EXPERIMENTAL BIOMECHANICAL CHARACTERIZATION AND NUMERICAL ANALYSIS OF THE TEMPOROMANDIBULAR JOINT

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1 15 th International Conference on Experimental Mechanics PAPER REF: 32 EXPERIMENTAL BIOMECHANICAL CHARACTERIZATION AND NUMERICAL ANALYSIS OF THE TEMPOROMANDIBULAR JOINT María Jesús Lamela 1(*), Pelayo Fernández 1, David Dorantes 1, Alberto Ramos 1, Eiji Tanaka 2, Antonio Argüelles 1, Alfonso Fernández-Canteli 1 1 Department of Construction and Manufacturing Engineering, University of Oviedo, Spain 2 Department of Orthodontics and Dentofacial Orthopedics, University of Tokushima Graduate School, Japan (*) mjesuslr@uniovi.es ABSTRACT Recent studies have shown that up to 3% of the population could suffer from temporomandibular joint (TMJ) disorders during their life. Up to now, there is no permanent solution for replacing the temporomandibular joint disc, so that a more precise knowledge of load regimes and an exhaustive definition of the biomechanical properties of the TMJ components are essential. The aim of this work is twofold, first, to provide a novel experimental methodology for the TMJ based on the adjustment of a three-degree of freedom testing machine, in terms of hardware and software, in order to simulate the real jaw kinematics and series of loading and second, to characterize the viscoelastic behaviour of the disc and the rest of the components of the TMJ by means of static and dynamic relaxation and creep testing. Keywords: biomechanics, TMJ, viscoelastic characterization, experimental techniques. INTRODUCTION The TMJ (see Fig. 1) is one of the most complex joint in the human body enabling movements of opening and closing, lateral excursion, jaw protrusion and retrusion by combining rotations and translations (Tanaka, 23) For the final purpose to perform ex vivo tests to recreate the normal operation conditions of the disc and the rest of components of the TMJ, a three-degree of freedom machine made by walter + bai company was adapted (see Fig. 2), using anatomical models to simulate the work surfaces and mathematic models to implement the control of jaw kinematics taking into account medical information. Since the TMJ disc is regularly subjected to large strain and stress levels, the study of its nonlinear response under compression is of practical interest, especially for analysis of medical dysfunctions (Tanaka, 28 and Koolstra, 29). With this aim, relaxation and creep tests were carried out using round specimens cut off from the central, anterior, posterior, lateral and medial zones of porcine discs to investigate the regional differences in the mechanical properties. ICEM15 1

2 Porto/Portugal, July 212 Fig. 1. Image of the TMJ structure Fig. 2. Three-degree of freedom biomechanical machine TMJ TRAJECTORIES s, the different trajectories of the TMJ discs, To test in agreement with the real conditions of the disc were analysed in order to study how to programme and set the machine control system to reproduce a reliable movement of the TMJ. Since inquiring the movement of the disc directly is a difficult task, e.g., different trajectories exist for opening and closing, is useful to analyse the displacements of the bone parts and, then, use them as references to implement the movements (Gallo, 28). Due to the complexity of measuring the movements in real persons (Fričová, 26), few scientific documents about the TMJ movements exist. In order to study the TMJ paths, Magnetic Resonance Image (MRI) (Chen, 1993 and Drace, 199), Video-Analysis (Yatabe, 1995) or Ultrasonics techniques have been used (Braun, 2). In this work, data obtained from literature (Comisso, 21) was used as reference for a first setting of the machine control. In a first approach, the mandibular movement could be obtained by two directions (two translations) and an angle (rotation), considering, e.g., the starting point when the mouth is o define the TMJ movements is necessary to use closed, so the angle would be º. However, tto oposal, the reference known proposal, a reference point to establish the trajectory equations. With this pr as kinematic center (KC) was used. The kinematic center is define as the mandibular point for which the protrusive and opening movement trajectory showed a minimal difference. Since the protusive movement is, in general, only of translation, the KC is not influence by the rotational mandibular movements (Hou, 22). Parametric equations of the movements The trajectory of all the mandibular movements can be divided in two paths: movement of opening-closing and movement of protusive-retrusive. As the machine has two translational actuators and a rotational shaft (see Fig. 2), the mandibular trajectories will have to be fitted to those possibilities of movements. From the mandibular movement data a two axis (vertical and horizontal) equation can be fitted for the opening and closing path of the KC, respectively. The opening movement for the KC is presented in Fig. 3. 2

