BackgroundThe objective of the present study was to specify an optimum force system for intrusion and extrusion of maxillary central incisor and to compare the effects of bracket positioning at different heights from the incisal edge in Labial Orthodontics (LaO) and Lingual Orthodontics (LiO).MethodsA mathematical model of maxillary central incisor with normal inclination was developed. Four cases of heights of bracket slot from incisal edge were considered both in LaO and LiO viz. 3 mm, 4 mm, 5 mm and 6 mm. Based on a mathematical model, an optimum force system consisting of an intrusive or extrusive force (F) and a moment (M) was devised and moment (M) to force (F) ratio (M:F ratio) was estimated in each case. Then, three-dimensional Computer Aided Design (CAD) models of incisor and surrounding structures were prepared. To validate an optimum force system, finite element analysis was carried out and force system with derived M:F ratio was applied in each case.ResultsIn finite element analysis, results were shown in the form of vector graph of nodal displacements along with undeformed and deformed models. The desired intrusion or extrusion of incisor was observed. Thus, force system devised from a mathematical model was validated with finite element analysis in each case.ConclusionTo achieve intrusion or extrusion, M:F ratios required in LaO were same i.e. 8:1 for aforementioned heights of bracket slot from incisal edge but different in LiO i.e. 0:1, 1:1, 2:1 and 3:1 for the heights of 3 mm, 4 mm, 5 mm and 6 mm respectively.