1952 - Fernandez - Dimensions of the Cochlea - Guinea Pig

PATTERNS OF COCHLEAR MICROPHONICS 519

(3) The third "form of motion" is an dastic wave that depends on the mutual forces between adjacent elements in the cochlear partition. The pressure differences across the partition, whether delivered directly (first form) or as a surface wave (second form), set the cochlear partition in motion according to Eq. 3. Suppose, as an approximation, that over a certain range of frequencies the driving force, (pt--p-o)B in Eq. (3), is restricted to a region of the cochlea near the stapes. Then the more distant parts of the partition will carry a transverse wave described by the equation

M ( &øy/ O•) + R( Oy/ Ot)q- K y = r(a-oy/Ox•)-- U(O'y/Ox•). (7)

This transverse wave depends solely upon the solid structure of the partition and not upon the difference in the hydrostatic pressure across the partition. In this respect it differs from the second form of wave motion described above. Our failure to modify the pattern of the actual wave in the cochlea (observed by the electrical means) by producing an "acoustical short circuit" supports our view that this third form of motion cannot be neglected in considering the actual motion in the cochlea. When the driving frequency is high and the wavelength short, the elastic waves should become prominent because the effects of the "mutual forces" in the partition depend on the curva- ture of the structures along the partition.

It is our present opinion that the amazing complexity of the phase and amplitude patterns of cochlear motions can be understood, at least qualitatively, in terms of Ihe three different types of motion: direct driving, surface waves, and transverse elastic waves.

APPENDIX

Table of Mathematical Symbols and Notations

B: width of the basilar membrane (a function of x). F•: coefficient for the frictional force acting upon an

elementary box of fluid in scala vestibuli in its longitudinal motion.

F-o: similar value of the fluid in scala tympani. F: average of F• and K: coefficient for the elastic force acting upon the

cochlear partition. M: mass of the cochlear partition per unit length. pt and p.o: pressure at point x in the scala vestibuli

and tympani, respectively. R: coefficient for the frictional force acting on the

cochlear partition. Sx, S2: cross-section area of the scala vestibuli and

scala tympani, respectively. S: a{•erage of S• and S•. T: longitudinal tension of the cochlear partition. U: coefficient for the shear force acting upon the

cochlear partition. m, u-o: average longitudinal velocity of the fluid in

scala vestibuli and tympani, respectively. x: distance along the cochlear partition. y: average displacement of the cochlear partition at

point x. t: time.

p: density of the fluid. c0: 2•r times the frequency of the sound. co,: (K/M) •, namely 2•r times the resonance frequency

at point x.

THE JOURNAL OF THE ACOUSTICAL soCIETY' OF AMERICA VOLUME 24. NUMBER $ SEPTEMBER. 1052

Dimensions of the Cochlea (Guinea Pig)*

Central Institute for the Deaf, St. Louis, Missouri (Received April 27, 1952)

Measurements have been made under the microscope of many structures in the cochlea of the guinea pig and the results plotted graphically as a function of position along the cochlea. The structures measured are the spiral lamina, Rosenthal's canal, the basilar membrane (length, width and thickness), the channels and windows of the cochlea (cross-section area) and the hair cells (angles of orientation).

INTRODUCTION

HE dimensions of the structures of the cochea and the way in which they vary as a function of

position along the cochlea have long been a matter of interest because of their bearing on the dynamics of

* This work was earfled out under Contract N6onr-272 between the Office of Naval Research and the Central Institute for the Deaf. The author is indebted to Dr. Walter P. Coyell of the Department of Otolaryngology of Washington University for the use of laboratory radiities and for helpful criticism and guidance.

the cochlea2 More recently they have become important also for calculations of the probable distribution of electrical current flow and potential fields within the cochlea.: Wever a has published many useful measurements on the human cochlea. The present study was undertaken to supply similar data for the guinea pig,

• H. Fletcher, J. Acoust. Soc. Am. 23, 637 (1951). a G. v. B6kisy, J. Acoust. Soc. Am. 23, 18 (1951). a E.G. Wever, Theory of Hearing (John Wiley and Sons, Inc.,

New York, 1949).

