Determination of the Effects of Dissipation in the Cochlear Partition by Means of a Network Representing the Basilar Membrane

Abstract

Results are given of measurements made on a 175-section network representing the basilar membrane, which was modified to include the effects of dissipation in the cochlear partition. The results show that the dynamical theory of the cochlea, when dissipation is considered, is in good agreement with experimental evidence.T is the purpose of this paper to describe some results, determined experimentally, pertinent to a dynamical theory of the cochlea. This theory, developed in a recent paper, x gives equations which govern the dynamics of a theoretical model of the cochlea. The equations include the effects of dissipation in the cochlear partition and viscous losses in the fluids filling the scalas vestibula and tympani. Solutions were given only for the case in which dissipation in the cochlear partition was disregarded. The equations referred to give the pressures in the fluids on either side of the cochlear partition and the displacement of the basilar membrane, both as a function of frequency and the distance along the membrane from the stapes to the helicotrema.In the course of the work described in reference 1, an electrical network was builff' which would act as an analog to three of the equations* whose solutions were ß desired. The network, as originally designed and built, was to give solutions to the equations for the case in which dissipation was neglected. Such unwanted dissipation as actually existed in the network was due to unavoidable loss in the constituent elements. The quantities found by the network are the pressure differx L. C. Peterson and 13. P. 13ogert, J. Acoust. Soc. Am. 22, 369 (1950). ' B. P. Bogerr, Bell Labs. Record 28, 11, 481-485 (1950). * Equations (14), (15), and (16) of reference 1. ence across the cochlear partition (P_) and the displacement of the basilar membrane (Y), as functions of distance x from the stapes and angular frequency co. The network, shown in Fig. 1, was subsequently modified to include the effect of dissipation or damping in the cochlear partition. In this manner, the effect of r(x), representing the damping, could be determined with reasonable accuracy and with much less labor than by numerical calculations. The effect of viscosity of the fluids filling the scalas is ignored. The network has 175 sections, each section with the configuration shown in Fig. 2. The series inductance Lx represents the mass of the fluid in the scalas vestibula and tympani, and the dotted condenser Cx represents the compressibility of the fluids.• The shunt impedance represented by the coil L•., resistance R1, and set of three condensers C2, Ca, and C4 corresponds to the assumed dynamical properties of the cochlear partition. The voltage across the line corresponds to the pressure difference P_(x, co), and the voltage at the junction of the condensers Ca and C4 corresponds to the membrane displacement Y(x, co).The addition of resistance R1 to the shunt impedance enabled the determination of the results to be described here.

On the adequacy of the Peterson-Bogert model and on the effects of viscosity in cochlear dynamics

“…on the partition) and with regard to x when l u o(x, y, 0) l, that is I Po,~ (x, y, 0) 1 is largest. The calculations of Peterson and Bogert [2], [7] and of Hubbard and Geisler [5] show that Op/#x is maximal near the helicotrema for low frequencies. For high frequencies the maximum moves towards the windows.…”

“…Taken per unit area the mass increases slightly from the basal to the apical end, the order of magnitude being 0.1 g/cm 2, the resistance and the stiffness decrease rapidly (order 10 3 g/cm 2. s and 10 6 dyn/cm 3 respectively). These figures are due to [2,6,7,11], all of which refer to experiments of Von B6k6sy.…”

“…The numerical values, used by Peterson and Bogert [2], [7] are c = 1.72 x 109 e 2(x-t ) dyn/cm 3 , k = 6.737 x 103 e x-t g/cm 2 . s, m = 0.143 g/cm 2 , Po = 1 g/cm 3 , while h~0.1 cm and 102< co< 105 c.p.s.…”

Parameter Analysis of 2d Cochlear Model and Quantitative Research on the Traveling Wave Propagation

“…15 Though some kind of dissipation is widely used in almost all numerical cochlear models, little theoretical or experimental research is seen on the source of BM damping and its influence on traveling wave. Viergever 16 discussed the physical background of BM impedance based on a viscoelastic plate assumption of BM.…”

Cochlear Dynamics: The Evolution of a Mathematical Model

“…The expression, r/E(x), for the time envelopes of ,/sT(X, t) is simply rlE(x)= +A(x).It turns out that the transient portion makes no contribution to the time envelope of r/(x, t). Hence, we need study only the upper half, A (x) => 0, of the envelopes (which are symmetrical with respect to the x axis) given by(38).Downloaded 12/03/14 to 137.112.220.81. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php…”