What middle ear parameters tell about impedance matching and high frequency hearing

Acoustic energy enters the mammalian cochlea aided by an anatomical impedance matching performed by the middle ear. The purpose of this paper is to analyse the functional consequences of changes in scale of the middle ear when going from the smallest mammals to the largest. Our anatomical measurements in mammals of different sizes ranging from bats to elephants indicate that middle ear proportions are largely isometric. Thus the calculated transformer ratio is basically independent of animal size, a typical value lying between 30 and 80. Similarly, the calculated specific acoustic input impedance of the inner ear is independent of animal size, the average value being about 140 kPa s/m. We show that if the high frequency hearing limit of isometric ears is limited by ossicle inertia, it should be inversely proportional to the cubic root of the ossicular mass. This prediction is in reasonable agreement with published audiogram data. We then present a three-parameter model of the middle ear where some obvious deviations from perfect isometry are taken into account. The high frequency hearing limits of different species generally agree well with the predictions of this simple model. However, the hearing limits of small rodents clearly deviate from the model calculation. We interpret this observation as indicating that the hearing limit towards very high frequencies may be set by cochlear transduction mechanisms. Further we discuss the exceptional high frequency hearing of the cat and the amphibious hearing of seals.