Nonlinear dependency of tooth movement on force system directions.

INTRODUCTION Moment-to-force ratios (M:F) define the type of tooth movement. Typically, the relationship between M:F and tooth movement has been analyzed in a single plane. Here, to improve the 3-dimensional tooth movement theory, we tested the hypothesis that the mathematical relationships between M:F and tooth movement are distinct, depending on force system directions. METHODS A finite element model of a maxillary first premolar, scaled to average tooth dimensions, was constructed based on a cone-beam computed tomography scan. We conducted finite element analyses of the M:F and tooth movement relationships, represented by the projected axis of rotation in each plane, for 510 different loads. RESULTS We confirmed that a hyperbolic equation relates the distance and M:F; however, the constant of proportionality ("k") varied nonlinearly with the force direction. With a force applied parallel to the tooth's long axis, "k" was 12 times higher than with a force parallel to the mesiodistal direction and 7 times higher than with a force parallel to the buccolingual direction. CONCLUSIONS The M:F influence on tooth movement depends on load directions. It is an incomplete parameter to describe the quality of an orthodontic load system if it is not associated with force and moment directions.

[1]  C. Burstone,et al.  Axes of resistance for tooth movement: does the center of resistance exist in 3-dimensional space? , 2013, American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics.

[2]  B. Melsen,et al.  Moment-to-force ratio, center of rotation, and force level: a finite element study predicting their interdependency for simulated orthodontic loading regimens. , 2008, American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics.

[3]  S. Barone,et al.  Computer-aided modelling of three-dimensional maxillofacial tissues through multi-modal imaging , 2013, Proceedings of the Institution of Mechanical Engineers. Part H, Journal of engineering in medicine.

[4]  Dietmar Kubein-Meesenburg,et al.  Initial forces generated by three types of thermoplastic appliances on an upper central incisor during tipping. , 2009, European journal of orthodontics.

[5]  B Melsen,et al.  Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyzed by finite element. , 2009, Orthodontics & craniofacial research.

[6]  C. Burstone,et al.  Mechanics of tooth movement. , 1984, American journal of orthodontics.

[7]  Christoph Bourauel,et al.  Determination of the Elasticity Parameters of the Human Periodontal Ligament and the Location of the Center of Resistance of Single-rooted Teeth A Study of Autopsy Specimens and Their Conversion into Finite Element Models , 2002, Journal of Orofacial Orthopedics / Fortschritte der Kieferorthopädie.

[8]  Werner Götz,et al.  Correlation of stress and strain profiles and the distribution of osteoclastic cells induced by orthodontic loading in rat. , 2004, European journal of oral sciences.

[9]  Sandro Barone,et al.  Creation of 3D Multi-Body Orthodontic Models by Using Independent Imaging Sensors , 2013, Sensors.

[10]  F. Sander,et al.  Experimentelle Untersuchung der Zahnbeweglichkeit am Menschen „in vivo“ , 2002 .

[11]  R. Pryputniewicz,et al.  Holographic determination of centers of rotation produced by orthodontic forces. , 1980, American journal of orthodontics.

[12]  Jie Chen,et al.  Load system of segmental T-loops for canine retraction. , 2013, American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics.

[13]  Dietmar Kubein-Meesenburg,et al.  Influence of thermoplastic appliance thickness on the magnitude of force delivered to a maxillary central incisor during tipping. , 2009, American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics.