Modal analysis of maxillary central incisor tooth

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1 African Journal of Biotechnology Vol. 8 (19), pp , 5 October, 2009 Available online at ISSN Academic Journals Full Length Research Paper Modal analysis of maxillary central incisor tooth Li, Ming-Yong 1, Li, Bin 2, Yan, Hong 3, Li, Yu-Long 2 *, Zhao, Ling-Cheng 2, Yan, Zi-Qiang 1, Li, Zhun 1 and Ma and Xuang-Xiang 4 * 1 Department of Stomatology, No.451 Hospital of PLA, Xi an , P.R. China. 2 School of Aeronautic, Northwest Polytechnical University, Xi an , P.R. China. 3 Tangdu Hospital, Fourth Military Medical University, Xi an , P.R. China 4 College of Stomatology, Fourth Military Medical University, Xi an , P.R. China. Accepted 25 August, 2009 The purpose of this study was to investigate the vibration modes of tooth and explain the vibration characteristics of tooth. By using the finite element method (FEM) software, the Eigen vibration of 3-D finite element model of maxillary central incisor tooth was analyzed. Crown vibration was dominantly present in the natural modes. In general, tooth vibration was mostly dominated by the first 4 natural modes and the natural frequencies of the tooth studied were , , and Hz, respectively. Corresponding natural mode shapes were as follows: 1 st, the whole tooth vibrates along its axis in crown to root direction; 2 nd, the crown swings mainly in labio-lingual direction; 3 rd, the crown twists about its axis; and 4 th the crown swings mainly in mesio-distal direction. The present data suggest that the modal analysis can be successfully applied in the field of study on the tooth under the loading of masticatory force. Key words: Tooth, vibration, modal analysis, frequency. INTRODUCTION The force on tooth can be analyzed by solid mechanics. Solid mechanical analysis includes statics analysis and dynamics analysis (Liu et al., 1998). Statics analysis has no consideration of the effect of inertia force. In other words, the force on the object does not change. Most previous mechanical studies in stomatology were statical analyses (Ilie et al., 2006; Ghassemieh, 2008) and dynamical analysis was rarely involved. But the practical force on tooth in nature is related with time. For instance, the chewing requires definite time. And the chewing force varied periodically in chew cycle (Pi, 2006). So it needs to introduce dynamics into stomatology and the force in nature may need further investigation. Some patients may feel ache and tingle during scaling or odontal-operation. Perhaps it is due to temporality hyperaemia which is caused by periodicity vibration of scaling handpiece or dental drill. People may feel ache and tingle on tooth when they take a long trip on train due to vibration caused by the roll of the wheel. Furthermore, the vibration of airplane could affect the oral health of *Corresponding author. lmy1018@sina.com. Tel: aviator. Study on the dynamics of tooth should analyse the Eigen vibration firstly. Modal analysis shows the natural properties of vibration system (Liu et al., 1998). Natural frequency, an important parameter to describe system dynamics, is correlated with modulus of elasticity, density and boundary conditions (Liu et al., 1998). So the natural frequency of tooth is associated with many factors in mouth. These factors include its size, density, height of alveolar bone, elastic module of periodontal ligament and the health state of periodontal ligament. Different tooth has different natural frequency. Normal value of natural frequency of healthy tooth is limited in a definite range. The periodical chewing impact can give bad influence on the health of tooth or dental pulp. Lee et al. (2000) reported an innovative method to evaluate periodical condition by surveying natural frequency of tooth. Huang et al. (2000) assessed the implant/bone interface by using natural frequency analysis. These studies revealed that natural frequency has close relationship with the state of tooth or implant. The natural frequencies are arranged according to its value, ascending from low to high, as first order, second order and so forth. When the frequency of external loading is close to one natural frequency, the response vibration is mostly dominated by the corresponding modal

