The dynamic characteristics of human ossicle responses to stimulus frequencies of 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz were analyzed using a 3D image model that was constructed using the finite element method. The 3D image model of the ossicle chain was based on images previously obtained from highresolution computed tomography (CT) scans of the middle ear region of patients. The displacement at the footplate in the 3D model showed essentially no response when the ossicles were subjected to sound stimuli with frequencies above 2 kHz. However, the ossicles responded to sound stimuli with frequencies below 1 kHz, and the vibration of the ossicles was equivalent to the amplitude of the sound stimuli

Ching-I Chen

Jen-Fang Yu

English

Yu, Jen-Fang

Chen, Ching-I

JVE International

  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1494 875. Modeling the dynamic characteristics of human ossicles    Jen-Fang Yu1, 2, Ching-I Chen3 1Graduate Institute of Medical Mechatronics, Chang Gung University, Taoyuan, Taiwan, R. O. C.  2Taiouan Interdisciplinary Otolaryngology Lab, Chang Gung University, Taoyuan, Taiwan, R. O. C.  3Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan, R. O. C.  E-mail: 1, 2jfyu.phd@gmail.com, 3meching@chu.edu.tw  (Received 10 August 2012; accepted 4 December 2012)  Abstract. The dynamic characteristics of human ossicle responses to stimulus frequencies of 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz were analyzed using a 3D image model that was constructed using the finite element method. The 3D image model of the ossicle chain was based on images previously obtained from high-resolution computed tomography (CT) scans of the middle ear region of patients. The displacement at the footplate in the 3D model showed essentially no response when the ossicles were subjected to sound stimuli with frequencies above 2 kHz. However, the ossicles responded to sound stimuli with frequencies below 1 kHz, and the vibration of the ossicles was equivalent to the amplitude of the sound stimuli.   Keywords: ossicles, finite element method, vibration analysis, high resolution computed tomography.   Introduction   Otorrhea and tympanic membrane perforation are common symptoms of chronic suppurative otitis media (CSOM). CSOM is associated with bacterial infection in the middle ear. Damage to the tympanic membrane may be corrected using ossiculoplastic surgery. Congenital hearing losses associated with ossicular disruptions resulting from congenital abnormalities of the middle ear can also be improved by ossiculoplasty [1].  However, ossicle conduction may be reduced following ossiculoplasty. The vibration of ossicles can also be affected by the positive and negative non-atmospheric pressures that may result in the middle ear [2-3], inducing conductive hearing losses. To address such problems, the generalized circuit model has been used to simulate the vibration of ossicles [4]. The malleus vibration audiometer has also been used for the evaluation of ossicular function and integrity [5]. However, the heavier parts of ossicles, such as the malleus head and the incus body, could not be measured directly. The finite element method was developed to analyze the vibration mode of ossicles [6-7]. The finite element model of ossicles was constructed based on histological section images [6] and computed tomography (CT) images of human ossicles in vivo [7].  The objectives of our study were to construct a 3D model of ossicles that was based on the geometry of ossicles calculated from CT images of in vivo ossicles obtained during clinical evaluations, and to characterize the harmonic vibration characteristics of ossicles using a finite element method.  Materials and Methods  The geometry of ossicles was calculated based on the CT images of patients that were previously evaluated. The 3D model of ossicles was constructed using the medical imaging software Amira®. Note that the format of 3D model was STL. Then, the file format of the 3D model was transformed from STL into SAT by CAD, and the SAT file was imported into the finite element analysis software ANSYS®. The finite element model of ossicles was constructed 875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. JEN-FANG YU, CHING-I CHEN     VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1495 using the SOLID185 (SolidWorks®) and the free meshing methods. The repeated nodes between ossicles were combined into a single node. The finite element model of ossicles was then built. The joint between the incus and stapes was considered because of the large value of Young's modulus. The COMBIN14 Spring-Damper was used for the vertical and horizontal axes on the stapes footplate. The vertical and horizontal spring elements are shown in Figures 1(a) and 1(b), respectively.  