## 1 Introduction
[PERSON] [36] reported a spontaneous adaptation of the mandible after a change in the transversal dimension of the maxilla, which included a correction of the inclination of the teeth in both the lateral and frontal areas, which was also due to a change in the balance between the tongue and the bucciinator muscles. Some rotations of the maxillary anterior teeth, corrections, counter-clockwise rotation, and medialization of the mandible are reported. Spontaneous correction of class III malocclusion has been described by other authors [37; 38; 39]. One of the most important parameters in orthodontic diagnostics is the perimeter of the dental arch (PA). Many methods have been developed to measure it and predictions have been made about its expected normal values. The fastest and most accurate in modern orthodontic practice is its digital measurement on scanned models with specialized software [40; 41; 42; 43]. For patients, the new digital methods in dental practice are interesting and well accepted and are associated with less discomfort due to their precision [44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. Many authors propose their own methods for digital measurement of the dental arch perimeter, dividing dental arch in segments and measurement of the individual parameters [63; 64; 65; 66; 67; 68]. Other authors use well-known equations in geometry such as [PERSON]'s [69; 70] to calculate the perimeter of the dental arch accepting the condition that the form of the arch is elliptical [71; 72]. The changes in the parameters of the arch--width and length--affect both the perimeter and its shape. A number of scientists, through software and analysis of parameter values, report the existence of a relationship between parameter values and the shape of the dental arch [73; 74; 75]. There is no standardized method for digital measurement of the dental arch perimeter, and many authors propose their own methodologies [62; 63; 64; 66; 76]. Based on the digital measurements made, dependencies between the parameters are derived, and a model for the prediction of perimeter is created, most often in the form of an equation [64; 68; 70; 72; 77; 78; 79; 80; 81; 82]. The gained space in the dental arch perimeter, after treatment with the RME appliance, is highly important in borderline cases when the clinical decision is between extraction and non-extraction treatment. [PERSON] [82] finds that the maxillary arch perimeter increases at a rate of approximately 0.7 mm for each millimeter change in first premolar width. [PERSON] [83] reports an increase in the dental arch perimeter with the same magnitude as the increase in maxillary width. [PERSON] [84], in a long-term evaluation, examined the records of 112 patients treated with RME followed by fixed appliances and examined the changes in dental arch dimensions. The study is of high clinical importance and gives full information about all parameters of the dental arch. [PERSON] [85] examines the effects of rapid maxillary expansion in the early mixed dentition. He finds a 4 mm increase in maxillary dental arch perimeter and proves that the results are reliable and stable with time. In the reviewed literature, a lot of authors investigated the outcomes and results with RME appliances, analyzing only the changes in the transversal dimension of the dental arch. There is a need for deeper research on the changes in the sagittal dimension of the maxilla and for exploration of whether there is a relationship between dental arch parameters such as dental arch perimeter, width, and length. The aim of the present study is to evaluate the change in dental arch parameters--perimeter, width, and length--after treatment with a printed RME appliance. The investigation follows the dynamics of changes in all parameters from a period before treatment until the removal of the RME and explores the correlational connections between them.