Determination of individual angular characteristics of the teeth positions according to the computer tomography in Ukrainian adolescents with orthognathic bite

positions according to the computer tomography in Ukrainian adolescents with orthognathic bite Dmitriev М. О., Volkov K. S., Glushak A. A., Kyrychenko Yu. V., Balynska M. V., Chugu T. V., Kovalchuk О. І. National Pirogov Memorial Medical University, Vinnytsya, Ukraine SHEE "Ternopil Ivan Horbachevsky State Medical University of the Ministry of Healthcare of Ukraine", Ternopil, Ukraine Shupyk National Medical Academy of Postgraduate Education, Kyiv, Ukraine


Introduction
Cone-ray computed tomography provides significant advantages for working with images in orthodontics, allows you to describe the craniofacial anatomy more precisely and provide comprehensive information on anatomical relationships and individual patient characteristics for improved diagnosis, treatment planning and prediction of dental anomalies [5,19,23].But the lack of standard assessment methods, the unified protocol of orthodontic research, the existence of various methods for obtaining a three-dimensional image and the impossibility of their association defines a set of tasks that need to be resolved for the widespread introduction of computed tomography into orthodontic and surgical practice [28].The issues of determining and controlling the three-dimensional position of the teeth have always been central to clinical orthodontic practice.The main characteristics of the position of the central axis of the tooth in the form of various sets of standard characteristics formed the basis of the production of bracket systems in the form of a prescription, which determines the position of the tooth in relation to the orthodontic arc [21].
Difficulties in production, individual morphological variety of teeth, different variants of positioning lead to the fact that the doctor often fails or difficult to implement the bracketed angular characteristics.The lack of the ability to determine the individual standard angle characteristics of the position of the teeth and the technical provision of their control often does not lead to the expected result and in each case requires individualization, the vision of which is based, as a rule, on the experience and intuition of the doctor.In order to solve such a situation, in addition to improving the positioning protocols of the non-removable equipment, the physician should be able to clearly identify the individual angular characteristics of the tooth-jaw system.
The purpose of the study -by studying computer tomography and cephalometric indices and conducting direct stepwise regression analysis to develop in Ukrainian adolescents with orthognathic bite mathematical models of individual angular positions of teeth.

Materials and methods
Dental tomograms and side teleroentgenograms were obtained and analyzed using the Veraviewepocs 3D device, Morita (Japan) in 38 young men (17 to 21 years of age) and 55 angle P_OR_N (by 3.9%).In young women, most frequently models included -angle N_POG_ (14.3%); angle AB_NPOG (10.2%); indicator WITS (8.2%); angle ММ, angle ANB, length of the branch of the mandible R_ASC (by 6.1%).Thus, in the work with the help of the method of step-by-step regression with inclusion, among Ukrainian adolescence, on the basis of peculiarities of computer-tomographic and teleroentgenography indices, reliable models of computer-tomographic individual linear angular characteristics of the position of teeth necessary for constructing the correct three-dimensional geometry of dental arches are developed and analyzed.Keywords: regression analysis, vestibular-lingual tilt of the tooth (tork), mesiodistal inclination of the tooth (angulation), tooth rotation (rotation), computed tomography, teleroentgenography, young men, young women, orthognathic bite.[11,14,15,24,29,30,31,33]. Anatomical points were determined taking into account the recommendations of A. E. Athanasiou [3], S. I. Doroshenko and Y. A. Kulginsky [10].
The analysis of telerentgenograms and the results of their researches for Ukrainian adolescents are described in detail and set out in a number of articles [6,7,8,9,12,13].The determined cephalometric indices were combined and then divided into three groups.The first group included metric characteristics of the skull, which usually do not change during surgical and orthodontic treatment.Most of these       indicators are basic in modern cephalometric analyzes.In relation to them, lateral teleroentgenograms determine the inclination, anterior-posterior or vertical position of the gnatic structures (upper and lower jaw, closure plane, separate teeth).The second group includes indicators of the toothjaw system, the definitions of which most often need to be oriented when performing orthodontic treatment of patients who are in the process of growth, as well as in individuals with a formed bone skeleton who may with orthodontic surgery change the width, length, angles and positions of the upper and lower jaws.The third group includes indicators that actually characterize the position of each individual tooth relative to each other, to the bony cranial structures and profile of the face.It is this group of indicators most often corrected in the process of orthodontic treatment of tooth-jaw abnormalities.
For modeling, we selected the following CT-indicators of the third group (Fig. 1-6), depending on the characteristics of the indicators of the first and second groups.
For a more universal clinical use, the position of the occlusion plane in relation to the palatine plane was investigated (YGOCLPL).This indicator can be determined both on dental tomograms on and on teleroentgenogramі (Fig. 7 and 8).
The statistical processing of the obtained results was carried out in the license package "Statistica 6.0" using a direct stepwise regression analysis.In the case of direct stepwise regression analysis, we have identified several conditions: 1) -the final version of the regression polynomial must have a determination coefficient of not less than 0.50, that is, the accuracy of the description of the feature being simulated is not less than 50.0%; 2) -the value of the Fcriterion is not less than 3.0, that is, the contribution of the variable to the regression should be sufficiently significant; 3) -the number of free members included in the polynomial should be as low as possible.In all cases, after selecting the equation of multiple regression, we carried out the analysis of the residues, since emissions can substantially shift the results and lead to erroneous conclusions.When the observations fell beyond the ±3 standard quadratic deviations from the mean value, we carried out a repeated analysis with and without emissions, in order to be sure that their impact on the bias of the final results is not affected.