Downloaded 08 Feb 2011 to 128.151.79.113. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.jsp

$20 CI•SAR FERNANDEZ

FIG. 1. Projection of the basilar membrane of guinea pig on a plane perpendicular to the axis of the modiolus. Line AB is a mid-modiolar section which cuts the cochlea at 8 points. Line CD is also a mid-modiolar section but at right angles to AB; it cuts the cochlea at 8 points which alternate with the points on Line A B. The numerals indicate the distances in millimeters of thes• inter- sections from the round window, measured along the basilar membrane under the tunnel of Corti.

the animal which serves so well for studies of the

electrical phenomena of the ear. METHOD

Six adult guinea pigs were perfused with fixing solution; their temporal bones were then removed and mounted in celloidin. Four cochleas were sectioned

serially with the axis of the modiolus oriented in the horizontal plane and turned so that the sections were parallel to line AB in Fig. 1. Two other cochleas were sectioned parallel to the plane indicated by CD. The sections were stained with hematoxylin-eosin and the most representative mid-modiolar section of each ear was selected for measurement.

DISTANCE ACROSS ROSENTHALJ S

CANAL AND SPIRAL LAMINA

I N GUINEA PIG

• ,.o- jc L • .

0 .

DISTANCE ON •SILAR MEMBRANE IN MILLIMETERS

•. 2. •he wid• of •e o•en•s spiral la• m•urcd between the •ts indi•t• by A in'the inner fi•re. In the •t three qu•em of •e •t turn •e is a second real (C) betwe• •e

Drawings at magnification of about 250 diameters were made with a camera lucida of the cochlear passages (scalae vestibuli, tympani, and media) and of the organ of Corti, including the inner and outer tunnel of Corti and Nuel's space. The cross-sectional areas of these structures were measured with a plankmeter. The organ of Corti was also drawn with the camera lucida at high maguification, and lines parallel to the axes of the inner and the outer hair cells were superimposed as in the sketch in Fig. 6. The angles formed by these two lines with one another and with the basilar mem-

brane were measured with a protractor. The total length of the basilar membrane and also

the distance along the basilar membrane from the round window to each point of intersection with the axes indicated in Fig. 1 were measured by the recon- struction method of Guild. 4 The length of the basilar

PERCENTAGE OF LENGTH 0 20 40 60 80 100

O-5- • •.• • 0.4- i-.-"•'?ø :• o.3- .o...-'ø .y .... ' \

'o.•- "•" ! :. I•. SA / i JI 'm' [ APICAL

MILLIMETERS ON BASlEAR MEMBRANE (C•IINEA

F/o. 3. Width of the basilar membrane in the guinea pig. The curves X and ¾ represent our own measurements made according to the criteria shoa n in the sketch. The criterion Y' was used in the upper tums where the bony spiral lamina does not extend beyond the limbus. The lowest curve, X--X, represents Guild's data for the guinea pig measured from spiral ligament to the spiral lamina. The upper curve (HUMANI) shows Wever's measurements. For these data use the scale for percentage of length (at the top). To convert these percentages into millimetem multiply by the factor 0.315.

membrane was also determined directly as described elsewhereS: The basilar membrane was carefully dis- sected out under a dissection microscope and measured with a calibrated eye piece.

The width and thickness of the basilar membrane, the width of Rosenthal's canal and of the spiral lamina were determined by measurements, made by the use of a calibrated eyepiece, on the mid-modiolar sections described above.

RESULTS

Spiral Lamina

The osseous spiral lamina of the guinea pig does not have a uniform width along the cochlea. It tapers from a broad lamina 0.5 mm wide at the middle of the first

turn until it disappears at the beginning of the apical • S. R. Guild, Science 65, 67 (1927). s C. Femtindez, Laryngoscope 61, 1152 (1951).


DIMENSIONS OF THE COCHLEA 521

turn (Fig. 2). In the apical turn the nerve fibers are contained in channels formed by fibrous tissue and continuations of the fibers of the basilar membrane.

The part of the lamina lying between the limbus and habenula perforata is so thin that it seems probable that it can vibrate as part of the basilar membrane.

RosenthaPs Canal

Rosenthal's canal has an average width of 0.30 mm in the first turn and in the basal half of the second turn.

