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Updated: May 2, 2026

A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
Published on: April 8, 2020
An analytical approach to 3D orthodontic load systems.
Thomas R Katona1, Serkis C Isikbay, Jie Chen
1a Associate Professor, Department of Orthodontics and Oral Facial Genetics, Indiana University School of Dentistry, and Department of Mechanical Engineering, Purdue University School of Engineering and Technology, Indianapolis, Ind.
A new pseudo three-dimensional (3D) analytical approach accurately characterizes orthodontic force and moment systems. This method improves upon flawed traditional two-dimensional (2D) analyses for better orthodontic treatment planning.
Area of Science:
- Orthodontics
- Biomechanics
- Dental Mechanics
Background:
- Orthodontic treatment relies on precise application of forces and moments.
- Traditional analysis often simplifies complex three-dimensional (3D) load systems into two-dimensional (2D) planes, potentially leading to inaccuracies.
- Accurate characterization of orthodontic load systems is crucial for predictable treatment outcomes.
Purpose of the Study:
- To introduce and validate a pseudo three-dimensional (3D) analytical method for characterizing orthodontic force and moment systems.
- To compare the efficacy of this novel 3D approach with traditional 2D methods.
Main Methods:
- Utilized previously measured 3D load systems.
- Evaluated and compared load systems using both the traditional 2D planar approach and the proposed vector-based 3D method.
- Focused on analyzing loop designs for translatory space closure.
Main Results:
- Both the 2D and 3D methods identified loop designs as suboptimal for translatory space closure.
- However, the reasons provided by each method were distinct and contradictory, highlighting the limitations of the 2D approach.
- The new 3D method offered a more comprehensive understanding of the load system's behavior.
Conclusions:
- The traditional 2D analysis of 3D orthodontic load systems is fundamentally flawed.
- Established 2D orthodontic principles can be adapted to 3D analysis by employing a modified coordinate system aligned with the intended tooth movement.
- This adapted 3D approach allows for the preservation of core orthodontic concepts while improving analytical accuracy.
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