Results
Results of simulation of CT indicators that characterize the position of individual teeth relative to each other, to the bone cranial structures and the profile of the appearance in young men and women with orthognathic bite, depending on the metric characteristics of the skull, which usually do not change during surgical and orthodontic treatment, as well as indicators of width, length, angles and positions of the upper and lower jaws that may be altered by orthodontic surgery, have the form of the following linear equations.
For young men:   where, here and in the future, R 2 -coefficient of determination; F (!,!!) =!!,!! -critical (!,!!) and got (!!,!!) value of -is formed by lines S-N (the front part of the skull base) and S-Ba; GL_SNPOG (angle Gl'SnPog' or index of convexity of the soft tissue profile) -is formed by lines Gl'-Sn and Sn-Pog'; H (H-angle) -is formed by lines Pо-Or (Frankfurt plane) and Pn (nasal perpendicular, perpendicular to the line from the point N' to the line Se-N), defines the angle of inclination of the Frankfurt plane to the base of the skull; ARGOME (angle Ar-Go-Me, or the angle of the lower jaw) -is formed by lines Ar-tGo and tGo-Me; GL_SN_S (index Gl'_Sn_Sn_Gn' or facial vertical index) -distance ratio Gl'-Sn and Sn-Gn' (defines vertical relationships in the face profile); N_SP_SP (coefficient N_Sp'_Sp'_Me) -distance ratio N-Sp' and Sp'-Ме (ratio of the upper and lower height of the face); ANB (angle ANB) -is formed by lines A-N and N-B (indicates an angular interstitial relationship in the anterior-posterior direction); POR_GNS (У-axis or angle POr_GnS) -angle formed by lines Po-Or and S-Gn (angle of inclination of the У -axis relative to the Frankfurt plane); P_OR_N (a soft tissue face angle, or an angle P_Or_N'Hold_Pog') -is formed by lines Po-Or and N'Hold-Pog'; POR_NPOG (angle POr_NPog) -is formed by lines Po-Or and N-Pog; AFH_PFH (AFH_PFH ratio) -ratio between the values of the front (AFH) and the rear (PFH) face height; S_L (distance S_L or the anterior length of the base of the skull by Steiner) -from point S to a constructive point L, which is formed at the intersection of the perpendicular carried out from the point Pog to the line Se-N; R_ASC (length of the branch of the mandible) -distance from the constructive point R.asc to the constructive point tGoS.
For young women: TORK_11 = 27.88 - where, SNB (angle SNB) -is formed by lines S-N and N-В (the angle points to the anterior-posterior position of the lower jaw to the base of the skull); I (inclination angle, angle I) -angle of inclination of the upper jaw (spinal plane) to the nasal perpendicular); NAPOG (the angle of the skeletal obliquity or angle NаPog) -is formed by lines N-A and A-Pog; A_N_Po (distance A_N_Pog) -distance from point А to line N-Pog (the face plane, characterizes the degree of convexity of the face); PN_POG (distance PN_Pog) -distance from point Pog to nasal perpendicular PN (perpendicular line from point N to the line Po-Or).
Regression models of all other CT indicators that characterize the position of individual teeth in young men and women with orthognathic bite have a determination coefficient of less than 0.5 and therefore not significant for practical dentistry.

