Bite force and contact area evaluation in a physical-virtual environment

Transcription

1 HOME Proceedings of IDMME - Virtual Concept 2010 Bordeaux, France, October 20 22, 2010 in a physical-virtual environment Roberto Meneghello, Gianpaolo Savio, Andrea Cerardi DAUR Laboratory of Design Tools and Methods in Industrial Engineering Faculty of Engineering University of Padova Phone /Fax {roberto.meneghello, gianpaolo.savio, andrea.cerardi}@unipd.it Abstract: An integrated physical-virtual methodology for the in-vitro study of the occlusion is proposed. Both the contact area and the bite force are investigated in order to evaluate the functional characteristics of removable complete dentures and its relation to teeth morphology, position and orientation in the dental prosthesis and to relative position between antagonist teeth. The force is experimentally estimated by a 6-axis strain gauges sensor, while the contact areas are virtually identified by reverse engineering techniques. The proposed method is aimed to assist the functional design of artificial teeth for removable complete as well as the prototyping phases of the prosthesis. Key words: Virtual dentistry, occlusion simulation, force measurement, reverse engineering, complete dentures 1- Introduction In this work a multidisciplinary approach to the investigation of factors influencing force and contact mechanism in occlusion is proposed. 1.1 Human mastication Both mechanical and biological issues of the stomatognathic system have been studied in order to characterise its functional performances. Functional aspects are usually put in relation with the force and the contact areas which arise in chewing, swallowing and speaking. These parameters strictly depend to the patient health status, to teeth morphology, position and orientation, and to biomechanic activity. An useful indicator of the functional status of the masticatory system is the maximum bite force in complete occlusion, which increases with the number of contact areas and the total contact area, while the mean pressure remain constant [B1,KS1, HI1]. Maximum bite force is influenced by several factors and its quantification depends on the measurement methods adopted. In literature values ranging from 200 N [FS1], N [B1], up to 1500 N [HI1] are recorded. These values decrease when a dental prosthesis is used [FS1]. Experimental in vivo measurement of the force acting on an implanted tooth was proposed [YK1, KK1]. In these studies, it is observed that as the magnitude of the load increase, the direction of the load tended to correspond with the direction of the palatal root of the tooth, thus offering a 3D representation of the local bite force. Moreover, within the aim of investigating prostheses stability during mastication it was emphasized its correlation to the position of the resultant force in alveolar ridge and to the space for the tongue movement in swallowing and speaking [H1]. 1.2 Force sensors Many contributions are available in literature which adopt a load cell based on strain gauges or piezoelectric crystals to assess the load effect during occlusion. Strain gauges sensors (load cell) are typically constitued of metal elastic structures to which full bridge strain gauges are bonded: when the structure is loaded, an elastic deformation occurres which changes the electric properties of strain gauges. In the literature, different structural flexible element geometries were adopted, as depicted in figure 1: a) regular beam, b) parallel beam [KT1], c) octagonal ring [HI1], d) binocular shape [KK2], e) cylindrical column [KK3], and f) Pylon structure [FN1]. 1.3 Contact area analysis In the past, traditional methods in dental occlusion analysis were based on articulation paper, waxes, pressure indicator paste, etc., and were adopted by dentists to assess and balance occlusal forces/contacts, [W1]. Most of these methods are not sensitive enough to detect simultaneous contacts, and none of them can measure both biting time and force. Carey [CC1] showed that a linear relationship between applied load and articulating paper mark area could not be found. ViRMAN_P Copyright of IDMME - Virtual Concept

