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J Dent Res 86(1):73-78, 2007
© 2007 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Smart Bracket for Multi-dimensional Force and Moment Measurement

B.G. Lapatki1,*, J. Bartholomeyczik2, P. Ruther2, I.E. Jonas1, and O. Paul2

1 Department of Orthodontics, School of Dental Medicine, University of Freiburg, Hugstetter Str. 55, D-79106 Freiburg i.Br., Germany; and
2 Department of Microsystems Engineering (IMTEK), University of Freiburg, Germany

* corresponding author, bernd.lapatki{at}uniklinik-freiburg.de


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
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. 1AGo), 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. 1BGo), were computed for the plane of a virtual sensor chip surface (xy-plane) oriented parallel to the bracket-cube interface.


Figure 1
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  		Figure 1. Numerically simulated stress distributions within an orthodontic bracket resulting from 3D force and moment application. (A) Finite-element model of an orthodontic bracket with inserted wire and underlying (cubic) tooth crown. The model was constructed with 87,253 elements (ANSYS element Solid 92) leading to a total number of 126,673 nodes. These tetrahedral structural elements having 10 degrees of freedom are highly suitable for structural mechanical simulations. The model was selectively loaded at the cube’s center with the 6 force and moment components by exertion of adequate couples of forces with equal or opposite directions on opposing cube surfaces, while keeping both wire ends fixed. Black arrows: spatial orientation of the x, y, and z axes. (B) Illustration of the 2 stress components (shear stress {sigma}xy and normal stress difference {sigma}xx-{sigma}yy) extractable from piezoresistive microsensors positioned in the xy-plane. Grey: Unloaded form. Black: Forces and resulting deformations. (C) Shear and normal stress fingerprints in the xy-plane, resulting from selective application of each of the 6 force or moment components. Red: Positive stress. Blue: Negative stress.

 
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. 2AGo). This stress sensor system was first attached to a printed circuit board, wire-bonded (Fig. 2BGo), 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. 2CGo) had a base of 8 x 8 mm2, and was about 2.5 times as large as a standard bracket.


Figure 2
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  		Figure 2. Microsystem chip before and after encapsulation into a smart bracket. (A) (left) Micrograph of the sensor chip (used for construction of the smart bracket) with 32 stress sensors distributed over the chip area, analogue signal conditioning, and digital control unit. Center: sensor element with switches. Right: octagonal sensor with 8 contacts allowing for application of the spinning-current method. (B) Schematic illustration (cross-section) of the smart bracket model. The sensor chip was wire-bonded to a printed circuit board and encapsulated in a plastic bracket. (C) Photograph of the manufactured smart bracket with a base of 8 x 8 mm2 (scale of approximately 2.5:1 compared with normal bracket size). For the mechanical experiments, the archwire was adhesively attached.

 
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
The interrelation between the stress sensor signals and the 6 force and moment components externally applied to the smart bracket model can be mathematically described in a response matrix. Theoretically, the rank of this matrix is 6 even if only 3 sensors providing 2 stress components each are used. However, a stress sensor system providing a larger number of stress sensor signals (i.e., an over-determined system) results in a more accurate estimation of the externally applied force-moment components. Numerical experiments showed that a selection of 24 (out of the 64 available) stress sensor signals was sufficient to establish accurate agreement between externally applied and reconstructed force-moment combinations. The inclusion of additional stress sensor signals led to no further significant improvement. Thus, the externally applied force components Fi and moment components Mi with i = x, y, z can be written as


Formula

and


Formula

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.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
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. 1CGo. 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
The comparison of the applied force components with the force components inferred from the stress sensor signals showed excellent agreement (Fig. 3Go). The standard deviations for the differences between applied and inferred forces were 0.045 N, 0.032 N, and 0.034 N for the 3 components Fx, Fy, and Fz, respectively, with a mean value of 0.037 N.


Figure 3
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  		Figure 3. Comparison of applied force components Fx, Fy, and Fz and corresponding values inferred from the stress sensor signals for the second sequence of 396 load cases. (A) Component Fx. (B) Component Fy. (C) Component Fz. Applied force values (blue line) were registered by the calibration system. Smart bracket values (red triangles) were inferred from the 24 most relevant sensor signals.

 
In comparison, the corresponding differences between applied and inferred moment components (Fig. 4Go) were slightly larger (mainly for Mx, Fig. 4AGo), 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.


Figure 4
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  		Figure 4. Comparison between applied moment components Mx, My, and Mz and corresponding values inferred from the stress sensor signals for the second sequence of 396 load cases. (A) Component Mx. (B) Component My. (C) Component Mz. Applied moment values (blue line) were registered by the calibration system. Smart bracket values (red triangles) were inferred from the 24 most relevant sensor signals.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
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.


   ACKNOWLEDGMENTS
 
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.


   FOOTNOTES
 
A supplemental appendix to this article is published electronically only at http://www.dentalresearch.org.

Received May 16, 2006; Last revision September 29, 2006; Accepted October 5, 2006


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 DISCUSSION
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This Article
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