INTRODUCTION

The three-dimensional (3D) application of forces and moments onindividual 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 animportant 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 orthodontictreatment (Bergius et al., 2000), are correlated with the magnitudes of theload therapeutically exerted on the teeth. Several recent experimental studiesin humans revealed that, apart from individual predisposition as a probablemain determinant, the application of heavy forces and moments must beregarded as a significant causative factor for root resorption and irreversibleloss of dental hard tissue and attachment (Casa et al., 2001; Chan andDarendeliler, 2005).

Despite these risks and requirements, objective monitoring of all 6force and moment components applied to the teeth during orthodontictreatment with fixed appliances remains an unsolved methodologicalproblem. Although several systems have been introduced for the evaluationof force-moment systems in the laboratory (Solonche et al., 1977; Bourauelet al., 1992; Menghi et al., 1999; Gunduz et al., 2003; Wichelhaus et al.,2004), only one apparatus allowing for 3D force and momentmeasurements in situ, i.e., on the patient, has been realized (Friedrich et al.,1998). The complex configuration of this system (consisting of separablebrackets and an extra-orally supported force-moment transducer) isresponsible for several significant limitations hampering clinicalapplication: (1) the long time needed for fixation and adjustment, (2) theimpossibility for force-moment systems to be determined simultaneously atseveral teeth, and (3) the limited measurement accuracy associated with thelimited rigidity of the system itself and its support by the movable andresilient facial skin. Simpler alternative techniques for force measurementspracticable in the orthodontic office (e.g., spring balances) have similardisadvantages. Moreover, they do not allow for multi-dimensional forceand moment measurements. Due to the manipulation of the appliancenecessary for the measurement—usually the active element (wire, loop, orelastic module) must be uncoupled from the corresponding bracket(s)—measurement bias is relatively high, and the unknown amount of frictionbetween the wire and bracket (normally present in the non-manipulatedcondition) is often not taken into account (Proffit, 2000a).

Previous work in the field of microelectromechanical systems hassuccessfully demonstrated that an encapsulated microelectronic chipequipped with stress sensors can be used for the quantitative determinationof externally applied loads (Sweet et al., 1999; Suhling and Jaeger, 2001;Schwizer et al., 2003). Recently, such integrated systems have consisted ofmultiple diffused silicon resistors distributed over the chip surface(Bartholomeyczik et al., 2005), each capable of measuring 2 different

ABSTRACTAtraumatic, well-directed, and efficient toothmovement is interrelated with the therapeuticapplication of adequately dimensioned forces andmoments in all three dimensions. The lack ofappropriate monitoring tools inspired thedevelopment of an orthodontic bracket with anintegrated microelectronic chip equipped withmultiple piezoresistive stress sensors. Such a'smart bracket' was constructed (scale of 2.5:1)and calibrated. To evaluate how accurately theintegrated sensor system allowed for thequantitative determination of three-dimensionalforce-moment systems externally applied to thebracket, we exerted 396 different force-momentcombinations with dimensions within usualtherapeutic ranges (± 1.5 N and ± 15 Nmm).Comparison between the externally applied force-moment components and those reconstructed onthe basis of the stress sensor signals revealed verygood agreement, with standard deviations in thedifferences of 0.037 N and 0.985 Nmm,respectively. We conclude that our methodologicalapproach is generally suitable for monitoring therelatively low forces and moments exerted onindividual teeth with fixed orthodontic appliances.

KEY WORDS: smart bracket, intelligent bracket,force control, fixed appliance, microsensor.

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

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

Smart Bracket for Multi-dimensional Force and Moment Measurement

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

1Department of Orthodontics, School of Dental Medicine,University of Freiburg, Hugstetter Str. 55, D-79106Freiburg i.Br., Germany; and 2Department of MicrosystemsEngineering (IMTEK), University of Freiburg, Germany;*corresponding author, bernd.lapatki@uniklinik-freiburg.de

J Dent Res 86(1):73-78, 2007

RESEARCH REPORTSBiomaterials & Bioengineering

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mechanical stress components by exploiting the piezoresistiveeffect in silicon (Smith, 1954; Tufte and Stelzer, 1963).

