Numerical analysis of ossicular chain lesion of human ear

Transcription

1 Acta Mech Sin (2009) 25: DOI /s RESEARCH PAPER Numerical analysis of ossicular chain lesion of human ear Yingxi Liu Sheng Li Xiuzhen Sun Received: 8 January 2008 / Revised: 11 September 2008 / Accepted: 24 September 2008 / Published online: 11 November 2008 The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH 2008 Abstract Lesion of ossicular chain is a common ear disease impairing the sense of hearing. A comprehensive numerical model of human ear can provide better understanding of sound transmission. In this study, we propose a three-dimensional finite element model of human ear that incorporates the canal, tympanic membrane, ossicular bones, middle ear suspensory ligaments/muscles, middle ear cavity and inner ear fluid. Numerical analysis is conducted and employed to predict the effects of middle ear cavity, malleus handle defect, hypoplasia of the long process of incus, and stapedial crus defect on sound transmission. The present finite element model is shown to be reasonable in predicting the ossicular mechanics of human ear. Keywords Finite element model Ossicular chain lesion Acoustic structural coupled analysis Middle ear cavity Sound transmission 1 Introduction The human ear includes complex morphological structures consisting of canal, middle ear and inner ear to transfer sound from environment into central auditory system. The external The project was supported by the National Natural Science Foundation of China ( , , and ). Y. Liu S. Li (B) X. Sun State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China lishengdlut@163.com X. Sun ENT Department, The Second Affiliated Hospital of Dalian Medical University, Dalian, China canal collets sound pressure waves and stimulate the air media in the ear canal to induce vibration of the tympanic membrane. The middle ear consists of three small ossicles (i.e., malleus, incus, and stapes) which are suspended in the airfilled middle ear cavity by attached ligaments and muscle tendons and connected by two joints: incudomalleolar and incudostapedial joints. The middle ear builds a mechanism (ossicular chain) for transmitting vibrations of the tympanic membrane. The output portion of the middle ear is a stapes footplate, which sets into the oval window and transmits vibrations into cochlear fluid. A number of parameters, such as shape and stiffness of the tympanic membrane, shape and volume of the external ear canal, and volume and pressure of the middle ear cavity, affect directly acoustic mechanical transmission through the ear. Changes of these parameters are often related to patho-physiological conditions in the ear. The ossicular chain plays an important role in auditory mechanics. If a patient suffers from different diseases, the ossicular bones may be damaged in different part and the efficiency in the sound transmission of the middle ear may also be reduced. Frequent occurrence of ossicular chain lesions is one of the factors urging physicians to seek out the most cost-effective clinical strategies for managing the condition. A number of clinical studies have been dedicated to symptoms of the diseases of ossicles in human [1 3] using experimental method. However, the effects have not been quantitatively clarified because removal of any part of ossicular bones is difficult. And, direct measurements of certain performances are difficult to carry out. When the dynamic behavior of biological structures is analyzed, the finite element method would be one of the powerful tools. The finite element method is always capable of modeling the complex geometry, ultrastructural characteristics, and non-homogenous and anisotropic material properties of biological systems. The first

2 242 Y. Liu et al. finite element model of the ear (for cat tympanic membrane) was reported by Funnell and Laszlo in 1978 [4]. In 1992, a three-dimensional finite element model of middle ear was proposed by Wada and Metoki [5] for investigating vibration patterns of the middle ear system. Since then, the finite element modeling of the static and dynamic behaviors of the middle ear subsets or entire middle ear has become a rapid growing field in ear mechanics. A thorough literature survey about the FE modeling of ear mechanics is summarized in our previous publication [6]. In 2004, Gan et al. construct a complete finite element model of the human ear on the basis of histological section images of human temporal bone [7] for analyzing the transmission of sound wave. But, the specimen has to be decalcified and embedded before the actual risky process of sectioning and mounting the slices on microscope glass plates. In 2007, Lee et al. develop a finite element model using high-resolution computed tomography for cartilage myringoplasty [8]. However, some factors have not been considered in Lee s model, e.g., the middle cavity and the canal. Using the spiral CT technology, Liu et al. [9] construct a finite element model of human ear which incorporated the canal, the tympanic membrane, the ossicular bones, the middle ear suspensory ligaments/muscles, and the inner ear fluid. The validity of the model is confirmed by comparing the displacements of tympanic membrane and stapes footplate obtained by the finite element model with published experimental data. In the present study, the effect of middle ear cavity is taken into consideration [10]. The acoustic structural coupling effect of the canal, the tympanic membrane, the ossicules, and the middle ear cavity is investigated and the effects of the middle ear cavity and the ossicular chain lesions are predicted by using the finite element model. 2 Methods 2.1 Construction of finite element model A healthy living volunteer (male, age 25, right ear) is scanned using spiral computerized tomography to show the whole temporal bone. The spiral data set is reconstructed with an interval of 0.1 mm, and the images from the spiral computerized tomography machine are digitized using self-programming of Matlab along the outlines of the ear structures identified by the otologic surgeon. The data of digitized images are input into ANSYS to generate a finite element model and appropriate boundary conditions. Figure 1a d show the finite element model of human ear incorporating the ear canal, the tympanic membrane, the ossicular bones, the middle ear suspensory ligaments/muscles, the middle ear cavity and the inner ear fluid. The connections of components are showed in Fig. 1e and f. The tympanic membrane is meshed by three-node shell elements with a total of 3,626 elements, the canal, the middle cavity and inner ear fluid are meshed by four-node acoustic elements with a total of 149,747 elements, and the other parts are meshed by four-node tetrahedral solid elements with a total of 36,270 elements. Fig. 1 a d Finite element models of ear components, e, f illustration for the connection of components