From the middle of the second turn it tapers off until the apical turn is reached. In the apical turn the canal is no longer clearly defined. Here the spiral ganglion consists of a cluster of bundles of nerve cells and fibers, sometimes, but not consistently, separated by bony walls. In the first half of the first turn there is an

additional channel (C in Fig. 2) about 0.35 mm wide that lies between Rosenthal's canal and the modiolus.

This channel plus Rosenthal's canal proper have a total width of 0.7 mm in this part of the cochlea.

7

3.5 7 10.5 12.5 14.25 16.5 I•,•,

LENGTH OF THE BASILAR MEMBRANE (MM)

Fro. 4.

Basilar Membrane

(.4) Direct measurements and the method of reconstruc-

tion agree in showing that the average length of the basilar membrane in the guinea pig is 18.8 mm with extreme individual differences of +0.5 ram. (In all of our references to distances from the round window the

distances are measured along the basilar membrane under the tunnel of Corti.) The average lengths of each of the four turns, as indicated in Fig. 3, are 8.5, 4.8, 3.4, and 2.1 mm, respectively.

(.•) Wi•t•, It is difficult to measure the width of the basilar

membrane because the boundaries are not clearly defined. We undertook to measure the width of the

section that would probably participate in vibratory motion. We therefore chose as our outer reference

point the junction between the basilar membrane and the spiral ligament as indicated in Fig. 3. The two inner reference points were (1) the outer end of the habenula perforata, and (2) the edge of the osseous spiral lamina (Y in Fig. 3). When the osseus spiral

CROSS SECTION AREA OF'

THE THREE CHANNELS

OF THE COCHLEA OF

2 I THE GUINEA PiG !

I

I% .... •' I fi , l]I • , 0 • ' •' I•0 .... 1•,5 ' ' 20

DISTANCE I N MILLIMETERS

Fro. 5. The abscissa is distance in millimeters along the basilar membrane. The points represent averages of measurements in six ears. The broken lines were obtained by extrapolation. To obtain the area of scala vestibuli at any point, the area of scala media must be substracted.

lamina did not extend beyond the limbus the latter was used as the inner boundary (Y• in Fig. 3). The width of the basilar membrane measured to the habenula perforata (X) increases rapidly over the'first 2 mm of the basilar membrane from 0.07 to 0.15 ram. Thereafter it increases more slowly until it reaches its maximum

RATIO OF CROSS SECTION I I

AREAS OF SCALA VESTIRUI..I i TO SCALA TYMPANI I

I 3 (GUINEA PiG) t

• t

"! ß • Jh • • Sv

• .• .... •: ..........

I x • • • 0 / .... • . . . • . .,• . ß .* . •,• . •. .

0 5 •u DISTANCE IN M•LIMETERS ALONG BASILAR

Fro. 6. The broken cu•e represents the ratio of the cross- •ctional areas of scala vestibuli plus scala medea to s•la tympani, and the solid line the ratio of •ala vestibu• alone to •la tympani. The broken portion of_•e solid l•e w• obt•ed by •te•olation.


522 Ci•SAR FERNANDEZ

I00-

o 0 .• I•0 lift ,

DISTANCE IN MILLIMETERS ALONG BASILAR MEMBRANE

Fro. 7. The angles of the hair cells with the basilat membrane as measured in two ears. The points and triangles represent average measurements. No measurements were made between 0 and 3.5 ram, but examination of other sections (not cut exactly at right angles to the tunnel of Corfi) shows that A does not change significantly while B seems to increase and then to decrease slightly and gradually toward the round window.

of 0.25 mm at the middle of the apieal turn where it then rapidly tapers off. The measurements made to the osseous spiral lamina or to the limbus (Y or Y') show a similar curve, although of course the width is always greater than the width measured to the habenula perforata. The maximum width of Y is 0.34 mm and is reached at about the same position as for X in the apical turn.

The width of the basilar membrane in the guinea pig was measured by Guild. s His data are also plotted in Fig. 3 as the lowest curve. He states that he measured from the edge of the spiral lamina to the attachment to the spiral ligament, and also that "some were measured from the foramina nervosa" (habenula pefforata). The agreement with our curve labeled X is very satisfactory if we assume that by the phrase "edge of the spiral lamina" he means the first thickening of the membrane under the foot of the internal pillar.

