Evaluation of the Force System Acting Within an Orthodontic Appliance

Background: Implant-prosthetic rehabilitation of single-tooth edentulism often requires orthodontic reshaping of the potential implant-prosthetic space because its dimensions change due to the migration of adjacent teeth. In this context, it is very important to understand the force system generated by orthodontic arches in order to control tooth movement and to achieve, at the end of orthodontic treatment, the correct dimensions of the potential implant-prosthetic space for dental implant placement. Materials and Methods: The study was based on CBCT images acquired from a 25-year-old female patient with maxillary and mandibular lateral edentulism. The images were processed using InVesalius and Geomagic to obtain a patient-specific three-dimensional reconstruction of the dento-maxillary structures. Orthodontic brackets, adhesive components, and round-section nickel–titanium archwires were subsequently modeled and positioned within a common three-dimensional coordinate system. The reconstructed geometry was used to extract local geometric parameters of the archwire. These parameters were subsequently introduced into a local equivalent Euler–Bernoulli beam formulation to estimate elastic force components and transverse reactions associated with the bracket-related points. Results: The study revealed an uneven distribution of forces along the orthodontic arches. For the upper arch, the elastic force values ranged from 0.044 to 0.383 N, and for the lower arch, from 0.050 to 0.308 N. The calculated reactions at the bracket components also varied depending on the orthodontic archwire geometry and the position of the support points. Conclusions: Patient-specific three-dimensional reconstruction combined with a local analytical beam approximation provides a framework for estimating geometry-dependent elastic force components within an orthodontic appliance. The calculated values should be interpreted as equivalent local force estimates derived from the reconstructed geometry and not as a complete three-dimensional force–moment system.