I read with interest the article, “Does the center of resistance depend on the direction of tooth movement?” (Meyer BN, Chen J, Katona TR. Am J Orthod Dentofacial Orthop 2010;137:354-61). It deals with the resistance center during tooth movement. The authors are to be applauded for several aspects of their study, especially for the modeling of the periodontal ligament as a composite material consisting of a fiber-reinforced matrix. I want to draw attention to some ideas regarding the study of tooth movement.

Many studies are concerned with tooth movement during orthodontic treatment, but it is still something of a paradox. Therefore, some new concepts should be introduced to eliminate these limitations and provide a more comprehensive description of tooth movement. As those authors said in their article, orthodontic tooth displacement is described as translation, rotation, or a combination thereof. Any such movement can be characterized by its associated center of rotation. Tooth movement includes the rotational and translational components. That is, on average, tooth movement starts with both rotation and translation, and this relationship remains constant throughout tooth displacement. In solid mechanics, the helical axis (also called screw axis, twist axis, or axis of rotation) is used to describe the movement of a rigid body. In this system, the infinitesimal spatial displacement of a rigid body is described by the instantaneous helical axis—ie, a combination of translation along an axis in space and rotation around it. During the movement and displacement of a rigid body, the instantaneous helical axis keeps on changing its position and orientation, and a group of instantaneous helical axes make up a continuous and smooth pathway. Actually, the helical axis is not a new concept in oral science. It has been used previously, mainly in describing movement of the mandible and the temporomandibular joints. But only the instantaneous center of rotation—simply a bidimensional analysis—could be analyzed, because of the complexity of the computing methods and the anatomic structures and the mandibular movement tracks. With the development of computing and measurement techniques, we can more comprehensively describe tooth movement using the concept of the helical axis. Describing tooth movement using the helical axis has a distinguishing advantage over just using the rotation center. It describes the 3-dimensional movement of a rigid body and contains information on the components of both rotation and translation of the tooth, not only the buccolingual but also the mesiodistal and occlusal-gingival directions, thus yielding a more comprehensive description of tooth movements than does a single center point, such as the center of rotation, the center of resistance, and so on. The helical axis can be computed from the initial and last positions of the tooth movement during an infinitesimal period. Conversely, the motion of any point of the rigid body can be determined from the orientation and position of the helical axis. Moreover, the finite helical axes might not be located in the tooth. For the molars, it might be located at the bifurcated area between the roots.

The orthodontic load (force and moment) is certain to achieve displacement, which depends on the property of the periodontal tissues, especially the alveolar bone and periodontal ligament. The helical axis and rotation center of tooth movement are not constant, and are influenced by several factors, including force applied, point of action, and magnitude and direction of resistance. Furthermore, even after minimal displacement, all these factors will be changed accordingly, as well as the helical axis, the rotation center, and the resistance center of the tooth movement.

Both the computing methods for the helical axis and rotation center are based on the hypothesis that the tooth and the alveolar bone are rigid objects, and the periodontal ligament is elastic and uniform. The viscoelastic property of the periodontal tissues makes it even more difficult to define these changes precisely.

The x-ray transmissivity of the tooth is low, and its surface reflection is high. During microcomputed tomography scanning and image reconstruction, artifacts occur around the tooth, and discrepancies are generated. These will influence the quality of the digitized tooth model, whereas accurate geometry is the key to realistic and validated simulations and successful finite element model analysis.

Theoretically, the locations of both the helical axis and rotation center for tooth movement will be more apical than the calculated results. This might be because of the following reasons: the enlarged tooth image reconstructed from computed tomography scans, the viscoelastic property of the periodontal tissues (meaning that more displacement occurred, and more resistance was generated), and the friction from neighboring teeth.

Tooth movements are intricate and difficult to describe appropriately; 3-dimensional analysis is the right tool for better teaching and understanding. In our study funded by the Chinese Nature Science Foundation (No. 30801307), we attempted to analyze the position and the orientation of the finite helical axis and the functional long axis of the tooth during movement. We wanted to obtain a thorough kinematic description of tooth movement, not only during orthodontic treatment, but also during tooth displacement under various patterns of occlusal contact.