a)12XYZXYZ                                                                                b)12XYZXYZ                                                                                 Fig. 1. The spring element at stapes footplate: a) the vertical direction, b) the horizontal direction  The material parameters for each part of the ossicles were different. Poisson's ratio for overall structure was assumed to be 0.3 based on the results of similar previous studies, and the analysis of the dynamic characteristics of ossicles were not significantly affected by the value of the Poisson ratio used [8]. The damping matrix was calculated as [ ] [ ] [ ]C M Kα β= + , where [M] and [K] are the mass matrix and stiffness matrix, respectively, and α and β are the damping parameters.  The overall structure consisted of 3 ossicles, the joints between the incus and the stapes, and the springs of the stapes. The incudomalleolar joint was adopted based the results of a previous study that showed no relative motion between the malleus and the incus at frequencies less than 3 kHz [9]. Therefore, Young's modulus was assumed to be 14.1 GPa, which indicated a linearly elastic material of equal quality and equal direction. The density of the various parts of the ossicles is shown in Table 1. The nodes that connected the malleus and incus were combined into one node in our study. The joints between the incus and the stapes were adopted according to a previous study that showed no stiffness displacement in the joints under various conditions of noise and pressure [10]. Although there was some relative motion between the incus and stapes, we concluded that the inner ear was protected, and that it would not be damaged by the large displacement of the stapes footplate. In addition, the joints between the incus and the stapes were assumed to comprise homogeneous materials, with a Young's modulus of 0.6 MPa [11, 12].  Table 1. The density of the various parts of the ossicles   Density (kg/m3) Head 2.55×103 Neck 4.53×103 Malleus Handle 3.70×103 Body 2.36×103 Short process 2.26×103 Incus Long process 5.08×103 - 2.20×103 Stapes I-S joint 1.2×103 875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. JEN-FANG YU, CHING-I CHEN     VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1496 For harmonic analysis, 6 x-y plane springs were on the vertical side of the stapes footplate. The total constant of the springs, K, was 60 N/m. The total damping was 0.054 N/(m/s). The K value for the nine 3D vertical springs on the horizontal side was assumed to be 9 N/m. The vertical and horizontal springs of the stapes footplate were fixed to the UX, the UY and the UZ direction movements of the nodes of ossicles, respectively. To simulate the response of the sound transmitted through the cochlear fluid by the ossicles, the vertical direction was constrained to the 2D spring damper that could be pulled in the vertical direction only. The horizontal direction was used to simulate the actual motion of the stapes footplate. Therefore, the 3D spring damper was assumed. The ossicles and the ligament and the spring damper of the stapes footplate were analyzed. The degrees of freedom of the 3 directions of the nodes that connected the spring damper and the stapes footplate were fixed, as shown in Figure 2. The nodes on the base area of the manubrium of the malleus were excited in the X direction by 90 dBSPL, as shown in Figure 3. Based on the modal superposition (MSUP) theorem, the results of the MSUP analysis were obtained by transforming to the original coordinate system. The results of the MSUP analysis were extended to the overall structure to interpret the response of the sound transmitted to the inner ear through the ossicles following excitement with the sound pressure (90 dBSPL) under stimulus frequencies of 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz,  6 kHz, 7 kHz, and 8 kHz.   1                                                                                 1XYZ                                                                                 Fig. 2. The degree of freedom for the nodes at the stapes footplate Fig. 3. The external load (90 dBSPL) for the harmonic analysis  Results and Discussion  The harmonic analysis focused on the joints of the malleus head and the tympanic membrane. The surface area of the malleus head, 3.081 mm2, was excited by 90 dBSPL    (0.623 Pa). The frequency and the amplitude response of the specific nodes (Figure 4) on the stapes footplate at 250 Hz to 8 kHz, respectively, are shown in Figure 5. The results were also observed along the X, Y and Z axes, as shown in Figures 6 to 13. Based on the data presented in Figures 6 to 13, there was an apparent transition point for the 9 nodes of the stapes footplate at 1 to 2 kHz. The ossicles were excited by the stimuli at frequencies below 1 kHz. The displacement corresponded to the amplitude of the sound stimuli that were transmitted to the stapes footplate. In contrast, significant displacement was not detected when the ossicles were subjected to stimuli with frequencies above 2 kHz, and the transmission power of ossicles was adopted directly.   