure on the point velocity. ß 2001 Published by Elsevier Science B.V. Key words: Tympanic membrane; Tympanometry; Laser Doppler velocimetry

1. Introduction The tympanic membranes (TMs) of most mammals consist of two parts: pars tensa and pars £accida. Current knowledge about TM morphology and histology is quite extensive (Lim, 1995; Funnell and Laszlo, 1982) and there are signi¢cant interspecies variations in size, shape, and thickness as well as the microstructure of these components (Kohllo«¡el, 1984; Lim, 1968a,b, 1970). As for their functions, p. tensa is tightly coupled

* Corresponding author. Tel.: +1 (617) 573-4237; Fax: +1 (617) 720-4408; E-mail: [email protected]

to the malleus forming a part of the transformer that converts the sound pressure acting on the TM into mechanical vibrations of the ossicles. The function of p. tensa has been fairly well studied experimentally (Zwislocki, 1962 ; Tonndorf and Khanna, 1970; Decraemer et al., 1989), and variations in p. tensa's response that result from the application of static pressure are the foundation of clinical tympanometry. P. £accida, on the other hand, is known to be commonly involved in the pathology of middle-ear diseases, but its actual function remains unclear. A role in regulating middleear pressure has been hypothesized since Henry Jones Shrapnell (1832) ¢rst described the p. £accida. More recently Stenfors et al. (1979) and Hellstro«m and Sten-

0378-5955 / 01 / $ ^ see front matter ß 2001 Published by Elsevier Science B.V. PII: S 0 3 7 8 - 5 9 5 5 ( 0 0 ) 0 0 2 6 9 - 0

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

fors (1983) suggested the primary function of the p. £accida was as a pressure equalizer that bu¡ered gas absorption by passive movement of the p. £accida. The changes in middle-ear volume that resulted from p. £accida motion minimize static-pressure di¡erences between the ear canal and middle-ear cavity, though in the later study Hellstro«m and Stenfors suggested the contribution of p. £accida to equalizing such di¡erences was small. This view of a limited pressure-regulation function of p. £accida is consistent with Dirckx et al. (1998) who recently described how the p. £accida of a gerbil was nearly completely distended by pressure differences of þ 40 daPa (V4 cm H2 O). In terms of acoustic function, Tonndorf and Khanna (1970) pointed out that the limp p. £accida might facilitate the rotation of the malleus. A minor acoustic role for p. £accida in peripheral sound transmission was suggested by Aritomo et al. (1988) and von Unge et al. (1991). Kohllo«¡el (1984), using an acoustic model of the ear, suggested that p. £accida shunts part of volume velocity available in the ear canal around the p. tensa and thereby reduces the response of the middle ear to low-frequency sound. This suggestion was supported by a series of studies in gerbils by Teoh et al. (1997) and Rosowski et al. (1997). In the present paper we investigate the relationship between the pressure-regulation and acoustic-shunt functions of the p. £accida by determining how changes in middle-ear static pressure a¡ect the acoustic behavior of the gerbil p. tensa and p. £accida. Static pressure has long been used to investigate the mechanisms of the middle ear both in the laboratory (Wever and Lawrence, 1954; MÖller, 1965; Lynch, 1981) and in the clinic (Lide¨n et al., 1970; Creten and van Camp, 1974 ; Margolis and Shanks, 1985). The clinical use of static pressure has been in the form of the immittance (impedance or admittance) tympanogram where the middle-ear immittance, measured with a pure-tone stimulus, is monitored while the static pressure in the ear canal is varied (Creten and van Camp, 1974). Tympanometry has therefore been an important component of the clinical auditory test battery for many years and is now a well-established method for physiologic assessment of the middle ear. Though there are only limited correlations between tympanometry and speci¢c middle-ear pathologies, tympanometry has often been used to estimate middle-ear pressure, determine the presence or absence of £uid in the middle ear, and estimate the condition of the ossicular chain. While tympanometry can provide useful information about the mechanoacoustic property of the middle ear, it treats the TM as a uniform interface between the external and middle ear. Therefore, tympanometry is not sensitive to di¡erences in the behavior of p. tensa and p. £accida. With the introduction of point measurement

147

of TM velocity by laser Doppler velocimetry, it is possible to separate the vibration of the p. tensa and p. £accida (Rosowski et al., 1997). The purpose of this article is to report how, in the gerbil ear, the middle-ear static-pressure changes the individual acoustic behavior of p. tensa and p. £accida. The di¡erences between the responses of the two membrane components will be discussed. We also hypothesize concerning the e¡ect of the di¡erences we ¢nd and apply this hypothesis to the human middle ear. 2. Materials and methods 2.1. Animal preparation This study protocol was approved by the Animal Care and Use Committee of the Massachusetts Eye and Ear In¢rmary, and meets the guidelines of the National Institute of Health. Healthy young female Mongolian gerbils were used, with body weights of 50^80 g. This study is based on nine ears of nine animals, three right ears and six left ears. Gerbils have a prominent p. £accida with well-studied middle ears (Ravicz et al., 1992, 1996, 1997 ; Teoh et al., 1997). Fig. 1 shows the middle ear and TM of the Mongolian gerbil with its prominent p. £accida (approx. 10% of the total TM area). Two anesthesia regimens were used. In the earlier experiments gerbils were anesthetized with sodium pentobarbital (Nembutal) at a dose of 70 mg/kg body weight and followed by supplemental doses on positive withdrawal re£ex. These early measurements demonstrated that sodium pentobarbital by itself can lead to respiratory problems, so later animals underwent anesthesia with a combination of sodium pentobarbital, fentanyl citrate and droperidol1 . Body temperature was monitored throughout the experiment and maintained around 34^39³C with a heating pad. Tracheotomy with cannulation was performed after anesthetization. Then the pinna and cartilaginous portion of the external-ear canal of the experimental ear were removed to expose the bony ear canal. Part of the lateral inferior bony ear canal was removed with care (to prevent opening the middle-ear cavity) in order to allow better access of the laser beam to the umbo. A brass ring 6 mm in inner diameter and 2.5 mm high was cemented in place around the bony ear canal (Fig. 2). A small brass tube with a side-mounted microphone and 1

The Mongolian gerbils were ¢rst anesthetized with a cocktail of Nembutal (25 mg/kg i.p.), droperidol (10 mg/kg i.m.), and fentanyl (0.2 mg/kg i.m.). On positive withdrawal re£ex, boosters of Nembutal (1/3 original dose) or droperidol and fentanyl (1/3 original dose) were administered.

HEARES 3635 15-2-01

148

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

Fig. 1. The ear of the Mongolian gerbil. (a) The middle ear, coronal view. Drawing from Rosowski et al. (1997). (b) The tympanic membrane, inferior lateral view. Drawing adapted from Teoh et al. (1997).

