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Smart Bracket for Multi-dimensional Force and Moment Measurement
1 Department of Orthodontics, School of Dental Medicine, University of Freiburg, Hugstetter Str. 55, D-79106 Freiburg i.Br., Germany; and Correspondence: * corresponding author, bernd.lapatki{at}uniklinik-freiburg.de
Atraumatic, well-directed, and efficient tooth movement is interrelated with the therapeutic application of adequately dimensioned forces and moments in all three dimensions. The lack of appropriate monitoring tools inspired the development of an orthodontic bracket with an integrated microelectronic chip equipped with multiple piezoresistive stress sensors. Such a ‘smart bracket’ was constructed (scale of 2.5:1) and calibrated. To evaluate how accurately the integrated sensor system allowed for the quantitative determination of three-dimensional force-moment systems externally applied to the bracket, we exerted 396 different force-moment combinations with dimensions within usual therapeutic ranges (± 1.5 N and ± 15 Nmm). Comparison between the externally applied force-moment components and those reconstructed on the basis of the stress sensor signals revealed very good agreement, with standard deviations in the differences of 0.037 N and 0.985 Nmm, respectively. We conclude that our methodological approach is generally suitable for monitoring the relatively low forces and moments exerted on individual teeth with fixed orthodontic appliances.
Key Words: smart bracket • intelligent bracket • force control • fixed appliance • microsensor
The three-dimensional (3D) application of forces and moments on individual teeth with an orthodontic multibracket appliance results in a complex, statically indeterminate system (Proffit, 2000a; Burstone, 2005). Unexpected and unwanted tooth movement can easily result when an important component of the applied force-moment system is overlooked (Proffit, 2000a). Trauma of dental and periodontal tissues (Proffit, 2000b; Brezniak and Wasserstein, 2002), and possibly pain during orthodontic treatment (Bergius et al., 2000), are correlated with the magnitudes of the load therapeutically exerted on the teeth. Several recent experimental studies in humans revealed that, apart from individual predisposition as a probable main determinant, the application of heavy forces and moments must be regarded as a significant causative factor for root resorption and irreversible loss of dental hard tissue and attachment (Casa et al., 2001; Chan and Darendeliler, 2005). Despite these risks and requirements, objective monitoring of all 6 force and moment components applied to the teeth during orthodontic treatment with fixed appliances remains an unsolved methodological problem. Although several systems have been introduced for the evaluation of force-moment systems in the laboratory (Solonche et al., 1977; Bourauel et al., 1992; Menghi et al., 1999; Gunduz et al., 2003; Wichelhaus et al., 2004), only one apparatus allowing for 3D force and moment measurements in situ, i.e., on the patient, has been realized (Friedrich et al., 1998). The complex configuration of this system (consisting of separable brackets and an extra-orally supported force-moment transducer) is responsible for several significant limitations hampering clinical application: (1) the long time needed for fixation and adjustment, (2) the impossibility for force-moment systems to be determined simultaneously at several teeth, and (3) the limited measurement accuracy associated with the limited rigidity of the system itself and its support by the movable and resilient facial skin. Simpler alternative techniques for force measurements practicable in the orthodontic office (e.g., spring balances) have similar disadvantages. Moreover, they do not allow for multi-dimensional force and moment measurements. Due to the manipulation of the appliance necessary for the measurement—usually the active element (wire, loop, or elastic module) must be uncoupled from the corresponding bracket(s)—measurement bias is relatively high, and the unknown amount of friction between the wire and bracket (normally present in the non-manipulated condition) is often not taken into account (Proffit, 2000a). Previous work in the field of microelectromechanical systems has successfully demonstrated that an encapsulated microelectronic chip equipped with stress sensors can be used for the quantitative determination of externally applied loads (Sweet et al., 1999; Suhling and Jaeger, 2001; Schwizer et al., 2003). Recently, such integrated systems have consisted of multiple diffused silicon resistors distributed over the chip surface (Bartholomeyczik et al., 2005), each capable of measuring 2 different mechanical stress components by exploiting the piezoresistive effect in silicon (Smith, 1954; Tufte and Stelzer, 1963). The progress in miniaturized sensor systems engineering, together with the limitations of methods for monitoring the forces and moments exerted during orthodontic therapy, has inspired smart bracket development. In previous attempts to apply miniaturized sensors to orthodontic brackets, only a single force component was measured (Tseng et al., 2004). Our approach to brackets was aimed at the quantitative determination of the complete force-moment system exerted by the archwire via the bracket on the tooth, and was based on the hypothesis that the 6 externally applied force and moment components can be reconstructed by measurement of the mechanical stress at multiple locations within the bracket. The aim of this study was to prove the validity of our hypothesis (1) theoretically, by finite-element simulations, and (2) in practice, by constructing a bracket model (scale of 2.5:1) with an embedded microelectromechanical sensor system, and by examining whether this smart bracket model is capable of quantitatively characterizing externally applied force-moment systems of dimensions within orthodontic therapeutic ranges with sufficient resolution and accuracy.