875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. JEN-FANG YU, CHING-I CHEN     VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1497  Fig. 4. The nodes, 1-9, on the footplate of stapes  100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.1UXUYUZ Fig. 5. The displacement at node 1 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz  100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.2UXUYUZ 100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.3UXUYUZ Fig. 6. The displacement at node 2 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,   3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz Fig. 7. The displacement at node 3 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. JEN-FANG YU, CHING-I CHEN     VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1498 100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.4UXUYUZ 100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.5UXUYUZ Fig. 8. The displacement at node 4 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,   3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz Fig. 9. The displacement at node 5 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz  100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.6UXUYUZ 100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.7UXUYUZ Fig. 10. The displacement at node 6 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz Fig. 11. The displacement at node 7 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz   100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.8UXUYUZ 100 1000 10000FREQUENCY (Hz)1E-0211E-0191E-0171E-0151E-0131E-011AMPLIDUTE (mm) No.9UXUYUZ Fig. 12. The displacement at node 8 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz Fig. 13. The displacement at node 9 on the footplate under stimulus frequencies including 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz  Conclusions  To meet the clinical needs of otolaryngologists, a dynamic model of human ossicles was constructed from in vivo CT images to aid clinicians in the assessments of ossicle function. The 3D image of the ossicles was successfully imported into the finite element analysis software ANSYS®, and the finite element model of ossicles was constructed using the SolidWorks® SOLID185 program. When the ossicles were excited with sound stimuli at frequencies below   875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. JEN-FANG YU, CHING-I CHEN     VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 1499 1 kHz, the vibration of the ossicles was equivalent to the amplitude of the sound stimuli. Significant displacement of the ossicles was not observed in response to sound stimuli at frequencies above 2 kHz, and the sound was transmitted by the ossicles directly. Analyses of the dynamic characteristics of ossicles based on this finite element model system may aid clinicians in the pre-op evaluation of substitute implants for the correction of hearing loss, such as that resulting from ossiculoplasty for the treatment of CSOM.  References  [1] Samy R. N., Pensak M. L. Revision ossiculoplasty. Otolaryngol. Clin. North Am., 39(4), 2006,       p. 699-712. [2] Petrova P., Freeman S., Sohmer H. The effects of positive and negative middle ear pressures on auditory threshold. Otol Neurotol., 27(5), 2006, p. 734-738. [3] Puria S., Kunda L. D., Roberson J. B. Jr., Perkins R. C. Malleus-to-footplate ossicular reconstruction prosthesis positioning: cochleovestibular pressure optimization. Otol Neurotol., 26(3), 2005, p. 368-379. [4] Hudde H., Weistenhofer C. Key features of the human middle ear. ORL J. Otorhinolaryngol. Relat. Spec., 68(6), 2006, p. 324-328. [5] Maassen M. M., Rodriguez Jorge J., Herberhold S., Vonthein R., Zimmermann R., Baumann I., Brosch S., Mauz P. S., Pfister M., Zalaman I. M., Lowenheim H., Zenner H. P. Safe and reliable sound threshold measures with direct vibration of the ossicular chain. Laryngoscope, 114(11), 2004, p. 2012-2020. [6] Gan R. Z., Feng B., Sun Q. Three-dimensional finite element modeling of human ear for sound transmission. Ann. Biomed. Eng., 32(6), 2004, p. 847-859. [7] Koike T., Shinozaki M., Murakami S., Homma K., Kobayashi T., Wada H. Effects of individual differences in size and mobility of the middle ear on hearing. JSME International Journal, 48(4), 2005, p. 521-528. [8] Funnell W. R. J., Laszlo C. A. A critical review of experimental observations on eardrum structure and function. ORL J. Otorhinolaryngol. Relat. Spec., 44, 1982, p. 181-205. [9] Vlaming M. S. M. G. Middle Ear Mechanics by Laser Doppler Interferometry. Techniche Universiteit Delft, Netherlands, 1987. [10] Hüttenbrink K. B. The mechanics of the middle-ear at static air pressures: the role of the ossicular joints, the function of the middle-ear muscles and the behaviour of stapedial prostheses. Acta Otolaryngol. Suppl., 451, 1988, p. 1-35. [11] Ferris P., Prendergast P. J. Middle-ear dynamics before and after ossicular replacement. J. Biomech., 33(5), 2000, p. 581-590. [12] Wada H., Koike T., Kobayashi T. Three-dimensional finite-element method (FEM) analysis of the human middle ear. In: Hüttenbrink K. B. (ed.), Middle Ear Mechanics in Research and Otosurgery. Department of Oto-Rhino-Laryngology, Dresden University of Technology, 1996, p. 76-80. [13] William A. Yost Fundamentals of Hearing: An Introduction. 4th Edition, Academic Press, 2000. 

