Regression models of teleroentgenograhic indicators of the position of teeth and the profile of face soft tissues in juvenile aged persons with different face types according to Schwarz A.M

Considering the differences in the values of teleroentgenograhic (TRG) indicators in different racial, gender, ethnic, age, population, geographical population groups and numerical methods of TRG analysis, determination of normative values of cephalometric, gnatometric TRG-indicators, their interdependencies in the population of different countries is extremely important both for human anatomy and for the practice of dentists. This fully applies to residents of Ukraine of different age groups. The aim of the work is to develop and analyze regression models of teleroentgenograhic indicators of tooth position and facial soft tissue profile according to Schwarz A.M. in Ukrainian young men and young women with different facial types. Lateral teleroentgenograms of 49 young men (aged 17 to 21 years) and 76 young women (aged 16 to 20 years) with physiological occlusion as close as possible to orthognathic were analyzed. In the license package "Statistica 6.0" regression models of indicators of position of teeth and profile of soft tissues of the face according to the method of Schwarz A.M. depending on basic cephalometric and gnatometric indicators separately for boys and for girls with different types of the face are constructed. In young men, 16 of the 24 possible reliable regression models were constructed, in which the coefficient of determination is greater than 0.6 (R2=from 0.609 to 0.998). For young men with 1st (back face type) and 3rd (front face type) face types, the following models were created with respect to 5 indicators from 8 possible (respectively, angles Max1-SpP S-arz, distances Sn-Pn and Pog'-Por, angles Gl'LsPog' and SnPog'-Pn; R2 = from 0.609 to 0.998 and angles Max1-SpP S-arz and Mand1-MP Schwars, distances Sn-Pn and Pog'-Por, angle Gl'LsPog'; R2 = from 0.609 to 0.946), and for young men with 2nd face types (average face type according to Schwarz AM) for 6 indicators (angles Max1-SpP S-arz and Mand1-MP Schwars, distances Sn-Pn and Pog'-Por, angles Gl'LsPog'and SnPog'-Pn; R2 = from 0.690 to 0.990). In young women, 17 of the 24 possible reliable models with R2 greater than 0.6 (R2 = 0.628 to 0.958) were constructed. For young women with 1st type of face 6 indicators are modeled angles Max1-SpP S-arz, distances Sn-Pn and Pog'-Por, angles Gl'LsPog'and SnPog'-Pn, the distance of Li-SnPog'(R2= from 0.663 to 0.958). For young women with 2nd face type, the following models were created for 7 indicators angles Max1-SpP S-arz and Mand1-MP Schwars, distances Sn-Pn and Pog'-Por, angles Gl'LsPog' and SnPog'-Pn, distances Li-SnPog'(R2= from 0.628 to 0.891). For young women with 3rd face type the smallest number of models with R2 larger than 0.6 was built, compared to all groups of persons with different face types only 4 models for Max1-SpP S-arz angle, Pog'-Por distance, angles Gl'LsPog' and SnPog'-Pn (R2 from 0.718 to 0.847).


Introduction
Determination of cephalometric parameters, morphometry of parameters of craniofacial structures, indicators of the human dental apparatus have always occupied an important place both in anatomical research and in the practice of dentists, surgeons, cosmetologists, etc. The most valuable, informative and accessible method for determining such indicators was X-ray cephalometric analysis using lateral teleroentgenography. The method of teleroentgenography allows to obtain a lifetime image of the head and its bone structures, soft tissues of the face in full accordance with their actual size and location, allows to obtain both qualitative and quantitative linear and angular morphometric parameters [1,16,18]. But there are still a number of unresolved problems in determining and interpreting the results of teleroentgenography -there are dozens of author's methods of such research, which are used by researchers and practitioners intuitively, based on their own experience and preferences, or the priorities of their choice in a particular country or medical institution; frequent discrepancy between the author's indicators established on certain samples of the population and the indicators received by researchers on other samples depending on racial [2,14,17], ethnic [21,25,32], population [13,22] features of the population of different geographical zones, different countries [12,20,23].
Therefore, determining the features of cephalometric, gnatometric teleroentgenograhic (TRG) indicators of the population of different countries is extremely important for both human anatomy and practice, especially dentists, orthopedists, orthodontists, specialists in maxillofacial surgery. In recent years, a number of scientific and practical developments in this direction have appeared in Ukraine [8,9,27]. An important place among such studies is occupied by works on mathematical modeling of individual teleroentgenograhic indicators of various methods of cephalometric analysis, inherent in persons with orthognathic occlusion, which is necessary primarily for practical use in dentistry [5,6,10,15,24].
The aim of the work is to develop and analyze regression models of teleroentgenograhic indicators of tooth position and facial soft tissue profile according to Schwarz A.M. in Ukrainian young men and young women with different face types.