available water-¢lled manometer connected to the middle ear via the vent tube in the bullar wall. Motion of the umbo or p. £accida was measured by a Polytec0 ¢ber-optic laser velocimeter ; the laser beam was focused through the cover glass onto either the umbo or p. £accida re£ector (see Fig. 2). The angle between the umbo plane and the laser beam was around 60³ and that between p. £accida and laser beam around 80³. These viewing angles introduced errors as large as 15% to the velocity data that are not corrected in this article. A calibrated microphone that was integrated with the brass coupler (see Fig. 2) measured sound pressure at the entrance to the ear canal. An Ariel0 DSP-16+ data-acquisition board and Sysid0 software were used to generate broad-band chirp stimuli (50 Hz^25 kHz) and record the umbo and p. £accida velocity and ear-canal sound pressure. The stimulus level of the chirps varied between 70 and 100 dB SPL. The chirps contained sound energy at the ¢rst through 512th harmonic of 50 Hz, and allowed rapid measurement of the response at multiple frequencies. In order to keep the data set we discuss of reasonable size we extracted the measurements from seven frequencies for presentation as tympanograms. The extracted measurements at 250, 500, and 1000 Hz represent the magnitude and angle data at those individual frequency points. At frequencies of 2000, 4000, 6000, and 8000 Hz we observed some microstructure in the frequency

sound tube was sealed to the brass ring. The lateral opening of this brass tube was sealed with a glass coverslip. The posterior auditory bulla was exposed, and a small hole was made in which a vent tube was inserted and sealed with dental cement to the bullar wall. Triangles of re£ective tape ( 6 500 Wm per side) were placed near the center of p. tensa at the umbo and in the center of the p. £accida. The mass of each piece of tape was around 20 Wg, which is small compared to the mass of the TM and ossicles in gerbils. The re£ectors were necessary to generate su¤cient re£ected light for the laser to measure velocity reliably. The area of the re£ector was about 6% of the area of the p. £accida and about 1% of the area of the p. tensa. These small re£ectors had no noticeable e¡ect on the motions of the TM produced by static pressure. 2.2. Methods 2.2.1. Instrumentation Middle-ear pressure, generated by a manually controlled syringe, was measured with a commercially

Fig. 2. Schematic drawing of the measuring system. Pinna, cartilaginous ear canal removed. Drawing modi¢ed from Teoh et al. (1997).

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

response that was smoothed by reporting narrow band averages (base frequency þ 150 Hz) of the magnitude and angle. 2.2.2. Experimental procedure Each chirp sequence provided a measurement of the velocity-to-ear-canal-sound-pressure transfer ratio. These transfer ratios were measured at each step of two sets of stepped pressure sweeps. At the start of the ¢rst sweep the laser was focused on the umbo re£ector. Then, middle-ear pressure, starting with a pressure of +30 cm H2 O relative to atmospheric pressure, was stepped to values of +25, +20, +15, +10, +5, +2, +1, 0, 31, 32, 35, 310, 315, 320, 325, 330 cm H2 O. The pressure was then reduced to 0 cm H2 O ; the laser was focused on the p. £accida re£ector and the pressure series repeated. For each re£ector at each pressure level, two laser and microphone measurements were made. If the two were not repeatable, a third measurement was made.

149

The di¡erence between the two repeated measurements was less than þ 2.5 dB for 98% of the measurements. Each pressure level was maintained for around 1 min. The second set of sweeps of measurements was made with the laser focused on the umbo and then p. £accida while the pressure was brought to 330 cm H2 O and then stepped in the ascending direction. This sequence of large positive pressures that are swept to large negative pressures, and vice versa, mimics the pressure changes in normal tympanometry. Our pressure sweep procedure evolved with time. Only the ¢nal six gerbils were done with the precise methods described above. Thus, we report data from these six ears. In order to estimate the mean and range of data from six ears, we selected the velocity measured at seven frequencies from 250 Hz to 8 kHz. The noise £oor was determined by recording the point velocity while there was no stimulus. All of the reported data meet a signal-to-noise criterion level of a factor of 10 or greater.

Fig. 3. Umbo velocity normalized by ear-canal sound pressure (MHU M) as a function of middle-ear pressure for two ears from two gerbils, individual measurement at seven frequencies. The pressure sweep from +30 to 330 cm H2 O is indicated as the solid line, reverse as the dash-dot line. Signal-to-noise ratio is higher than 10. (1 cm H2 O = 98.06 Pa.) The units of the transfer function are those of velocity per sound pressure.

HEARES 3635 15-2-01

150

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

3. Results We report velocity-transfer functions, i.e. measures of velocity normalized by the measured ear-canal sound pressures, with the units of a speci¢c acoustic admittance. The transfer function HU equals the ratio of umbo velocity to ear-canal sound pressure while HPF equals the ratio of p. £accida velocity to ear-canal pressure. However, since the measured sound pressure acts over the entire surface of the TM and since parts of the TM may be coupled to the measurement point in complicated ways, the measured transfer function does not describe a driving-point admittance. Therefore we might expect phase angles of the transfer function that fall outside the þ 0.25 period range especially at frequencies and static pressures that produce complicated patterns of membrane displacement.

3.1. HU and HPF , individual measurement at seven frequencies Fig. 3 shows examples from two animals of the e¡ect of middle-ear static pressure on the magnitude of HU (MHU M). The seven columns show results at seven frequencies. The solid curve in each plot denotes MHU M measured while the middle-ear pressure was stepped from an over-pressure of +30 cm H2 O to an underpressure of 330 cm H2 O (downward sweep). The dash-dot curve denotes MHU M measured while stepping in the reverse direction (upward sweep). Regular di¡erences in the magnitude with the direction of the pressure sweep are apparent, where the MHU M is usually larger for the downward sweeps especially with small under-pressures. Also apparent is an asymmetry in MHU M measured with middle-ear over- and under-pressure, where the magnitude at each frequency is usually larger for middle-ear over-pressures. HU tympanograms (MHU M vs. middle-ear static pressures) with a single peak

Fig. 4. P. £accida velocity normalized by ear-canal sound pressure (MHPF M) as a function of middle-ear pressure. Individual measurements are plotted at seven frequencies, from the same two ears in Fig. 3. (1 cm H2 O = 98.06 Pa.) The units of the transfer function are those of velocity per sound pressure.

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

appear at 2 kHz and lower while the shape of the HU tympanogram varies at frequencies higher than 4 kHz. The peak MHU M increases as the frequency goes from 250 Hz to 2 kHz. The MHU M measurements made at the extreme static pressures ( þ 30 cm H2 O) generally di¡er between the two sweeps. These di¡erences can be associated with di¡erences in the history of pressurization, e.g. the pressure at each extreme is stepped either directly from 0 cm H2 O at the start of a sweep or from a slightly smaller static pressure of identical sign at the end of the sweep. Also, measurements were made on p. £accida between each of the illustrated pressure sweeps. HPF tympanograms (MHPF M vs. middle-ear static pressures) for the same two animals are shown in Fig. 4. Di¡erent magnitudes appear between the two pressure

151

sweeps especially for the peak magnitudes at 2 kHz and lower where the peak MHPF M during the downward sweep is usually larger than that during the upward sweep. An asymmetry between the MHPF M at middleear over- and under-pressure at each frequency is similar to the asymmetry of MHU M. HPF tympanograms with a single peak appear at 2 kHz and lower, the peak is sharper than those in the HU tympanograms and the peak magnitude is usually larger than the peak of the HU tympanogram. The shape of the HPF tympanogram varies at frequencies higher than 4 kHz. In general the two directions of pressure sweep result in similar tympanometric patterns except for the two pressure sweeps at 8 kHz for one animal (gerbil 5) as noted in Fig. 4. The magnitude of the single peak in HPF increases somewhat from 250 Hz to 2 kHz.

Fig. 5. MHU M and MHPF M (with units of velocity per sound pressure) means for each pressure sweep from six ears at seven frequencies. The pressure sweep from +30 to 330 cm H2 O is indicated as the solid or dash line, reverse as the dash-dot or dot line. The minimum and maximum standard errors of mean velocity magnitude for each frequency are illustrated with bars at the right lower corner of each panel. The static pressures with statistically di¡erent point-velocity magnitudes between two pressure directions are indicated with diamonds. Means of data that come from fewer than six ears are marked as circle for ¢ve ears, square for four ears, asterisk for three ears, x for two ears and plus for one ear. (1 cm H2 O = 98.06 Pa.) The units of the transfer function are those of velocity per sound pressure.