Modeling the dynamic characteristics of human ossicles

Journal of Mechatronics and Artificial Intelligence in Engineering

Journal of Vibroengineering

  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1494 
875. Modeling the dynamic characteristics of human 
ossicles  
  
Jen-Fang Yu
1, 2
, Ching-I Chen
3
 
1Graduate Institute of Medical Mechatronics, Chang Gung University, Taoyuan, Taiwan, R. O. C.  
2Taiouan Interdisciplinary Otolaryngology Lab, Chang Gung University, Taoyuan, Taiwan, R. O. C.  
3Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan, R. O. C.  
E-mail: 1, 2jfyu.phd@gmail.com, 3meching@chu.edu.tw 
 
(Received 10 August 2012; accepted 4 December 2012) 
 
Abstract. The dynamic characteristics of human ossicle responses to stimulus frequencies of 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
were analyzed using a 3D image model that was constructed using the finite element method. 
The 3D image model of the ossicle chain was based on images previously obtained from high-
resolution computed tomography (CT) scans of the middle ear region of patients. The 
displacement at the footplate in the 3D model showed essentially no response when the ossicles 
were subjected to sound stimuli with frequencies above 2 kHz. However, the ossicles responded 
to sound stimuli with frequencies below 1 kHz, and the vibration of the ossicles was equivalent 
to the amplitude of the sound stimuli.  
 
Keywords: ossicles, finite element method, vibration analysis, high resolution computed 
tomography.  
 
Introduction  
 
Otorrhea and tympanic membrane perforation are common symptoms of chronic 
suppurative otitis media (CSOM). CSOM is associated with bacterial infection in the middle 
ear. Damage to the tympanic membrane may be corrected using ossiculoplastic surgery. 
Congenital hearing losses associated with ossicular disruptions resulting from congenital 
abnormalities of the middle ear can also be improved by ossiculoplasty [1].  
However, ossicle conduction may be reduced following ossiculoplasty. The vibration of 
ossicles can also be affected by the positive and negative non-atmospheric pressures that may 
result in the middle ear [2-3], inducing conductive hearing losses. To address such problems, 
the generalized circuit model has been used to simulate the vibration of ossicles [4]. The 
malleus vibration audiometer has also been used for the evaluation of ossicular function and 
integrity [5]. However, the heavier parts of ossicles, such as the malleus head and the incus 
body, could not be measured directly. The finite element method was developed to analyze the 
vibration mode of ossicles [6-7]. The finite element model of ossicles was constructed based on 
histological section images [6] and computed tomography (CT) images of human ossicles in 
vivo [7].  
The objectives of our study were to construct a 3D model of ossicles that was based on the 
geometry of ossicles calculated from CT images of in vivo ossicles obtained during clinical 
evaluations, and to characterize the harmonic vibration characteristics of ossicles using a finite 
element method. 
 
