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

                                         Resembling Mode 1                    Resembling Mode 2





                       FEM


                                       59.47 Hz   75.62 Hz              103.76 Hz   104.77 Hz  121.32 Hz





                       RPIM



                                                                            116.83Hz    124.37Hz
                                             61.70 Hz




                     NNRPIM


                                       60.15 Hz   63.50 Hz                  115.86 Hz   120.03 Hz

           FIG. 2.7  Two first modes and natural frequencies of the two-dimensional cupula with endolymph using FEM and RPIM and NNRPIM.


                                                  One otoconia          Three otoconia





                                      Model




                                                RM 1       RM 2       RM 1       RM 2




                                    Resembling
                                    Modes (RM)


                                               61.42 Hz  115.02 Hz   61.80 Hz  113.06 Hz


           FIG. 2.8  Two first modes and natural frequencies of the cupula with endolymph and otoconia.




              In conclusion, it was possible to understand that the natural frequency of the cupula ranges between 51 and 61Hz
           for all the analyzed situations. Moreover, all the other vibration frequencies possess very distinct values. Since theo-
           retically the resonance phenomena will force the cupula to vibrate, the induced vibration will allow detaching the oto-
           conium particles from the cupula, reducing the vertigo symptoms. This could be achieved with noninvasive ways,
           such as listening to music with a predominant set of bass sounds.



                                                       I. BIOMECHANICS
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