2 Recently new approaches based on pressure grid sensors have been introduced in dental occlusion analysis [W1, G1], but these new techniques are not able to offer a complete 3- dimensional quantification and representation of the acting forces. reference system. By associating the 3D coordinate system defined on the load cell with the 3D virtual reference system of the complete denture in occlusal configuration both the orientation and the position of forces and contact areas on the digitalized denture can be visualized and quantified. c) d) Figure 2: Occlusal configuration and the digitalized virtual condition. 2.1 Six-component load cell e) f) Figure 1: Different geometries of a structural flexible element 1.4 This work In this work an integrated method based on 3-dimensional force measurement and reverse engineering techniques is proposed for the study of the bite force and occlusion mechanic in removable complete dentures. Force and moment vectors measurement is performed by a 6- axis strain gauges sensor, while contact areas are made available by reverse engineering actual prostheses and executing distance analysis between reconstructed CAD model of upper and lower dentures in occlusion. The integration of the two proposed techniques makes possible to represent and study the prosthesis, the contact areas in occlusion and the forces in the same 3D virtual environment Design and manufacturing The proposed load cell is constitued by four column sensible elements constrained by two support plates (figure 3a). The column elements (figure 3b) consist of a double parallel beams perpendicular to each other. Two full bridge strain gauges are positioned in each column as depicted in figure 3c. Signals are acquired by a CRONOS-PL IMC data acquisition system (figure 3d). 2- Method The proposed method is based on the integration of force data deriving from direct measurement with virtual (CAD) geometric models of a complete denture. By a specifically designed 6-axis load cell, the resultant bite force acting in the occlusal configuration between the maxillary and the mandibular dentures of a complete denture can be measured (figure 2a). Force vectors versus time are thus represented in a 3D coordinate system defined on the load cell. Adopting reverse engineering techniques, the dentures can be digitalized separately and then together as aligned in the occlusal configuration (figure 2b). In this way a geometrical model is obtained, which can be represented in a 3D virtual c) d) Figure 3: Load cell design: a) columns and support plates assembly, b) column sensible element, c) strain gauges and d) data acquisition system. In the design phase three main aspects were considered: - two flexible hinges are located on the ends of the columns, in order to reduce the mutually influence between different parallel beams and different columns; - two safety C-shape elements to avoid the yield of the horizontal parallel beams, are placed on each column; - one safety step-shape element to avoid the yield of the horizontal vertical beams, are placed on each column. Both the columns and the plates are manufactured in ViRMAN_P Copyright IDMME - Virtual Concept

3 aluminium by EDM technologies Calibration With the aim to obtain numerical information relevant to the force, the load cell must be calibrated as proposed in literature [HD1], adopting the reference frame illustrated in figure 4. The strain gauge signal [mv/v] in the i column (i=1,2,3,4 see figure 4) is identified as Ci,j, where j=1 if the signal is relevant to horizontal parallel beams (upper beams in figure 3b, which detect vertical load) and j=2 if the signal is relevant to vertical parallel beams (lower beams in figure 3b, which detect horizontal load). 2 3 z y P = (4), ( C11, C12, C21, C22, C31, C32, C41, C ) T C = 42 (5). The calibration matrix gives the relation between the signal vector V and the load vector F: V = K F (6). The rows of K matrix are derived applying a unidirectional known load and measuring the relevant V vector. Moreover, in order to apply the calibration loads a suitable modular structure has been designed as presented in figure 5. x 1 4 Figure 4: Reference frame adopted on the upper plates of the load cell. The vector V, apparent loads [HD1], are defined as the signal vector whose components, in ideal condition, are proportional to the components of the load vector F: VFx C12 - C32 VFy C42 - C22 V C11 C21 C31 C41 V = = (1). VMx C31+ C41- C11- C21 VMy C21+ C 31- C41- C11 VMz C12 + C22 + C32 + C42 F ) T = ( Fx, Fy,, Mx, My, Mz (2) The vector V can be written as: with P and C: V = P C (3) c) Figure 5: Structure designed for calibration. Different configurations are proposed in order to apply unidirectional component load: a) Fx, Fy, b), Mx, My, c) Mz. Applying an external force to the load cell, it is possible to calculate the load components by the sensitivity matrix K -1 : F = K V = K 1 1 P C = T C where the transfer matrix T is defined as: T = K P 2.2 Digitalization and contact areas reconstruction 1 (7). (8). Reverse engineering techniques were applied for the reconstruction of a virtual (CAD) geometrical model of the load cell and its reference frame, of both the dentures and of its relevant alignment. The digitalization instruments used (figure 6) are: - Dental Wings 5Series: a 3D scanner laser. In this work, the scanner is adopted to digitalize the dentures and the relevant supports; ViRMAN_P Copyright IDMME - Virtual Concept