Materials and Methods 
 
The geometry of ossicles was calculated based on the CT images of patients that were 
previously evaluated. The 3D model of ossicles was constructed using the medical imaging 
software Amira
®
. Note that the format of 3D model was STL. Then, the file format of the 3D 
model was transformed from STL into SAT by CAD, and the SAT file was imported into the 
finite element analysis software ANSYS
®
. The finite element model of ossicles was constructed 
875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. 
JEN-FANG YU, CHING-I CHEN 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1495 
using the SOLID185 (SolidWorks
®
) and the free meshing methods. The repeated nodes 
between ossicles were combined into a single node. The finite element model of ossicles was 
then built. The joint between the incus and stapes was considered because of the large value of 
Young's modulus. The COMBIN14 Spring-Damper was used for the vertical and horizontal 
axes on the stapes footplate. The vertical and horizontal spring elements are shown in Figures 
1(a) and 1(b), respectively. 
 
a)
1
2
X
Y
Z
X
Y
Z
                                                                                b)
1
2
X
Y
Z
X
Y
Z
                                                                                 
Fig. 1. The spring element at stapes footplate: a) the vertical direction, b) the horizontal direction 
 
The material parameters for each part of the ossicles were different. Poisson's ratio for 
overall structure was assumed to be 0.3 based on the results of similar previous studies, and the 
analysis of the dynamic characteristics of ossicles were not significantly affected by the value of 
the Poisson ratio used [8]. The damping matrix was calculated as [ ] [ ] [ ]C M Kα β= + , where 
[M] and [K] are the mass matrix and stiffness matrix, respectively, and α and β are the damping 
parameters.  
The overall structure consisted of 3 ossicles, the joints between the incus and the stapes, and 
the springs of the stapes. The incudomalleolar joint was adopted based the results of a previous 
study that showed no relative motion between the malleus and the incus at frequencies less than 
3 kHz [9]. Therefore, Young's modulus was assumed to be 14.1 GPa, which indicated a linearly 
elastic material of equal quality and equal direction. The density of the various parts of the 
ossicles is shown in Table 1. The nodes that connected the malleus and incus were combined 
into one node in our study. The joints between the incus and the stapes were adopted according 
to a previous study that showed no stiffness displacement in the joints under various conditions 
of noise and pressure [10]. Although there was some relative motion between the incus and 
stapes, we concluded that the inner ear was protected, and that it would not be damaged by the 
large displacement of the stapes footplate. In addition, the joints between the incus and the 
stapes were assumed to comprise homogeneous materials, with a Young's modulus of 0.6 MPa 
[11, 12]. 
 
Table 1. The density of the various parts of the ossicles  
 Density (kg/m3) 
Head 2.55×103 
Neck 4.53×103 Malleus 
Handle 3.70×103 
Body 2.36×103 
Short process 2.26×103 Incus 
Long process 5.08×103 
- 2.20×103 
Stapes 
I-S joint 1.2×103 
875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. 
JEN-FANG YU, CHING-I CHEN 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1496 
For harmonic analysis, 6 x-y plane springs were on the vertical side of the stapes footplate. 
The total constant of the springs, K, was 60 N/m. The total damping was 0.054 N/(m/s). The K 
value for the nine 3D vertical springs on the horizontal side was assumed to be 9 N/m. The 
vertical and horizontal springs of the stapes footplate were fixed to the UX, the UY and the UZ 
direction movements of the nodes of ossicles, respectively. To simulate the response of the 
sound transmitted through the cochlear fluid by the ossicles, the vertical direction was 
constrained to the 2D spring damper that could be pulled in the vertical direction only. The 
horizontal direction was used to simulate the actual motion of the stapes footplate. Therefore, 
the 3D spring damper was assumed. 
The ossicles and the ligament and the spring damper of the stapes footplate were analyzed. 
The degrees of freedom of the 3 directions of the nodes that connected the spring damper and 
the stapes footplate were fixed, as shown in Figure 2. The nodes on the base area of the 
manubrium of the malleus were excited in the X direction by 90 dBSPL, as shown in Figure 3. 
Based on the modal superposition (MSUP) theorem, the results of the MSUP analysis were 
obtained by transforming to the original coordinate system. The results of the MSUP analysis 
were extended to the overall structure to interpret the response of the sound transmitted to the 
inner ear through the ossicles following excitement with the sound pressure (90 dBSPL) under 
stimulus frequencies of 125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz,  
6 kHz, 7 kHz, and 8 kHz.  
 