3 15 th International Conference on Experimental Mechanics 1.5 Real path (opening) Fitted model Veritcal Axis (mm) Horizontal Axis (mm) Fig. 3. KC mandibular movement: opening (sagittal plane view). In a same way, data of the protusive-retrusive trajectory (see Fig. ) was fitted to polynomial model in order to have all the parametric equations of the mandibular movement. In this case and, taking into account the symmetry in the movements, the protusive-retrusive paths were considered the same. The fitted models for each movement were: Opening = (1) Closing = (2) Protu.-Retru. = (3) 1 Real path Fitted model Vertical Axis [mm] Horizontal Axis [mm] Fig.. KC mandibular movement: protusive (sagittal plane view). Movement equation implementation Once the movement equations are fitted, the next step is to convert the equations in a way that can be programmed easily in the actuators of the machine. As the mandibular paths are quite ICEM15 3

4 Porto/Portugal, July 212 complex and the machine can only develop translations (vertical and horizontal in the same plane), it is necessary to combine different waves in the machine for each actuator in order to fit the equations with the actuators control. Besides the previous movement descriptions, it is necessary to add a new variable for the mandibular complete movement: the time. Therefore both, e.g., opening-closing trajectories must be combined in order to obtain the mandibular close loop that will be carried out in a cyclic way. With this proposal complex harmonic motion was used define as: = sin + () where is the motion amplitude, is the circular frequency and the phase. Fitting Eqs. (1) and (2) with Eq. (), the parameters (,, of the complex movement are obtained (see table 1). It can be seen that, in this case (see table 1), only two waves (subscripts (1) and (2)) are needed for each actuator (vertical and horizontal) for fitting the cyclic movement. Table 1. Parameters of the complex harmonic motion for the opening-closing mandibular movement. Parameter Vertical (1) Actuator 1 Vertical (2) Actuator 1 Horizontal (1) Actuator 2 Horizontal (2) Actuator 2 Amplitude (mm) Frequency (Hz) Phase (º) In Fig. 5. both mandibular movement and the fitted complex model are presented. From this figure can be inferred that the complex model, carried out with only two orthogonal actuators (horizontal and vertical, respectively), presents good agreement with the real mandibular movement. It is important to remark the possibility of adding the third degree of motion of the machine (in-plane rotation) for other different complex trajectories..5 Vertical Axis / Actuator 1 (mm) Fitted model Opening path Closing path Horizontal Axis / Actuator 2 (mm) Fig. 5. Fitted model and experimental data [a8] for the opening-closing mandibular movement.

5 15 th International Conference on Experimental Mechanics EXPERIMENTAL PROGRAMME Biomechanical machine design As the Fig. 6 shows (Dorantes, 211), to adapt the three-degree of freedom biomechanical machine (see Fig. 2) for ex vivo testing, firstly, the hardware design was performed using some technologies for medical imaging, such as CT (Computer Tomography) and MRI (Magnetic Resonance), obtaining a series of 3D models of the mandibular bones, which were processed using commercial CAE (Computer Aided Engineering) and FEA (Finite Element Analysis) software to get the final pieces to be installed in the machine. Secondly, in order to make data processing easier, a new software tool was created providing an easy-to-use graphical user interface (GUI). This software tool imports the information from the machine and process this data according to the desired results. Fig.6. Hardware and software design of the biomechanical machine. Viscoelastic characterization To study the viscoelastic characterization of the whole disc and the regional variation of the material properties (Allen, 26 and Kuo, 21) round samples were cut off in the five characteristic zones of the disc: central, anterior, posterior, lateral and medial (see Fig. 7), using a tissue punch. The diameter of the specimens was about mm from the central, anterior and posterior zones, and about 5 or 6 mm for the lateral and medial zones. Table 2 indicates the sample thickness in each specific location. Table 2 Thickness of samples in each disc zone Sample location Medial Central Lateral Posterior Thickness (mm) 1.78 ±.3 2 ± ± ±.15 Anterior 2.26 ±.25 To analyse the possible non-linear material behaviour under compression, relaxation and creep tests were carried out at different strain and stress levels, respectively, in each disc zone to obtain the corresponding relaxation and creep moduli as a function of time, E(t) and D(t). ICEM15 5

6 Porto/Portugal, July 212 Fig.7 Zones of the TMJ disc The tests were conducted in a Dynamomechanical Analyzer, DMA RSA 3 of TA Instruments, showed in Fig. 8a. In order to simulate human body conditions during testing, the temperature was maintained at 37 ºC by a climate chamber and the samples were immersed in saline solution, using a special accessory adapted to the compression sion tool of the DMA (see Fig. 8b). a) b) Fig. 8 a) DMA RSA 3 of TA Instruments equipment and b) Accessory adapted to the DMA compression tool EXPERIMENTAL RESULTS Fig. 9 a) and b) show, respectively, the regional variation of viscoelastic properties of TMJ disc and the dependence of E(t) results from the strain level applied, inferring a non-linear material behaviour (F Pelayo,, 211 and Lamela, 211). Analogously, the results of creep modulus, D(t), plotted in Fig. 1 a) and b), confirm the regional variation of material properties and its non-linear behaviour with respect to the stress level applied. 6

