Three-dimensional analysis of orthodontic tooth movement based on XYZ and finite helical axis systems

The purpose of this study was to demonstrate the advantage of the finite helical axis (FHA) system in the biomechanical analysis of orthodontic tooth movement by comparing it with the rectangular coordinate (XYZ) system. Ten patients (6 females and 4 males, mean age 23 years 7 months) were selected. Maxillary canine retraction using light continuous forces of two different magnitudes (0.5 and 1 N) was used to retract the right and left maxillary canines in subjects who required maximum posterior anchorage. The findings were compared based on midpalatal implants that provided a fixed reference for measurement. The significance of the difference between the results with the two different force magnitudes was determined using Wilcoxon's signed-rank test. With both the XYZ and the FHA system, no significant differences in the amount of distal movement of the canines over 2 months were found between the two force magnitudes. However, the results showed that the canine was likely to incline distally during tooth retraction with a force of 1 N compared with a force of 0.5 N (P < 0.05). With the FHA system, the result indicated that the canine was likely to incline palatally during tooth retraction with a force of 0.5 N compared with a force of 1 N (P < 0.05). In this study, the combination of these two different approaches for describing tooth movement clearly showed a difference between light continuous forces of 0.5 and 1 N.