The vibration analysis of bone conduction for bone anchored hearing aids: In-vivo human mastoid

Transcription

1 The vibration analysis of bone conduction for bone anchored hearing aids: In-vivo human mastoid Jen-Fang Yu Graduate Institute of Medical Mechatronics Chang Gung University Taoyuan, Taiwan Ching-I Chen Department of Mechanical Engineering Chung Hwa University Hsinchu, Taiwan Abstract The 3D model of mastoid was reconstructed noninvasively based on the image of in-vivo mastoid reconstructed by computed tomography scan to observe the geometry and the measurements of the mastoid in this study. Then the finite element model was built by ANSYS. The finite element model included two phases. The first phase was to discuss the natural vibration frequencies and vibration mode of mastoid. The second phase was to investigate the harmonic response. The base center and central line were established in the external auditory meatus and the 0 degree direction, respectively. The amplitude force was applied along central line and ± 15 degrees direction with distance of 30 mm, 35 mm and 40mm from the center. The amplitude of the bone anchored hearing aids is approximately 550 g excited by the vibrator. The frequency responses and the characteristics of the BAHA vibrator on the mastoid at the frequencies of 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz, 5 khz, 6 khz, 7 khz, 8 khz, with sound pressure 0 db and 70 db, were discussed. Based on the results of modal analysis of mastoid, the 9 natural frequencies, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, were similar to the pure-tone stimuli frequency for the clinical hearing test. Based on the results obtained by the harmonic analysis of mastoid, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees. Keywords- Mastoid; Vibration analysis; Finite element method; Computed tomography image INTRODUCTION The sound waves can be transmitted to the human inner ear by two ways: (1) the air conduction: the transmission of sound to the inner ear through the outer ear, middle ear, inner ear, auditory nerve and central auditory processing; () the bone conduction: the transmission of sound to the inner ear by the vibration thru the bone, auditory nerve and central auditory processing [1]. The sound is transmitted to the cochlea directly through the skull without through the outer ear and the middle ear by the bone conduction. The cochlea is excited by the vibration. However, the normal human ear for bone conduction is less sensitive than that for air conduction. When the transmission of sound waves is blocked due to the outer and middle ears diseases, the hearing can be recovered by the characteristics of bone conduction. Therefore, the bone conduction is mostly used for hearing aids. There were some disadvantages for the general bone conduction hearing aids: (1) the offered magnifying power was seldom at the frequencies of 3 khz to 4 khz; () the mastoid and the vibrator could not be closed completely, and the stability of the sound volume and the tone quality could be affected; (3) the patients would feel pained for their skin and head. In order to improve the disadvantages, the bone anchored hearing aids (BAHA), a kind of hearing aids that the titanium was implanted into the bone by surgery, was concerned [, 3]. The effective range of frequency was the most common disadvantage for the bone conduction hearing aids and the bone anchored hearing aids. The sound was transmitted well at low frequency through bone conduction, whereas the sound was not transmitted well at high frequency through bone conduction. The transmission of sound was unstable at the mastoid behind the ear. If the vibrator was not placed on the mastoid properly, the bone conduction at high frequency would be affected and the patients would loss their high-frequency hearing. Hence, this study was to reconstruct the 3D geometric model of the mastoid and then conduct the modal analysis by the finite element model to discuss the dynamic characteristics of the free vibration of mastoid. Additionally, the location where the vibrator was placed on the mastoid affect the transmission of sound by bone conduction would be discussed by harmonic analysis; and further, the optimal location for placing the BAHA vibrator on the mastoid would be determined. MATERIALS AND METHODS High-Resolution Computed Tomography of Mastoid The CT image of a patient s mastoid was obtained by the high-resolution computed tomography at Chung-Gung Memorial Hospital shown in figure 1. A 39-year-old female patient with normal hearing for bilateral ears who sometimes suffered from tinnitus was studied. 