A novel method to define personalized post-orthodontic treatment dental arch form

The dental arch is a fundamental aspect of orthodontic treatment and has considerable implications in planning and therapy. Since arch forms differ (e.g. tapered, ovoid, square), determination of posttreatment arch form should take each patient's dental arch features into account. This study aims to develop a method to predict optimal post-orthodontic treatment dental arch form.

Mandibular dental casts of 55 patients who underwent non-extraction treatment and presented with functional occlusion according to functional occlusion criteria were selected. The casts were scanned and digitalized, 18 landmarks were collected and the spatial coordinates were utilized to compute tooth size and intermolar width. Several mathematical functions were then used to ensure a best-fitting mandibular arch form, including beta function, polynomial equations and polynomial combined with circle equations.

After applying several mathematical functions, we developed a mixed model made of two simple geometrical curves. The anterior segment of the dental arch was fitted with a circle and the posterior segment with a quartic curve; both could be calculated simply using tooth size.

The present study presents a new approach to determine an individualized post-orthodontic treatment dental arch form, using the combined width of the lower teeth. The proposed method offers a simple and practical solution that can be easily implemented in clinical practice. These findings hold great promise for digital personalized treatment and the development of customized orthodontic appliances.