Materials and methods
We analyzed lateral teleroentgenograms in residents of Ukraine of the youth age group -49 young men (aged 17 to 21 years) and 76 young women (aged 16 to 20 years) with a physiological bite that was as close as possible to orthognathic (hereinafter "orthognathic bite"). Teleroentgenograms were obtained on a dental cone-beam tomograph Veraviewepocs 3D Morita (Japan). Some of the primary indicators of teleroentgenograms were obtained from the database of the research center of National Pirogov Memorial Medical University, Vinnytsya.
The obtained teleroentgenograhic indicators were divided into 3 groups [6,7]. Indicators of group 1 -metric characteristics of the skull, defined in the classical methods of A. Bjork [3], C.J. Burstone [4], J.R. Jarabak [19], R.M. Ricketts [28], A.M. Schwarz [29,30] and S.S. Steiner [31] and which in the process of surgical and orthodontic treatment usually do not change, but act as basic indicators of cephalometric analysis in relation to which the lateral radiographs determine the inclination, position of the upper and lower jaws, closing plane and individual teeth. The second group of indicators -teleroentgenograhic indicators of the upper and lower jaws, inter-jaw indicators according to the method of A.M. Schwarz [29,30], the definition of which is most often focused during orthodontic surgery when necessary to correct the length, width, angles and position of the upper and lower jaws.
The third group of indicators included teleroentgenograhic indicators of the position of the teeth and the profile of the soft tissues of the face according to the method of A.M. Schwarz [29,30]: angle Max1-SpP S-arz (°)is formed by lines Ap1u-Is1u (inclination of the central axis of the upper medial incisor) and ANS-PNS (palatal plane, SpP); angle Mand1-MP Shwars (°) -is formed by lines Ar1L-Is1L and Me-Im and determines the position of the axes of the mandibular incisors relative to the mandibular plane according to A.M. Schwarz; angle II (°) -inter-cutter angle, formed by lines Ap1u-Is1u (central axis of the upper medial incisor) and Ar1L-Is1L (central axis of the lower medial incisor); distance Sn-Pn (mm) -determines the position of the point Sn relative to the perpendicular Pn; Pog'-Por distance (mm) -the distance from the Pog' point to the orbital perpendicular Por (determines the position of the chin relative to the perpendicular to the Frankfurt plane, drawn through the orbit); angle GI'LsPog' (°) -formed by lines Gl'-Ls and LsPog' (determines the convexity of the face); the angle SnPog'-Pn (°) -formed by the lines SnPog' and the perpendicular Pn and the distance Li-SnPog' (mm) -determines the position of the point Li relative to the line SnPog'.
Young men and young women were divided into separate groups with different face types according to A.M. Schwarz [29] depending on the values of the facial angle F, which is determined between the Se-N lines (line from the constructive point Se) (sellia turcica entru) in the middle of the distance between back and front inclined wedgeshaped processes to point N (nasion)) and N-A ((line from point N (nasion) to point A (subspinale), the most posterior point of the anterior contour of the upper jaw)): 1 type (back face type according to Schwarz A.M.) -13 young men or 23 young women, angle F up to 83°; 2 type (average face type according to Schwarz A.M.) -18 young men or 24 young women, angle F from 84° to 87°; 3 type (front face type according to Schwarz A.M.) -18 young men, or 29 young women, angle F>87°.
Conducted mathematical modeling of teleroentgenograhic indicators of 3 groups depending on TRG indicators of 1 or 2 groups in young men and young women with different face types according to Schwarz A.M. using the method of step-by-step regression analysis in the license package "Statistica 6.0". The following conditions were observed during the regression analysis: the final version of the obtained model must have a coefficient of determination (R 2 ) of not less than 0.60; the value of the F-criterion is not less than 3.0; the number of independent variables of the equation should be as small as possible.
The Biomedical Ethics Commission of National Pirogov Memorial Medical University, Vinnytsya, Ukraine has established that the conducted research and applied research methods correspond to the international and domestic bioethical and moral and legal requirements and laws of Ukraine (protocol №8 dated 5.10.2017).

Results
The results of simulation of teleradiographic indicators of the position of the teeth and the profile of the soft tissues of the face in adolescents with different types of faces according to Schwarz A.M. have the form of the following regression equations.

