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U radu su prikazani analitički modeli za predviđanje naprezanja u parodontnom ligamentu kod ortodontske terapije. Ortodoncija kao specijalistička grana stomatologije predstavljena je u uvodnom prvom poglavlju. Navedeni su primarni ciljevi i trenutni izbori liječenja te njihove prednosti i nedostaci. U drugom poglavlju prikazana je klasifikacija i morfologija zubi te je opisana građa i funkcija zubi kao i okolnih tkiva. Posebno su naglašeni parodontni ligament i alveolna kost jer imaju značajnu ulogu kod ortodontskog pomaka zuba. Osnovni pojmovi ortodontske terapije prikazani su u trećem poglavlju. Zbog potpunog razumijevanja procesa ortodontskog pomaka zuba, objašnjena je biomehanika koja stoji iza pomaka zuba, kao i pojam središta otpora zuba. Četvrto poglavlje obuhvaća razvoj analitičkih modela. Korijen zuba aproksimiran je pomoću dva modela, a to su paraboloid i eliptični paraboloid. Uvedene su određene pretpostavke i ograničenja modela na temelju kojih su dobivene analitičke formule. Izvod je proveden pomoću klasične teorije elastičnosti, a odnosi se na horizontalnu translaciju jednokorijenskog zuba. U petom poglavlju prikazani su rezultati provedenih analiza naprezanja za oba modela. Raspodjela komponenti naprezanja prikazana je: grafički, jednadžbom i tablično. Kako su za oba modela korištene iste dimenzije i svojstva parodontnog ligamenta, dobiveni rezultati su međusobno uspoređeni pomoću relativne razlike. Naknadno su grafička raspodjela i rezultati usporedbe potkrijepljeni dokazima. Na kraju je dan zaključak na temelju provedenih analiza naprezanja. This study focuses on analytical models for stress prediction of periodontal ligament in orthodontic therapy. Orthodontics as specialist branch of dentistry is introduced in the first chapter. The primary goals and current choices of treatment as their advantages and disadvantages are listed in introductory chapter. The second chapter presents the classification and morphology of the teeth and describes the structure and function of the teeth as well as the surrounding tissues. Periodontal ligament and alveolar bone are particularly emphasized as they play a significant role in orthodontic tooth movement. The basic concepts of orthodontic therapy are presented in the third chapter. To fully understand the process of orthodontic tooth movement, it is necessary to explain the biomechanics behind the tooth movement, as well as the term center of tooth resistance. Chapter four covers the development of analytical models. The root of the tooth was approximated by two models, namely the paraboloid and the elliptical paraboloid. Certain assumptions and limitations of the model were introduced, on the basis of which analytical formulas were obtained. The excerpt was performed using the classical theory of elasticity, referring to the horizontal translation of a single root tooth. Section five presents the results of the stress analyzes performed for both models. The distribution of stress components is shown: graphically, by equation and in tabular form. As the same dimensions and properties of periodontal ligament were used for both models, the obtained results were compared by relative difference. Subsequently, the graphical distribution and results of the comparison were supported by the evidence. Finally, a conclusion is made based on the performed stress analyzes. |
