ORIGINAL ARTICLE

Influence of the expansion screw height onthe dental effects of the hyrax expander:A study with finite elements

Rafael Marques de Sousa Araugio,a J�anes Landre, Jr,b Diana de Lourdes Almeida Silva,c Wellington Pacheco,d

Matheus Melo Pithon,e and Dauro Douglas Oliveiraf

Belo Horizonte, Minas Gerais, and Jequi�e, Bahia, Brazil

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Introduction:Our objective was to evaluate the influence of the expansion screw height of a hyrax expander onthe degree of dental inclination during rapid maxillary expansion by using the finite element method. Methods:The hyrax expander and the maxillary arch were modeled by using Solidworks software (Dassault Syst�emes,Paris, France). Three distinct finite element method models were created by simulating different screw heightsrelative to the plane that intersected the center of resistance of the maxillary first molars. These 3 relative posi-tions were 10 mm below the maxillary first molars’ center of resistance, at the same level as the maxillary firstmolars’ center of resistance, and 10 mm above the maxillary first molars’ center of resistance. The initial activa-tion of the expanders was simulated, and tooth displacements for each finite element method model were reg-istered in the buccolingual, corono-apical, and mesiodistal directions. Results: The simulations tested showedthat the 3 hyrax screw heights had different dental tipping tendencies. When the screw was simulated below themaxillary first molars’ center of resistance, buccal tipping of the crowns and lingual tipping of the roots were reg-istered. This tendency decreased when the screw was simulated at the same level as the maxillary first molars’center of resistance. However, when the screw was simulated above the maxillary first molars’ center of resis-tance, the tipping tendency was inverted, with the crowns displaying lingual tipping and the roots displaying buc-cal tipping. Conclusions: These findings might explain the importance of carefully planning the height of thehyrax expander screw, since, depending on this position, different tooth movements can be achieved. Froman orthopedic perspective, the ideal screw position might be slightly above the maxillary first molars’ center ofresistance; this would generate less dental tipping. (Am J Orthod Dentofacial Orthop 2013;143:221-7)

Studies performed since the 1950s have proven theviability of rapid maxillary expansion (RME) and itscapacity to aid in the treatment of posterior cross-

te practice, and former orthodontic resident, Pontifical Catholic Universitynas Gerais, Belo Horizonte, Brazil.ciate professor, School of Engineering, Pontifical Catholic University ofGerais, Belo Horizonte, Minas Gerais, Brazil.er undergraduate student, Mechanical Engineer, School of Engineering,cal Catholic University ofMinas Gerais, Belo Horizonte, Minas Gerais, Brazil.nct professor, Department of Orthodontics, Pontifical Catholic University ofGerais, Belo Horizonte, Minas Gerais, Brazil.ssor, Department of Orthodontics, Southwest Bahia State University, Jequi�e,, Brazil.am director, Department of Orthodontics, Pontifical Catholic University ofGerais, Belo Horizonte, Minas Gerais, Brazil.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.spondence to: Dauro Douglas Oliveira, P�os-graduac~ao em Odontologia,f�ıcia Universidade Cat�olica de Minas Gerais, Avenida Dom Jos�e Gaspar,Pr�edio 46, sala 106, Belo Horizonte, MG 30535-610, Brazil; e-mail,.bhe@gmail.com.itted, June 2012; revised and accepted, September 2012.5406/$36.00ight � 2013 by the American Association of Orthodontists./dx.doi.org/10.1016/j.ajodo.2012.09.016

bites, especially in patients with maxillary arch constric-tion.1-5 Various studies have analyzed the effects of RMEon the maxilla and its adjacent structures,1-4,6,7 as well asthe forces exerted by the rapid maxillary expanders.8,9

Several authors have stressed the importance of opti-mizing the orthopedic effects of RME. Buccal inclinationof the posterior teeth is an undesired side effect thatmight limit the amount of orthopedic expansion ob-tained.7,10 Sometimes, RME must be prematurelyinterrupted to prevent a posterior buccal crossbitewithout achieving adequate orthopedic correction ofthe transverse deficiency. Although RME has beenwidely used in orthodontics for several decades, westill need to better understand its effects and toimprove the control of its undesired side effects.