3 Numerical analysis of ossicular chain lesion of human ear 243 Table 1 Material properties of ear components ρ/(kg m 3 ) E/Pa Tympanic membrane [11] [12] Malleus (head) [13] [14] (neck) (handle) Incus (body) [13] [14] (short process) (long process) Stapes [13] [15] Incudomalleolar joint [6] [6] Incudostapedial joint [6] [16] Manubrium [6] [6] Tympanic annulus [6] Superior mallear ligament [17] [12] Lateral mallear ligament [12] Anterior mallear ligament [6] Superior incudal ligament [6] Posterior incudal ligament [16] Stapedial annular ligament [18] Tensor tympani tendon [16] Stapedial tendon [17] Table 2 Acoustic properties of ear components ρ/(kg m 3 ) v/(ms 1 ) Air Cochlear fluid 1,000 1, Governing equations The structural dynamics equation of the acoustic structural coupled system is Mü + C u + Ku = f + Rp, (1) 2.3 Material properties The human ear is described as a linear system under a regular sound intensity at an audible level. Material properties and boundary conditions are assigned from published data (Table 1), while acoustic properties of air and water are listed in Table 2. The Poisson s ratio is assumed to be 0.3 [7], the Raleigh damping parameters for all materials of the middle ear system are α = 0s 1 and β = s [7] and the thickness of the tympanic membrane is 0.05mm. The surfaces of acoustic elements next to the movable structure, such as the tympanic membrane, ossicles, and suspensory ligaments, are where M, C, K, and R are structural mass matrix, structural damping matrix, structural stiffness matrix, and coupling matrix, respectively; u is the displacement vector; u is the velocity vector; ü is the acceleration vector; f is the applied load vector, and p is the sound pressure on the coupled surface. The acoustic wave equation of the acoustic structural coupled system is M p p + K p p = ρ 0 R T ü, (2) where M p, K p, and R are fluid mass matrix, fluid stiffness matrix, and coupling matrix, respectively; p is the sound pressure; ü is the acceleration vector on the coupled surface; ρ 0 is mean fluid density. Fig. 2 Finite element model of the middle ear cavity with different volume. a Cavity closed I, b cavity closed II

4 244 Y. Liu et al. Fig. 3 Effects of the middle ear cavity on tympanic membrane (a) and stapes footplate (b) displacements Fig. 4 Finite element model of malleus handle defect defined as fluid structural interface (FSI) where the acoustic pressure distribution is coupled into structural analysis as the force input in ANSYS. 3 Result and discussion 3.1 Effects of middle ear cavity Effect of the middle ear cavity on sound transmission is examined in this section. The finite element models with different volumes: (a) mm 3 and (b) mm 3 are shown in Fig. 2, and the state of the middle ear cavity can be either open or closed for simulation. An open middle ear cavity refers to a finite element model in which the middle ear air space connects directly to ambient pressure, whereas a closed middle ear cavity refers to a model where the entire middle ear air space is sealed. Figures 3a and b show the calculated displacements of tympanic membrane and stapes footplate based on the finite element model with three states of cavity: cavity open, cavity closed I and cavity closed II. Opening the middle ear cavity increases the magnitude of the displacements at tympanic membrane. Moreover, the displacements will be reduced when the cavity volume is decreased. The effects of cavity states on displacements are sensitive for frequencies below 2,000 Hz. Results of stapes footplate show similar differences between the open and sealed cavity configurations. The analysis demonstrates that the volume of the middle ear cavity plays an important role in determining hearing loss. The trend of simulation results is consistent with that previously published [19]. 3.2 Effects of malleus handle defect The handle of the malleus secured to the tympanic membrane plays an important role in sound transmission from Fig. 5 Effects of malleus handle defect on tympanic membrane (a) and stapes footplate (b) displacements