Discussion
A number of works have proved the fundamental possibility of modeling teleroentgenograhic parameters of the dental apparatus in Ukrainian young men and young women depending on cephalometric parameters. However, the coefficients of determination R 2 , which in the evaluation of regression models are interpreted as the conformity of the model to the data and indicate the efficiency of the model in different researchers differ significantly. I.V. Gunas and co-authors [15] constructed and analyzed regression models of TRG parameters used in the method of C.J. Burstone in young men and young women with normal occlusion and a harmonious face. Moreover, the authors managed to obtain regression models with R 2 >0.6 for all 6 studied indicators of the second group and for all 7 indicators of the third group, depending on the indicators of the first group.
A.V. Chernysh and co-authors [6] built regression models of individual cephalometric parameters in young men and young women used in the method of E.P. Harvold: young men have all possible models of TRG-indicators, which are included in the second group, depending on the indicators of the first group with R 2 from 0.616 to 0.940, and young women have built such models only for indicators of the length of the upper and lower jaws with R 2 , respectively, 0.857 and 0.792. Also, these researchers built reliable models of the third group (angle Ap1uAp1l-DOP) depending on the indicators of the first and second groups, both for young men (R2 = 0.626) and for young women (R 2 = 0.584).
A.V. Chernysh also performed simulations of the cephalometric parameters used in the R.M. Ricketts method [5]. For young women built almost the same number of models -17 of the 24 possible reliable regression models in which the coefficient of determination is greater than 0.6 (R 2 = from 0.628 to 0.958). But the number of models for certain groups of people with different face types, as well as the indicators for which such models were created in young women differed slightly. For young women with the first type of face, the following models were created for 6 indicators -in addition to the same five indicators (R 2 = from 0.699 to 0.958), as for young men of the first group, a model was built for the distance Li-SnPog' (R 2 = 0.663). For young women with the second type of face, the following models were created for 7 indicators -in addition to the same six indicators (R 2 = from 0.660 to 0.891), as for young men with the second type of face, a model was also built for the distance Li-SnPog' (R 2 = 0.628). Instead, for young women with the third type of face, the smallest number of models with coefficients of determination greater than 0.6, compared to all groups, both young men and young women with different facial types -only 4 models for the angle Max1-SpP S-arz, Pog'-Por distances, Gl'LsPog' and SnPog'-Pn angles (with R 2 from 0.718 to 0.847). Compared with the group of young men with the third type of face, young women with this type of face were not built models with a coefficient of determination greater than 0.6 for the angle Mand1-MP Schwars and the distance Sn-Pn, instead -such a model was created for the angle SnPog'-Pn.
It should be noted that for Max1-SpP S-arz, Gl'LsPog' and Pog'-Por distances, models with a coefficient of determination greater than 0.6 have been developed for both young men and young women of all face types. For the Sn-Pn distance, such models are designed for young men of all face types and for young women of all face types except the third type, and for the SnPog'-Pn angle, on the contrary, for young women of all face types and for young men of all face types except the third type. The Mand1-MP Schwars angle was modeled with a coefficient of determination greater than 0.6 in young men with the second and third facial types and in young women with the second facial type, and the Li-SnPog' distance was modeled only in young men with the first and second facial types.
The inter-incisor angle II in all models of young men with different face types and young women with the first and second face types was modeled with coefficients of determination less than 0.6, and in young women with the third face type the model of this indicator was not built at all.
Regression equations of Li-SnPog' distance values had coefficients of determination less than 0.6 in young men of all face types (R 2 from 0.312 to 0.574) and in young women with 3 face types (R 2 = 0.494), and coefficients of determination of regression equations of Mand1-MP Schwars angle values were less than 0.6 in young men with 1 facial type (R 2 = 0.569) and in young women with 1 and 3 facial types (respectively, R 2 = 0.121 and R 2 = 0.597).
In young men with different types of faces to the constructed models of teleroentgenograhic indicators, which were included in the third group according to the method of Schwarz A.M. most often includes the following TRG indicators of the first and second groups: profile angle T (21.4%), angle H according to A.M. Shwars (16.1%) and angles MM (maxillary-mandibular angle), B (basal angle, angle between upper and lower jaws) and distance R.asc. (length of the branch of the mandible) (7.1%).
In young women models of teleroentgenograhic indicators of the third group according to the method of A.M. Schwarz most often includes the following TRG indicators of the first and second groups: profile angle T and angle H according to A.M. Shwars (13.9% each), angle MM (maxillarymandibular angle) (11.1%) and angle F (facial angle) (6.9%).
In our opinion, the practical application of the created regression models of teleroentgenograhic indicators of tooth position and soft tissue profile of the face depending on the basic cephalometric indicators and gnatometric indicators of the upper and lower jaws based on sex, face type will provide an individual approach to the patient and the best consequences of treatment in case of need of surgical correction of these indicators at inhabitants of Ukraine of youthful age.

Conclusions
1. In young men, residents of Ukraine with orthognathic occlusion and with different types of faces according to A.M. Schwarz, constructed 16 of 24 possible reliable regression models with coefficients of determination greater than 0.6 (R 2 = from 0.609 to 0.998) groups of teleroentgenograhic indicators of the position of the teeth and the profile of soft tissues of the face, which can be corrected during surgery, orthopedic interventions in dentistry depending on the group of basic, invariable cephalometric indicators and the group of teleroentgenograhic indicators of the upper and lower jaws. In young women with different face types, 17 of the 24 possible models in which the coefficient of determination is greater than 0.6 (R 2 = from 0.628 to 0.958) were constructed.
2. The created models are suitable for use in the practice of dentists, cosmetologists in order to provide an individualized approach to determining the tactics, scope and improvement of the consequences of interventions when necessary to correct these indicators in adolescents.