The use of the finite element method is an establishedand important research tool in dentistry. The finite ele-ment method has recently been used to analyze the ef-fects of RME on the teeth and craniofacial bones.11-13

Undoubtedly, a major advantage of this researchmethod in the health care field is the possibility of

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Fig 1. Hyrax expander closely fit to the molars and pre-molars, simulating the horizontal restriction of the move-ment that would be imposed by bands on the first molars.

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simulating different treatment approaches withoutexposing animals or humans to any adverse effects ofexperimental ideas and procedures.14

Hyrax and Haas appliances are the 2 rapid maxillaryexpanders mostly used in orthodontics. Although bothexpanders generate similar orthopedic effects, many or-thodontists prefer to use the hyrax expander because itfacilitates the patient’s oral hygiene compared with theHaas expander.9,15

Various studies have analyzed the stresses and strainsimposed on the craniofacial complex by RME.11-13

However, at present, no studies in the literature haveresearched the influence of the position of theexpansion screw on the orthodontic and orthopedicresponses to RME. Therefore, the purposes of this studywere to use the finite element method to simulatedifferent hyrax screw heights and to evaluate theirinfluence over posterior tooth inclination during RME.

MATERIAL AND METHODS

The construction of the 3-dimensional finite elementmethod model was initiated by using 2-mm sections ofamultiplanar computerized tomography scan of a youngadult with a complete permanent dentition, except forthe third molars. Our research protocol was approvedby the ethics research committee of the Pontifical Cath-olic University of Minas Gerais in Brazil.

A total of 195 computerized tomography images (2-dimensional) were stacked with the computer designsoftware Solidworks with the Simulation package (Das-sault Syst�emes, Paris, France) to accurately develop the3-dimensional model. During the development of thismodel, the maxilla and the teeth were built indepen-dently and considered to be independent parts with uni-form mechanical properties. The maxillary graphicreproduction was made without considering the maxil-lary sinus because its anatomic variations would signif-icantly increase the drawing complexity. In addition, themaxilla was drawn up to an upper horizontal limit de-fined by a plane passing through the anterior nasal spineand the external acoustic meatus on both sides. After allbony structures were graphically represented, each of the14 teeth was drawn separately, with no differentiationbetween enamel, dentin, or pulp, and with each toothconsidered an independent part.

Once the maxilla and the teeth were created, the hy-rax expansion screw was modeled in Solidworks basedon the measurements of the Palex Mini-12 expansionscrew (Dentaurum, Newtown, Pa). The modeled appara-tus featured an expansion screw and 2 segments of steelwire that were 0.9 mm in diameter, following the lingualcontour of the crowns of the maxillary first and secondpremolars and the first and second molars (Fig 1).

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Three distinct finite element method models werecreated, with different heights of the screw relative tothe plane that intersected the center of resistance ofthe maxillary first molars defined by the furcal regionof these 2 teeth (Fig 2). The first model (FEM 1) hadthe screw positioned in a plane parallel to the occlusalplane that intersected the crowns of the maxillary teethin the center of their crown, 10 mm below the maxillaryfirst molars’ center of resistance. The secondmodel (FEM2) had the screw simulated at a higher and intermediateposition that was coincident with the plane that inter-sected the maxillary first molars’ center of resistance.The final model (FEM 3) simulated the screw closer tothe palate, 10 mm above the maxillary first molars’ cen-ter of resistance (Fig 2).

The frame of the expansion screw was substituted fora frame with a rectangular section. Since a goal of thisstudy was to evaluate the inclinations of the premolarsand molars, soft elements were incorporated into thebuccal surfaces of the roots of these teeth.