4 - FARO CAM2 Platinum 7-axis: an articulated arm that provides a tactile probe and a laser head. In this work, the articulated arm is adopted to identify the position of the load cell and of the upper and the lower dentures in the occlusal configuration. The loads applied are equal to 50 N and 100 N. Dentures are placed in the ideal occlusal condition (derived from the articulator in which the prosthesis was manufactured). From this position the lower denture is moved in x and y directions in the range from -2 mm to +2 mm. 3.3 Contact areas analysis The contact areas are studied in dentures manufactured with Strack geometric artificial teeth [S1] Acry Plus [W2] (Ruthinium ). Figure 6: Instruments adopted in the digitalization: a) cnc scanner laser, b) articulated arm with laser head. By the alignment (registration) of the two virtual single dentures with the virtual complete denture in occlusion configuration it is possible to identify the contact areas: areas of the virtual single dentures where the distance between the two shells is lower than a threshold value ( mm). Alignment and contact areas identification are performed in Rapidform (INUS Technology). 2.3 Techniques integration The magnitude of the resultant force is given by: 2 2 F = Fx + Fy + while the direction of the resultant force is parametrized as: z Fx Mz x =, z Fy + Mx y = 2 (9), (10). Finally the prostheses, the resultant force (magnitude and direction) and the contact areas can be shown together in the same virtual reference frame (figure 7) by using a conventional CAD software (Rhinoceros, McNeel and Associates) 3- Validation Several occlusal configurations were studied to evaluate the potentialities of the proposed method. 3.1 Load cell calibration With the aim of calculate the K matrix, 6 calibrated weights are adopted each about 50 N. The 6 weight are used in order to obtain unidirectional load (force or moment of the force) variable between -300 N to 300 N or -39 Nm to 39 Nm. 3.2 Force analysis In this test a vertical load is applied to the upper prosthesis, constrained by a ball joint (free or locked), while the lower denture is constrained to a micro-positioner, as in figure 2a. The manual positioners are used in order to simulate the mandibular movements. 3.4 Integrated test To simulate a typical masticatory configuration, a steel sphere with radius 3 mm is placed in different position between the prostheses. 4- Results 4.1 Load cell calibration By the calibration procedure the K matrix has been derived which lead to the transfer matrix T, through K -1 P: T = T (11). 4.2 Experimental force analysis in virtual model In figure 7 the representation of the force vectors on the digitalized virtual prosthesis are shown. Points of application of the force vectors are estimated on the Fox plane of a virtual articulator. Results are obtained with the ball joint unlocked. Force vectors converge in a single location, the centre of the ball joint, as it was expected. By the analysis of the resultant force, the stability of the prosthesis can be deduced: if the force is within the alveolar ridge a stabilization effect is obtained. 4.4 Contact areas analysis In figure 8, results of the virtual contact areas analysis compared with articulation paper analysis are shown. The best correspondance is obtained with a threshold for the distance analysis equal to 0.5 mm. Reducing the value of the threshold it is possible to identify smaller contact areas (contact points) with no correspondance with articulating paper and an increasing measurement uncertainty. ViRMAN_P Copyright IDMME - Virtual Concept

5 Figure 9: Force vectors and contact areas corrisponding to local load condition with a 3 mm steel sphere. x [mm] c2.1: -2 c2.2: -1 c2.3: 1 c2.4: 2 y [mm] c3.1: -2 c3.2: -1 c3.3: 1 c3.4: 2 Figure 7: Resultant force represented in the prosthesis virtual model: a) protrusive movement, b) lateral movement. 5- Conclusion An experimental-virtual methodology for force measurement and contact area identification is proposed. In addition, some preliminary applicative examples and results for the investigation of removable complete dentures functional characterization are proposed. This methodology is being applied to the design and manufacture of a new generation of artificial teeth, based on the Neuromuscular approach in dentistry, where the accurate verification of contact requirements as well as the control of force balancing during clenching are of primary relevance. 6- Acknowledgments This research was supported by Dental Manufacturing Spa. The authors are grateful for the cooperation to: A. Caivano, M. Ferrari, M. Saraceni, R. Scola, and M. Turchetto. Figure 8: Comparison between contact areas detected by the proposed method and by articulation paper. 4.4 Integrated results In figure 9 both the resultant force relevant to experimental measurement and the contact area derived by reverse engineering techniques are shown in a common virtual reference frame, together with the digitalized denture model. The resultant force is directed through the centre of the steel sphere in contact with the occlusal surface of the molar tooth (figure 9a). The resultant force and the relevant contact areas relevant to different sphere positions are shown in figure 9b. The stability of the prosthesis can be furtherely analyzed in different mastication condition. 7- References [B1] Bakke M., Bite force and occlusion. Seminars in Orthodontics, vol.12, 2, pp , [CC1] J. P. Carey, M. Craigb, R. B. Kerstein and J. Radke, Determining a relationship between applied occlusal load and articulating paper mark area, The Open Dentistry Journal, 1, pp1-7, [FN1] Fowler N.K., Nicol A.C., A force transducer to measure individual finger loads during activities of daily living. Journal of Biomechanics, vol.32, 7, pp , [FS1] Fontijn-Tekamp F.A., Slagter A.P., Van Der Bilt A., Van 'T Hof M.A., Witter D.J., Kalk W., Jansen J.A., Biting and chewing in overdentures, full dentures, and natural dentitions. Journal of Dental Research, vol.79, 7, pp , [G1] Garg A. K., Analyzing Dental Occlusion for Implants: Tekscan s TScan III. Dental Implantology Update, vol.18, 9, pp , [H1] I. Hayakawa, Principles and practices of complete dentures creating a dental image of a denture, Quintessence Publishing Co., Ltd. Tokyo, ViRMAN_P Copyright IDMME - Virtual Concept

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