HEARES 3635 15-2-01

152

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

Table 1 Enumeration at each frequency of the number of +/3 pressure sweeps, number of 3/+ sweeps, the mean peak magnitude for each sweep direction ( þ S.E.M.), the peak of the mean curves for each sweep direction and the peak magnitude of the bidirectional mean (the mean of all of the sweeps) for both p. tensa and p. £accida Peak magnitude (mm/s/Pa) P. tensa N +/3 N 3/+ Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean P. £accida N +/3 N 3/+ Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean

250 Hz

500 Hz

1 kHz

2 kHz

6 6 0.0973 (0.0276) 0.1024 (0.0309) 0.1008 0.0973 0.0917

6 6 0.2099 (0.0732) 0.1850 (0.0469) 0.1850 0.1959 0.1810

6 6 0.4899 (0.0822) 0.4388 (0.0940) 0.4335 0.4604 0.4470

6 6 1.1399 (0.4524) 1.0910 (0.4840) 0.9801 1.0056 0.9918

6 6 0.4373 (0.3048) 0.2216 (0.1776) (n = 5) 0.2757 0.1883 0.2007

6 6 1.1839 (0.9751) 0.3401 (0.2881) 1.0590 0.3357 0.5610

6 6 1.3758 (1.0875) 0.6257 (0.3155) 1.2853 0.5116 0.7662

4 4 2.7877 (1.5803) 1.2594 (0.1923) 1.5897 0.8078 0.9708

Because MHPF M varies so greatly with small pressures near 0 cm H2 O, it is possible that our sampling resolution of 1 cm H2 O between þ 2 cm H2 O caused us to miss the precise peak pressure of MHPF M which would lead us to underestimate the peak magnitude. The limited pressure resolution in our measurements has less in£uence on the HU data because the HU tympanograms are not as peaked. 3.2. HU and HPF , mean data for each pressure sweep at seven frequencies Fig. 5 shows the mean MHU M and MHPF M from six individuals at each of the seven middle-ear static pres-

sures for each pressure sweep direction. These mean data curves are generally consistent with the individual measurements of Figs. 3 and 4. However, there are di¡erences in the peak magnitude, peak pressure and sharpness (as quanti¢ed by the width at half the peak value) of these single-peaked HU and HPF tympanograms (Tables 1^3). An obvious di¡erence between the mean and individuals is the lower peak magnitude of the mean of HPF while the peak magnitudes of the mean of HU are similar to the individuals. The broadening and lowering of the mean HPF peaks (Fig. 5 and Tables 1 and 3) is a consequence of inter-individual variation in the static pressure at the peak and the sharpness of HPF tympanogram. The standard errors

Table 2 Enumeration at each frequency of the mean pressure where the peak magnitude occurred for each sweep direction ( þ S.E.M.), the peak pressure of the mean curves for each sweep direction and the peak pressure of the bidirectional mean (the mean of all of the sweeps) for both p. tensa and p. £accida Peak pressure (cm H2 O) P. tensa Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean P. £accida Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean

250 Hz

500 Hz

1 kHz

2 kHz

1.0000 (0) 0.1667 (0.4082) 1 0 1

0.6667 (0.5164) 0 (0) 1 0 1

0 (1.0954) 0.3333 (0.5164) 0 0 0

0.1667 (1.3292) 0.5000 (0.5477) 1 1 0

0.3333 (0.5164) 1.0000 (0) (n = 5) 0 1 1

0.3333 (0.5164) 1.6667 (1.6330) 0 1 0

0.1667 (0.9832) 1.6667 (1.7512) 0 1 0

0.2500 (1.2583) 1.5000 (0.5774) 0 1 0

The number of peaked tympanograms that are averaged at each frequency is the same as that in Table 1.

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

153

Table 3 Enumeration at each frequency of the mean half width of the peak (as quanti¢ed as the pressure range where the magnitude equals or is greater than 50% of the peak magnitude) for each sweep direction ( þ S.E.M.), the half width of the mean curves for each sweep direction and the half width of the bidirectional mean (the mean of all of the sweeps) for both p. tensa and p. £accida Half width (cm H2 O) P. tensa Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean P. £accida Mean (S.E.M.) +/3 Mean (S.E.M.) 3/+ Mean curve +/3 Mean curve 3/+ Bidirectional mean

250 Hz

500 Hz

1 kHz

2 kHz

7.6811 (2.2750) 4.2699 (3.0804) 7.0367 4.3686 6.5277

6.8456 (3.1717) 5.3257 (3.1221) 6.5445 4.9712 6.2498

6.4030 (3.1072) 4.5193 (2.3153) 6.1935 4.1736 5.2315

6.6113 (1.9094) 5.3381 (2.6989) 8.2243 5.1319 6.5172

3.0019 (4.4424) 2.1779 (1.1789) (n = 5) 2.0291 1.3834 2.1342

2.9147 (4.0717) 3.6683 (4.1779) 1.1934 1.4443 1.6429

2.9284 (2.3227) 4.6019 (3.5086) 1.2108 5.1484 1.7642

5.3366 (7.8101) 4.5999 (2.7863) 2.4745 6.0896 4.7437

The number of peaked tympanograms that are averaged at each frequency is the same as that in Table 1.

varied quite a bit from pressure to pressure and frequency to frequency. (The maximum and minimum standard errors of the mean at each frequency are noted by the bars in the lower right of each panel of the ¢gure.) The downward sweeps generally produce the larger magnitude of HU and HPF except at 32 cm H2 O at 4 kHz for HU where the upward sweep produces the larger MHU M. Such di¡erences in the magnitude between the two pressure sweeps were analyzed statistically using ANOVA2 . The results revealed that the di¡erence between the magnitudes of HU or HPF measured with the two pressure sweeps is signi¢cant at only a few frequencies and static pressures. (Due to variations in the standard error at each pressure and frequency, the largest visible di¡erences in Fig. 5 do not always yield signi¢cant di¡erences.) The directionally (pressure sweep) dependent di¡erence for MHU M is statistically signi¢cant at 310 cm H2 O at 1 kHz, 2 kHz and 4 kHz (P = 0.0039, 0.0093, 0.0067). A statistically signi¢cant di¡erence is also noted at 32 cm H2 O at 4 kHz (P = 0.0148) and +2 cm H2 O at 6 kHz (P = 0.0268). The directional di¡erence for MHPF M is statistically signi¢cant at 0 cm H2 O at 250 Hz, 500 Hz, 1 kHz, 2 kHz, 4 kHz, and 6 kHz (P = 0.0257, 0.0110, 0.0302, 0.0186, 0.0124, 0.0321), the di¡erence at 6 kHz extends to 31 and 32 cm H2 O (P = 0.0464, 0.0257).

2

Independent analyses compared the data for the two directions at each frequency and pressure. Such analyses ignore the observed correlation between nearby pressure points but also make no assumptions about the interdependence of the data at di¡erent pressures.

3.3. HU and HPF , bidirectional mean data at seven frequencies 3.3.1. Pressure dependence of HU and HPF Because the directionally dependent di¡erences in HU and HPF are signi¢cant at only a few combinations of static pressure and frequency, we averaged the results from the two directions to compare the behavior of p. tensa and p. £accida. Fig. 6 shows the mean of MHU M and MHPF M from six individuals at each of the seven middle-ear static pressures from both pressure sweeps. The bidirectional mean HU and HPF tympanograms look much like the individual HU and HPF tympanograms. However, the single-peak magnitude of the bidirectional mean HPF tympanograms is again not as high as in the individual HPF tympanogram and the bidirectional mean HPF tympanograms are not as sharp as the individual HPF tympanograms (Tables 1 and 3). This di¡erence between the individual HPF tympanograms and the bidirectional mean is again explained by an interaction of the very sharp individuals and variations in static pressure of the peak between individuals, which together tend to £atten the bidirectional mean HPF tympanogram. Speci¢cally, the peak pressures of all HPF pressure sweeps (both upward and downward) varied between 31 and +5 cm H2 O, with a mean of 0.9 cm H2 O. At 1 kHz, the individual peak MHPF M varied between 2.9 and 1.08 mm/s/Pa, with a mean of 1.01 mm/s/Pa. The peak of the bidirectional mean of the MHPF M measurements at 1 kHz occurred at 0 cm H2 O but its magnitude is only 0.77 mm/s/Pa. This peak of the mean pressure sweeps is smaller than the mean of the individuals.

