The article presents a methodology for creating a computer program based on a three-dimensional model of the dento-mandibular segment to determine the optimal individual parameters of solid cast-cult structures in the treatment of patients with defects in hard tissue of the teeth during the tooth root action of various loads in the periodontal stress and strain. The stress-strain state depends on various factors, such as the length of the root canal, the thickness of its walls, the size of the pin. The study of the influence of these factors is one of the important tasks of orthopaedic dentistry. To solve problems related to the restoration of damaged teeth, a three-dimensional computer model of the dental-maxillary segment was created using mathematical calculation of finite elements. The first stage is the project task. At the heart of the project is the choice of the type of scheme. We have chosen 5 types of general form systems. Each of the model elements with this system has 6 degrees of freedom (3 angles of rotation, 3 linear deformations behind the coordinate axes). The next step is the description of the tooth geometry, which we expect. According to the schematic image of the tooth we set the nodes of the finite element model. For each calculation, we obtained normal and tangential stresses along all coordinate axes; we also investigated equivalent stresses along four basic strength theories. Thus, the investigated three-dimensional tooth models allowed us to calculate the individual parameters of the future orthopedic design, to display digital data that will maximize individualization of the selection of optimal parameters for the restoration of damaged teeth of each patient. The root of the natural tooth has the shape of an elliptical cone. The periodontal thickness is constant over the entire root surface. The force of the tooth is 10 kg at an angle of 120 ° to the horizontal axis. The force is applied to a section that is 3.2 mm away from the cone axis. The height of the tooth is 15 mm, the angle of the cone is 12°, and the periodontal thickness is 0.25 mm with a modulus of elasticity of 1.07 kg / mm2. After the calculations were made, the coordinate of the center of resistance 9.8 mm at 10.2 mm, for example, was almost completely consistent, and the vertical tooth displacement was 0.0296 mm at 0.0309 mm, for example. But the horizontal displacement of the tooth differed very strongly 0,0289 mm at 0.0111 mm, for example.

Keywords: three-dimensional computer model, dentition segment, deformation, pin-stump constructions, stress, modeling

Full text: PDF (Ukr) 477K

1. Persan VS. Pidsumky roboty stomatologichnoyi sluzhby Ukrayiny za 2006‒2009 roky [Results of work of the dental service of Ukraine for 2006‒2009]. Dentalni tekhnologiyi. 2010; Spetsvyp: 58‒73. [Ukrainian]
2. Kostenko YeYa, Pavlenko OV, Radko VI. Ortopedychne likuvannya zubiv, zruynovanykh nyzhche rivnya yasen [Orthopedic treatment of teeth destroyed below the gum level]. Zubnoe protezyrovanye. 2008; 2: 17‒21. [Ukrainian]
3. Kostenko YeYa, Radko VI. Matematychnyy rozrakhunok elementiv fiksatsiyi sutsilnolytoyi kombinovanoyi shtyftovoyi vkladky pry likuvanni zubiv, zruynovanykh nyzhche rivnya yasennogo krayu [Mathematical calculation of the fixation elements of a solid cast combined pin insert in the treatment of teeth destroyed below the level of the gum margin]. Novyny stomatologiyi. 2008; 3: 54‒8. [Ukrainian]
4. Chulak LD, Bas AA, Kravchenko LS. Byokhymycheskye pokazately rotovoy zhydkosty u bolnykh s vosstanovlennymy kornyamy zubov, razrushennykh nyzhe urovnya desny [Biochemical parameters of oral fluid in patients with restored tooth roots, destroyed below the level of the gums]. Visnyk stomatologiyi. 2002; 2: 35‒7. [Russian]
5. Rytter RG. Vybor shtyftovoy konstruktsyy dlya estetycheskogo vosstanovlenyya frontalnoy gruppy zubov [The choice of a pin design for aesthetic restoration of the frontal group of teeth]. Panorama ortopedycheskoy stomatologyy. 2007; 3: 12‒3. [Russian]
6. Godovanyy VO, Sudova OYa, Pikh AZ. Shtyftovi konstruktsiyi v ortopedychniy stomatologiyi [Pin designs in orthopedic dentistry]. Novyny stomatologiyi. 2010; 3: 49‒54. [Ukrainian]
7. Godovanyy VO, Sudova OYa, Pikh AZ. Shtyftovi konstruktsiyi v ortopedychniy stomatologiyi [Experimental study of the functional properties of cast crown-root inserts]. Novyny stomatologiyi. 2016; 4: 125‒30. [Russian]
8. Olesova VN, Balguryna OS, Musheev YU, y dr. Yzuchenye byomekhanyky lytoy shtyftovoy vkladky v uslovyyakh trekhmernogo matematycheskogo modelyrovanyya [Study of biomechanics of a cast pin in the conditions of three-dimensional mathematical modeling]. Rossyyskyy stomatologycheskyy zhurnal. 2012; 2: 19‒21. [Russian]
9. Kassaro A, Dzherachy D, Pytyny A. Teoretycheskoe y eksperymentalnoe yssledovanye po povodu pereloma v systeme shtyftovaya vkladka [Theoretical and experimental study of a fracture in the pin tab system]. Klynycheskaya stomatologyya. 2000; 2: 26‒30. [Russian]
10. Pavlenko AV, Tymofeev AA. Nespetsyfycheskaya obshchaya rezystentnost organyzma pry yspolzovanyy metallycheskykh konstruktsyy nesemnykh zubnykh protezov [Nonspecific general resistance of the body when using metal structures of non-fixed dentures]. Sovremennaya stomatologyya. 2014; 1: 122‒4. [Russian]
11. Matros‒Taranets YN. Byomekhanycheskye yssledovanyya v eksperymentalnoy stomatologyy [Biomechanical research in experimental dentistry]. Donetsk: Typ Don GMU PKF “BAO”: 2008. 122 p. [Russian]
12. Chuyko AN, Bocharova EV. Osobennosty napryazhyonno‒ deformyrovannogo sostoyanyya pry zabolevanyyakh parodonta [Features of stress-strain state in periodontal diseases]. Stomatolog. 2000; 11: 31‒5. [Russian]
13. Shvarts AD. Byomekhanyka y okklyuzyya zubov [Biomechanics and occlusion of teeth]. M: Medytsyna; 2011. 208 p. [Russian]
14. Saakyan ShKh. Prymenenye shtyftovykh vkladok s estetycheskym pokrytyem pry polnom razrushenyy koronkovoy chasty zubov [Application of pin tabs with aesthetic coated with complete destruction of the crown of the teeth]. Abstr. PhDr. (Med.). М; 2012. 26 p. [Russian]
15. Demydova YY, Lysenkov VV. Parodont: byomekhanycheskye svoystva (chast 1) [Periodontics: biomechanical properties (part 1)]. Parodontologyya. 2015; 4: 6‒8, 22‒26. [Russian]
16. Solovyov MM, Lysenkov VV, Demydov YY. Byomekhanycheskye svoystva tkaney parodonta [Biomechanical properties of periodontal tissues]. Stomatologyya. 2013; 76(4): 47‒51. [Russian]
17. Ortopedycheskaya stomatologyya: Prykladnoe materyalovedenye [Orthopedic Dentistry: Applied Materials Science]. Uchebnyk dlya medytsynskykh vuzov. Pod red prof VN Trezubova. SPb: SpetsLyt; 2011. 351 p. [Russian]
18. Logynova NK, Guseva YE, Zaytseva YV. Okklyuzyonnye syly [Occlusal forces]. Stomatologyya. 2011; 78(6): 51‒6. [Russian]