1
                                                                                 
1
X
Y
Z
                                                                                 
Fig. 2. The degree of freedom for the nodes at 
the stapes footplate 
Fig. 3. The external load (90 dBSPL) for the 
harmonic analysis 
 
Results and Discussion 
 
The harmonic analysis focused on the joints of the malleus head and the tympanic 
membrane. The surface area of the malleus head, 3.081 mm
2
, was excited by 90 dBSPL    
(0.623 Pa). The frequency and the amplitude response of the specific nodes (Figure 4) on the 
stapes footplate at 250 Hz to 8 kHz, respectively, are shown in Figure 5. The results were also 
observed along the X, Y and Z axes, as shown in Figures 6 to 13. 
Based on the data presented in Figures 6 to 13, there was an apparent transition point for the 
9 nodes of the stapes footplate at 1 to 2 kHz. The ossicles were excited by the stimuli at 
frequencies below 1 kHz. The displacement corresponded to the amplitude of the sound stimuli 
that were transmitted to the stapes footplate. In contrast, significant displacement was not 
detected when the ossicles were subjected to stimuli with frequencies above 2 kHz, and the 
transmission power of ossicles was adopted directly. 
 
 
875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. 
JEN-FANG YU, CHING-I CHEN 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1497 
 
Fig. 4. The nodes, 1-9, on the footplate of stapes 
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.1
UX
UY
UZ
 
Fig. 5. The displacement at node 1 on the footplate 
under stimulus frequencies including 125 Hz, 250 Hz, 
500 Hz, 750 Hz, 1 kHz, 2 kHz, 3 kHz, 4 kHz, 5 kHz, 
6 kHz, 7 kHz and 8 kHz 
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.2
UX
UY
UZ
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.3
UX
UY
UZ
 
Fig. 6. The displacement at node 2 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,   
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
Fig. 7. The displacement at node 3 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. 
JEN-FANG YU, CHING-I CHEN 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1498 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.4
UX
UY
UZ
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.5
UX
UY
UZ
 
Fig. 8. The displacement at node 4 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,   
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
Fig. 9. The displacement at node 5 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.6
UX
UY
UZ
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.7
UX
UY
UZ
 
Fig. 10. The displacement at node 6 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
Fig. 11. The displacement at node 7 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
  
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.8
UX
UY
UZ
 
100 1000 10000
FREQUENCY (Hz)
1E-021
1E-019
1E-017
1E-015
1E-013
1E-011
A
M
P
L
ID
U
T
E
 (
m
m
) No.9
UX
UY
UZ
 
Fig. 12. The displacement at node 8 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz, 
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
Fig. 13. The displacement at node 9 on the 
footplate under stimulus frequencies including 
125 Hz, 250 Hz, 500 Hz, 750 Hz, 1 kHz, 2 kHz,  
3 kHz, 4 kHz, 5 kHz, 6 kHz, 7 kHz and 8 kHz 
 
Conclusions 
 
To meet the clinical needs of otolaryngologists, a dynamic model of human ossicles was 
constructed from in vivo CT images to aid clinicians in the assessments of ossicle function. The 
3D image of the ossicles was successfully imported into the finite element analysis software 
ANSYS
®
, and the finite element model of ossicles was constructed using the SolidWorks
®
 
SOLID185 program. When the ossicles were excited with sound stimuli at frequencies below   
875. MODELING THE DYNAMIC CHARACTERISTICS OF HUMAN OSSICLES. 
JEN-FANG YU, CHING-I CHEN 
 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2012. VOLUME 14, ISSUE 4. ISSN 1392-8716 
1499 
1 kHz, the vibration of the ossicles was equivalent to the amplitude of the sound stimuli. 
Significant displacement of the ossicles was not observed in response to sound stimuli at 
frequencies above 2 kHz, and the sound was transmitted by the ossicles directly. Analyses of 
the dynamic characteristics of ossicles based on this finite element model system may aid 
clinicians in the pre-op evaluation of substitute implants for the correction of hearing loss, such 
as that resulting from ossiculoplasty for the treatment of CSOM. 
 
References 
 
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Modeling the dynamic characteristics of human ossicles

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