115 CT images of mastoid were acquired. The slice thickness was 0.3 mm. The acquisition matrix was The pixel size was mm mm. Image Reconstruction of Mastoid The image was processed by the medical image software, Amira, in this study. The needed parts of the image were selected through brush and Magic Wand for image segmentation. The boundary of the mastoid was found by noise elimination and image threshold, and then the spatial distribution model of mastoid could be reconstructed based on its original geometry. Besides, the selected D section was

2 constructed to 3D model by the compute tool, Surface Gen. After reconstructing the 3D model, it was time-consuming for computation because the points and the surfaces of the model were too large. Therefore, the model was simplified by the Simplifier function in Amira. Additionally, the surface of the 3D image model was smoothed by Smoothsurface in order to avoid the singular point occurring on the reconstructed 3D model of mastoid. Note that Smoothsurface was provided by Amira. After being smoothed, the reconstructed 3D model of mastoid would be more similar to the geometry of in-vivo mastoid shown in figure. The boundary of the reconstructed 3D model was obtained based on the contours of the CT image. To compute the geometry of the 3D model of mastoid, the curve of each slice of the 3D model was transformed to the curve surface and the gaps between each slice were combined. Moreover, the file format of 3D model was transformed from STL into SAT by CAD and then imported the SAT file into the finite element analysis software, ANSYS. Finite Element Analysis of Mastoid The image was processed by the medical image software, Amira, the modal analysis and the harmonic analysis of in-vivo mastoid were then conducted by the finite element analysis software, ANSYS. The modal analysis was to discuss the natural frequency and the vibration mode of mastoid. The harmonic analysis was to discuss the location where the BAHA vibrator was placed on the mastoid, and to observe the frequency and amplitude response by 550g force and by 0 db-spl and 70 db-spl pure-tone stimuli. The bone was excited by the stimuli directly without concerning the soft tissue. The 550g force was utilized because the amplitude of the bone anchored hearing aids is approximately 550g excited by the vibrator [5]. The 0 db-spl and 70 db-spl pure-tone stimuli were utilized to compare the characteristics of the bone conduction of mastoid through the BAHA vibrator by different pure-tone stimuli. To build the finite element model, the finite element model of mastoid was built by adopting the Solid9, 10-Node tetrahedral element type of the 3D model of mastoid and by the Free Meshing method. Beside, some parameters were utilized: the Young's modulus was (N/mm ); the density was (kg/mm 3 ); the Poisson's ratio was 0.3 [6, 7]. The finite element model of mastoid contained 3,769 elements and 6,080 nodes. As for the modal analysis, the free-free condition was adopted for the finite element model of mastoid. The dynamic characteristics of the free vibration of mastoid were analyzed by the damped free vibration equation shown as follows: du du + + = 0 M C Ku dt dt Where M indicated the mass matrix; C indicated the damping matrix; K indicated the stiffness matrix; the u indicated the displacement vector. The modal solution at the frequency from 100 Hz to 10 khz was obtained by Block Lanczos. The dynamic characteristics of the free vibration of mastoid were discussed at the 1 frequencies: 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz, 5 khz, 6 khz, 7 khz and 8 khz. The 1 frequencies were utilized as the standard frequency of pure-tone stimulus for the clinical hearing test. As for the harmonic analysis, the degrees of freedom of the three directions, X, Y and Z on each boundary of mastoid, were fixed. The harmonic analysis of mastoid was analyzed by the damped force vibration equation shown as follows: du du M + C + Ku= f cos wt dt