For all 3 models, the materials of both the teeth andthe expander were defined. The teeth were considered tohave isotropic properties, with an elastic modulus of21,400 MPa and a Poisson coefficient of 0.31. The ex-pander was defined with the properties of AISI 304 steelfrom the database of the SolidWorks software, with anelastic modulus of 190,000 MPa and a Poisson coeffi-cient of 0.29. Elastic supports were incorporated intothe buccal surfaces of the roots of the teeth, with anelastic constant of 1 3 106 (N/m)/m2. A force of 1 Nwas applied in a direction normal to the medial surfaceof the body of the apparatus. The values used for theelastic and force constants were standardized across all3 configurations.

The elastic constant is a way of simulating the resis-tance to the displacement caused by the labial boneplate. Because there is no value for this resistance inthe literature, a standard value was arbitrarily selected.

Journal of Orthodontics and Dentofacial Orthopedics

Fig 2. Expander apparatus: A, lowest position, screwsimulated in a plane parallel to the occlusal plane at thecenter of the maxillary teeth and 10 mm below the maxil-lary first molars’ center of resistance; B, intermediate po-sition, screw parallel to the occlusal plane at the samelevel as the maxillary first molars’ center of resistance;C, the highest position, with the screw closest to the pal-ate, 10 mm above the maxillary first molars’ center of re-sistance.

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Since this value was not real, the magnitude of the forceis relatively unimportant, because this magnitude hasbeen standardized based on our assumed resistancevalue. Therefore, for the 3 models, meshes were gener-ated with elements measuring 2 mm with a toleranceof 0.1 mm. Static studies were performed, and the toothdisplacements for each of the 3 models were registeredin the buccolingual (x-axis), corono-apical (y-axis),and mesiodistal (z-axis) directions.

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RESULTS

The number of elements and nodes of the mesh foreach finite element method model differed because ofthe different lengths of the screw arms. The modelwith the lowest configuration (FEM 1) contained11,378 elements and 19,299 nodes. The model withthe intermediate screw position (FEM 2) generated11,417 elements and 19,414 nodes. The expander simu-lated with the highest screw position (FEM 3) had a meshwith 11,616 elements and 19,761 nodes.

In FEM 1, the crowns of the premolars and molarsshowed buccal displacements that gradually decreasedin the apical-cervical direction. The roots exhibited lin-gual displacements.

In FEM 2, the crowns of the 4 teeth had displace-ments in the buccal direction that gradually decreasedin the apical-cervical direction. Only the apices of theroots had lingual displacements. The tooth displace-ments from this configuration were smaller than thoseregistered in FEM 1.

In FEM 3, the tooth crowns displayed displacementsin the lingual direction that gradually decreased in theapical-cervical direction. All roots exhibited buccal dis-placements (Fig 3).

In FEM 1, displacement in the apical-cervical direc-tion was identified for the 4 teeth examined, indicatinga tendency toward intrusion.

In FEM 2, there were displacements in the apical-cervical direction of the 4 teeth, indicating a tendencytoward intrusion. However, the magnitude of this intru-sion tendency was smaller than that registered in FEM 1.

Conversely, in FEM 3, displacement in the coronaldirection was identified in the 4 teeth, indicating a ten-dency toward extrusion (Fig 4).

In FEM 1, the crowns of the 4 teeth had displace-ments in the mesial direction that gradually decreasedin the apical-cervical direction. The roots exhibited distaldisplacements.

In FEM 2, the crowns of the 4 teeth showed mesialdisplacements that gradually decreased in the apical-cervical direction. The roots exhibited distal displace-ments. The magnitude of these displacements wassmaller than those noted in FEM 1.

In FEM 3, the crowns of the 4 teeth had displace-ments in the distal direction that gradually decreasedin the apical-cervical direction. The roots exhibitedmesial displacements (Fig 5).