Finite-element Model Simulations To establish the interrelationships between externally applied force or moment components and the resulting mechanical stress distributions within the bracket base theoretically, we designed a finite-element model of a bracket with an inserted (straight) orthodontic wire and an underlying (cubic) tooth crown (Fig. 1A  ), using the finite-element simulation tool ANSYS Multiphysics (ANSYS Inc., Canonsburg, PA, USA). Forces and moments in all 3 dimensions were applied to this model at the cube’s center, while both wire ends were kept fixed. The 2 in-plane stress components detectable by diffused silicon resistors, i.e., the shear stress and the difference of normal stresses (Fig. 1B), were computed for the plane of a virtual sensor chip surface (xy-plane) oriented parallel to the bracket-cube interface.
Construction of a Smart Bracket A microelectromechanical system with 32 stress sensors distributed over the chip area (providing 64 stress values in total) was developed and fabricated (Fig. 2A ). This stress sensor system was first attached to a printed circuit board, wire-bonded (Fig. 2B), and then positioned in a silicone form for the casting of an orthodontic bracket with epoxy encapsulant (Emerson & Cuming, Billerica, MA, USA). The smart bracket model (Fig. 2C) had a base of 8 x 8 mm2, and was about 2.5 times as large as a standard bracket.
Mechanical Characterization of the Smart Bracket To calibrate and test this smart bracket mechanically, we used an experimental set-up for 3D application and measurement of forces and moments in a three-bracket model, as described in detail in the APPENDIX. For calibration, the smart bracket was exposed to 56 representative force-moment combinations (load cases) between ± 1.5 N and ± 15 Nmm that approximately corresponded to therapeutically exerted loads on the teeth (Ricketts et al., 1979; Proffit, 2000a). In this calibration run, we evaluated the interrelations between the stress signals provided by the encapsulated sensor chip and the force-moment systems externally applied to the bracket monitored by the experimental set-up. To evaluate quantitatively how accurately the calibrated sensor system permits the determination of externally applied force-moment systems, we exposed the smart bracket to a second sequence of 396 load cases.
Data Evaluation and Statistical Analysis
and
respectively. The symbols sj with j = 1,...,24 denote the 24 measured sensor signals considered. The quantities aij, ai0, bij, and bi0 are fit parameters that were determined on the basis of the applied force and moment values and the sensor signals of the 56 load cases of the calibration run. We obtained the values of the fit parameters by minimizing the deviation between the applied and inferred force and moment values using least-squares fitting. We then used these fit parameter values to infer the 6 external force-moment components from the stress sensor signals acquired during the second sequence of 396 load cases. We statistically evaluated the differences between applied and inferred force and moment components by calculating their standard deviations over the 396 load cases separately for each component.
Finite-element Simulations The stress distribution on the pre-defined virtual sensor chip plane, resulting from selective application of the 6 distinct force or moment components, is shown in Fig. 1C  . The diagrams reveal that characteristic in-plane stress profiles occurred for both extractable stress components and for all 6 force and moment components.
Mechanical Experiments
In comparison, the corresponding differences between applied and inferred moment components (Fig. 4 ) were slightly larger (mainly for Mx, Fig. 4A), but were still relatively small. For the differences between applied and inferred moment values, we calculated standard deviations of 1.453 Nmm, 0.759 Nmm, and 0.742 Nmm for Mx, My, and Mz, respectively, with a mean value of 0.985 Nmm.
