Mechanism of bone-conducted hearing: mathematical approach

For better understanding of bone-conducted (BC) hearing, a mechanical BC model is formulated using the Wentzel–Kramers–Brillouin (WKB) method. The BC hearing can be generally described by three main mechanisms: (1) cochlear fluid inertia, (2) in-phase motion of the outer bony shell, and (3) out-of-phase motion of the outer bony shell. Specifically, the second and third mechanisms can be identically explained by symmetric pressure compression–expansion and anti-symmetric compression–expansion, respectively. In this study, simulation results show that both the symmetric and anti-symmetric compression–expansion modes become significant at frequencies above 7 kHz while the fluid inertial mode is dominant at lower frequencies. The density difference between the scala fluid and soft cells of basilar membrane and the amplitude of the anti-symmetric compression–expansion input are identified as the difference between the air conduction and bone conduction. The natural frequency of the cochlear duct wall determines the magnitudes between the three mechanism and is approximated to be in the order of 10 MHz and above.