Optimization Analysis of Two-Factor Continuous Variable between Thread Depth and Pitch of Microimplant under Toque Force

Abstract

Microimplant, an anchorage device, is widely applied in clinical orthodontic treatment. Since tooth torque is required to be controlled during orthodontic tooth movement, a novel microimplant needs to be developed to apply better torque force during orthodontic. In this study, the optimal value ranges of thread depth and pitch under toque force were studied for choosing microimplant with relevant value ranges in clinical design from biomechanical perspective. Finite element analysis (FEA) and optimization design technology were used for accessing the optimal value ranges of thread depth and pitch under toque force. Thread depth ( $D$ ) (0.1 mm to 0.4 mm) and pitch ( $P$ ) (0.4 mm to 1 mm) were used as continuous variables, with the other parameters as constant, and the optimal value ranges were obtained by analyzing the tangent slope and sensitivity of the response curve. When a torque force of 6 Nmm was applied on the microimplant, the maximum equivalent stress (Max EQV) of cortical bone and maximum displacements (Max DM) of microimplant were analysis indexes. When $0.55\text{mm}\le P\le 1\text{mm}$ , the Max EQV of cortical bone was relatively smaller with less variation range. When $0.1\text{mm}\le D\le 0.35\text{mm}$ , the Max DM of microimplant was relatively smaller with less variation range. So in conclusion, the initial stability of microimplants with pitch $0.55\text{mm}\le P\le 1\text{mm}$ and thread depth $0.1\text{mm}\le D\le 0.35\text{mm}$ was better with the torque force applied.