Introduction: In the absence of adequate animal or in vitro models, the biomechanics of human malocclusion must be studied indirectly. Finite element analysis (FEA) is emerging as a clinical technology to assist in diagnosis, treatment planning and retrospective analysis. The hypothesis tested is that instantaneous FEA can approximately predict long-term, mandibular occlusal plane rotation to plan the correction of a skeletal Class III malocclusion. Methods: Seventeen published case reports were selected for patients treated with statically determinate mechanics, utilizing posterior mandible (PM) or infrazygomatic crest (IZC) bone screw anchorage, to retract the lower arch. Twodimensional (2D) measurements were made for incisor and molar movement, lower arch rotation, and retraction relative to the upper arch. A patient with cone-beam computed tomography (CBCT) imaging was selected for a retrospective finite element analysis (FEA). Results: The mean age (+SD) for the sample was 23.3±3.3 years; seven were male and 10 were female. Mean incisor movement was 3.35±1.55mm of retraction and 2.18±2.51mm of extrusion. Corresponding molar movement was retraction of 4.85±1.78mm and intrusion of 0.85±2.22mm. Retraction of the lower arch relative to the upper arch was 4.88±1.41mm. Mean posterior rotation of the lower arch was -5.76±4.77° (counterclockwise). The mean treatment time (n=16) was 36.2±15.3 mo. Bone screws in the PM region were more efficient for intruding molars and decreasing the vertical dimension of occlusion (VDO) to close an open bite. The fullcusp, skeletal Class III patient selected for FEA was treated to an ABO CRE score of 24 points in ~36mo by en masse retraction and posterior rotation of the mandibular arch: the bilateral load on the lower segment ~200cN. The lower arch was retracted ~5mm, posterior rotation was ~16.5°, and molar intrusion was ~3mm. There was a 4° decrease in the mandibular plane angle (MPA) to close the skeletal openbite. Retrospective sequential iterations (FEA animation) simulated the clinical response, as documented with longitudinal cephalometrics. The level of PDL stress was relatively uniform (<5kPa) for all teeth in the lower arch segment. Conclusions: En masse retraction of the lower arch is efficient for conservatively treating skeletal Class III malocclusion. PM anchorage results in intrusion of molars to close the VDO and MPA. Instantaneous FEA as modeled here could be used to reasonably predict the clinical results of an applied load.

DEDICATIONTo my parents, who have supported my education. iv ACKNOWLEDGMENTSOne of the most important things I have learned during my PhD is the necessity of the existence of a working network of people that can help you achieve your goals. The more effectively this network functions, the higher the chance you will achieve the goals quickly.I would first like to thank my parents, who have unconditionally supported my decision to abandon a profitable private practice in Orthodontics, and return to humble student conditions while aiming for a full time academic career.I also thank my girlfriend Laura Kruter who has (almost always) been ok with my, some might say, not very sane ideas. Sometimes they do turn out fine, though (like this "PhD" one).I can hardly think of anyone else that could have complemented my work and ideas during this Program as well as Dr. Thomas Katona. While I was passionately conditioned to an idea, he was always rational and careful. While I was sometimes furious with a shortcoming, he was always temperate and humorous. When I ran into his office with some news about a project, he would always listen and almost never seem too busy to see me. While I was working and something went wrong, he would listen and wonder with me about the "whys" and "hows", instead of telling me what to do or express disappointment. He was even subject to some of my home culinary experiments. I was extremely fortunate to find someone that thought about science the same way I did, and that actually helped me with my project instead of just telling me what to do. I felt like we worked as a team, and that helped to increase my motivation during my studies. The third part of this project tested the role of the P2X7 receptor in the dentoalveolar morphology of C57B/6 mice. P2X7R KO (knockout) mice were compared to C57B/6 WT to identify differences in a maxillary molar and bone. Tooth dimensions viii were measured and 3D bone morphometry was conducted. No statistically significant differences were found between the two mouse types. P2X7R does not have a major effect on alveolar bone or tooth morphology.The final part examines the role of the P2X7 receptor in a controlled biomechanical model. Orthodontic mechanotransduction was compared in wild-type (WT) and P2X7R knock-out (KO) mice. Using Finite Element Analysis, mouse mechanics were scaled to produce typical human stress levels. Relationships between the biological responses and the calculated stresses were statistically tested and compared.There were direct relationships between certain stress magnitudes and root resorption and bone formation. Hyalinization and root and bone resorption were different in WT and KO. Orthodontic responses are related to the principal stress patterns in the PDL and the P2X7 receptor plays a significant role in their mechanotransduction.

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Optimum stresses for a favorable response to orthodontics are still unknown. Here, we compared the effects of initial periodontal ligament (PDL) stresses over time in orthodontic external root resorption (OERR), necrosis, and the TRAP+ cell population. Forty-two rats (Fischer CDF) were treated with 10 cN of force for 5 different time periods. Finite element (FE) models of the first maxillary molars were constructed from μCT scans to calculate initial PDL stresses. The scans were also used for OERR measurements before histology. Time, stress, and their interaction were significant to result in an OERR increase only in the regions of medium and high stress. OERR was not significantly different between control and treated animals over time in the region of low stress. After 30 days, OERR was increased by 5- and 3-fold in the zone of high- and medium-stress regions, respectively. The TRAP+ cell population initially followed the stress gradient, but changed after bone and necrotic tissue resorption. In the 30-day modeling cycle, the correspondent 3rd principal stress range to promote direct bone resorption and insignificant OERR was between -9.92 and -7.75 KPa. These translate to approximate forces of 30 to 40 cN applied at the bracket level (tipping) of a human maxillary canine.

The M:F influence on tooth movement depends on load directions. It is an incomplete parameter to describe the quality of an orthodontic load system if it is not associated with force and moment directions.