Finite-element modelling of the 3D motion of the malleus-incus complex validated with 3D laser Doppler vibrometry

Three-dimensional (3D) motions of the middle ear (ME) are investigated with finite-element (FE) modelling by comparison with 3D laser Doppler vibrometer (LDV) measurements of the malleus-incus complex. 3D point velocity measurements are converted to 3D rigid-body motion (RBM) components of the malleus and incus under acoustic excitation of the ME from 0.2 kHz to 8 kHz. The parameters in the FE model are adjusted to provide qualitative agreement with the 3D motion measurements for three separate model geometries. The results show a dominant hinge-like motion for malleus and incus across the frequency range, but with an increase of other components at high frequencies to yield a more complex motion. Incudomallear joint flexibility increases the relative motion between malleus and incus and is shown to contribute most to the ME transformer ratio at low and especially high frequencies, including the phase delay across the two ossicles. The dominant motion direction of the umbo coincides with the medial-lateral axis across the frequency range. The malleus head, incus head and incus long process show a deviation from this motion direction between 1.5 kHz and 5 kHz, associated with dips in the corresponding velocity magnitude. Motion trajectories at these points follow a line below 1.5 kHz but alternate between a line and ellipse at higher frequencies. While the tympanic membrane influences the 3D motion of malleus and incus in a similar way, the ME suspensory ligaments affect the motion components of the ossicles to varying degrees depending on the location on the ossicles.