Discussion
Today, at the disposal of the orthodontist doctor available bracket systems with various unified characteristics that were proposed by various researchers [1].With the availability and wider use of dental computer tomography, doctors have developed a tool to control the position of the roots of the teeth after orthodontic treatment, even by conducting only one preliminary diagnostic radiological examination [20].
By conducting an analytical analysis of the treatment outcomes, more and more studies appear that present unexpected findings.So Jain M. et al. [16] argues that the use of braces with different authoring prescriptions does not affect the overall clinical outcome and the quality of treatment depends entirely on the judgment of the clinician and his experience, and that the use of standard systems, even with given angular characteristics, still requires individual arc correction [34].A number of studies prove the inconsistency of the angular characteristics of the standard braces that are obtained by teeth at the end of the orthodontic treatment [4,26].
The existence of such a situation can be explained by the absence of taking into account the variations of the individual anatomy of the teeth when positioning the bracket [27], the presence of errors in various manufacturers, which under one type of prescription can produce different angular characteristics [2,25] and the impossibility of using one standard and unified system for biological diversity various variations and types of anatomical structure of the toothjaw system.So, a number of studies indicate that the normative characteristics of the spatial position of the teeth differ significantly in different races and ethnic groups [18,22] and require the study and development of updated indicators [32].It is also noted that there is an individual variation regarding the angular positions of the teeth [17], which necessitates the development of individual prognostic techniques.
In our study, based on the peculiarities of the metric characteristics of the skull, which usually do not change during surgical and orthodontic treatment, as well as the parameters of the width, length, angles and position of the upper and lower jaws, which may be altered by orthodontic surgery, using the stepwise regression method with inclusion, in young men and women, reliable models of CT-indicators that characterize the position of individual teeth relative to each other, to the bony cranial structures and profile of the face are developed.It was established that in young men from 40 possible models, 23 were constructed with determination coefficient R 2 from 0.557 to 0.832, while young women had only 8 models with determination coefficient R 2 from 0.581 to 0.832.Moreover, in young men -out of 10 possible 9 models of vestibular-tongue inclination of corresponding teeth were constructed (R 2 from 0.557 to 0.832); out of 10 possible 5 models of mesio-distal inclination of corresponding teeth (R 2 from 0.558 to 0.769) were constructed; of the possible 14 constructed 6 models of rotation of the corresponding teeth (R 2 from 0.579 to 0.737); and in young women -only 5 models of the vestibular-tongue inclination of the corresponding teeth (R 2 from 0.603 to 0.665).In addition, in both in young men and women, models of the magnitude of the inter-incision angle (R 2 0.748 in young men and 0.581 in young women), the magnitude of the angle of inclination of the lower canine in the jet plane (R 2 respectively 0.729 and 0.793) and the values of the inclination of the closing plane relative to the palatal plane (R 2 is respectively 0.808 and 0.832).
The analysis found that in young men models most often included -the WITS score, indicating a linear interjaw ratio in the anterior-posterior direction (7.0%); angle GL_SNPOG, or the index of convexity of the soft tissue profile (5.4%); distance S_E, maxillo-mandibular angle ММ, defines the angle at which the upper jaw is located in relation to the lower jaw in the jet plane, angle NSBA (by 4,7%); angle AB_NPOG, angle N_POG_, distance N_SE, coefficient N_SP_SP, which determines the ratio of the upper and lower facial heights, as well as the soft tissue facial angle P_OR_N (by 3.9%).In young women most often models included -angle N_POG_ (14.3%); angle AB_NPOG (10.2%); indicator WITS (8.2%); angle ММ, angle ANB, indicating the angular inter-jaw ratio in the anterior-posterior direction, as well as the length of the branch of the mandible R_ASC (by 6.1%).
In further research, it is necessary to develop a computer program that will allow orthodontists to automatically calculate the necessary CT indicators that characterize the position of individual teeth relative to each other, to the bone cranial structures and profile of the face, which will enable the dentist to achieve the treatment of maximum physiological and aesthetic results.

