Mathematical appraisal of arch form of non-extraction therapy of crowding

Aim : Patients (n=22) with severe crowding in the upper as well as in the lower jaw before treatment were treated with the Damon®-System (3MX, Ormco, Orange, CA) without performing any extractions or approximal enamel reduction to evaluate the tooth changes with appraisal of the arch form before and after treatment.
Material and Method :
The obtained digital models were analyzed with the OrthoProof® software (Nieuwegein, Nederland) to investigate the tooth movements. On each tooth at least one reference point is located before treatment. Through these points we then fit a curve. After treatment a new curve is fitted through the new positions of the reference points. The movement of the teeth is measured by numerically computing the area between the two curves. The area between the curves before and after treatment was computed in the 22 cases using the octave numerical package (www.gnu.org/software/octave) in order to estimate the expansion. This is done by numerically integrating the difference between the two spline interpolated curves whose origin is centered between the two front incisors. Statistical analysis was performed with SPSS15.0 software package.
Results : Significant increase in upper arch length and arch width were noted after the correction of crowding. Both molar distalization and incisor protrusion contributed to the increase in arch length. A mean expansion of 1.08 (8%) resp 1.04 (lower) and 1.12 (upper) was calculated.
Conclusion :
During the correction of upper arch crowding with non-extraction Damon® technique, arch perimeter is gained by the increase in both arch length and inter-bicuspid arch width. Arch form could be reconstructed using the above described method based on the given parameters