Referring to figure 8.2, the occluded ear canal is terminated by a 2-port network, which describes the response o f eardrum together with the ossicular chain and enclosed tympanic cavity. is loaded by an impedance, Z^, representing the cochlear input impedance. Thus, the ear canal acoustic environment is made explicitly a function o f the middle ear loaded by the cochlea.
The action o f the ME is commonly referred to as an impedance transformation (von Békésy, 1960). An ideal transformer has zero capacity for energy dissipation, i.e., lossless, and is generically known as a positive immittance converter, a term which reveals the transformation: with a turns ratio o f n :\, the load impedance on port 2-2’ is modified by n^ at the 1-1’ port (Lampton, 1978). The transmission matrix representing an ideal transformer is given in equation 8.4.
Chapter 8; Cochlear parameters inferred from ear canal measurements
A transformation from the characteristic impedance o f the cochlear fluid to that o f air, such that the energy loss o f the compressional wave in both fluids is minimised, is incorrect for the following reasons. The effective stimulus is not the launching o f a compressional wave within the cochlear fluid, which equates to the fast wave as discussed in section 2.7, but rather the initiating o f a slow, hydro-mechanical, travelling wave (Zwislocki, 1950). The effective cochlear driving point impedance is therefore a function o f the fluid flow between the OW to RW and its interaction with the mobile cochlear partition. Hence, the net pressure across the cochlear partition, i.e., the transpartition sound pressure, at the base initiates the TW. Hence, to ensure efficient energy transfer, the function o f the middle ear is to couple, or transform (equation 8.2), the cochlear input impedance to that o f the characteristic impedance o f the ear canal.
If the middle ear acted as an optimal coupling device, achieved through the use o f an ideal transformer o f appropriate turns ratio, the input impedance at the TM would equal the ear canal characteristic impedance, . Since under such a condition no reflection would occur at the TM, the ear canal energy reflectance would be zero, a finding which is not observed in experimental data at high stimulus levels (figure 7.4; Keefe et al, 1993). Although the use o f a transformer which optimally couples the cochlea to the ear canal is inappropriate, modelling the ME as a transformer with a turns ratio equal to 1/30, which results in realistic values for ear canal energy reflectance, will be used because o f its simplicity.
Zwislocki (1962) proposed a quantitative model o f the middle ear, developed from measurements on pathological ears and anatomical data, and represented as a network o f electrical elements based upon functional anatomy. The measure employed as 'the goodness o f fif between model predictions and experimental measurements was the acoustic input impedance at the TM. The link between middle ear mechanisms and circuit topology is shown in figure 2 (Zwislocki, 1962). Due to the position o f the block representing the effect o f middle ear cavities, which precedes the blocks associated with the ossicles, it is made explicit that the cochlea can only be stimulated through the transmission path effected by motion o f the ossicular chain.
Chapter 8: Cochlear parameters inferred from ear canal measurements
Utilising the formalism given in Lampton (1978) which provides a link between network topology and the transfer matrix coefficients, the Zwislocki middle ear, less the cochlear complex branch is represented as a single 2-port network (figure 8.3). Parameter values are those given in Zwislocki (1962).
F ig u re 8,3: N etw ork topology o f Zw islocki analogue netw ork o f m iddle ear less the stapes/cochlear com plex branch, relating each block on the basis o f fu n c tio n a l anatomy. Z ,, im pedance representing m iddle ear cavities, eardrum, Z^ eardrum - m alleus-incus com plex and Z^ incudo-stapedial joint. is the driving p o in t adm ittance given by 1/Z„ .
Z; Zj T = 1 Z, 0 1 1 0 1 Z3 1 0 1 1 0 ^4 1 (8.6)
A major drawback o f the models derived from Zwislocki's ME network topology is the failure to model ears in which a dislocation or complete interruption o f the ossicular chain occurs. This pathway is termed ossicular coupling, while the mechanism for the initiation o f a cochlear hydro-mechanical wave via an air-home sound pressure difference across the OW and RW is identified as acoustic coupling (Peake et al, 1992). The latter mechanism explains the less than profound hearing loss experienced by subjects with dislocated or interrupted ossicular chain pathologies, which is further ameliorated by creating a greater pressure difference between the OW and RW, a surgical procedure known as type IV Tympanoplasty (Peake et al, 1997). However, studies indicate that the acoustic coupling provides little or no effect, o f the order o f 40 dB below ossicular coupling in terms o f pressure, for otologically normal subjects (Voss
et al, 1996).
Chapter 8: Cochlear parameters inferred from ear canal measurements
The contraction o f the stapedius muscle, which is attached to the stapes, occurs during high intensity sound input; this phenomenon is known as the acoustic reflex. A study o f the acoustic reflex using an extension o f Zwislocki's model is developed in Lutman and M artin (1979), whereby the change in stiffiiess due to stapedial contraction is modelled by an additional element, a variable capacitor, Cy ; under no reflex Cy is negligibly small, while the reflex is present Cy is increased.
Due to the simplicity o f the ideal transformer and the common use o f the Zwislocki analogue model, both networks will be used to model