Marrying critical oscillators with traveling waves shapes nonlinear sound processing in the cochlea

Abstract: The cochlea's capacity to process a broad range of sound intensities has been linked to nonlinear amplification by critical oscillators. However, while the increasing sensitivity of a critical oscillator upon decreasing the stimulus magnitude comes with proportionally sharper frequency tuning and slower responsiveness -- critical slowing down, the observed bandwidth of cochlear frequency tuning and the cochlear response time vary little with sound level. Because the cochlea operates as a distributed system rather than a single critical oscillator, it remains unclear whether criticality can serve as a fundamental principle for cochlear amplification. Here we tackle this challenge by integrating tonopically distributed critical oscillators in a traveling-wave model of the cochlea. Importantly, critical oscillators generically provide spatial buildup of energy gain from energy pumping into the waves and a key nonlinearity. In addition, our nonlinear model accounts for viscoelastic coupling between the oscillators. The model produces, with a single set of parameters, a family of cochlear tuning curves that quantitatively describe experimental data over a broad range of input levels. Overall, the interplay between generic nonlinear properties of local critical oscillators and distributed effects from traveling waves gives rise to a collective nonlinear response that preserves the power-law responsiveness afforded by criticality, but without paying the price of critical slowing down.