Three-dimensional finite element analysis on the effects of maxillary protraction with an individual titanium plate at multiple directions and locations

Abstract

Objective: : A three-dimensional-printed individual titanium plate was applied for maxillary protraction to eliminate side effects and obtain the maximum skeletal effect. This study aimed to explore the stress distribution characteristics of sutures during maxillary protraction using individual titanium plates in various directions and locations.

Methods: : A protraction force of 500 g per side was applied at forward and downward angles between 0° and 60° with respect to the Frankfort horizontal plane, after which the titanium plate was moved 2 and 4 mm upward and downward, respectively. Changes in sutures with multiple protraction directions and various miniplate heights were quantified to analyze their impact on the maxillofacial bone.

Results: : Protraction angle of 0-30° with respect to the Frankfort horizontal plane exhibited a tendency for counterclockwise rotation in the maxilla. At a 40° protraction angle, translational motion was observed in the maxilla, whereas protraction angles of 50-60° tended to induce clockwise rotation in the maxilla. Enhanced protraction efficiency at the lower edge of the pyriform aperture was associated with increased height of individual titanium plates.

Conclusions: : Various protraction directions are suitable for patients with different types of vertical bone surfaces. Furthermore, when the titanium plate was positioned lower, the protraction force exhibited an increase.

Keywords: Face mask; Finite element analysis; Miniplate; Three-dimensional printing.

Figure 1

The three-dimensional finite element model of the craniomaxillary complex and titanium plate. (1) Frontomaxillary suture, (2) zygomaticofrontal sutures, (3) zygomaticotemporal sutures, (4) zygomaticomaxillary sutures.

Figure 2

The direction of protraction. (1) Frontomaxillary suture, (2) zygomaticofrontal sutures, (3) zygomaticotemporal sutures, (4) zygomaticomaxillary sutures, (5) pterygopalatine sutures.

Figure 3

Maxillary protraction with varying heights of titanium plates.

Figure 4

Linear graph and distribution nephogram of von Mises stress in sutures with varying protraction directions (protraction angle: from 0° to 60° with respect to the Frankfort horizontal plane). The colors in the stress distribution nephogram denote the magnitude of stress. The stress values increase as the color approaches red, whereas decreasing stress levels are indicated by colors closer to blue.

Figure 5

Linear graph and distribution nephogram of the first principal stress in sutures with varying protraction directions (protraction angle: from 0° to 60° with respect to the Frankfort horizontal plane). The colors in the stress distribution nephogram represent the magnitude and direction of stress. As the color shifts toward red, it indicates increased tensile stress, whereas a shift toward blue signifies higher compressive stress.

Figure 6

Linear graph and distribution nephogram of von Mises stress in sutures with varying heights of titanium plates. A, 4 mm upward movement; B, 2 mm upward movement; C, original position; D, 2 mm downward movement; E, 4 mm downward movement. The stress distribution nephogram reflects the magnitude of stress, with red indicating higher stress values and blue indicating lower stress levels.

Figure 7

Linear graph and distribution nephogram of the initial principal stress in sutures with varying heights of titanium plate. A, 4 mm upward movement; B, 2 mm upward movement; C, original position; D, 2 mm downward movement; E, 4 mm downward movement. The colors in the stress distribution nephogram depict both the magnitude and direction of stress. Intensity increases as the color shifts closer to red, indicating higher tensile stress. Conversely, as the closer the color approaches blue, the stress tends to be closer to zero.