Page 34 - Advances in Biomechanics and Tissue Regeneration

28 2. BIOMECHANICS OF THE VESTIBULAR SYSTEM: A NUMERICAL SIMULATION

(A)

(B)
FIG. 2.5 (A) Three-dimensional model of the semicircular duct with a cupula and (B) three-dimensional model of the vestibular system.

To obtain numerically the free vibration modes of the cupula, 2-D and 3-D discrete models were built using the
standard dimensions and the approximated mechanical properties found in the literature [39]; the applied boundary
conditions were correlated with a real situation. Three different scenarios were simulated: the cupula itself, the cupula
with the surrounded fluid, and the cupula with the attached otoconia and the surrounded fluid.
The free vibrations of the cupula were obtained with the software FEMAS, which is a finite element and meshless
analysis software fully developed in an academic environment [27], and it possesses a graphical user interface (GUI)
running in a MATLAB environment.
The formulations used to study the discrete models of the cupula were the FEM and two distinct meshless methods
detailed in the previous section: RPIM and NNRPIM.
The results presented in this chapter include the vibration modes (Fig. 2.6) and the corresponding frequencies
(Table 2.1) of the cupula 2-D with 417 nodes and 382 elements.
To visualize automatically the vibration mode, the results of the figures correspond to a fictitious displacement field.
With this visualization technique, it is possible to visualize in each figure the magnitude of the fictitious displacement
corresponding to the indicated vibration mode, since the red color corresponds to the higher displacement values and
the blue color to the lower ones. In Table 2.1 the corresponding 10 first vibration frequencies of the cupula are
presented.
The results indicate that the first vibration frequency is between 51.48 and 54.70Hz. Note that the following vibra-
tion frequencies are much higher, which allows identifying with enough precision the magnitude of frequency of the
first mode.
All the vibration frequencies obtained are contained in the human hearing range, since it goes from 20 to 20,000Hz.
In general, the vibration frequencies obtained with both meshless methods used (RPIM and NNRPIM) are lower than
the ones obtained with FEM.

I. BIOMECHANICS