Conclusions
1.In young men with normal occlusion close to orthognathic bite of 40 possible regression models of CT indicators that characterize the position of individual teeth relative to each other, to the bone cranial structures and profile of the face, 23 with a determination coefficient R 2 of 0.557 to 0.832 were constructed, and in young womenonly 8 models with determination coefficient R 2 from 0.581 to 0.832.
young women (aged 16 to 20 years) with normal occlusion close to orthognathic bite.Cephalometric points and measurements were performed according to recommendations of A. M. Schwarz, J. McNamara, W. B. Downs, R. A. Holdway, G. P. F. Schmuth, C. C. Steiner and C. H. Tweed

Fig. 1 .
Fig. 1.The angle between the central canines axis of the jaw of the upper jaw in the frontal projection (54) (YG13_23) -formed by lines I13-Apx13 and I23-Apx23 in the frontal projection; the angle between the central axis of the jaw of the lower canines in the frontal projection (55) (YG33_34) -formed by lines I33-Apx33 and I43-Apx43 in the frontal projection.Here and thereafter: -Apx (apex) -the top of the root of the corresponding tooth; I -the middle of the cutting edge of the corresponding tooth.

Fig. 2 .
Fig. 2. Mesio-distal inclination !! of the corresponding tooth (56) (ANGUL_!!) -formed by line I!!-Apx!! (the central axis of the corresponding tooth) and perpendicular to the closure plane (OclPl) in the frontal area of the studied tooth (in the calculation the average value of the angle of the symmetrical teeth of the right side to left side on one jaw is then taken).

Fig. 3 .
Fig. 3. Vestibular-lingual inclination !! of the corresponding tooth (57) (TORK!!) -formed by line I!!-Apx!! (the central axis of the corresponding tooth) and perpendicular to the closure plane (OclPl) in a sagittal plane of investigating tooth (in the calculation the average value of the angle of the symmetrical teeth of the right side to left side on one jaw is then taken).

Fig. 4 .
Fig. 4. Rotation !! of the corresponding tooth (58) (ROT!!) -formed by the median-sagittal plane of the tooth and the median-sagittal plane of the head, allows to determine the tooth rotation relative to the median-sagittal plane (in the calculation the average value of the angle of the symmetrical teeth of the right side to left side on one jaw is then taken).

Fig. 5 .
Fig. 5. Angle of inclination of the upper canine in the sagittal plane (61) (MDYG13) -formed by lines I13-Apx23 and line ANS-PNS in the sagittal projection (the angle formed by the central canine axis of the upper jaw and the palatal plane in the sagittal projection); angle of inclination of the lower canine in the sagittal plane (62) (MDYG33) -formed by lines I43-Apx43 and line ANS-PNS in the sagittal projection (the angle formed by the central canine axis of the lower jaw and the palatal plane in the sagittal projection).

Fig. 6 .
Fig. 6.Inter-cutter angle (YGRES) -formed by the central axes of the middle incisors of the upper I11-Apx11 and lower jaws I41-Apx41 (the indicator characterizes the angle formed by median cutters of the upper and lower jaws in the sagittal projection), (the calculation takes averaged magnitude of the angle of the symmetrical teeth of the right and left sides on one jaw).

Fig. 7 .
Fig. 7. Determination of the inclination of the closure plane relative to the palatal plane.

