A Time-Domain Model for the Generation of Spontaneous Otoacoustic Emissions in Resonant Cavities

A long-standing question in hearing science is whether spontaneous otoacoustic emissions (SOAEs) arise from a specific active site on the basilar membrane-they have a local origin-or whether they derive from distributed active elements working together in a resonant cavity-a global picture. This paper uses numerical modelling to investigate the difference between local and global activity in the ear. The cochlea is modelled as a graded array of discrete oscillators, each of fixed natural frequency and coupled only by the surrounding fluid. We examine what happens when the damping parameters of the system are varied in particular ways. Do the continuous oscillations that emerge at the middle ear carry the tell-tale frequency of a specific oscillator-pointing to a local origin-or is the oscillation one that arose from the global activity of multiple interacting oscillators? The basic oscillating element considered here is made up of two feedback-coupled masses, a general arrangement first proposed by Neely and Kim. An important parameter is the amount of undamping of the element, such that high undamping (low damping) energizes the system and tends to generate spontaneous oscillations. We use the time-domain state-space formalism to describe the interacting system of oscillating elements. We find that the entire system can be made local or global depending on the size and distribution of the undamping parameters. Thus, if a single element is made to continuously oscillate by increasing its undamping, a spontaneous otoacoustic emission (SOAE) will emerge at the oscillator's natural frequency-it can be considered to have a local origin. On the other hand, if all the elements are provided with sufficient undamping, an SOAE can again emerge even though each individual element remains below its oscillation threshold-the conclusion being that the oscillation now arises from global coupling. In this manner, our numerical modelling shows that even when undamping is supplied irregularly all along the array (but not enough to make any individual element continuously oscillate), one or more SOAEs can still be produced. When such a system is examined, we see an underlying pattern of standing waves, but even so, we see no clear evidence of a more or less regular process for the reflection of waves from irregularities at the apical side of a resonant cavity-which is what the generally accepted global model of SOAE generation by coherent reflection calls for.