2 Li et al Table 1. The first 6 natural frequencies and mode shapes of a maxillary central incisor tooth. Order of modes Frequency (Hz) Vibration mode Plunge along the axis of tooth, in crown to root direction Pitch in labio-lingual direction, crown mostly Twist about the axis of tooth Swing in mesio-distal direction, crown mostly Swing in labio-lingual direction, root mostly Swing in mesio-distal direction, root mostly motion. Generally, the first 6 Eigen modal motions are the major vibration forms. Higher frequency modal motions have no significant effects on vibration problem. By using modal analysis structural dynamic, response of an object can be elicited. Based on the parameters, further study on dynamics can be developed. For example, Bo et al., (2000) has built a dynamical model of human skull by using modal analysis, suggesting that the vibration of skull structure under outer loading was mostly dominated by the shape of the first mode. The first 4 modes indicate that the modal analysis produces important information on dynamic response and injury mechanism of human skull under impact loading. The skull dynamics deduced from modal analysis has certain reliability. By the rapid development of computer technique, the application field of finite element method (FEM) has been spread out extensively (Soares et al., 2008; DeHoff et al., 2006; Sorrentino et al., 2007). And maxillary central incisor is usually used as a typical tooth to analyze any kinds of force pressed on tooth (Zaroneb et al., 2006). In this study, the vibration of 3-D finite element model of maxillary central incisor tooth was introduced. Then the natural frequency of tooth was determined by using FEM software. OBJECT AND ANALYSIS METHODS USED Object 3-D model of maxillary central incisor tooth: Based on the data of Chinese natural maxillary central incisor tooth (Wang 1959). The software: MARC2001 (purchased from MSC Co. Ltd.) and 3D Max. Methods of analysis Firstly, the 3 dimensional model of maxillary central incisor tooth was established by using 3D Max. Then this model was input to Marc2001 and the Mentat software was used to generate the finite element meshes (Li et al., 2003). The length of the tooth was 22.8 cm (Wang 1959). According to the anatomic structural properties of maxillary central incisor tooth, the finite element model was divided into two parts: the crown part and the root part. The two parts were assumed to be isotropic linearelastic. The crown part has physical parameters E = Mpa, = 0.30 and the root part has E = MPa, = 0.30 (Van et al., 1990). The thickness of peridental membrane was 0.2 mm (Pi, 2006). And alveolar bone around peridental membrane was considered to be rigid boundary. So an elastic foundation boundary condition was imposed on the surface of tooth root. Physical parameters of peridental membrane are E = 3.45 MPa, = 0.45 (Skinner, 1960). Based on the finite element model, modal analysis of maxillary central incisor tooth was performed. First 10 natural frequencies and mode shapes were obtained. RESULTS By using FEM software, for the maxillary central incisor tooth, the first four molars having significant effects on vibration problem could be calculated. In this paper the first 6 natural frequencies and modes of the maxillary central incisor tooth studied were obtained and listed in Table 1. Also the mode shapes were shown in Figures 1-6. In these figures, difference colors denoted different displacement amplitudes of the tooth in the vibration modes. Different colours, from yellow to blue, denote vibrational amplitudes from small to large. DISCUSSION Vibration analysis of tooth The present results showed that the first natural frequency of maxillary central incisor tooth was Hz and the vibration mode was whole tooth vibration along its axis in crown to root direction. Under the impact of chewing force, the tooth vibration will be mostly dominated by the first vibration mode shape. Chewing force on maxillary central incisor tooth is transferred along its axis and will be cushioned by the periodontal ligament. The second natural frequency of maxillary central incisor tooth was Hz and the vibration mode was crown swing mainly in labio-lingual direction. It is also one of the chief vibration modes of the tooth. Under the impact of chewing force, crown will swing in labio-lingual direction rather evidently. At the same time, part of the force will be transferred to root and cushioned by periodontal ligament. The third natural frequency of maxillary central incisor tooth was Hz and the vibration

3 5090 Afr. J. Biotechnol. Figure 1. The first vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: plunge along the axis of tooth, in crown to root direction. mode was twist about the axis of tooth. The fourth natural frequency of maxillary central incisor tooth was Hz and the vibration mode was crown swing mainly in mesio-distal direction. In normal condition, the possibility of occurrence of these two vibration modes is little, because of the presence of adjacent teeth. The values of these two Eigen frequencies are close to that of the second. It means that part of the force may be transferred to adjacent teeth by contacting area under the loading of chewing force.

4 Li et al Figure 2. The second vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: pitch in labio-lingual direction, crown mostly. The fifth natural frequency of maxillary central incisor tooth was Hz and the vibration mode was root Hz and the vibration mode was root swing mainly in mesio-distal direction. The results suggest that the chewing force can cause root vibration. But the vibration of root is weaker than that of the crown by the restriction of alveolar bone. These may be secondary vibrations. Vibration modes higher them 6 th order were root twist. The possibility of occurrence of these vibration modes is very little and can be ignored in modal analysis. swing mainly in labio-lingual direction. The sixth natural frequency of maxillary central incisor tooth was Moreover, vibration modes also revealed that swing range of crown was greater than that of the root in the second and the fourth modes and there is a fixed point, which locates on the 1/3 of upper root during the swing vibration. It is the rotating center of the tooth. This result is consistent with Zhou Su-Min s report by using 2D FEM (Zhou and Wu, 1984). It indicates that when an orthodontic force is applied on the tooth, the crown and root