7 15 th International Conference on Experimental Mechanics 8 x 15 Anterior 12 x 15 ε = 2 % 6 Posterior Lateral 8 E(t) [Pa] 2 Central Medial E(t) [Pa] ε = 15 % ε = 1 % Time [s] ε = 5 % Time [s] Fig. 9 a) Local variation of the relaxation modulus E(t) for ε = 15% and b) Variation of the relaxation modulus E(t) with the strain applied for the lateral disc zone. 1 x 1-5 Medial 8 x 1-5 σ = 2.5 kpa 8 D(t) [Pa -1 ] 6 Central Lateral Posterior Anterior 6 D(t) [Pa-1] σ = 5 kpa σ = 1 kpa 2 σ = 15 kpa Time [s] Time [s] Fig. 1 a). Local variation of the creep modulus D(t) for σ = 2.5 kpa and b). Variation of the creep modulus D(t) with the strain applied for the disc lateral zone. CONCLUSION This study shows the following conclusions: A new biomechanical testing system was developed with tree-degree of freedom that allows us to obtain the complex trajectories of the TMJ by means of the combination of two orthogonal translations and one rotational movements. The local variation of the compressive mechanical properties of the TMJ disc has been verified by the experimental results obtained in the relaxation and creep tests performed, as it was expected from previous works already published. To take into account the non-linear material behaviour of the TMJ disc under compression, an additional consideration of the strain and stress as variables is required. ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support given by the Spanish National and Asturias Regional Research Programmes (Projects DPI C2, FC--EQP-21 and ICEM15 7

8 Porto/Portugal, July 212 FC-IB9-136), as well as the research grants conceded by the Council of Gijón through the IUTA and by the University of Oviedo through the Excellence Mobility and the CajAstur Fellowship Programmes. REFERENCES Tanaka E, van Eijden T (23) Biomechanical behaviour of the temporomandibular joint disc. Crit Rev Oral Biol Med, 1, Tanaka E, Koolstra JH (28). Biomechanics of the temporomandibular joint. J Dent Res, 87, Koolstra JH, Tanaka E (29). Tensile stress patterns predicted in the articular disc of the human temporomandibular joint. J Anat, 215, Gallo LM, Gössi DB (28) Relationship between kinematic center and TMJ anatomy and function. Journal of Dental Research 86, Fričová M, Konvičková S (26) Modelling of temporomandibular joint and FEM analysis. Acta of Bioengineering and Biomechanics 8, 1. Chen J, Buckwalter K (1993) Displacement analysis of the temporomandibular condyle from magnetic resonance images. Journal of Biomech. 26, 12, Drace JE, Enzmann DR (199) Defining the normal TMJ: closed-, partially open-, and openmouth MR imaging of asymptomatic subjects. Radiology 177, Yatabe M, Zwijnenburg A (1995) The kinematic center: A reference for condylar movements. Journal of Dental Research 7, 1, Braun S, Hicken JS (2) Ultrasound imaging of condylar motion: a preliminary report. Angle Orthodontist 7, Comisso MS, Martínez J, Pérez del Palomar A (21) A model of the human mastication process including the TMJ. 17th International Congress of the European Society of Biomechanics, 17. Hou Z, Feng H, Li G (22) Trace features of the mandibular condylar kinematic center during jaw protrusive and open-closing movements in healthy subjects. Chinese Journal of Stomatology, 37, 2, Dorantes D (211) Adaptation of temporomandibular joint trajectories and adjustment of a three-degree-of-freedom biomechanical machine. Master Thesis, University of Oviedo. Allen DK, Athanasiou KA (26) Viscoelastic characterization of the porcine temporomandibular joint disc under unconfined compression. J Biomech, 39 (2), Kuo J, Zhang L, Bacro T, Yao H (21) The region-dependent biphasic viscoelastic properties of human temporomandibular joint discs under confined compression. J Biomech, 3 (7), F Pelayo, Lamela-Rey MJ, Fernández-Canteli A (211) Viscoelastic characterization of the temporomandibular joint disc in bovines. Strain, 7, Lamela MJ, Prado Y, F Pelayo, Fernández-Canteli A, Tanaka E (211) Non-linear viscoelastic model for behaviour characterization of temporomandibular joint discs. Experimental Mechanics, 51 (8),