HEARES 3635 15-2-01

154

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

Fig. 6. MHU M and MHPF M (with units of velocity per sound pressure), bidirectional means at seven frequencies. The MHU M is indicated with solid lines while dash lines denote the MHPF M. The static pressures with statistically di¡erent magnitude between HU and HPF are indicated with diamonds. Standard errors are illustrated at some static pressures with bars on lines (n = 6, mean þ S.E.M.). Means of data that come from fewer than six ears are marked as circle for ¢ve ears, square for four ears, asterisk for three ears, x for two ears and plus for one ear. Other standard errors with similar magnitude are omitted for clarity. (1 cm H2 O = 98.06 Pa.) The units of the transfer function are those of velocity per sound pressure.

The data in Fig. 6 point out that while there are similarities in the pressure dependence of MHU M and MHPF M, there are also di¡erences. In general the HPF tympanograms appear sharper. The di¡erences between MHU M and MHPF M at each pressure and frequency were analyzed statistically using ANOVA. The results revealed that MHU M and MHPF M are signi¢cantly di¡erent at 31 cm H2 O at 250 Hz, 500 Hz, and 1 kHz (P = 0.0032, 0.0009, 0.0006); at 32 cm H2 O at 250 Hz, 500 Hz, 1 kHz, 2 kHz, and 4 kHz (P = 0.0044, 0.0058, 0.0139, 0.0076, 0.0499); at 35 cm H2 O at 2 kHz, 4 kHz, and 8 kHz (P = 0.0072, 0.0097, 0.0476). Di¡erences are also found at 330 cm H2 O at 2 kHz (P = 0.0418) and at 310, +1, and +30 cm H2 O at 8 kHz (P = 0.0461, 0.0488, 0.0390). In summary, the di¡erences between MHU M and MHPF M are mostly found at small under-pressures where MHU M is always larger than MHPF M. There are also signi¢cant di¡erences with the largest absolute static pressures we used, but only at 2 kHz and 8 kHz.

3.3.2. Frequency dependence of HU and HPF To better display the frequency dependence of HU and HPF and the e¡ects of middle-ear static pressure on the phase angle of the transfer function, we replot the data from Fig. 6 against frequency in Figs. 7 and 8 respectively. In Fig. 7 at ambient pressure, the magnitude of HU increases with frequency from 250 Hz up to 2 kHz and then decreases at higher frequencies. The phase angles show sti¡ness control (0.125 9 angle 9 0.25) of HU at low frequency and mass control (30.25 9 angle 9 30.125) at high frequency. MHU M decreases as the middle-ear static-pressure shifts away from ambient pressure at frequencies below 2 kHz. Fractional decreases of MHU M are larger with middle-ear under-pressure. Di¡erent responses of HU to over- and under-pressure are noted at 4 kHz, 6 kHz, and 8 kHz where the middle-ear over-pressure mostly increases the MHU M while under-pressure decreases MHU M. However, the direction of the e¡ect varies with the magnitude of the static pressure and the frequencies.

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

155

Fig. 7. Magnitude and angle of HU (with units of velocity per sound pressure) as a function of frequency at seven di¡erent static pressures, bidirectional means at seven frequencies. Solid lines represent HU for 0 cm H2 O, dash-dot lines for þ 1 cm H2 O, dot lines for þ 10 cm H2 O and dash lines for þ 30 cm H2 O. Standard errors for bidirectional mean data of 0 and þ 30 cm H2 O pressures are illustrated at each frequency with bars on lines (n = 6, mean þ S.E.M.). Means of data that come from fewer than six ears are marked as circle for ¢ve ears, square for four ears, asterisk for three ears, x for two ears and plus for one ear. (a) At middle-ear under-pressure. (b) At middle-ear over-pressure. (1 cm H2 O = 98.06 Pa.)

Both middle-ear over- and under-pressure increase the sti¡ness of the p. tensa leading to a decrease of MHU M at low frequency and an increased frequency range where the angle of HU is about +0.25 period. At higher frequency, the e¡ect of static pressure on the angle of HU is more variable. The e¡ect of static pressure on HPF is illustrated in Fig. 8. At ambient pressure, the MHPF M increases with frequency from 250 Hz up to 2 kHz and then decreases at higher frequencies. Angles show sti¡ness control of HPF at low frequency and mass control at high frequency. The sti¡ness control shifts to mass control at a little lower frequency compared to HU . A similar pattern of decreasing magnitude with altered middleear pressure is displayed, though HPF is more sensitive to pressure than HU (i.e. the change in MHPF M for a given pressure is larger than the change in MHU M). Both over- and under-pressure extend the range of sti¡ness control of HPF towards the higher frequencies ex-

cept for +1 cm H2 O where the angle is around +0.1 period at low frequency. The e¡ect of static pressure on the angle is variable at higher frequencies. The sensitive pressure response of HPF is better demonstrated in Fig. 9a,b, which compares the e¡ect of pressure on the frequency dependence of HU and HPF . With a þ 1 cm H2 O change of static pressure, MHPF M decreases more than MHU M decreases at frequencies below 4 kHz with the larger di¡erence occurring as middle-ear pressure changes from 0 to 31 cm H2 O. As for the þ 30 cm H2 O static pressure (Fig. 9c), the magnitudes of HU and HPF are similar at +30 cm H2 O and MHU M is lower than MHPF M at 330 cm H2 O between 1 kHz and 4 kHz. This is the same frequency range where HU is mass-dominant. The larger magnitude for both HU and HPF at +30 cm H2 O at each frequency is consistent with the asymmetry of the HU and HPF tympanograms at each frequency in Fig. 6.

HEARES 3635 15-2-01

156

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

Fig. 8. Magnitude and angle of HPF (with units of velocity per sound pressure) as a function of frequency at seven di¡erent static pressures, bidirectional means at seven frequencies. Means of data that come from fewer than six ears are marked as circle for ¢ve ears, square for four ears, asterisk for three ears, x for two ears and plus for one ear. (a) At middle-ear under-pressure. (b) At middle-ear over-pressure. (1 cm H2 O = 98.06 Pa.)

