Malanchuk V. A., Tsylenko A. L., Hrabovetskyy P. V.

MATHEMATIC MODELLING OF BLOOD CIRCULATION WHICH IS LOCATED IN IMAGINARY BONE CAVITY AFTER IMPANT PLACEMENT IN THE LOWER JAWBONE

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About the author:	Malanchuk V. A., Tsylenko A. L., Hrabovetskyy P. V.
Heading	CLINICAL MEDICINE
Type of article	Scentific article
Annotation	Having placed an impant in the bone and its surrounding soft tissue, certain patological changes take place. The absence of definite assessment criteria for the performed treatment as well as the clear mathematical ground for the chosen method of surgical measure, the amount and type of implant – all of it does not allow to provide substantial ground for the treatment given and to avoid complications. Therefore, it is only mathematical objectiveness and biological adequacy that will let us build an individual approach to every patient. While considering the variables that define geometry of hemorrhage borders around the implant which had been placed in the bone, we came to studying the models which met the following requirements: Model 1. Conditions: 1) bone tissue of lower jawbone is almost completely represented by a compact layer, or a correlation of both compact and spongy layers 1:1, (I-II bone type); 2) the height of bone cavity for the implant, depending on implants that are possible to use amounts to: a) 8 mm; b) 10 mm; c) 11,5mm; d) 13mm; 3) the diameter of bone cavity, depending o the implants that are possible to use amounts to: a) 2,8 mm; b) 3,2 mm; c) 3,65 mm; d) 4,3 mm. Model 2. Conditions: 1) 1/3 of side wall length around bone cavity is represented by compact bone tissue while 2/3 of bone cavity is occupied by spongy bone tissue (III-IV bone type); 2) the height of bone cavity for the implant, depending on implants that are possible to use amounts to: a) 8 mm; b) 10 mm; c) 11,5mm; d) 13mm; 3) the diameter of bone cavity, depending o the implants that are possible to use amounts to: a) 2,8 mm; b) 3,2 mm; c) 3,65 mm; d) 4,3 mm. Model 3. Conditions: 1) The mean of the first and second variants, a correlation of compact an spongy tissues (II-III bone type); 2) the height of bone cavity for the implant, depending on implants that are possible to use amounts to: a) 8 mm; b) 10 mm; c) 11,5mm; d) 13mm; 3) the diameter of bone cavity, depending o the implants that are possible to use amounts to: a) 2,8 mm; b) 3,2 mm; c) 3,65 mm; d) 4,3 mm. We have come up with the data as to the possible radius of intraosseous hematoma in the course of schematic placement of cylindrical and cylindrical-conic (correlation of cylindrical and conic part amounted to 1:1) implants in the lower jawbone based on the theory of mathematic modelling of blood circulation which is located in bone cavity depending on the bone type. While comparing the data as to the size of intraosseous hematoma which is formed when using cylindrical and cylindrical-conic implants, we have received the following data: intraosseous hematoma which is formed when using conic implants is on the average 72,67 mm smaller compared to the size of intraosseous hematoma which is formed when using cylindrical implants, independent of the bone tissue type. Taking into account the aforementioned calculations and on the basis of the filtration laws, the imaginary hematoma of bone tissue will spread across intertrabecular spaces and will occupy the bigger amount of bone tissue the higher the sponginess (σ) and the bigger length (h) and diameter (d) of the used implant is. Its shape, however, will be absolutely optional. Hemorrage will circulate across the intertrabecular spaces and according to our calculations, will occupy the bigger part the bigger the length and width of the implant which is being used is, notably while using cylindrical implants blood will take up bigger capacity of intertrabecular space than when using the conic ones.
Tags	dental implant, bone injury, hemorrhage, mathematical model
Bibliography	Bojko Ju. G. Kliniko-anatomicheskij analiz vrachebnyh oshibok / Ju. G. Bojko, N. F. Siljaeva // – Minsk, - 1994. – 107 s. Zhusev A. I. Dental'naja implantacija / A. I. Zhusev, A. Ju. Remov // – M.: Centr dental'noj implantacii, - 1999. – 168 s. Zamaraev E. P. Dopolnitel'nye dannye ob uchastii kal'cija v regeneracii kosti pri perelomah / E. P. Zamaraev // materialy nauchnoj konf. (Cheljabinsk, 1965) – t. ІІ. – S. 318 – 320. Kaplan A. V. Tehnika lechenija perelomov kostej / A.V. Kaplan // – M.: Medicina. – 1948. Mirgazizov M. 3. Matematicheskoe modelirovanie razlichnyh sposobov postanovki zubov v polnyh s#emnyh protezah, fiksirovannyh na vnutrikostnyh implantatah: sb. tezisov nauch. trudov k 70-letiju V.N. Kopejkina / M. 3. Mirgazizov // – MMSI, Moskva, - 1999. – S. 172 – 173. Musheev I. U. Prakticheskaja dental'naja implantologija / I. U. Musheev, V. N. Olesova, O. Z. Fromovich // – M.: Paradiz, - 2000. – 272 s. Malanchuk V. O. Hіrurgіchna stomatologіja ta shhelepno-liceva hіrurgіja / V. O. Malanchuk, І.P. Logvіnenko, T.O. Malanchuk ta іn. // – K.: LOGOS, - 2011. – T. 2. – S. 443 – 465. Perova M. D. Standartizacija ocenki vnutrikostnoj dental'noj implantacii / M. D. Perova // Novoe v stomatologii. – 1999. – №5. – S. 37 – 45. Sumarokov D. D. Jeksperimental'noe issledovanie roli reguljatornyh faktorov v processe reparativnoj regeneracii kostnoj tkani na modeli pereloma nizhnej cheljusti: avtoref. dis. na prisvoenie uchen. stepeni dokt. biol. nauk: spec. 03.00.30 «Biologija razvitija, jembriologija» / D. D. Sumarokov // – M., - 1988. – 44 s. Sumarokov D. D. Ontogenez / D. D. Sumarokov, M. B. Shvyrkov, A. H. Shamsudinov // Stomatologija. – 1988. – №5. – S. 468 – 473. Sumarokov D. D. Rol' destruktivnoj fazy regeneracii v reparativnom processe / D. D. Sumarokov, D. V. Gutkin, M. B. Shvyrkov // Patol. fiziol, i jeksper. ter. – 1991. – №2. – S. 40 – 42. Surov O. N. Zubnoe protezirovanie na implantatah / O. N. Surov – M.: Medicina, - 1993. – 205 s.
Publication of the article	«World of Medicine and Biology» №2(50) 2 part 2015 year, 068-071 pages, index UDK 616.314-089.843-031:616-005.1:001.891.573