## 2 Materials and Methods  
The FEA solid model of a 3D skull was reconstructed from CBCT images of a male subject by using medical image reconstruction of the Avizo software (version 7.0; Visualization Sciences Group, Burlington, MA, USA). The boundary of cortical and cancellous bone of the maxillpalatal arch was determined and selected from each CT section to build the 3D model for preparing a standard maxillpolatal model in this study. The 3D maxillpolatal model was a homogenized FEA model, which was assumed to have linear elastic, homogenous, and isotropic properties. The total number of elements and nodes in the FEA model was 153,954 and 237,842, respectively. The ranges of element size, with edges from 0.3 to 1.5 mm, were considered to mesh in the FEA model according to investigating importance of the maxillpolalatine and the expansion devices. Figure 1 is the solid model of the skull, which included the cortical shell, cancellous bone, and midpalatal suture. The virtual skull model excluded other sutures, such as pterygomaxillary, zygomaticomaxillary, and zygomaticotemporal sutures. In this stage, teeth displacement was disregarded when analyzing effects of MARME on midpalatal suture opening. Hence, maxillary dentition, which was assumed to have the same material properties as cortical bone, was not isolated when tooth models were reconstructed from CBCT images. The skull model had a cortical bone thickness and a midpalatal suture width of 2 mm and 1.5 mm, respectively. The mini-implants (2.0 mm in diameter; 6, 8, 10, 12, 14, and 16 mm in length; A1 Series; Bio-Ray, Biotech Instrument Co., Taipei, Taiwan) and a specified bone-borne maxillary expander design (skeletal maxillary expander, SME; Bio-Ray, Biotech Instrument Co.) were constructed with CAD software (SolidWorks 2010, Solidworks Corp, Waltham, MA, USA) according to design specifications provided by the manufacturer. The CAD model of the SME included the expansion screw (diameter, 2 mm), transverse rods (diameter, 1.5 mm), expansion sliders, support wires (diameter, 1 mm) (Figure 2), and fixed bands. Six expansion miniscrews of varying lengths were selected to investigate the effect of transverse displacement of palatal bone under application of expansion force caused by increased mechanical resistance in the midpalatal suture. Varying combinations of two different lengths of miniscrews inserted into the palatal bone were modeled to study the mechanical effect in clinical treatment. Figure 3 shows the FEA models with different miniscrews in lengths in this study. The miniscrews were placed on both sides in the palatal aspect. Model A of monocortical anchorage was modeled using monocortical miniscrews 6 mm in length located at the posterior and anterior positions; model B of monocortical deepening anchorage was modeled using monocortical miniscrews 8 mm in length located at the posterior and anterior position; model C of bicortical anchorage was modeled using bicortical miniscrews 10 mm in length located at the posterior position and 12 mm in length located at the anterior position; model D of bicortical deepening anchorage was modeled using bicortical miniscrews 14 mm in length located at the posterior position and 16 mm in length located at the anterior position. Two different miniscrew compositions, stainless steel and titanium alloy, were  
Figure 1: The 3D skull FEA model with midpalatal suture. Point A, the most anterior point of nasal floor; point B, the most anterior inferior point on the maxillary alveolar process; point C, the most posterior point at the posterior margin of the hard palate. also investigated. The mechanical properties of the cortical bone, cancellous bone, suture, titanium alloy, and stainless steel in the model were defined according to previous studies, as shown in Table 1[21; 22; 23; 24]. The boundary condition of the FEA model was fixed at the whole surface of cutting plane in the skull to restrict degree of freedom in the translation and rotation.