Bio-Medical Materials and Engineering 28 (2017) S169–S177 S169 DOI 10.3233/BME-171638 IOS Press Mechanical equilibrium of forces and moments applied on orthodontic brackets of a dental arch: Correlation with literature data on two and three adjacent teeth Delphine Wagner a,b,∗ , Yves Bolender b , Yves Rémond a and Daniel George a a ICube Laboratory, University of Strasbourg, CNRS, 2 rueBoussingault, 67000 Strasbourg, France b Faculty of Dental Surgery, University ofStrasbourg, 8 rue Sainte-Elisabeth, 67000 Strasbourg, France Abstract. Although orthodontics have greatly improved over the years, understanding of its associated biomechanics remains incomplete and is mainly based on two dimensional (2D) mechanical equilibrium and long-time clinical experience. Little experimental information exists in three dimensions (3D) about the forces and moments developed on orthodontic brackets over more than two or three adjacent teeth. We define here a simplified methodology to quantify 3D forces and moments applied on orthodontic brackets fixed on a dental arch and validate our methodology using existing results from the literature by means of simplified hypotheses. Keywords: Orthodontic, tooth movement, force, moment, friction, periodontium 1. Introduction Modern orthodontic appliances have been introduced by E.H. Angle in the early twentieth century [1] and many innovations have followed since, even if the fundamental principles remain unchanged [2]. Slotted brackets are fixed on the teeth buccal or lingual surfaces and wires are inserted and secured in the bracket slots. The “straight wire technique” introduced by Andrews in the 70’s [3,4], where the orthodontist is taking advantage of pre-informed brackets and pre-shaped wires, is nowadays in current use among almost 70% of American orthodontists. This association of brackets and wire generates a set of forces and moments and three dimensional tooth movements are initiated [5] through the bone remodeling process. When these forces and moments are applied on a bracket, periodontal reactions occur [6–10]. However, even if the biological events during orthodontic tooth movement are nowadays better understood [11–13], the correlation between orthodontic force systems, desmodontal reaction and bone remodeling is not yet well established despite the heavy use of numerical and finite element models [14–24]. * Corresponding author. E-mail: delphine.wagner@chru-strasbourg.fr. 0959-2989/17/$35.00 © 2017 – IOS Press and the authors. All rights reserved