Summed Tissue Resistance of Periodontal Ligaments and Alveolar Bone in Orthodontic Distal Retraction of Maxillary Canines: Mathematical Simulation of Clinical Data and Interpretation of Results

<b>Background</b>: The mechanical properties of either alveolar bone or periodontal ligaments under orthodontic loading, as well as orthodontic tooth movement, have been studied in recent years using computational approaches. In previous studies, we developed a theoretical mathematical approach that uses a weighting coefficient of the summed resistance of periodontal structures, namely the bone and periodontal ligaments, in relation to apex movement, the center of rotation, orthodontic force loading, and time in order to quantify the biological response to orthodontic biomechanics. <b>Methods</b>: We analyzed the distal retraction of three maxillary canines and integrated the clinical data obtained in the previously developed mathematical programs. <b>Results</b>: The values of the (σ) weighting coefficient of the tissue resistance were interpreted in the context of the clinical data obtained: the smaller the value of (σ), the higher the actual tissue resistance, with a greater difference between the crown and root movement; also, the higher the value of (σ), the lower the actual tissue resistance, with a small difference between the crown and apex movement. <b>Conclusions</b>: The clinical interpretation of the results allows us to set a premise for the refinement of the mathematical programs so that we can use them in assessing the orthodontic biomechanics of larger patient groups over longer periods of time and create premises of treatment protocol simplification and adjustment.