dt where M indicated the mass matrix; C indicated the damping matrix; K indicated the stiffness matrix; u indicated the displacement vector; the f indicated the external force; w indicated the angular frequency. The solution was obtained by full method. The coordinate system was built at the ear canal. The coordinate of the central surface of ear canal in the coordinate system was determined based on the model of temporal bone. The horizontal part of the ear canal was determined as 0 degree. The surface of the mastoid would be divided into three parts for discussion, which were the superior, the middle and the inferior parts. The superior part was the area at the 15 degrees with distance of 30 mm, 35 mm and 40 mm from the ear canal; the middle part was the area at the 0 degree with distance of 35 mm, 40 mm and 45 mm from the ear canal; the inferior part was the area at the -15 degrees with distance of 30 mm, 35 mm and 40 mm from the ear canal, respectively. The areas were excited by 550g force from BAHA and by pure-tone stimuli at 0 db-spl and 70 db-spl to observe the dynamic characteristics of the vibrator at the 1 frequencies. RESULTS Geometry of Mastoid After obtaining the boundary of the 3D model reconstructed by CT image, the geometry of the 3D model was computed. The geometry of the 3D model of mastoid was measured by the curve surface with the gap between each slice. Note that the curve surface was transformed by the curve of each slice. The area and the volume of the geometry of the 3D model of mastoid were 4,53 mm and 10,68 mm 3, respectively. The 3D model contained 95,66 surfaces and 47,635 points. After reconstructing the 3D model, it was timeconsuming for computation because the points and the surfaces of the model were too large. Therefore, the model was simplified by the Simplifier function in Amira. The surface area and the volume of the geometry of the simplified 3D model of mastoid were 3,953 mm and 10,585 mm 3, respectively. The simplified 3D model contained 1,000 surfaces and 50 points. The difference between the simplified and the original 3D models of mastoid was within 0.91%. Additionally, the surface of the 3D model of mastoid was smoothed by Smooth Surface in order to avoid the singular point occurring on the reconstructed 3D model of mastoid. After being smoothed, the reconstructed 3D model of mastoid would be more similar to the geometry of in-vivo mastoid shown. The surface area and the volume of the geometry of the 3D model of mastoid by smoothed were 3,470 mm and 10,604 mm 3, respectively. The smoothed 3D model contained 1,000 surfaces and 50 points. The difference between the

3 smoothed and the original 3D models of mastoid was within 0.73%. The measurements of the geometry of the original, the simplified and the smoothed 3D models of mastoid were shown in table 1. Modal Analysis of Mastoid The free-free condition was utilized for modal analysis. The displacement was approximately zero because the former six modal frequencies were rigid motion. The modal solution at the frequency from 100 Hz to 10 khz was obtained by Block Lanczos. The vibration mode and the vibration mode shape of the mastoid at the 1 frequencies, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz, 5 khz, 6 khz, 7 khz and 8 khz, were observed. The 1 frequencies were utilized as the standard stimulus frequency for the clinical hearing test. Based on the natural frequency obtained from the free vibration analysis of the mastoid at 100 Hz to 10 khz frequencies, the 9 natural frequencies, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, were similar to the frequencies of pure tone stimulus for the clinical hearing test. Harmonic Analysis of Mastoid The 9 locations of the mastoid were discussed by harmonic analysis. The superior, the middle and the inferior parts of the mastoid were at the 15 degrees, 0 degree and -15 degrees of the ear canal, respectively. The places were excited by 550g force from BAHA and by pure-tone stimuli at 0 db- SPL and 70 db-spl to observe the dynamic characteristics of the BAHA vibrator at the frequencies from 15 Hz to 8 khz. The amplitude was approximately 550g excited by BAHA vibrator. The frequency response of BAHA vibrator on the mastoid at 15 degrees with distance of 30 mm, 35 mm and 40 mm from the ear canal, at 0 degree with distance of 35 mm, 40 mm and 45 mm from the ear canal, and at -15 degrees with distance of 30 mm, 35 mm and 40 mm from the ear canal were discussed shown in figure 3. The horizontal and vertical axes indicated the frequency and the amplitude, respectively. The solid line, the dotted line and the dashed line indicated the 15 degrees, 0 degree and -15 degrees with three locations from the ear canal, respectively. The dynamic characteristics of BAHA vibrator at 0 dbspl and 70 dbspl were shown in figures 4 and 5, respectively. Based on the results obtained by the harmonic analysis of mastoid at the 9 locations, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees. The frequency was approximately 3 khz. Therefore, the performance of bone conduction for the BAHA placed at the superior part was better than that placed at the middle and inferior parts on the mastoid. DISCUSSION Modal Analysis of Mastoid Among the natural frequencies obtained from the free vibration analysis of mastoid at 100 Hz to 10 khz frequencies, the 9 natural frequencies, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, were similar to the stimulus frequencies for the clinical hearing test. The other natural frequencies were quite different from 5 khz, 7 khz and 8 khz. The 9 frequencies of pure-tone stimuli, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, could be transmitted by resonance thru the bone conduction with BAHA vibrator. Harmonic Analysis of Mastoid The results obtained by the harmonic analysis of mastoid were shown in figure 3. The amplitude on the mastoid was approximately 550g excited by the BAHA vibrator. Based on the figure of the frequency response, the performance of bone conduction of BAHA vibrator at 35 mm of 15 degrees was better than that at 30 mm and 40 mm, and the frequency was approximately 3 khz; the performance of bone conduction of BAHA vibrator at 35 mm of 0 degree was better than that at 40 mm and 45 mm, and the frequency was approximately khz; the performance of bone conduction of BAHA vibrator at 40 mm of -15 degree was better than that at 30 mm and 35 mm, and the frequency was approximately khz. Based on the results, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees, and the frequency was approximately 3 khz. However, the performance of bone conduction would be decreasing while the frequency of the pure tone transmitted was over 3 khz. The energy of bone conduction would be diminished gradually. Only the 550g force for the vibration of BAHA was discussed. Figure 4 showed the performance of bone conduction for the 0 db-spl pure tone stimuli transmitted by BAHA vibrator on the surface of mastoid. Based on the figure of the frequency response, the performance of bone conduction of BAHA vibrator at 35 mm of 15 degrees was better than that at 30 mm and 40 mm, and the frequency was approximately 3 khz; the performance of bone conduction of BAHA vibrator at 35 mm of 0 degree was better than that at 40 mm and 45 mm, and the frequency was approximately khz; the performance of bone conduction of BAHA vibrator at 40 mm of -15 degrees was better than that at 30 mm and 35 mm, and the frequency was approximately khz. Based on the results, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees, and the frequency was approximately 3 khz. However, the performance of bone conduction would be decreasing while the frequency of puretone stimuli was over 3 khz. The energy of bone conduction would be diminished gradually. Figure 5 showed the performance of bone conduction for the 70 db-spl pure-tone stimuli transmitted by BAHA vibrator on the surface of mastoid. Based on the figure of the frequency response, the performance of bone conduction of BAHA vibrator at 35 mm of 15 degrees was better than that at 30 mm and 40 mm, and the frequency was approximately 3 khz; the performance of bone conduction of BAHA vibrator at 35 mm of 0 degree was better than that at 40 mm and 45 mm, and the frequency was approximately khz; the performance of bone conduction of BAHA vibrator at 40 mm

