The Three-dimensional Finite Element Stress Analysis Of The Mandibular Second Molar Moving Mesially With The Molar Tip-back Bend In Different Angles

ObjectiveThree-dimensional finite element model of a human mandibular second molar and "Australian Wire Special Plus"(0.018 inch) arch form with molar tip-back bend in different angles had been established to investigate the displacements of the tooth and the stress distributions of periodontal ligaments when the tooth moved mesially under different loading force systems of archwires.This can provide theoretical references for understanding the biomechanics of mandibular second molar moving mesially.MethodsUsing a normal Chinese mandible as an anatomy foundation,the finite element model of mandibular second molar,and "Australian Wire Special Plus"(0.018 inch) arch form,with molar tip-back bend in different angles,were built with CT scanning aided model building, AutoCAD software and ANSYS software.The wire was assumed to be an elastic beam.The force systems on mandibular second molar conducted by archwires with molar tip-back bend in different angles were calculated by ANSYS software.Along with the force systems of archwire,the mesial force of 1N,1.5N,2N were respectively loaded at buccal sites or on both buccal and palatal sites of the tooth by simulating mesial movement with molar tip-back bend in different angles.The displacements of the tooth and the stress distributions of periodontal ligaments were studied.Results1 The three-dimensional finite element modes of the mandibular second molar had been constructed with a good geometry and mechanics resemblance.2 Under the archform with molar tip-back bend in different angles,there was occlusal force at mesial point of mandibular second molar,and gingival force at distal point.The magnitude of the force increased with the raise of the angle,and the magnitude at mesial point is greater than that at distal. 3 When the mandibular second molar moved mesially under the archform with molar tip-back bend in different angles,the stress of periodontal ligaments concentrated at the cervix, and the stress distributions were relatively uniform when the mesial force of 1N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 15°,when the force of 1.5N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 20°,and when the force of 2N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 25°4 When the mesial force of 1N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 15°,when the force of 1.5N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 20°,and when the force of 2N loaded at both buccal and palatal sites of the tooth with the tip-back bend in 25°,the mandibular second molar almost bodily moved.Conclusions1 A complicated tooth model with good geometry and mechanics resemblance can be reconstructed by applying the finite element method.2 The molar tip-back bend archwire delivered distal-tipping moment to mandibular second molar,which made them present distal upright tendency.3 When the mandibular second molar moved mesially with the molar tip-back bend in proper angle,the stress distributions of periodontal ligaments was more uniform when the force was loaded on both buccal and palatal sites with equal force than the mesial force was loaded at buccal sites.4 The molar tip-back bend in special angle should match the mesial force when the mandibular second molar moved mesially.