Asymmetric Outer Bow Length and Cervical Headgear Force System: 3D Analysis Using Finite Element Method

Original Article Asymmetric Outer Bow Length and Cervical Headgear Force System: 3D Analysis Using Finite Element Method Allahyar Geramy1, Mehdi Hassanpour2, Elham sadat Emadian Razavi3 1 Professor, Dental Research Center, Dentistry Research Institute, Tehran University of Medical Sciences, Tehran, Iran; Department of Orthodontics, Faculty of Dentistry, Tehran University of Medical Sciences, Tehran, Iran 2Orthodontist, Tehran, Iran 3 Postgraduate Student, Department of Orthodontics, Tehran University of Medical Sciences, Tehran, Iran Abstract  Corresponding author: A. Geramy, Professor, Department of Orthodontics, Tehran University of Medical Sciences, Tehran, Iran Received: 14 August 2014 Accepted: 28 December 2014 Objectives: This study sought to assess distal and lateral forces and moments of asymmetric headgears by variable outer bow lengths. Materials and Methods: Four 3D finite element method (FEM) models of a cervical headgear attached to the maxillary first molars were designed in SolidWorks 2010 software and transferred to ANSYS Workbench ver. 11 software. Models contained the first molars, their periodontal ligament (PDL), cancellous and cortical bones, a mesiodistal slice of the maxillae and the headgear. Models were the same except for the outer bow length in headgears. The headgear was symmetric in model 1. In models 2 to 4, the headgears were asymmetric in length with differences of 5mm, 10mm and 15mm, respectively. A 2.5 N force in horizontal plane was applied and the loading manner of each side of the outer bow was calculated trigonometrically using data from a volunteer. Results: The 15mm difference in outer bow length caused the greatest difference in lateral (=0.21 N) and distal (= 1.008 N) forces and also generated moments (5.044 N.mm). Conclusion: As the difference in outer bow length became greater, asymmetric effects increased. Greater distal force in the longer arm side was associated with greater lateral force towards the shorter arm side and more net yawing moment. A difference range of 1mm to 15 mm of length in cervical headgear can be considered as a safe length of outer bow shortening in clinical use. Keywords: Orthodontic; Extraoral Traction Appliances; Force; Unilateral; Finite Element Analysis Journal of Dentistry, Tehran University of Medical Sciences, Tehran, Iran (2015; Vol. 12, No. 3) INTRODUCTION A shift to non-extraction orthodontic treatment seems to be occurring in contemporary orthodontics [1]. Therefore, space regaining treatment modalities are highly important in order to alleviate crowding and establish an ideal occlusion. Molar distalization is one method for space regaining, for example, in unilateral www.jdt.tums.ac.ir March 2015; Vol. 12, No. 3 class II malocclusions. This type of malocclusion is often a challenge for practitioners [2]. Treatment modalities for this malocclusion include asymmetric headgear (AHG), asymmetric extractions, differential elastic patterns, intraoral anchorage appliances, and, more recently, temporary skeletal anchorage devices (TADs) [3-6]. 216 Geramy et. al Asymmetric Outer Bow Length and Cervical Headgear Force System… Extensive clinical data have demonstrated the effectiveness of AHG in unilateral distalization [2]. Traction with headgears has some important advantages such as maximum anchorage to adjust the force and control of bodily or tipping movement [7]. Unlike most of the other fixed appliances for molar distalization, headgear does not lead to protrusion of anchorage teeth [8]. Different modifications of AHG have been designed and evaluated, such as anterior swivel joint for the connection between inner and outer bows, an internal hinge on the inner bow, and use of long and short outer bows [9]. Undoubtedly, AHG applies an unequal distal force; but it should be noticed that the common side effect in all designs is the lateral force produced. Although many theoretical and experimental studies were performed to evaluate the effect and side effects of AHGs, the results were confusing. Nobel and Waters [10] showed that AHG produced a buccal displacement in the transverse dimension as a side effect. On the other hand, Hershey and his colleagues [11] found some buccal-buccal displacement and some lingual-buccal displacement of the molars; the buccal-buccal displacement was attributed to the arch expansion effect of the inner bow. Martina et al, [12] and Yoshida et al. [9] stated that AHG often produced buccal cross bite in the light force side and lingual cross bite in the heavy force side; however, they believed that the magnitudes were not equal on both sides. Geramy analyzed the cervical headgear force system using FEM and reported the same distalizing force in both side molars when all dimensions were considered ideal [13]. In some instances, asymmetries may arise inadvertently. Geramy et al. analyzed the force system in detail when a modification in molar situation or inner bow form resulted in different distalizing forces and an asymmetric headgear was produced [14]. www.jdt.tums.ac.ir March 2015; Vol. 12, No. 3 The FEM, as a numerical analysis to find approximate solution to complex problems, was first introduced in aerospace industry and soon entered into different fields of biology. Its efficacy in different fields of science has been well proven. Three-dimensional FEM is a powerful discipline used to examine complex mechanical behaviors of dental structures. It can be used for designing, analysis and finding answers to dental biomechanical problems [15-20]. MATERIALS AND METHODS Five 3D finite element models of a mesiodistal slice of the maxillae were designed. The models contained upper first molars, their PDLs, cancellous bone, cortical bone, stainless steel molar bands fitted to molar crowns, and a cervical headgear. The difference in models was in the outer bow length in the cervical headgear, which was symmetric in the first model and asymmetric in models 2 to 4. The length difference (shortening of the left outer bow) was 5 mm (model 2), 10 mm (model 3), and 15 mm (model 4). Wire diameter was 1.6 mm in the outer bow and 0.9 mm in the inner bow (Fig. 1). The last model was the same as the fourth one except for the molar teeth, which were replaced by two blocks. This replacement was done to simplify viewing the details of displacements occurred in headgear loading and to make an unforgettable image of the molar reaction (in the fourth model). The models were designed in SolidWorks 2010 (SolidWorks Corp., MA, USA) and were then transferred to ANSYS Workbench ver. 11 (ANSYS, PA,USA) for the solving process. To find the angles formed between the outer bow and its tangent to the neck, accurate trigonometric calculations were made using SolidWorks. Distances needed to draw Fig. 2 were derived from a volunteer dental student by a clinical vernier caliper. In this way, the exact force components in the anteroposterior and mediolateral directions were found. 217 (...truncated)