5 5092 Afr. J. Biotechnol. Figure 3. The third vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: twist about the axis of tooth. will transfer the force with movements in reverse directions. Significance of the vibration analysis for tooth Vibration is a back and forth periodic motion about the equilibrium position of the system (Liu et al., 1998). Periodic motion of tooth can produce different effects in mouth. Crown is the physiological functional part and its stiffness is highest. Root is fixed in alveolar cavity by periodontal ligament. Periodontal ligament is of soft compact tissue with considerable elasticity (Pi, 2006). The vibration property is determined by its unique character of

6 Li et al Figure 4. The fourth vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: swing in mesio-distal direction, crown mostly. structure. When the chewing force on maxillary central incisor tooth does not exceed the physiological loading limit, it may cause tooth vibration and be buffered by periodontal ligament and adjacent teeth. This is advantageous for human body. On the other hand vibration may also be disadvantageous if the chewing force exceeds physiological loading limit or the chewing relationship is abnormal, then vibration caused by chewing force will lead to loosen the tooth. The modal analysis of tooth can reveal the essence of

7 5094 Afr. J. Biotechnol. Figure 5. The fifth vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: swing in labio-lingual direction, root mostly. tooth vibration and explain the mechanical properties of tooth under chewing force. Important information on dynamic response and injury mechanism of human tooth under chewing loads could be obtained. Based on this study, the application of dynamics in stomatology may expand the study field of biomechanics.

8 Li et al Figure 6. The sixth vibration mode of maxillary central incisor tooth. Frequency: Hz. Vibration mode: swing in mesio-distal direction, root mostly. REFERENCES Liu Y, Chen W, Chen L (1998). Vibrate mechanics.beijing: Higher education publishing company. Ilie N, Kunzelmann KH, Hickel R (2006). Evaluation of micro-tensile bond strengths of composite materials in comparison to their polymerization shrinkage. Dent. Mater. 22(7): Ghassemieh E (2008). Evaluation of sources of uncertainties in microtensile bond strength of dental adhesive system for different specimen geometries. Dent. Mater. 24(4): Pi X (2006). Anatomy and physiology of stomatology. (6rd edit). Beijing: People s sanitation publishing company. Lee SY, Huang HM, Lin CY, Pan LC (2000). In vivo and in vitro natural frequency analysis of periodontal conditions: an innovative method. J. Periodontal. 71(4): Huang HM, Pan LC, Lee SY, Lin CY (2000). Assessing the implant/ bone interface by using natural frequency analysis. Oral Surg. Med. Oral. Pathol. 90(3): Bo B, Zhou SX, Bai XG, Zhang YF (2000). Upbuilding a dynamic model of human skull by using modal analysis. Chin. J. Trau. 16(12): Soares CJ, Santana FR, Castro CG, Santos-Filho PCF, Soares PV, Qian F, Armstrong SR (2008). Finite element analysis and bond strength of a glass post to intraradicular dentin: comparison between microtensile and push-out tests. Dent Mater, 24(10): DeHoff PH, Anusavice KJ, Gotzen N (2006). Viscoelastic finite element analysis of an all-ceramic fixed partial denture. J. Biomech. 39(1): Sorrentino R, Aversa R, Ferro V, Auriemma T, Zarone F, Ferrari M, Apicella A (2007). Three-dimensional finite element analysis of strain and stress distributions in endodontically treated maxillary central incisors restored with different post, core and crown materials. Dent. Mater. 23(8): Zaroneb F, Sorrentinob R, Apicella D, Valentino B, Ferrari M, Aversa R, Apicella A (2006). Evaluation of the biomechanical behavior of maxillary central incisors restored by means of endocrowns

9 5096 Afr. J. Biotechnol. compared to a natural tooth: A 3D static linear finite elements analysis. Dent. Mater. 22(8): Wang HY (1959). Mensuration and statistic of chinese tooth. Chin. J. Stoma. 7(3): Li MY, Li B, Ma XX, Li YL, Wang MQ, Zheng XJ, Zhao GW (2003). Generating three-dimensional FEM model of teeth by CAE software. J. Prac. Stoma. 19(2): Van Rossen JP, Brauk LH, De Putter C, De Groot K (1990). Stress absorb element in dental implant. J. Prosthet. Dent. 64(2): Skinner P (1960). The Science of dental material. (5 th Ed). Philadelphia: Saunder. Zhou S, Wu Z (1984). Stress analysis on different altitude sustain tissue of mandibular molar by using FEM. J. Beijing Med. College, 16(4):

Prosthetic Options in Implant Dentistry. Hakimeh Siadat, DDS, MSc Associate Professor

Prosthetic Options in Implant Dentistry. Hakimeh Siadat, DDS, MSc Associate Professor Prosthetic Options in Dentistry Hakimeh Siadat, DDS, MSc Associate Professor Dental Research Center, Department of Prosthodontics & Dental s Faculty of Dentistry, Tehran University of Medical Sciences