Fig. 8 .
Fig. 8. Determination of the inclination of the closure plane on the teleroentgenogram relative to the palatal plane. 1 -the angle of inclination of the closure plane in contact with the cutting edge of the median lower incisors (Is1L) and the further buccal edges of second molars of the mandible (DPOcl) relative to the palatal plane that passes through the point passing through the anterior (ANS) and posterior (PNS) nasal spine.
Fisher's criterion; St. Error of estimate -standard error of the standardized regression coefficient; AB_NPOG -angle formed by lines A-B and N-Pog, (defines the position of the plane AB in relation to N-pog); T (profile angle Т) -is formed by lines Sn-Pоg' and Pn (nasal perpendicular, perpendicular to the line from the point N' to the line Se-N); G (angle G, gonial angle, mandibular angle) -is formed by lines ppCond-MT2 and T2-Me, which intersect at the point tGoS; N_POG_ (angle N'Hold_Pog'_Hline) -the angle between the lines Ls-Pog' (H line, Holdway line) and N'Hold-Pog'; WITS (Wits indicator) -the distance between the constructive points AOclP and BOclP (indicates a linear intra-jaw ratio in the anteriorposterior direction); N_SE (distance Se_N or the length of the front of the skull base by Steiner) -distance from the point Se to the point N; PN_A (distance PN_A) -distance from the point А to the line PNm (perpendicular line from the point N to the line Po-Or); S_E (distance S_E or the length of the back of the skull base by Steiner) -distance from the point S to a constructive point Е, which is located at the crossroads of the perpendicular conducted from the point ppCond to the line S-N; MAX_MAND (maxillo-mandibular difference) -difference between distances Cond-A (42') and Cond-Gn (42''); AFH (distance AFH or front height of the face) -distance from the point Мe to the line ANS-PNS; NL_NSL (angle NL_NSL, also angle SNSpP) -is formed by lines ANS-PNS and S-N (angle of the palatal plane to the base of the skull inclination); LPALAT (the size of the base of the upper jaw) -distance between points ANS and PNS; COND_GN (effective length of mandible, or distance COND_GN) -distance from the point Cond to the point Gn; PFH (distance PFH or back height of the face) -distance from the point Ar to the point tGo; FMA (POr_MeGo, angle FMA, Frankfort Mandibular Angle) -is formed by lines tGo-Me (mandibular plane Mp) та Pо-Or (Frankfurt plane Fp); SND (angle SND) -is formed by lines S-N and N-D (indicates the anterior-posterior arrangement of the symphysis of the mandible to the base of the skull); ML_NL (SpP_GoMe, base angle) -is formed by lines ANS-PNS and tGo-Me (the angle between the palatal SpP and the mandibular MP planes); B (base angle) -is formed by lines ANS-PNS (palatine plane SpP) and Im-Me (mandibular plane MPS by Schwarz) (indicates the angle between the upper and lower jaws); COND_A (effective length of the upper jaw) -distance from the point Cond to the point A; SNA (angle SNA) -is formed by lines S-N and N-A, (the angle indicates the anterior-posterior position of the upper jaw to the base of the skull); MAND (length of mandible) -distance from the constructive point tGoS to the constructive point apMandS; F (facial angle or angle F) -is formed by lines Se-N and N-A (determines the location of the anterior contour of the upper jaw in the jet plane to the base of the skull); ANS_ME (lower face height) -distance from the point ANS to the point Ме; ML_NSL (angle ML_NSL or angle SN_GoMe) -is formed by lines tGo-Me and S-N, (inclination angle of the mandibular plane to the base of the skull); NBA_PTGN (angle NBa-PtGn or the angle of the front axle) -is formed by lines N-Ba and Pt-Gn (determines the direction of development of the mandible); SN_GOGN (angle SN_GoGn) -is formed by lines Go-Gn and S-N (inclination angle of the lower jaw plane by Steiner, to the base of the skull); MM (maxillo-mandibular angle) -is formed by lines A-B and ANS-PNS (defines the angle at which the upper jaw is located in relation to the lower jaw in the jet plane); MAX (length of the upper jaw) -distance from the constructive point apMax to the point PNS; NSBA (angle NSBA)