4. Discussion Our results describe the dependence on middle-ear static pressure of the velocity to sound-pressure transfer functions of gerbil p. tensa and p. £accida. Here : (1) we compare the pressure sensitivity of the two transfer functions, (2) we discuss the e¡ects of over-pressure and under-pressure on the frequency dependence of the transfer functions, (3) we compare our results to other results including clinical tympanometry, (4) we discuss our data in terms of the mechanisms of middle-ear pressure and volume regulation, and (5) we also discuss the e¡ect of static pressure on acoustic shunting by p. £accida. 4.1. The e¡ect of static pressure on pars tensa and pars £accida velocity The e¡ects of alterations in middle-ear static pressure on the velocity-transfer function of the center of the p. £accida and the p. tensa, measured at the umbo, show

many similarities and some di¡erences. The pattern of alterations in the magnitude of HU and HPF with staticpressure sweeps (Figs. 3^6) varied from single-peak, with the largest magnitude near 0 cm H2 O at frequencies less than 4 kHz, to almost sigmoid-shaped, with the largest magnitude occurring at large over-pressures at 6 and 8 kHz. As can be seen from the responses of individual ears (Figs. 3 and 4) the high-frequency sigmoid was not observed in all ears, e.g. in gerbil 5 at 8 kHz there is a clear peak in the pressure sweep near 0 cm H2 O static pressure. However, there was a clear increase of the complexity in the pressure dependence of HU and HPF with high-frequency sound in all ears. In general HPF was more sensitive to small changes in pressure near 0 cm H2 O (the p. £accida half widths in Table 3 are narrower than those for p. tensa), and therefore the pressure sweeps produced `sharper' alterations in HPF magnitude. This di¡erence in sharpness indicates that p. £accida is more sensitive to small alterations in middle-ear static pressure than is p. tensa. Both the measured HU and HPF were dependent on

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

157

Fig. 9. Comparison between HU and HPF as a function of frequency at di¡erent static pressures. Means of data that come from fewer than six ears are marked as circle for ¢ve ears, square for four ears, asterisk for three ears, x for two ears and plus for one ear. (1 cm H2 O = 98.06 Pa.) (a) Comparison at 0 and +1 cm H2 O. (b) Comparison at 0 and 31 cm H2 O. (c) Comparison at þ 30 cm H2 O.

the direction of the pressure sweep with the most signi¢cant directional di¡erences generally occurring at small middle-ear under-pressures (Figs. 3 and 4). Sweeps from under-pressure to over-pressure generally produced larger decreases in the transfer function magnitudes at these small middle-ear under-pressures. A comparison of this hysteresis-like phenomenon with similar directional dependences observed in clinical tympanograms is a point of later discussion. The velocity response of p. tensa and p. £accida to alterations in middle-ear static pressure of equal absolute value but di¡erent sign were asymmetric at all frequencies. The transfer-function magnitude measured with a middle-ear over-pressure was always larger than the magnitude with an under-pressure of similar absolute magnitude. This was a very robust phenomenon that was visible in all of our data. 4.2. The e¡ect of static pressure on the frequency dependence of TM velocity While we have already noted the frequency depen-

dence of the alterations of HU and HPF with static pressure, we have made no attempt to interpret this frequency dependence. In this section we use our measurements of HU and HPF with constant static pressure to describe our results in terms of simple acoustic quantities, e.g. acoustic sti¡nesses and inertances, and then discuss how these quantities are altered by static pressures. 4.2.1. The frequency dependence with zero static-pressure di¡erence across the TM The measurements of the frequency dependence of HU and HPF with ambient middle-ear pressure (Figs. 7^9) are consistent with some simple ideas of middleear mechanics. At the lowest frequencies (f = 0.5 kHz) the magnitudes of both transfer functions grow proportionally with frequency and the angles of both are near 0.25 periods. This behavior is consistent with a sti¡nesscontrolled membrane system. An acoustic sti¡ness continues to play a role in the response of p. tensa HU at 1 kHz (where the angle remains positive), while the near-zero angle and the broad peak of the mean p.

HEARES 3635 15-2-01

158

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

£accida transfer-function HPF imply a resonance in p. £accida mechanics at 1 kHz. A resonance in the mechanics of the p. tensa is suggested at 2 kHz, where the phase angle of HU is zero and the magnitude is peaked. Above the resonance frequency in both HU and HPF , the magnitude falls and the angle falls to between 30.1 and 30.2 periods. Such angles are consistent with a combination of resistance and inertance control of the mechanics. Above 1 kHz the angle of HPF is more negative than the angle of HU . The magnitude of HPF is generally larger than that of HU at frequencies 6 2 kHz and smaller at frequencies s 2 kHz (Fig. 9a). These results are generally consistent with the admittance measurements of Teoh et al. (1997) and the velocity measurements of Rosowski et al. (1997), which describe the p. £accida as a resonant membrane with a resonant frequency less than that of the p. tensa. However, the resonant response of the p. £accida described in those previous studies is generally sharper and has a lower resonant frequency (V500 Hz) than that observed here. One reason for this di¡erence is a di¡erence in the state of the middle-ear cavity. The earlier reports described the frequency dependence of the velocity of the p. £accida when the middle-ear cavity was opened, in an attempt to describe the mechanics of the isolated p. £accida. In this report, the middle-ear cavity is closed and our measurements re£ect the velocitytransfer function of the whole middle-ear system including the cavities. Rosowski et al. (1997) demonstrate a decrease in sharpness and an increase in the peak frequency of the p. £accida velocity when the cavity is closed ; however, these alterations are not large enough to completely explain the di¡erences in the two data sets. Another possible contributor to the disparity between the present and previous results is a broadening in these data that results from averaging the p. £accida response over six ears. 4.2.2. The e¡ect of middle-ear under-pressures on frequency dependence The e¡ect of middle-ear under-pressures on the frequency response of either the p. tensa or p. £accida is to decrease the response to lower sound frequencies where the a¡ected frequency range and the magnitude of the decrease increases with increasing static-pressure magnitude. The e¡ect of under-pressures on the angles of HU and HPF , in general, is to increase the range where the angle is close to 0.25 periods. However, at the extreme middle-ear under-pressures (325 and 330 cm H2 O), the angle of HU is close to 30.25 periods over the entire measured frequency range. Except at these largest under-pressures, our results are consistent with a sti¡ening of the p. tensa and p. £accida with increased middle-ear under-pressure. An increase in sti¡ness decreases the velocity response to

low-frequency sound stimuli (but in a manner such that the response still continues to grow with frequency), and increases the frequency range where the angle of the transfer function is near 0.25 periods. A variation from this pattern observed in the umbo response at 330 cm H2 O (Fig. 7a) may result from an interaction of the p. £accida and ossicular chain as the under-pressure pulls the p. tensa and p. £accida inwards and at the same time draws the malleus head up (Hu«ttenbrink, 1988). Under these circumstances the p. £accida and malleus head come into contact potentially altering the mechanics of the ossicles and the coupled p. tensa. The rate of change in sti¡ness with increasing underpressure is faster for p. £accida than p. tensa (Fig. 9b). An under-pressure of 31 cm H2 O on average produces a decrease in HU at low frequencies of about 10%, and at the same time reduces HPF by more than 70%. This di¡erential sensitivity to pressure is consistent with the greater sharpness of the HPF pressure sweeps near ambient pressure (Figs. 3^5; Tables 1 and 3). While the p. £accida is more sensitive to small underpressures, Fig. 9 points out that on average large underpressures produce larger alterations in HU . At frequencies below 2 kHz, the magnitude of HU with a 330 cm H2 O middle-ear pressure is about 1/100 of the magnitude measured at 0 cm H2 O middle-ear pressure. In the same frequency range, the magnitude of HPF with 330 cm H2 O is about 1/30 of the magnitude measured at 0 cm H2 O middle-ear pressure. 4.2.3. The e¡ect of middle-ear over-pressures on frequency dependence The e¡ects of middle-ear over-pressures on HU and HPF are also well approximated by an increase in sti¡ness as the absolute middle-ear pressure increases. However, there are some regular di¡erences between the e¡ects of middle-ear over- and under-pressures on the measured velocities. The most prominent di¡erence is in the magnitude of the e¡ect of pressure. As noted previously there is an asymmetry in the change in velocity magnitude with pressures of di¡erent sign: middle-ear over-pressures produce smaller reductions in velocity than under-pressures. Indeed, pressures of +10 to +30 cm H2 O can actually increase the magnitude of HU and HPF at sound frequencies greater than 2 kHz (Fig. 7b). The largest increases in MHU M and MHPF M generally occur at the locations of the new resonance frequencies that result from the increase in sti¡ness. (Figs. 7a and 8a,b show several examples of how the magnitude of the mean velocity with non-zero static pressures can be larger than those with zero static pressure at 4, 6, and 8 kHz.) Another di¡erence between over-pressure and underpressure is in the angle of the velocity-transfer functions at middle-ear pressures of larger absolute value. Where-