To better visualize the differences in the displace-ments for each of the 3 hyrax expander configurations,a Sonda tool (Dassault Syst�emes) was used tomark pointsalong the edges of each tooth in each finite elementmethod model. Thus, points were marked on the buccal

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Fig 3. Displacement in the buccolingual direction. Ineach image of this figure, positive values are representedby warm colors and indicate displacement in the buccaldirection; negative values are represented by cold colorsand indicate displacements in the lingual direction. How-ever, the scale of displacement magnitudes varies be-tween the different images, as does the relative positionand color of zero displacement. A, In FEM 1, zero dis-placement is represented by green; B, in FEM 2, zero isrendered in blue, close to the apices of the roots; C, inFEM 3, zero displacement is represented by green.

Fig 4. Displacement in the corono-apical direction. Ineach image of this figure, positive values are representedbywarm colors and indicate displacement in the apical di-rection; negative values are represented by cold colorsand indicate displacements in the occlusal direction.However, the scale of displacement magnitudes variesgreatly between the various images. A, FEM 1; B, FEM2; C, FEM 3.

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sides of the premolars and molars, and along the edgesthat had previously been defined along the long axesof these elements. For each point, or node, the Sondatool provided the corresponding displacement. Afterobtaining these points, comparative graphs of displace-ment were generated in the buccolingual direction ofeach tooth for the finite element method model (Fig 6).

The graphs of the 4 teeth illustrate the tendency to-ward crown tipping in the buccal direction for FEM 1and FEM 2, and in the lingual direction for FEM 3.

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However, FEM 2 had a tendency toward homogenousdisplacement, indicating that constructing the hyrax ex-pander with the screw positioned slightly higher than themaxillary first molars’ center of resistance might mini-mize dental tipping.

DISCUSSION

Although the viability of RME has been proven and itseffects have been studied over the last decades, the searchfor ways to improve RME efficiency continues. The finiteelement method has been successfully used to evaluatethe forces and deformations imposed on teeth and

Journal of Orthodontics and Dentofacial Orthopedics

Fig 5. Displacement in the mesiodistal direction. In eachimage of this figure, positive values are represented bywarm colors and indicate displacements in the mesial di-rection; negative values are represented by cool colorsand indicate displacements in the distal direction. How-ever, the scale of displacement magnitudes varies greatlybetween the various images. A zero value is representedby green for all parts of this figure, although the precisetint of this shade varies among the different figure parts.A, FEM 1; B, FEM 2; C, FEM 3.

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craniofacial bones when RME is performed.11,13,16,17

However, no study in the literature has examined theinfluence of the expansion screw’s position on theorthodontic and orthopedic responses of RME.

The simulations we performed in this study evaluatedthe initial effects of RME with the hyrax expander. Theinfluence of the hyrax screw’s height relative to the pal-ate was evaluated by assessing the displacements on themaxillary teeth used to anchor the expander.

This study proposal is validated by the importance totry to improve current RME appliances to maximize their

American Journal of Orthodontics and Dentofacial Orthoped

orthopedic effects and minimize their undesired sideeffects, such as buccal crown tipping, a long-standingconcern found in the dental literature.7,10 Animportant limiting factor of RME is the transverserelationship between the posterior maxillary andmandibular teeth. The activation of the expansionscrew must be interrupted before a posterior buccalcrossbite occurs.15 Thus, the greater the dental tipping,the smaller the orthopedic gain obtained from the sepa-ration of the midpalatal suture.

During RME, there is a tendency toward buccal crowntipping of the premolars and molars18,19 and alveolarbone folding also in the buccal direction.20 Bassarelliet al19 found a positive correlation between the amountof palatal expansion and the magnitude of buccalcrown tipping of the posterior teeth. These findingsare reinforced by the results of our study for the modelsimulating the hyrax screw below the maxillary firstmolars’ center of resistance (FEM 1). However, the re-sults of the intermediate (FEM 2) and higher (FEM 3)configurations indicated that it might be possible to re-duce the dental tipping tendency when the height of thehyrax expansion screw is properly chosen.

