Construction of a Three-Dimensional Model of Teeth for Experimental Biomechanical Investigation by the Method of Finite Elements

Abstract

Problemi s proučavanjem odgovora zuba na djelovanje sustava sila mnogo su složeniji i teze ih rješavamo od jednostavnog mjerenja same sile. Svrha je ovoga istraživanja razraditi vlastitu metodu trodimenzionalne digitalizacije zuba kako bi se što vjernije mogao izraditi njegov matematički model. Izraditi vlastiti trodimenzionalni matematički model zuba s pripadajućim potpornim strukturama u svrhu biomehanič- kih istraživanja metodom konačnih elemenata. Kao predložak za izradu matematičkog modela poslužio je gornji očnjak izvađen zbog paro- dontoloških razloga. Dobiven je trodimenzionalni matematički model gornjeg očnjaka koji se sastoji od 4000 elemenata oblika heksaedra i 2367 čvorova, što čini ukupno 7101 stupanj slobode cijelog modela. Periodontni ligament izmodeliran je cijelom duzinom korijena u širini od 0,25 mm. Sloj kompakte izmodeliran je u debljini od 2 mm. Zbog mogućnosti simulacije raznih položaja zubi, različite visine alveolarne kosti i terapijske situacije u kojima je izvršena ekstrakcija zubi, očekivati je da će se ova metoda u budućnosti još šire primjenjivati.Problems connected with the study of the response of the tooth to the effect of system forces are much more complex and difficult to solve than simple measurement of the forces themselves. The aim of this investigation was to develop a method for three-dimensional digitalization of teeth in order to produce a reliable mathematical model of a tooth. The construction of a three-dimensional mathematical model of a tooth with accompanying supporting structures for biomechanical investigations by the method of finite elements. An upper canine, extracted for parodontal reasons, served as the sample for construction of the mathematical model. A three- dimensional mathematical model of the upper canine was obtained, comprising 4000 elements of hexa- dic form and 2367 nodes, with a total of 7101 degrees of freedom for the whole model. The periodontal ligament was modelled for the whole length of the root, 0.25 mm in width. The layer of compact was modelled at a depth of 2 mm. It is anticipated that this method will be widely applied in the future, because of the possibility of simulating different positions of the tooth, and different heights of the alveolar bone and therapeutic situations in which teeth extractions are performed