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

as HU has an angle of 30.25 periods with 330 cm H2 O, at +30 cm H2 O both HU and HPF have angles that are more compliance-like (closer to 0.25 periods). These angles can even grow larger than 0.25 periods, producing `admittances' that are not consistent with simple passive mechanics. However, as pointed out earlier, while our transfer functions have units of a speci¢c acoustic admittance, they do not represent measurements of driving-point admittance in that the soundpressure stimuli act on regions of the membranes whose coupling to our velocity measurements may be complex. Indeed, to our mind, the non-admittance-like angles at large over-pressures and high sound frequencies suggest some change in the contribution of the di¡erent membrane components to the motion of the umbo in the center of the p. tensa. 4.3. Comparison to other data The measurements of the e¡ect of static pressure on sound transfer and input to the middle ear have been performed in various other animals and are a standard tool for the clinical evaluation of middle-ear function. 4.3.1. Measurements in other animals Several investigators have used middle-ear staticpressure variation as a probe of middle-ear sound transmission function. The measured parameters in these studies were of two di¡erent kinds. The ¢rst kind are measurements of middle-ear sound transfer, by measurements of either cochlear potential3 (Wever and Lawrence, 1954 ; MÖller, 1965) or ossicular motion (Murakami et al., 1997). The second kind are measurements of the e¡ect of static pressure on middle-ear input admittance (Mundie, 1963; MÖller, 1965; von Unge et al. 1991; von Unge and Bagger-Sjo«ba«ck, 1994). In general, these studies use methods similar to those of this report; the middle-ear static pressure is varied in steps during which measurements of admittance or sound transmission are made at multiple frequencies. All of the sound-transfer measurements are generally consistent with the work we report here. The earlier results demonstrate that middle-ear static pressure can reduce middle-ear sound transmission or admittance by a factor of 10 at frequencies below 1 kHz (Wever and Lawrence, 1954 ; MÖller, 1965) and that static pressure may actually increase sound transmission or admittance at higher frequencies. There is, however, a fundamental di¡erence within these measurements that is best observed by plotting the data in terms of iso-frequency pressure sweeps (Fig. 10). While our HU and HPF pres3

We consider the cochlear potential to indicate the output of the ossicular system and those parts of the tympanic membrane that are tightly coupled to the ossicles.

159

sure sweeps are asymmetric in that middle-ear underpressures tend to cause larger reductions in magnitude than over-pressures, the cochlear potential data and human cadaver velocity data are more symmetric ; middle-ear pressures of either sign with similar absolute value produce similar reductions in the measure of sound transmission (Fig. 10a). There is a di¡erence of another kind between our data and the admittance data from other animals. Fig. 10b illustrates that middle-ear static pressures produce asymmetric changes in the middle-ear input admittance of cat (MÖller, 1965; Lynch, 1981) and guinea pig (Mundie, 1963), but that the asymmetry is opposite of that observed in our data. Larger admittance changes are produced by middle-ear over-pressures. The di¡erences in symmetry between our data and the admittance and transmission data from other animals may indicate inter-species or methodological di¡erences in these measurements of the e¡ect of middle-ear static pressure. One point in favor of inter-species di¡erences is the work of von Unge and coworkers (1991, 1994), who measured admittance tympanograms in isolated gerbil temporal bones. In these measurements, larger admittance magnitude variations were seen when the middleear static pressure was less than the ear-canal static pressure. (The sign of the middle-ear to ear-canal static-pressure di¡erence with the larger change in admittance is the same as when we apply negative pressures in the middle ear.) 4.3.2. Comparisons with clinical tympanometry Our velocity measurements describe the e¡ect of static pressure on the sound-induced motion of individual points on the surface of the TM. The points in our measurements are the umbo, near the center of the p. tensa, and the center of the p. £accida. The static-pressure dependence of our measured point velocities (and the pressure sweeps from other data in Fig. 10) shares some features with clinical acoustic immittance tympanograms where acoustic immittance is a measure of the average sound-induced motion of the entire TM. Clinical tympanograms track changes in either admittance magnitude, susceptance, conductance, impedance magnitude, resistance, or reactance. We have expressed our velocity tympanograms (Figs. 3^6) in terms of transfer functions of a velocity normalized by the sound pressure in the ear canal. This ratio has the units of a speci¢c acoustic admittance (mm/s/Pa) and is analogous to an acoustic admittance magnitude. The shapes of the HU and HPF pressure sweep data (Figs. 3^6) have some features in common with admittance tympanograms measured in humans, but there are also clear di¡erences. 4.3.2.1. Frequency dependence of tympanograms. The frequency dependence of conventional tympanograms is

HEARES 3635 15-2-01

160

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

Fig. 10. A comparison of pressure sweeps at 1 kHz from our and other data. (1 cm H2 O = 98.06 Pa). (a) A comparison of measurements of middle-ear transmission, either of cochlear potential (CP) or of the velocity of the umbo (VUMBO ) in cat (Wever and Lawrence, 1954; MÖller, 1965) and human cadaver (Murakami et al., 1997), with the means of our + to 3 HU and HPF pressure sweeps in six ears. All of the measurements are normalized to the peak response magnitude. (b) A comparison of measurements of middle-ear input admittance in cat (MÖller, 1965; Lynch, 1981) and guinea pig (Mundie, 1963) with the mean + to 3 pressure sweeps of HU and HPF in six gerbil ears.

a well-known clinical phenomenon that is believed to arise from di¡erential pressure sensitivity of the physical components that limit middle-ear motion. A fairly simple classi¢cation scheme tracks the number of peaks in susceptance and conductance tympanograms as frequency is varied and uses these changes to determine a middle-ear resonance frequency (Vanhuyse et al., 1975 ; Lilly, 1984 ; Margolis et al., 1985). While we only illustrate our pressure sweeps in terms of the magnitude of the velocity-transfer function, examination of the real part (conductance) and imaginary part (susceptance) of the complex transfer functions yields tympanometric patterns similar to those described for the human. At 250 Hz and 1 kHz pressure sweeps of the speci¢c acoustic susceptance and conductance of the p. tensa show a single peak, while at 4 kHz there are three peaks in the conductance and two peaks in the susceptance pressure sweeps. There is a similar progression from single peaks at 250 Hz to multiple peaks at 1 kHz and higher in the p. £accida susceptance and conductance pressure sweeps. In general the frequency dependence of the gerbil pressure sweeps for both p. tensa and p. £accida is much like that described for the human acoustic immittance tympanograms (e.g. Vanhuyse et al., 1975 ; Margolis et al., 1985). 4.3.2.2. Hysteresis or directional dependence. The dependence of our velocity-transfer function on the direction of the pressure sweep also is a feature of clinical

tympanometry. It is well known that the peak magnitude, peak pressure, and the shape of the tympanogram vary slightly depending on the direction of the pressure sweep used in the tympanogram (Shanks and Lilly, 1981 ; Shanks and Wilson, 1986). It is also clear that these di¡erences appear more exaggerated as the rate of change used in the pressure sweep is increased (Shanks and Wilson, 1986). At least some of the directional dependence in tympanograms has been associated with rates of pressure change that are too fast for the pressure-measurement devices to follow. However, directional dependence is still observable in tympanograms even when the pressure is swept very slowly. Gaihede and co-workers (Gaihede et al., 1995; Gaihede, 1999) suggest that directional dependence is a fundamental feature of the response of the middle ear to static-pressure changes. These authors measure the pressures at the TM that results from a slow sinusoidal (1 cycle per 7 s) volume displacement (20 Wl in amplitude) of the TM. Such volume displacements produced displacements of the middle-ear structures that are on the order of 0.1^1 mm, and pressures on the order of tympanometric pressures ( þ 20 cm H2 O). The volume displacement is applied via a virtually incompressible column of warmed saline that ¢lls the ear canal and the system is capable of near-instantaneous measurement of the applied pressure. The data demon-

