Computational modeling of maxillary canine orthodontic movement

Abstract

Objectives: The current study aims to explore the stress distribution along the roots of palatally positioned maxillary canines during orthodontic movement using a novel computational spring model.

Methods: An experimental analysis based on the spring-model was utilized to calculate Orthodontic Tooth Movement (OTM) and the resulting stresses. Two sets of experiments were conducted: the first set compared stresses on a canine resulting from a single force and a force-couple, while the second set simulated canines' traction during instantaneous movement with varying original tooth angulations using different off-the-shelf orthodontic coils. In total, 130 simulations were performed.

Results: The model provided estimated stress distribution throughout the OTM with the expected movements, producing consistent outcomes with prior findings. In the first set of experiments, the force couple exhibited an average stress of 43 KPa, while a single force yielded 51 KPa on average. The maximum stress observed was 63 KPa for the force couple and 130 KPa for a single force. Note that the stress distribution attributed to the force couple was alleviated in comparison to the stress distribution caused by a single force. Force couples generated higher average stress. In the second experiment, the application of an occlusally-directed inclined force led to reduced stress levels overall. For instance, when a 200 g distal force was exerted on the canine, it generated an average stress of 20 KPa, whereas applying a force of the same magnitude in an occlusal-distal direction resulted in a lower average stress of 15.5 KPa.

Conclusions: Lower average stress levels when using a force couple indicate that larger loads might be safely applied for rotational movements. Given that areas under maximal stress are prone to damage, orthodontic treatment planning should carefully consider stress distribution to minimize potential harm in these high-stress zones. The results also suggest that force couples enable the use of stronger forces than a single force. Additionally, it is advisable to extrude the tooth initially before starting any horizontal movement towards the target position.

Clinical significance: Given that orthodontic treatment often relies on virtual planning, incorporating a variety of methods to evaluate stress distribution within the treatment strategy could offer numerous benefits. Such an approach holds the potential to improve both the efficiency and safety of orthodontic treatments, especially in complex cases that require the application of high forces.

Keywords: Impacted canine; Orthodontic tooth movement; PDL; Simulation; Stresses.

Fig. 1

PDL model: (a) Depicts a right maxillary canine with springs (colored in yellow) representing the relaxed state of the PDL before the initiation of orthodontic force (presented as red helix), the gingival line is outlined by a red mesh. (b) Depicts a single spring-block occupying a segment of the tooth surface (lower end) and anchored to the alveolar bone (upper end). Each block is comprised paired linear and torsional springs ((b) left). These springs undergo both linear ${\mathcal{l}}_i-{\mathcal{l}}_0$ and shear $\mathit{tan}\left({\theta }_i\right)$ deformations (right), where ${\mathcal{l}}_0$ denotes the spring's initial length. $O_i$ and $A_i$ denotes the spring's edges that are connected to the tooth and the alveolar bone edges, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 2

Tooth movement with remodeling. For display purposes the PDL springs (yellow) lengths are exaggerated. The initial position of the tooth is overlayed in green dashline. Orthodontic appliance displayed as red coil and gingival line is depicted as a red horizontal line. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3

Configurations of a single mesial force (a,c) and a mesial-distal force couple (b, d) applied over an upper-right canine. These configurations were set to study the stress distribution over the PDL throughout OTM under single-force and a force-couple loadings. c, d present an occlusal view.

Fig. 4

Tooth-load configurations for an upper-right canine, applied in the second simulation set. The orthodontic appliances are depicted as red coils. A single distal horizontal force (HF) or diagonal force (DF) was applied. The gingival line is displayed in red, and the orientation of the tooth denoted by α is determined by the angle between the perpendicular to gingival line and the vertical tooth axis. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5

Von Misses stress distribution over upper-right canine PDL tissue where a single 300gf mesial force was applied. The stress values are specified in the color bar (a). (b), (c),(d) a palatal-distal view at 0.25 mm, 1.5 mm and 3 mm anchorage movement. The black arrows display the direction of movement of each area in the tooth. (e), (f), (g) an apical view at 0.25, 1.5 and 3 mm movement. (h),(i),(j) a buccal view at 0.25,1.5 and 3 mm movement, note that the black arrows imply a tipping movement. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 6

Von Misses stress distribution over upper-right canine PDL tissue where a couple 300gf forces was applied. The stress values are specified in the color bar (a). (b),(c),(d) a palatal-distal view at 0.25 mm, 1.5 mm and 3 mm anchorage movement. (e), (f), (g) an apical view at 0.25, 1.5 and 3 mm movement. The black arrows display the direction of movement of each area in the tooth, implying a rotational movement. (h),(i),(j) buccal view at 0.25,1.5 and 3 mm movement. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 7

- The PDL's mean Von Misses stresses and their standard deviations (small fonts) given in [kPa], for various of-the-shelf orthodontic coils (see IOS [27]). The appliance model specifies the rest length of the coils in [mm] and the colors correspond to the stress values as in the sidebar. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 8

Maximal Von Misses stress calculated over the PDL tissue given in [kPa].