Wever's a data for the width of the basilar membrane

in man is also plotted in Fig. 3. The basilar membrane of humans and of the guinea pig is the same width for the first 30 percent of their lengths. After that the width in man increases more rapidly until it reaches its maximum of about 0.50 mm at the same percentage of its length from the round window as the position of maximum width in the guinea pig.

(C) Thickness

The thickness of the basilar membrane is 7.4• at the beginning of the first turn. It tapers gradually until it reaches 1.34• at the apical turn (Fig. 4). This measurement does not include the organ of Corti or the mesothelial cells that lie on the opposite side of the membrane.

Channels and Windows of the Cochlea

The area of the oval window, calculated from the major and minor axes, by the formula for an ellipse, is 1.41 mm 2. The opening of the scala vestibuli is 3.27

mm 2. The cross-sectional area of the scala vestibuli

first increases slightly and then diminishes rapidly until it reaches an area of 0.36 mm 2 at the middle of

the first turn (Fig. 5). From here on it tapers, with some irregularity and slight variations from one animal to another, until it reaches an area of 0.10 mm 2 close to the helicotrema. These measurements do not include the area of the scala media.

The cross-sectional area of scala media is practically uniform throughout the entire length of the cochlea. It tapers very gradually toward the helicotrema over the upper 8 mm of the cochlea. The final taper, both at the round window and at the helicotrema, is very abrupt. The typical cross-sectional area of the scala media is 0.10 mm 2.

The area of the round window, calculated from major and minor axes, is 1.02 mm • and the cross-sectional area of scala tympa•i at this level is 1.20 mm •. Scala tympani first increases and then diminishes rapidly until it reaches an area of 0.48 mm • at a distance of 5 mm from

the round window. From this point on it tapers on gradually to an area of 0.05 mm • close to the helicotrema (Fig. 5).

In Fig. 6 is plotted the ratio of the areas of scala vestibuli and also of scala vestibuli plus scala media to that of scala tympani. At approximately 1.5 and again about 6.0 mm from the round window the cross sections of scala vestibuli and scala tympani axe equal. From 0.15 mm scala vestibuli predominates with a maximum ratio of 2.2 at the opening of scala vestibuli. From 1.5 to 6.0 mm from'the round window scala

tympani predominates. The maximum ratio of 3.5 is reached at 3.5 mm from the round window. Beyond 6 mm the scala vestibuli again predominates, reaching a maximum ratio of 2.8 near the helicotrema.

If the area of scala media is included with that of

scala vestibuli the effect on the ratio is very slight for the first turn, but, as shown in Fig. 6, the ratio is altered more and more in favor of vestibuli-plus-media as the helicotrema is approached.

The most recent comparable measurements of the cross-sectional areas of the human cochlea were made

by Zwislocki. • The human scalas tympani and vestibuli do not show the great and abrupt reduction in area in the first half of the basal turn that is so evident in the

guinea pig. The openings of the scalas are of the same order of magnitude (2 to 3 mm •) as in the guinea pig, but the taper is less abrupt and less regular.

Organ of Corti

The total cross-sectional area of the organ of Corti, including the inner and outer tunnel of Corti and Nuel's space, was measured. The measurement included the fiupporting cells of the inner spiral sulcus and also the supporting cells of the outer spiral sulcus, as far as their junction with the spiral ligament. The total surface area amounts to at least 0.012 mm x. The measure-

i j. Zwlslockl, Acta Oto-Laryngol. Suppl. 72, 1-76 (1948).


DIMENSIONS OF THE COCHLEA 523

ment increases gradually over the second and third turns to a max'mum of 0.017 mm 2 at a distance of 17.5 mm from the round window and diminishes to 0.015 mm 2 near the helicotrema. The cross-sectional area of

the tunnels in the organ of Corti also increases slightly from 0.002 mm 2 in the first turn and in the first half of

the second turn to 0.005 mm 2 at the beginning of the apical turn. The total cross-sectional area of tissue (total area minus the area of the tunnels) thus varies from 0.010 mm • throughout the first turn to a maximum of 0.013 mm 2 at the beginning of the third turn. It then gradually falls to 0.011 mm • near the helicotrema.

Orientation of the Hair Cells

Figure 7 shows the angles formed by the axes of the outer and inner hair cells with one another and with

the basilar membrane. The angle between the inner ha/r cells and the basilar membrane (alpha in Fig. 7) is constant at about 65 ø throughout the cochlea. The angle (beta) formed by the outer hair ceils decreases progressively from base to apex and consequently the angle between the outer and the inner hair ceils increases. This apica] angle (gamma) is about 60 ø at 3.5 mm from the round window and increases to 92 ø, 0.5 mm from the he]icotrema.

THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA VOLUME 24. NUMBER 5 SEPTEMBER, 1952

The Masking of Tones by White Noise as a Function of the Interaural Phases of Both Components.* I. 500 Cycles

L•.o¾1) A. JEF•l•SS, HUaR C. BLODOErr, A•m BRUCE H. D•Al'tmR•V. Defense Research Laboratory and Department of Psychology, The University of Texas, Austin, Texas

(Received March 3, 1952)

Work by Hawkins, Hirsh, Licklider, Stevens, Webster, and others has shown the considerable reduction in masking which occurs when the interaural phase of either the signal or the noise is reversed, or when the interaural phase of the signal is shifted by various amounts. The present paper extends this work by shifting the interaural phases of the masking component of the noise and of the tone by various amounts between q-180 ø and - 180 ø, and also by shifting the noise timewise by amounts up to 4.0 milliseconds. The interaural phases of both the noise and the 500• tonal signal are therefore parameters of this study.

The results are in agreement with those already published, but show in addition large reductions in threshold even when the noise and the tone differ in their interaural phase positions by amounts less than 180 ø. They also show a periodic fall and rise of the masked threshold as the Enteraural time difference for the noise is varied. Finally, they show the importance of interaural correlation in determining the extent to which the binaural threshold will be lower than the mortaural.

INTRODUCTION

HE recent literature contains a number of papers upon the relation between the masking effect of

a noise and the interaural phases of the noise and the masked signal. In most cases •-• the phase change is a reversal of phase of the noise, the tone, or both. In one study • the tonal signal has also been shifted through angles other than 180 ø . The present work extends the investigation to a greater variety of noise and tone phase-combinations.

METHOD

The present experiments employed a tonal signal of 500• and a wide-band white noise. The interaural

phase position of the signal was adjusted by an R-C network. The noise position was altered, either by shifting the 500• masking component by means of an

* Resulting from research done under Bureau of Ships Research and Development Contract NObsr-52267.

x I. J. Hirsh, J. Acoust. Soc. Am. 20, 536 (1948). • J. C. R. Licklider, J. Acoust. Soc. Am. 20, 150 (1948). a I. J. Hirsh and F. A. Webster, J. Acoust. Soc. Am. 21, 496

(1949). • J. E. Hawkins, Jr. and S.S. Stevens, J. Acoust. Soc. Am. 22,

6 (1950). • F. A. Webster, J..Acoust. Soc. Am. 23• 452 (1951).

R-C network • (Experiment 1), or by displacing the whole noise band in time by means of a delay introduced into one channel of a binaural tape reproducer (Ex- periment 2). The R-C network could produce shifts up to 90 ø . Larger shifts were obtained by reversing the connections to one channel (180 ø ) and subtracting as necessary by means of the R-C network.

In both experiments the stimuli were presented automatically, two hundred at a sitting--twenty at each of ten intensity levels 1.5 db apart. The signals were 150 milliseconds in duration, and were presented at intervals of three seconds against a continuous noise background. Each was preceded by a 150 ms

• The phase-shift network was adapted from that described by H. J. Reich, Theory and Applications of Electron Tubes (McGraw- Hill Book Company, Inc., New York, 1944), p. 460. It consists of the low impedance secondary of a transformer, the center tap of which constitutes one terminal, and the common connection between a condenser from one leg and a variable resistor from the other leg constitutes the other terminal. The phase shift for the 50(P,• masking component of the noise was determined by sub- stituting a 500• tone for the noise, and then adjusting the network to give the appropriate Lissajou figure on an oscilloscope. Calculation shows that this will shift the extremes of the critical band through very nearly the same phase angles as the middle frequency when the ma•ximal phase shift is no greater than 90 ø. A similar device was used in the circuit for the signal tone.


Documents

1952 - Fernandez - Dimensions of the Cochlea - Guinea Pig