Geometrical prediction of post surgical Holdaway ratio following mandibular rotation and the need for genioplasty

This article is aimed at geometrical evaluation of antero-posterior displacement of incisor inferioris (Ii) and pogonion (Pog) following mandibular rotation and introducing a simple method to predict post surgical Holdaway ratio to evaluate the need for genioplasty. First the geometrical factors affecting the displacement of a landmark following the mandibular rotation are discussed; namely α (the amount of mandibular rotation), r (the distance of the landmark from the center of rotation), and θ (the angle of the radius of the landmark from true horizontal line), Then the amount of displacement is calculated as d=2r[sirt(α/2)sin(α/2+θ)]. Finally prediction method of post surgical Holdaway ratio is described as adding the amount of "d " for Pog and Ii to pre surgical Holdaway ratio. This ratio in addition to position of Pog relative to facial skelton was used to predict the need for genioplasty. The application of this method is also demonstrated on an open bite patient as an example and the outcome is compared with manual prediction method. The described method predicted the need for genioplasty the same way as manual prediction method. The geometrical prediction method can be of great value in determining the need of genioplasty following surgical mandibular rotation.