## 4 Discussion  
The surgically assisted rapid maxillary expansion therapy is successful when optimal widths of the upper dental arch are achieved. The increase in transverse dimensions should be skeletal, not dental, which determines stability in the treatment of the disorder [23; 24]. After bone growth is complete, it is necessary to perform surgical procedures to release the bone resistance sites in the midface region and therefore allow for maxillary expansion [13; 17]. The anatomical structure of the maxilla is reinforced by the aperture piriformis (anterior reinforcement), zygomaticoalveolar crest (lateral reinforcement) and pterygopalatine suture (posterior reinforcement). The reinforcements begin at the base of the maxillary alveolar process and run vertically, bending around the orbital rim down to the base of the skull [25; 26]. Le Fort I osteotomy with separation of all bone junctions around the maxilla and sagittal osteotomy without separation of the nasal septum is proposed by [PERSON] [13]. The inventor of the method of surgically assisted maxillary expansion using a bone-borne appliance (TPD--transpalatal distraction) declares that this method of expansion has good effects. The finite element analysis is a good simulation for evaluating surgical procedures performed on the facial skeleton in the method of surgically assisted rapid maxillary expansion [27; 28]. It allows one to evaluate complex stress distributions and displacement patterns on the facial skeleton model [29]. Interpretation of the results of the analysis should be made carefully and prudently, because it is a skeletal model created on the basis of a 3D computed tomography reconstruction of the facial skeleton with material properties assigned according to [PERSON] et al. [22]. Currently, in the literature, there is no agreement as to the scope of osteotomy in surgically assisted rapid maxillary expansion [17; 20; 30; 31]. What method should be chosen? It seems that the therapeutic team's experience and the surgeon's preferences are of great importance in this regard [17]. The authors' study presents six variants of the approach to the subject of surgically assisted maxillary expansion. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Variable** & **Model I** & **Model II** & **Model III** & **Model IV** & **Model V** & **Model VI** \\ \hline X & Mesial incision angle of maxillary tooth 1 & +0.04 & +0.31 & +0.04 & +0.04 & +0.31 & +0.4 \\ \hline  & Buccal cusp tip of maxillary tooth 5 & +0.04 & +0.22 & +0.04 & +0.13 & +0.31 & +0.31 \\  & Postrolateral surface of the maxilla & +0.04 & +0.22 & +0.04 & +0.04 & +0.22 & +0.22 \\  & Apertura piriforms—the lowest point & +0.04 & +0.22 & +0.04 & +0.04 & +0.22 & +0.22 \\ \hline Y & Mesial incision angle of maxillary tooth 1 & \(-\)0.05 & +0.05 & \(-\)0.5 & \(-\)0.5 & +0.05 & +0.07 \\ \hline  & Buccal cusp tip of maxillary tooth 5 & +0.01 & +0.03 & +0.01 & +0.03 & +0.03 & +0.01 \\  & Postrolateral surface of the maxilla & +0.01 & +0.03 & +0.03 & +0.05 & +0.03 & +0.01 \\  & Apertura piriforms—the lowest point & \(-\)0.03 & +0.03 & \(-\)0.03 & \(-\)0.03 & +0.03 & +0.05 \\ \hline Z & Mesial incision angle of maxillary tooth 1 & \(-\)0.03 & +0.01 & \(-\)0.03 & \(-\)0.03 & \(-\)0.05 & \(-\)0.05 \\ \hline  & Buccal cusp tip of maxillary tooth 5 & \(-\)0.03 & +0.07 & +0.01 & +0.03 & +0.07 & +0.05 \\  & Postrolateral surface of the maxilla & +0.03 & +0.07 & +0.03 & +0.07 & +0.07 & +0.07 \\  & Apertura piriforms—the lowest point & \(-\)0.03 & +0.01 & \(-\)0.03 & \(-\)0.03 & \(-\)0.05 & \(-\)0.05 \\ \hline  & X—buccolingual; (+)—buccal, (–)—lingual; Y—anteriorposterior (front-back); (+)—anterior, (–)—posterior; \(Z\)—superioinferior (upper part-lower part); (+)—superio, (–)—inferior. & & & & \\ \end{tabular}
\end{table} 
Table 4: Displacement values of selected anatomical structures (mm) along the X, Y, Z, with various surgical procedures and tooth born orthodontic appliance using finite element analysis.