The progress in miniaturized sensor systems engineering,together with the limitations of methods for monitoring theforces and moments exerted during orthodontic therapy, hasinspired smart bracket development. In previous attempts toapply miniaturized sensors to orthodontic brackets, only asingle force component was measured (Tseng et al., 2004). Ourapproach to brackets was aimed at the quantitativedetermination of the complete force-moment system exerted bythe archwire via the bracket on the tooth, and was based on thehypothesis that the 6 externally applied force and momentcomponents can be reconstructed by measurement of themechanical stress at multiple locations within the bracket.

The aim of this study was to prove the validity of ourhypothesis (1) theoretically, by finite-element simulations, and

(2) in practice, by constructing abracket model (scale of 2.5:1) withan embedded microelectro-mechanical sensor system, and byexamining whether this smartbracket model is capable of quan-titatively characterizing externallyapplied force-moment systems ofdimensions within orthodontictherapeutic ranges with sufficientresolution and accuracy.

MATERIALS & METHODS

Finite-element ModelSimulationsTo establish the interrelationshipsbetween externally applied force ormoment components and theresulting mechanical stressdistributions within the bracket basetheoretically, we designed a finite-element model of a bracket with aninserted (straight) orthodontic wireand an underlying (cubic) toothcrown (Fig. 1A), using the finite-element simulation tool ANSYSMultiphysics (ANSYS Inc.,Canonsburg, PA, USA). Forces andmoments in all 3 dimensions wereapplied to this model at the cube'scenter, while both wire ends werekept fixed. The 2 in-plane stresscomponents detectable by diffusedsilicon resistors, i.e., the shear stressand the difference of normal stresses(Fig. 1B), were computed for theplane of a virtual sensor chip surface(xy-plane) oriented parallel to thebracket-cube interface.

Construction of a Smart BracketA microelectromechanical systemwith 32 stress sensors distributedover the chip area (providing 64

stress values in total) was developed and fabricated (Fig. 2A). Thisstress sensor system was first attached to a printed circuit board,wire-bonded (Fig. 2B), and then positioned in a silicone form forthe casting of an orthodontic bracket with epoxy encapsulant(Emerson & Cuming, Billerica, MA, USA). The smart bracketmodel (Fig. 2C) had a base of 8 x 8 mm2, and was about 2.5 timesas large as a standard bracket.

Mechanical Characterization of the Smart BracketTo calibrate and test this smart bracket mechanically, we used anexperimental set-up for 3D application and measurement of forcesand moments in a three-bracket model, as described in detail in theAPPENDIX.

For calibration, the smart bracket was exposed to 56representative force-moment combinations (load cases) between ±1.5 N and ± 15 Nmm that approximately corresponded to

Figure 1. Numerically simulated stress distributions within an orthodontic bracket resulting from 3D forceand moment application. (A) Finite-element model of an orthodontic bracket with inserted wire andunderlying (cubic) tooth crown. The model was constructed with 87,253 elements (ANSYS element Solid92) leading to a total number of 126,673 nodes. These tetrahedral structural elements having 10degrees of freedom are highly suitable for structural mechanical simulations. The model was selectivelyloaded at the cube's center with the 6 force and moment components by exertion of adequate couples offorces 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 (shearstress �xy and normal stress difference �xx-�yy) extractable from piezoresistive microsensors positionedin the xy-plane. Grey: Unloaded form. Black: Forces and resulting deformations. (C) Shear and normalstress fingerprints in the xy-plane, resulting from selective application of each of the 6 force or momentcomponents. Red: Positive stress. Blue: Negative stress.

J Dent Res 86(1) 2007 Smart Orthodontic Bracket 75

therapeutically exerted loads on the teeth (Ricketts et al., 1979;Proffit, 2000a). In this calibration run, we evaluated theinterrelations between the stress signals provided by theencapsulated sensor chip and the force-moment systems externallyapplied to the bracket monitored by the experimental set-up.