4 of -15 degrees was better than that at 30 mm and 35 mm, and the frequency was approximately khz. Based on the results, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees, and the frequency was approximately 3 khz. However, the performance of bone conduction would be decreasing while the frequency of puretone stimuli was over 3 khz. The energy of bone conduction would be diminished gradually. Based on the comparison between the 0 db-spl and 70 db-spl pure-tone stimuli, the change of the frequency of bone conduction would not be affected by the level of sound intensity of stimuli. Only the energy consumption of bone conduction would be changed. CONCLUSION The 3D model of mastoid was reconstructed non-invasively based on the image of in-vivo mastoid reconstructed by computed tomography scan to observe the geometry and the measurements of the mastoid in this study. Then the 3D model of mastoid was transformed to ANSYS successfully by CAD software. The characteristics of the bone conduction of mastoid were analyzed by finite element analysis. Based on the modal analysis of mastoid, the 9 natural frequencies, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, among the natural frequencies obtained from the vibration mode of the mastoid at 100 Hz to 10 khz frequencies were similar to the pure-tone stimuli frequency for the clinical hearing test. The other natural frequencies were quite different from 5 khz, 7 khz and 8 khz. The 9 frequencies of pure-tone stimuli, 15 Hz, 50 Hz, 500 Hz, 750 Hz, 1 khz, khz, 3 khz, 4 khz and 6 khz, for the clinical hearing test could be transmitted by resonance thru the bone conduction with BAHA vibrator. Therefore, the results obtained by modal analysis could be the reference for the clinician to evaluate the BAHA surgery at pre-op. Based on the results obtained by the harmonic analysis of mastoid at the 9 locations, the performance of bone conduction at 35 mm of 15 degrees was better than those at 0 and -15 degrees. The frequency was approximately 3 khz. Therefore, the performance of bone conduction for the BAHA placed at the superior part was better than that placed at the middle and inferior parts on the mastoid. Additionally, the frequency of bone conduction would be affected by the location of the BAHA vibrator. The change of the frequency of bone conduction would not be affected by the level of sound intensity of stimuli. Only the energy consumption of bone conduction would be changed. The results obtained by the harmonic analysis would be helpful for the clinician to find out the optimal area on the mastoid to place the BAHA vibrator. Amplitude(mm) Figure 1. The computed tomography image of mastoid E-005 1E-006 1E-007 1E-008 1E-009 1E-010 Figure. The smoothed 3D image of mastoid mastoid_550g Figure 3. The frequency response of the 550g vibration of BAHA on the surface of mastoid at 15 degrees, 0 degree and -15 degrees

5 Amplitude(mm) 1E-009 1E-010 1E-011 1E-01 1E-013 1E-014 1E-015 1E-016 1E-017 1E-018 1E-019 1E-00 1E-01 1E-0 mastoid_70db [6] Z. Zong, H.P.L.a.C.L., A three-dimensional human head finite element model and power flow in a human head subject to impact loading. Journal of Biomechanics, : p [7] A. Boryor, M.G., A. Hohmann, A. Wunderlich, C. Sander, F. M. Sander and F. G. Sander, Stress distribution and displacement analysis during an intermaxillary disjunction A three- dimensional FEM study of a human skull. Journal of Biomechanics, : p Figure 4. The frequency response of 70 db on the surface of mastoid at 15 degrees, 0 degree and -15 degrees Amplitude(mm) 1E-011 1E-01 1E-013 1E-014 1E-015 1E-016 1E-017 1E-018 1E-019 1E-00 1E-01 1E-0 1E-03 1E-04 mastoid_0db Figure 5. The frequency response of 0 db on the surface of mastoid at 15 degrees, 0 degree and -15 degrees Table 1 The geometry measurement of the model of mastoid Surface area (mm ) Volume Surfaces Points Differences (mm 3 ) Original 4,53 10,68 95,66 47,635 Simplified 3,953 10,585 1, % Smoothed 3,470 10,604 1, % REFERENCES [1] S. Stefan and Goode, R.L., Bone-Conducted Sound: Physiological and Clinical Aspects. Otology Neurotology, : p [] James, B.C.P.a.A.L., Bone-Anchored Hearing Aids in Children. Operative Techniques in Otolaryngology Head and Neck Surgery, : p [3] Schüpbach J, K.M.a.H.R., Bone Anchored Hearing Aids (B.A.H.A.). Ther Umsch, : p [4] S. H. Bartling, K.P., T. Rodt, F. Kral, H. Matthies, R. Kikinis and H. Becker, Registration and Fusion of CT and MRI of the Temporal Bone. Comput Assist Tomogr, : p [5] Publishers, T.M., Strategies for Selecting and Verifying Hearing Aid Fittings (Hardcover). Michael Valrnte, 00.