Journal of Zhejiang University-SCIENCE B

, Volume 19, Issue 7, pp 535–546 | Cite as

A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

  • Jian-lei Wu
  • Yun-feng LiuEmail author
  • Wei Peng
  • Hui-yue Dong
  • Jian-xing Zhang


Excessive forces may cause root resorption and insufficient forces would introduce no effect in orthodontics. The objective of this study was to investigate the optimal orthodontic forces on a maxillary canine, using hydrostatic stress and logarithmic strain of the periodontal ligament (PDL) as indicators. Finite element models of a maxillary canine and surrounding tissues were developed. Distal translation/tipping forces, labial translation/tipping forces, and extrusion forces ranging from 0 to 300 g (100 g=0.98 N) were applied to the canine, as well as the force moment around the canine long axis ranging from 0 to 300 g·mm. The stress/strain of the PDL was quantified by nonlinear finite element analysis, and an absolute stress range between 0.47 kPa (capillary pressure) and 12.8 kPa (80% of human systolic blood pressure) was considered to be optimal, whereas an absolute strain exceeding 0.24% (80% of peak strain during canine maximal moving velocity) was considered optimal strain. The stress/strain distributions within the PDL were acquired for various canine movements, and the optimal orthodontic forces were calculated. As a result the optimal tipping forces (40–44 g for distal-direction and 28–32 g for labial-direction) were smaller than the translation forces (130–137 g for distal-direction and 110–124 g for labial-direction). In addition, the optimal forces for labialdirection motion (110–124 g for translation and 28–32 g for tipping) were smaller than those for distal-direction motion (130–137 g for translation and 40–44 g for tipping). Compared with previous results, the force interval was smaller than before and was therefore more conducive to the guidance of clinical treatment. The finite element analysis results provide new insights into orthodontic biomechanics and could help to optimize orthodontic treatment plans.

Key words

Biomechanics Optimal orthodontic force Finite element analysis Periodontal ligament 








对尖牙施加范围在0~300 g(100 g=0.98 N)的远中向、唇向和拔出向的整体移动力和倾斜移动力,以及范围在0~300 g·mm 的绕尖牙牙长轴向的扭转力矩,通过非线性有限元分析对牙周膜的应力应变进行定量评价。约定牙周膜应力在0.47 kPa(毛细血管压力)至12.8 kPa(人类心脏收缩压力的80%)之间的为最佳应力;以及牙周膜应变大于0.24%(尖牙最大移动速度时的牙周膜应变的80%)为最佳应变。


尖牙倾斜移动时的最佳正畸力范围(远中向为 40~44 g,唇向为28~32 g)小于其整体移动(远 中向为130~137 g,唇向为110~124 g);尖牙远 中向移动时的最佳正畸力范围(整体移动为 110~124 g,倾斜移动为28~32 g)小于其唇向移 动(整体移动为130~137 g,倾斜移动为40~44 g)。 与已有的研究结果相比,最佳正畸力范围进一步 缩小,对临床正畸治疗具有较好的指导意义。


生物力学 最佳正畸力 有限元分析 牙周膜 

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Supplementary material

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A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis


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Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ministry of Education & Zhejiang ProvinceKey Laboratory of E&M (Zhejiang University of Technology)HangzhouChina
  2. 2.Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, School of Mechanical EngineeringZhejiang UniversityHangzhouChina
  3. 3.Department of StomatologyZhejiang Provincial People’s HospitalHangzhouChina

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