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

strate a delay or hysteresis in the volume-displacement to sound-pressure tracking similar to the directional dependence observed in tympanograms. The authors argue that this hysteresis can only be explained by some visco-elastic mechanism within the middle ear with a memory of the previous middle-ear position as the position is varied by static pressures (Gaihede, 1999). Such a memory could also explain the di¡erences we see with di¡erent sweep directions. 4.3.2.3. Asymmetry of the tympanogram with large absolute pressures. All of the velocity measurements we measured showed a consistent asymmetry in their response to large middle-ear over- and under-pressures, where the velocity-transfer function (HU or HPF ) at any frequency measured with large over-pressures was always of higher magnitude than the transfer function measured with large under-pressures. At ¢rst glance, this appears similar to the common clinical tympanometric asymmetry, where admittance tympanograms show a larger admittance magnitude with large overpressures as compared to the admittance magnitude with large under-pressures (Margolis and Smith, 1977). However, in clinical tympanometry the static pressure is applied via the ear canal, such that an over-pressure is associated with an inward motion of the TM. In our experiment, the static pressure is applied via the middle ear and our over-pressures are associated with an outward motion of the TM. Therefore, there is a fundamental di¡erence in the sign of the trans-TM pressure di¡erence that evokes the larger admittance magnitude in humans and the larger velocitytransfer function in our preparation. Possible reasons for this di¡erence again include di¡erences between point velocity and acoustic admittance tympanometry, species di¡erences, and di¡erences in the site of action of ear-canal and middle-ear static pressures. The match between the larger e¡ect of middle-ear over-pressures in the cat and guinea pig admittance data of Fig. 10b and the larger e¡ect of negative external-ear pressures in human tympanograms suggest that di¡erences in admittance and velocity measurements are major contributors to variations in the direction of the asymmetry between our data and tympanograms. There is also a striking di¡erence between our p. tensa data and human tympanograms in the degree of the asymmetry observed at over- and under-pressures. Human tympanograms show di¡erences in the admittance magnitude measured with large over- and underpressures that are about a factor of 1.5 or less (Margolis and Smith, 1977) while our data show a factor-10 difference between the velocities measured with large overand under-pressures. At least part of the reduced asymmetry in human tympanograms can be accounted for by the presence of the ear-canal space, which limits changes in total admittance produced by static-pressure

161

alterations. The pressure sweeps we measured are not limited by the ear-canal air space. 4.4. The pars £accida as a pressure or volume regulator Hellstro«m and Stenfors (1983) showed that the p. £accida of rats moved from its most inward to its most outward position with a pressure change of 100 daPa (10 cm H2 O). In the recent study of Dirckx et al. (1998), the displacement of a gerbil's p. £accida reached its maximum at around 40 daPa (4 cm H2 O) middle-ear static pressure and remained nearly unchanged for pressure di¡erences greater than 4 cm H2 O. These data suggested a limited pressure-regulation function of the p. £accida for very small pressure changes around ambient pressure. Visual monitoring in our study is consistent with the quantitative data of Dirckx et al. (1998). The evident volume displacement to a small change of static pressure ( þ 1 cm H2 O) and the limited volume displacement to a large change of static pressure ( þ 30 cm H2 O) support the limited pressure-regulation function and the high sensitivity of the velocity of p. £accida to static pressure in this study. 4.5. The e¡ect of static pressure on the acoustic shunting function of pars £accida Kohllo«¡el (1985) suggested that the p. £accida acts as an acoustic shunt around the p. tensa that reduces the sensitivity of the middle ear to low-frequency sound. This suggestion has been supported by a series of middle-ear admittance and velocity measurements by Teoh and coworkers (Teoh et al., 1997 ; Rosowski et al., 1997). These earlier studies revealed a higher velocity of p. £accida compared to that of p. tensa at frequencies less than 500 Hz at ambient middle-ear pressure. The larger velocity of the p. £accida was associated with a signi¢cant shunting of volume velocity around the p. tensa. The p. £accida velocity led to an increase in the sound pressure in the middle-ear cavity that reduced the sound-pressure di¡erence across the p. tensa and therefore reduced the p. tensa velocity induced by low-frequency sounds. The larger velocity of the p. £accida as compared to umbo at ambient static pressure observed in this study is consistent with the previous results (Teoh et al., 1997; Rosowski et al., 1997). The data in this report suggest that the shunting of volume velocity by the p. £accida will be highly dependent on the static pressure across the TM, since even small static pressures of þ 1^2 cm H2 O greatly increase the sti¡ness of the p. £accida and reduce its sound-induced velocity. Furthermore, the p. £accida velocity appears much more sensitive than the umbo to small static-pressure di¡erences. Indeed it is possible that closing of the p. £accida shunt by small static pressure

HEARES 3635 15-2-01

162

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163

would help maintain the velocity of the p. tensa by increasing the di¡erence in sound pressure across the TM to compensate for the static-pressure-induced increase in p. tensa impedance. According to this hypothesis p. £accida can bu¡er the e¡ect of minor changes of middle-ear static pressure on p. tensa motion by counterbalancing the increase in p. tensa impedance by increasing the pressure di¡erence across the TM. A test of this hypothesis where we investigate the pressure sensitivity of the acoustic response of p. tensa before and after manipulating the p. £accida will be the subject of another publication (Lee and Rosowski, in preparation). 5. Conclusions The TM has two functionally distinct components, p. £accida and p. tensa. The acoustic behaviors of these two components are di¡erent from each other in many aspects (Teoh et al., 1997; Rosowski et al., 1997). The e¡ect of static pressure on the acoustic response of both structures is similar in that non-zero middle-ear pressures reduced the velocity of the two membrane components produced by sound frequencies of 2 kHz or less. With higher sound frequencies, middle-ear overpressures tend to increase membrane velocity, while middle-ear under-pressures tend to reduce the velocities of the membranes. In general middle-ear under-pressures produce bigger changes in membrane velocity than do middle-ear over-pressures. The major di¡erence between the two membrane components is that p. £accida appears more sensitive to small changes in static pressure and therefore yields sharper patterns of variation in velocity when static pressure is altered (Figs. 4^ 6; Table 3). This di¡erence in pressure sensitivity is related to the increased static compliance of p. £accida when the middle- and external-ear pressures are equal and to the extreme sensitivity of this compliance to static-pressure di¡erences across the membrane (Dirckx et al., 1998). This sensitivity of the p. £accida to small pressure di¡erences is consistent with the view that it plays a role in middle-ear pressure regulation (Hellstro«m and Stenfors, 1983) and also suggest that the acoustic shunting of the p. £accida (Kohllo«¡el, 1984 ; Teoh et al., 1997) can be modulated by variations in middle-ear pressure. Indeed, the bu¡ering of small changes in middle-ear volume by p. £accida and a simultaneous decrease in acoustic shunting across the p. £accida would both act to maintain the sensitivity of the p. tensa and coupled ossicles to low-frequency sound stimuli. The static-pressure-induced variations in velocity of the centers of the two components of the gerbil TM have many features in common with human tympano-

grams, including frequency dependence, hysteresis, and asymmetrical e¡ects of over- and under-pressures. However, there is a di¡erence in the direction of the asymmetry that seems to be related to a di¡erent e¡ect of static pressure on the average TM motion (as measured by acoustic admittance measurements) and on the velocity of the center of the p. tensa and p. £accida (as measured by laser vibrometry). Acknowledgements We thank W.T. Peake, N.Y.S. Kiang, T. Lin, M.E. Ravicz, and S.E. Voss for their comments on earlier versions of the manuscript. We also thank Robert Margolis PhD and an anonymous reviewer for detailed criticisms that improved the manuscript. This work was supported by the National Institute of Health. The experiments were performed in the Wallace Middle-Ear Research Unit of the Eaton-Peabody Laboratory of the Massachusetts Eye and Ear In¢rmary.

