The free vibration computational analysis of the cupula in the inner ear

The three semicircular canals, arranged in three orthogonal planes, are the main components of the inner ear with the balance function. They are sensitive to angular acceleration [1,2]. Each canal is composed of a circular path of fluid continuity, interrupted at the cupula, where the sensory epithelium is placed — known as hair cells, which is the focus of this work. The hair cells exhibit constant discharge of neurotransmitters that are modified by the direction of cupula deflection. One of the causes of vestibular disorders is the abnormal concentration of otoconia particles in the vicinity of the cupula. Thus, the accurate determination of the natural frequency (first vibration mode) of the cupula will allow to stimulate externally the cupula. Theoretically, the resonance phenomena will disperse the otoconia particles, reducing the vertigo symptoms. In order to understand the dynamic response of the cupula, first it is necessary to obtain its free vibration modes. Thus, a 2D and 3D geometrical model of the cupula was constructed. Then, a free vibration analysis was performed using two distinct numerical techniques, such as the finite element method (FEM) and a radial point interpolation meshless method (RPIM). Meshless methods are advanced discretization techniques that allow to discretize the problem domain using only a cloud of points, allowing them to discretize geometrical models directly from medical images. The results obtained with the 2D and 3D geometrical model show that RPIM is capable to deliver results very similar with the FEM. However, the RPIM solution is smoother. On the other hand, the FEM computational cost is lower than the RPIM.