To evaluate quantitatively how accurately the calibratedsensor system permits the determination of externally appliedforce-moment systems, we exposed the smart bracket to a secondsequence of 396 load cases.

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

Fi = �24j =1 aijsj + ai0

and

Mi = �24j =1 bijsj + bi0,

respectively. The symbols sj with j = 1,...,24 denote the 24measured sensor signals considered. The quantities aij, ai0, bij, andbi0 are fit parameters that were determined on the basis of theapplied force and moment values and the sensor signals of the 56load cases of the calibration run. We obtained the values of the fitparameters by minimizing the deviation between the applied andinferred force and moment values using least-squares fitting.

We then used these fit parameter values to infer the 6 externalforce-moment components from the stress sensor signals acquiredduring the second sequence of 396 load cases. We statisticallyevaluated the differences between applied and inferred force andmoment components by calculating their standard deviations overthe 396 load cases separately for each component.

RESULTS

Finite-element SimulationsThe stress distribution on the pre-defined virtual sensor chipplane, resulting from selective application of the 6 distinctforce or moment components, is shown in Fig. 1C. Thediagrams reveal that characteristic in-plane stress profilesoccurred for both extractable stress components and for all 6force and moment components.

Mechanical ExperimentsThe comparison of the applied force components with the forcecomponents inferred from the stress sensor signals showedexcellent agreement (Fig. 3). The standard deviations for thedifferences 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.

In comparison, the corresponding differences betweenapplied and inferred moment components (Fig. 4) were slightlylarger (mainly for Mx, Fig. 4A), but were still relatively small.For the differences between applied and inferred momentvalues, we calculated standard deviations of 1.453 Nmm, 0.759Nmm, and 0.742 Nmm for Mx, My, and Mz, respectively, with amean value of 0.985 Nmm.

DISCUSSIONIn this study, we explored the possibility of quantitativelydetermining all 6 force-moment components exerted via anorthodontic bracket on an individual tooth by means of a stresssensor system encapsulated in the bracket base. Asdemonstrated by the theoretical evaluations of thismeasurement principle by finite-element simulations, selectiveexertion of the 6 force-moment components on a bracket leavesunique two-dimensional "stress fingerprints" on a pre-definedplane within the bracket base. This finding suggests thatexternally applied 3D force-moment combinations can beidentified and reconstructed by a linear superposition of asuitable set of measured stress sensor signals. The stressfingerprints obtained by the finite-element simulations also

Figure 2. Microsystem chip before and after encapsulation into a smartbracket. (A) (left) Micrograph of the sensor chip (used for construction ofthe smart bracket) with 32 stress sensors distributed over the chip area,analogue signal conditioning, and digital control unit. Center: sensorelement with switches. Right: octagonal sensor with 8 contacts allowingfor 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 8mm2 (scale of approximately 2.5:1 compared with normal bracket size).For the mechanical experiments, the archwire was adhesively attached.

76 Lapatki et al. J Dent Res 86(1) 2007

indicate optimal locations for stress sensor placement on themicrosensor chip surface.

The successful application of internal stress measurementsfor 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 stressprofiles resulting from the relatively small forces and momentsapplied to the teeth during fixed-appliance therapy, e.g., forcesand moments in the order of ± 1.5 N and ± 15 Nmm. Theadvanced stress sensor array chip embedded in our bracket

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

Figure 4. Comparison between applied moment components Mx, My,and Mz and corresponding values inferred from the stress sensor signalsfor 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 (redtriangles) were inferred from the 24 most relevant sensor signals.

