不对称内弓头帽所产生力系统的有限元法（FEM）分析

Geramy Allahyar, Kizilova Natalya, Terekhov Leonid

Orthodontic Department, Tehran University of Medical Sciences, Tehran, Iran.

Aust Orthod J. 2011 Nov;27(2):125-31.

BACKGROUND

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.

AIM

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.

METHODS

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.

RESULTS

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.

CONCLUSION

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.

背景

口外牵引矫治器在一个多世纪以前就已问世，至今仍用于对上颌骨产生矫形和/或牙齿变化。虽然非对称外弓产生的力系统已得到广泛研究，但非对称内弓产生的力系统却被忽视了。

目的

分析当上颌第一磨牙受到以下情况影响时作用于其上的力：一个刺刀弯的尺寸增大；内弓上远中移动力的施力点移至一侧；一颗磨牙向腭侧移位。

方法

在SolidWorks 2010中设计了四个连接上颌第一磨牙的头帽的有限元模型，并将其转移到ANSYS Workbench Ver. 12.1中。模型1，每颗磨牙距腭中线23 mm，内弓对称；模型2，左磨牙向腭中线移位4 mm，内弓对称；模型3，磨牙距腭中线等距（23 mm），但左磨牙的刺刀弯大2 mm；模型4，磨牙距腭中线等距（23 mm），但内弓与外弓的连接处向左磨牙移位2 mm。在所有有限元模型中，在内弓与外弓的连接处向内弓施加2N的力，并评估传递至牙齿的能量以及磨牙牙周膜上的冯·米塞斯应力。