In this study, we explored the possibility of quantitatively determining all 6 force-moment components exerted via an orthodontic bracket on an individual tooth by means of a stress sensor system encapsulated in the bracket base. As demonstrated by the theoretical evaluations of this measurement principle by finite-element simulations, selective exertion of the 6 force-moment components on a bracket leaves unique two-dimensional "stress fingerprints" on a pre-defined plane within the bracket base. This finding suggests that externally applied 3D force-moment combinations can be identified and reconstructed by a linear superposition of a suitable set of measured stress sensor signals. The stress fingerprints obtained by the finite-element simulations also indicate optimal locations for stress sensor placement on the microsensor chip surface. The successful application of internal stress measurements for smart brackets is primarily confronted with the question, addressed in this study, as to whether currently available microsensor systems are sensitive enough to decode the stress profiles resulting from the relatively small forces and moments applied to the teeth during fixed-appliance therapy, e.g., forces and moments in the order of ± 1.5 N and ± 15 Nmm. The advanced stress sensor array chip embedded in our bracket model operates according to the so-called "spinning-current method" (Steiner et al., 1998). This method facilitates both the extraction of 2 stress components and their separation from other undesired transduction effects, such as the magnetic Hall effect and thermoelectric effects. The small standard deviations for the differences between the force-moment components applied externally and the values inferred from the stress sensor signals corroborated the hypothesis that such optimized sensor systems are indeed capable of measuring forces and moments of magnitude relevant for orthodontic therapy, with a sufficient resolution and accuracy. The reason behind the observation of slightly greater differences between applied and inferred moment components when compared with the force components must be subject to further investigation. The jagged course of the graph for the applied moment component Mx suggests that the sensor characteristics of the calibration system play a role in this respect. With regard to measurement accuracy and sensitivity, our approach to smart brackets has significant potential for further improvement. These perspectives are founded on (1) existing technical means of optimizing the stress sensor system (e.g., by using improved integrated amplifiers and analogue-digital converters), and (2) further miniaturization necessary for this principle to be applied to genuine brackets. In fact, in true-scale (i.e., smaller) brackets, forces and moments of the same magnitude act on a smaller cross-section of the bracket base. This leads to higher internal stresses, and thus higher measurement resolution can be expected. The feasibility of smart brackets demonstrated by this study is highly relevant for the field of orthodontic research and therapy and may prove to be an important milestone in the development of intelligent bracket technology. Our methodology has several advantages: (1) Simultaneous data acquisition is possible for all teeth included in the appliance; (2) all 6 components of the force-moment system can be quantitatively determined; and (3) the forces and moments are measured without manipulation of the appliance (e.g., taking out the archwire), directly at the location where the load is transmitted to the teeth. Thus, the unknown, highly variable friction between the bracket and wire (Kusy and Whitley, 1997) is accounted for, and the real load exerted on the tooth and periodontium is determined. The only forces and moments not taken into account by measurements within the bracket base are those exerted by adjacent or occluding teeth. A technique for complete monitoring of force-moment systems applied to individual teeth offers attractive perspectives in several respects. First, smart brackets would be highly useful tools for fundamental research, e.g., for experimental studies on tooth movement and for verifying biomechanical theories. Smart bracket systems could also prove to be valuable feedback tools for the education and further training of orthodontists. In this manner, the experience that the clinician needs to move teeth efficiently and with fewer side-effects could be acquired interactively and with objective control. The most attractive perspective is related to the method’s potential for clinical application. So far, orthodontists have had to rely substantially on their experience, feeling, and the properties of the wire material. Fixed-appliance therapy has undoubtedly benefited greatly from the development and introduction of innovative materials such as super-elastic wires. However, the use of even such advanced materials does not fully prevent the clinician from applying excessive forces and moments to the teeth, as has recently been confirmed (Fuck and Drescher, 2006). In conclusion, we have demonstrated, in an enlarged smart bracket model, that quantitative characterization of force-moment systems of dimensions within customary orthodontic therapeutic ranges is possible on the basis of in-plane stress measurements within the bracket base. From a short-term perspective, true-scale smart brackets with wire-mediated data and energy transmission seem already feasible with available technologies. Biomechanical research and the education of orthodontists could benefit significantly from such smart bracket versions. We believe that clinical therapy with intelligent multi-bracket systems has future prospects once the technical challenges concerning telemetric communication and energy transmission have been overcome. Significant contributions can be expected in that respect from parallel research in the fields of wireless sensor networks and telemetry-powered microelectromechanical systems. The future clinical application of smart brackets—for instance, in teeth or tooth segments requiring movements with a high predisposition for root resorption, or requiring complicated force systems—may contribute to reducing the negative side-effects of fixed-appliance therapy and increase therapeutic efficiency.
The authors gratefully acknowledge the technical support provided by J. Joos and J. Haefner. The set-up of the system used for calibration of the smart bracket was financially supported by the Deutsche Gesellschaft für Kieferorthopädie (Germany). All other financial support for this project was provided by the University of Freiburg (Germany). A preliminary report was presented at the IEEE MEMS Conference 2006, Istanbul, Turkey.
A supplemental appendix to this article is published electronically only at http://www.dentalresearch.org. Received for publication May 16, 2006. Revision received September 29, 2006. Accepted for publication October 5, 2006.
Journal of Dental Research, Vol. 86, No. 1,
73-78 (2007)
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ABSTRACT
INTRODUCTION
xy and normal stress difference 
