Finite element method (FEM) analysis of the force systems produced by asymmetric inner headgear bows

Extra-oral traction appliances were introduced more than a century ago and continue to be used to produce orthopaedic and/or dental changes in the maxilla. While force systems produced by asymmetric outer bows have been studied extensively, the force systems produced by asymmetric inner bows have been overlooked.

To analyse the forces acting on the maxillary first molars: when the size of one bayonet bend is increased; when the point of application of the distalising force on the inner bow is moved to one side; when one molar is displaced palatally.

Four FEM models of cervical headgear attached to maxillary first molars were designed in SolidWorks 2010 and transferred to an ANSYS Workbench Ver. 12.1. Model 1, each molar was 23 mm from the midpalatal line and the inner bow was symmetrical; Model 2, the left molar was displaced 4 mm towards the midpalatal line and the inner bow was symmetrical; Model 3, the molars were equidistant (23 mm) from the midpalatal line, but the left molar was engaged by a 2 mm larger bayonet bend; Model 4, the molars were equidistant (23 mm) from the midpalatal line but the join between the inner and outer bows was displaced 2 mm towards the left molar. In all FEM models, a 2N force was applied to the inner bow at the join between inner and outer bows and the energy transmitted to the teeth and the von Mises stresses on the molar PDLs were assessed.

There were marked differences in the strain energy on the teeth and the von Mises stresses on their PDLs. A 14 to 20 per cent increase in energy and force was produced on the tooth closer to the symmetric plane of the headgear. In addition, the increase in energy produced a 30 to 62 per cent increase in the von Mises stresses within the PDLs.

Small asymmetries in molar position, the size of a bayonet bend and the point of application of a force on an inner bow resulted in asymmetrical forces on the molars. These forces were higher on the molar closer to the symmetric plane of the headgear.