Magnitude and phase of three-dimensional (3D) velocity vector: Application to measurement of cochlear promontory motion during bone conduction sound transmission

Recent measurements of vibrational motion to assess sound transmission through ear structures and skull contents have included three-dimensional (3D) behavior. The 3D motion of a point has been described with the three orthogonal components in the 3D space. In this article, a method to represent the 3D velocity with the magnitude and phase of the resultant velocity is introduced. This method was applied to the measurement of cochlear promontory motion as an indication of bone conduction (BC) sound transmission. The promontory motions were measured on the ipsilateral and contralateral sides, and the transcranial attenuation and phase delay of the contralateral side relative to the ipsilateral side were calculated. The transcranial attenuation and phase delay calculated with the maximum magnitudes and corresponding phases of the resultant were a better fit to the interaural threshold difference and transcranial time interval between the ipsilateral and contralateral sides as reported in the literature, than the attenuation and phase delay calculated with any individual Cartesian motion component.