5 Numerical analysis of ossicular chain lesion of human ear Effects of incus with hypoplasia Fig. 6 Finite element model of incus lesion outer ear to inner ear. The trauma may lead to defects in the malleus handle. In the section, efforts are focused on the change of vibration at tympanic membrane and stapes because of the defect in melleus handle. Figure 4 shows the finite element model of normal malleus and melleus with lesion. The finite element model of the ear is used for predicting the effects of malleus handle on tympanic membrane and stapes movements. Figure 5a and b show the displacements of tympanic membrane and stapes footplate in response to the change of malleus handle. The results suggest that the lesion of malleus handle will have tremendous effects on tympanic membrane and stapes footplate movement and thus affect sense of hearing. The defect in malleus handle results in an overall increase of tympanic membrane displacement over the auditory frequency range (Fig. 5a). However, the defect results in an extensive reduction of stapes displacement (Fig. 5b). The results predicted by the finite element model may provide useful information for the diagnosis of isolated defect occurred in malleus handle of a patient with conductive hearing loss. The incus articulates with malleus and stapes by incudomalleolar joint and incudostapedial joint, respectively. Hypoplasia of incus would result in different otological diseases. In the study, it is assumed that the long process of incus has pathologic change. In the abnormal situation, bone tissue of the long process of incus is replaced by soft tissue (Fig. 6). To simulate the disorder of the long process of incus, it is assumed that the Young s modulus of the long process is decreased from Pa to Pa. Figures 7a and b show the model-predicted displacement curves at tympanic membrane and stapes footplate in response to the stiffness change of the long process of incus. The softer long process results in an obvious increase of stapes displacement. However, the influence of the softer long process on tympanic membrane is very limited. One explanation for the change is that less acoustic energy is transported to the stapes footplate through the softer long process. The results of the section indicate that the finite element model can be used to predicting clinical manifestation of incus prostheses for improving the patient s sense of hearing. 3.4 Effects of stapedial crus defect As the name implies, the stapes looks like a stirrup. It has four components: a footplate, anterior crus, posterior crus, and a head (Fig. 8). The head of the stapes articulates with the long process of the incus, and the footplate of the stapes covers the oval window. The hypoplasia of stapes may lead to defects in anterior crus or in posterior crus, both of which would be discussed in detail in the present section. The defect in crus has a little effect on tympanic membrane movement at all frequencies (Fig. 9a). Figure 9b and c show the displacement curves of the anterior part of stapes footplate and the posterior part of stapes footplate, respectively. As shown in the figures, the defect in anterior crus and posterior crus have substantial effect on the stapes footplate movement. The defect in anterior crus decreases the Fig. 7 Effects of the long process lesion of incus on tympanic membrane (a) and stapes footplate (b) displacements

6 246 Y. Liu et al. Fig. 8 Finite element model of stapedial crus defect Fig. 9 Effects of stapedial crus defect on the displacements of tympanic membrane (a), anterior part of stapes footplate (b) and posterior part of stapes footplate (c) displacement of the anterior part of stapes footplate (Fig. 9b) and increases the displacement of the posterior part of stapes footplate (Fig. 9c). When the posterior crus is damaged, the displacement is increased at the anterior part of stapes footplate (Fig. 9b) and decreased at the posterior part of stapes footplate (Fig. 9c). The results can give a better understanding of malformation of stapes and be referenced by stapedial surgery. 4 Conclusion In this study, a three-dimensional finite element model of human ear is created based on a complete set of CT images of a living human temporal bone. Numerical analysis based on the finite element model is conducted for otological applications to predicting the effects of the middle ear cavity, malleus handle defect, hypoplasia of the long process of incus, and stapedial crus defect on sound transmission. From this study, it is clear that the finite element method has great potential for analyzing the dynamical behavior of acoustic transmission in human ear. Predictions from this model may be useful to clinicians in researching new surgical reconstruction techniques and provide useful information for the design of middle ear implants to restore sense of hearing. Acknowledgments A special note of thanks is extended to all the doctors of the Department of ENT, Second Affiliated Hospital of Dalian

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