References Aritomo, H., Goode, R.L., Gonzalez, J., 1988. The role of pars £accida in human middle ear sound transmission. Otolaryngol. Head Neck Surg. 98, 310^314. Creten, W.L., van Camp, K.J., 1974. Transient and quasi-static tympanometry. Scand. Audiol. 3, 39. Decraemer, W.F., Khanna, S.M., Funnell, W.R., 1989. Interferometric measurement of the amplitude and phase of tympanic membrane vibrations in cat. Hear. Res. 38, 1^17. Dirckx, J.J.J., Decraemer, W.F., von Unge, M., Larsson, C.H., 1998. Volume displacement of the gerbil eardrum pars £accida as a function of middle ear pressure. Hear. Res. 118, 35^46. Funnell, W.R.J., Laszlo, C.A., 1982. A critical review of experimental observations on ear-drum structure and function. ORL J. Otorhinolaryngol. Relat. Spec. 44, 181^205. Gaihede, M., 1999. Mechanics of the middle ear system: computerized measurements of its pressure-volume relationship. Auris Nasus Larynx 26, 383^399. Gaihede, M., Felding, J.U., ElbrÖnd, O., 1995. The biomechanical characteristics of the middle ear system measured by a new method. II Clinical application and normal material. Acta Otolaryngol. (Stockh.) 115, 414^421. Hellstro¬m, S., Stenfors, L.E., 1983. The pressure equilibrating function of pars £accida in middle ear mechanics. Acta Physiol. Scand. 118, 337^341. Hu«ttenbrink, K.B., 1988. The mechanics of the middle-ear at static air pressures. Acta Otolaryngol. (Stockh.) 68 (Suppl. 11), 614^621. Kohllo«¡el, L., 1984. Notes on the comparative mechanics of hearing. iii. On Shrapnell's membrane. Hear. Res. 13, 83^88. Lide¨n, G., Peterson, J.L., Bjo«rkman, G., 1970. Tympanometry. Arch. Otolaryngol. Head Neck Surg. 92, 248^257. Lilly, D.J., 1984. Multiple frequency, multiple component tympanometry: New approaches to an old diagnostic problem. Ear Hear. 5, 300^308. Lim, D., 1968a. Tympanic membrane; Electron microscopy observation. i. pars tensa. Acta Otolaryngol. (Stockh.) 66, 181^198.

HEARES 3635 15-2-01

C.-Y. Lee, J.J. Rosowski / Hearing Research 153 (2001) 146^163 Lim, D., 1968b. Tympanic membrane. Part II. Pars £accida. Acta Otolaryngol. (Stockh.) 66, 515^532. Lim, D., 1970. Human tympanic membrane: An ultrastructural observation. Acta Otolaryngol. (Stockh.) 70, 176^186. Lim, D., 1995. Structure and function of the tympanic membrane: A review. Acta Otorhinolaryngol. Belg. 49, 101^115. Lynch, III, T.J., 1981. Signal Processing by the Cat Middle Ear: Admittance and Transmission, Measurements and Models. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA. Margolis, R.H., Shanks, J.E., 1985. Tympanometry. In: Katz, J. (Ed.), Handbook of Clinical Audiology. Williams and Wilkins, Baltimore, MD, pp. 438^475. Margolis, R.H., Smith, P., 1977. Tympanometric asymmetry. J. Speech Hear. Res. 20, 437^446. Margolis, R.H., van Camp, K.J., Wilson, R.H., Creten, W.L., 1985. Multifrequency tympanometry in normal ears. Audiology 24, 44^ 53. MÖller, A.R., 1965. An experimental study of the acoustic impedance of the middle ear and its transmission properties. Acta Otolaryngol. (Stockh.) 60, 129^149. Mundie, R., 1963. The impedance of the ear ^ A variable quantity. U.S. Army Med. Res. Rep. 576, 63^85. Murakami, S., Gyo, K., Goode, R.L., 1997. E¡ect of middle ear pressure change on middle-ear mechanics. Acta Otolaryngol. (Stockh.) 117, 390^395. Ravicz, M.E., Rosowski, J.J., Voigt, H.F., 1992. Sound-power collection by the auditory periphery of the Mongolian gerbil Meriones unguiculatus. I. Middle-ear input impedance. J. Acoust. Soc. Am. 92, 157^177. Ravicz, M.E., Rosowski, J.J., Voigt, H.F., 1996. Sound-power collection by the auditory periphery of the Mongolian gerbil Meriones unguiculatus. II. External-ear radiation impedance and power collection. J. Acoust. Soc. Am. 99, 3044^3063. Ravicz, M.E., Rosowski, J.J., Voigt, H.F., 1997. Sound-power collection by the auditory periphery of the Mongolian gerbil Meriones

163

unguiculatus. III. E¡ect of variations in middle-ear volume. J. Acoust. Soc. Am. 101, 2135^2147. Rosowski, J.J., Teoh, S.W., Flandermeyer, D.T., 1997. The e¡ect of pars £accida of the tympanic membrane on the ear's sensitivity to sound. In: Lewis, E.R., Long, G.R., Lyon, R.F., Narins, P.M., Steele, C.R., Hecht-Poinar, E. (Eds.), Diversity in Auditory Mechanics. World Scienti¢c, Singapore, pp. 129^135. Shanks, J.E., Lilly, D.J., 1981. An evaluation of tympanometric estimates of ear canal volume. J. Speech Hear. Res. 24, 557^566. Shanks, J.E., Wilson, R.H., 1986. E¡ects of direction and rate of earcanal pressure changes on tympanometric measures. J. Speech Hear. Res. 29, 11^19. Shrapnell, H.J., 1832. On the form and structure of membrane tympani. London Med. Gaz. 10, 120^124. Stenfors, L.-E., Salen, B., Windblad, B., 1979. The role of pars £accida in the mechanics of the middle ear. Acta Otolaryngol. (Stockh.) 88, 395^400. Teoh, S.W., Flandermeyer, D.T., Rosowski, J.J., 1997. E¡ect of pars £accida on sound conduction in ears of Mongolian gerbil: acoustical and anatomical measurements. Hear. Res. 106, 39^ 65. Tonndorf, J., Khanna, S.M., 1970. The role of tympanic membrane in middle ear transmission. Ann. Otol. Rhinol. Laryngol. 79, 743^ 753. Vanhuyse, V.J., Creten, W.L., van Kamp, K.J., 1975. On the W-notching of tympanograms. Scand. Audiol. 4, 45^50. von Unge, M., Bagger-Sjo«ba«ck, D., 1994. Tympanic membrane changes in experimental otitis media with e¡usion. Am. J. Otol. 15, 663^669. von Unge, M., Bagger-Sjo«ba«ck, D., Borg, E., 1991. Mechano-acoustic properties of the tympanic membrane: A study on isolated mongolian gerbil temporal bones. Am. J. Otol. 12, 407^419. Wever, E.G., Lawrence, M., 1954. Physiological Acoustics. Princeton University Press, Princeton, NJ. Zwislocki, J., 1962. Analysis of the middle-ear function. Part 1. Input impedance. J. Acoust. Soc. Am. 34, 1514^1523.

HEARES 3635 15-2-01