## 2 Materials and Methods
### Diagnosis and Treatment Plan  
Transversal measurements of the maxilla showed a distance of 21.86 mm between primary canines and 29.04 mm between primary second molars. According to the study of [PERSON] and coauthors [4; 24], a clinical value of inter-molar distances \(\leq\) 31 mm should be considered as a cut-off parameter for diagnosis of narrowed maxillary requiring treatment by maxillary expansion. However, considering that the patient was only 6 years old and that she presented full primary dentition, this cut-off could be higher considering the potential growth of the patient [24]. Thus, the maxillary contraction could be considered as moderate in severity.  
Emi-lateral distances to the MPP at the primary canines level were 12.24 mm at the right side and 11.60 mm at the left side. The same distances at the first molars level were 16.80 mm at the right side and 16.82 mm at the left side. Thus, no relevant differences were detected between right and left side concerning transversal linear measurements. Additionally, the deviation analysis of mirrored superimposed models of the maxilla revealed a good coincidence between the two models, as shown by the the colored map (green color). In particular, Figure 9 shows no areas of mismatching (intense blue and intense red contours) between the original and specular model either in the palatal vault or along the profile of the dento-alveolar processes.  
Thus, according to the diagnostic information obtained, the patient presented a slight bilateral symmetric contraction of the palatal vault with symmetric contraction of the alveolar process of the upper arch. As a consequence, our treatment goal was to correct the maxillary transverse deficiency by symmetrically expanding both the palatal vault and dento-alveolar processes, eliminating those occlusal interferences causing an altered posture of the mandible (mandibular shift). Along with this outcome, it was imperative to correct the anterior openbite in order to restore a correct functional posture of the tongue during swallowing and biting.  
We decided to construct a maxillary removable mono-block with a built-in Hyrax screw and with an anterior grid that was extended 3-4 mm below the lower incisor's marginal edge. This grid forced the tongue in a more physiologic position (backward and upward), with the tip of the tongue contacting the retro-incisal papilla (Figure 10 A,B). With the tongue in a more backward position, upper and lower incisor were left free to erupt facilitating the closure of the bite [25], without the application of orthodontic forces on these teeth. The screw was slowly activated, i.e., two times a week up to the clinical assessment of crossbite resolution and correction of mandible posture in centric relation, with both maxillary and mandibular midlines coincident.  
Figure 9: 3D deviation analysis between the two specular models. RGB colored scale bar (millimeters) is reported on the right side: the top (red colored) and the bottom (blue colored) of the scale indicate total mismatching. Green indicates matching percentage. As shown, both palatal shells (original and mirrored) were fairly matched. Some amount of mismatching (light blue and orange contours) were located along the cervical contour of posterior teeth, due to dento-alveolar positional differences.