J Dent Res 86(1) 2007 Smart Orthodontic Bracket 77

model operates according to the so-called "spinning-currentmethod" (Steiner et al., 1998). This method facilitates both theextraction of 2 stress components and their separation fromother undesired transduction effects, such as the magnetic Halleffect and thermoelectric effects. The small standard deviationsfor the differences between the force-moment componentsapplied externally and the values inferred from the stress sensorsignals corroborated the hypothesis that such optimized sensorsystems are indeed capable of measuring forces and momentsof magnitude relevant for orthodontic therapy, with a sufficientresolution and accuracy. The reason behind the observation ofslightly greater differences between applied and inferredmoment components when compared with the forcecomponents must be subject to further investigation. Thejagged course of the graph for the applied moment componentMx suggests that the sensor characteristics of the calibrationsystem play a role in this respect. With regard to measurementaccuracy and sensitivity, our approach to smart brackets hassignificant potential for further improvement. Theseperspectives are founded on (1) existing technical means ofoptimizing the stress sensor system (e.g., by using improvedintegrated amplifiers and analogue-digital converters), and (2)further miniaturization necessary for this principle to be appliedto genuine brackets. In fact, in true-scale (i.e., smaller)brackets, forces and moments of the same magnitude act on asmaller cross-section of the bracket base. This leads to higherinternal stresses, and thus higher measurement resolution canbe expected.

The feasibility of smart brackets demonstrated by this studyis highly relevant for the field of orthodontic research andtherapy and may prove to be an important milestone in thedevelopment of intelligent bracket technology. Ourmethodology has several advantages: (1) Simultaneous dataacquisition is possible for all teeth included in the appliance;(2) all 6 components of the force-moment system can bequantitatively determined; and (3) the forces and moments aremeasured without manipulation of the appliance (e.g., takingout the archwire), directly at the location where the load istransmitted to the teeth. Thus, the unknown, highly variablefriction between the bracket and wire (Kusy and Whitley,1997) is accounted for, and the real load exerted on the toothand periodontium is determined. The only forces and momentsnot taken into account by measurements within the bracket baseare those exerted by adjacent or occluding teeth.

A technique for complete monitoring of force-momentsystems applied to individual teeth offers attractiveperspectives in several respects. First, smart brackets would behighly useful tools for fundamental research, e.g., forexperimental studies on tooth movement and for verifyingbiomechanical theories. Smart bracket systems could alsoprove to be valuable feedback tools for the education andfurther training of orthodontists. In this manner, the experiencethat the clinician needs to move teeth efficiently and with fewerside-effects could be acquired interactively and with objectivecontrol. The most attractive perspective is related to themethod's potential for clinical application. So far, orthodontistshave had to rely substantially on their experience, feeling, andthe properties of the wire material. Fixed-appliance therapy hasundoubtedly benefited greatly from the development andintroduction 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 andmoments to the teeth, as has recently been confirmed (Fuck andDrescher, 2006).

In conclusion, we have demonstrated, in an enlarged smartbracket model, that quantitative characterization of force-moment systems of dimensions within customary orthodontictherapeutic ranges is possible on the basis of in-plane stressmeasurements within the bracket base. From a short-termperspective, true-scale smart brackets with wire-mediated dataand energy transmission seem already feasible with availabletechnologies. Biomechanical research and the education oforthodontists could benefit significantly from such smartbracket versions. We believe that clinical therapy withintelligent multi-bracket systems has future prospects once thetechnical challenges concerning telemetric communication andenergy transmission have been overcome. Significantcontributions can be expected in that respect from parallelresearch in the fields of wireless sensor networks andtelemetry-powered microelectromechanical systems. The futureclinical application of smart brackets—for instance, in teeth ortooth segments requiring movements with a high predispositionfor root resorption, or requiring complicated force systems—may contribute to reducing the negative side-effects of fixed-appliance therapy and increase therapeutic efficiency.

ACKNOWLEDGMENTSThe authors gratefully acknowledge the technical supportprovided by J. Joos and J. Haefner. The set-up of the systemused for calibration of the smart bracket was financiallysupported by the Deutsche Gesellschaft für Kieferorthopädie(Germany). All other financial support for this project wasprovided by the University of Freiburg (Germany). Apreliminary report was presented at the IEEE MEMSConference 2006, Istanbul, Turkey.

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