Bassarelli et al19 did not identify an increase in theheight of the crowns of the maxillary teeth duringRME. Reed et al,21 however, reported extrusion of themolars with banded and bonded expanders. In our study,tooth displacements in the corono-apical direction werealso evaluated to observe intrusion or extrusion tenden-cies with the different hyrax screw heights tested. Anextrusion tendency of the molars and premolars was reg-istered in FEM 3. It might be due to the upward tendencyof deformation registered in the central portion of theexpander, which generated a reactive tendency to de-form and displace the lateral portions of the expanderand the adjacent teeth in the opposite direction, thusdownward. Conversely, in FEM 1 and FEM 2, a down-ward tendency of deformation was observed in the cen-tral portion of the hyrax screw. Therefore, a reactive andupward deformation tendency was registered in theexpander extremities, thus generating the intrusion ten-dencies for both premolars and molars. The results ofthese simulations cannot be directly extrapolated tothe clinical setting. They represent mechanical tenden-cies, since some degree of approximation is a limitationof finite element method studies; our findings must beconfirmed in vivo before they are clinically applied.

There is a tendency toward deformation of the medialportion of the apparatus in the mesial direction for all 3apparatus configurations. This observation indicatesa force component in the anterior direction. For thelow and middle screw configurations, this force occursbelow the center of resistance of the teeth, resulting in

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Fig 6. Displacement in the buccolingual direction for the first premolar, second premolar, first molar,and second molar. Positive values indicate displacements in the buccal direction; negative values in-dicate displacements in the lingual direction.

226 Araugio et al

mesial movement for their crowns and distal movementfor their roots. In the highest screw configuration, theopposite occurs: the force component in the anterior di-rection is above the center of resistance of the teeth. Aswith the previous deformations discussed, these effectsare likely reduced when both halves of the apparatusare considered.

When the mesiodistal displacements were evaluated,a mesially directed deformation tendency of the hyraxcentral portion was registered in all finite elementmethods tested. This tendency indicated that an anteriorforce component acting on the extremities of the ex-pander and over the supporting teeth. In FEM 1 andFEM 2, the anterior force component was located below

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the centers of resistance of the teeth, indicating mesialcrown and distal root tipping. Inversely, in FEM 3, the re-sultant anterior force vector was observed above thecenters of resistance of the teeth. However, these dis-placements are unlikely to be observed clinically becauseof the bony and dental structures that were not simu-lated in the finite element method models tested.

The results of this study indicated that the construc-tion of the hyrax expander apparatus with the screw be-low the maxillary first molars’ center of resistancegenerated an increased tendency toward buccal tippingof the crown. The closer the screw is positioned to themaxillary first molar, the less the dental tipping tenden-cies. However, when the screw is located above the

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maxillary first molars’ center of resistance, the crowntends to tip in the lingual direction. When the screwwas tested far from the maxillary first molars’ center ofresistance (FEM 1 and FEM 3), the apices were displacedin the opposite direction from the crowns. This couldgenerate undesired compression in the root apices, espe-cially in the premolars. The intermediate configuration(FEM 2) appears to be close to ideal, producing nearlyhomogenous displacements. The likely ideal positionfor this evaluated situation would be slightly above themaxillary first molars’ center of resistance; this wouldgenerate bodily displacement in the buccal directionfor the 8 teeth, optimizing the orthopedic effects of RME.

CONCLUSIONS

The results of the finite element method simulationstested in this study indicated the following.

1. Greater amounts of buccal crown tipping were reg-istered when the hyrax screw was positioned closerto the occlusal plane.

2. There were extrusive tendencies when the screw wassimulated above the center of resistance of theteeth.

3. There were mesial displacement tendencies whenthe screw was simulated below the center of resis-tance of the teeth and distal displacements whenit was above the maxillary first molars’ center of re-sistance.

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