## 2 Materials and Methods  
The present numerical study is part of a larger step-by-step developed project [1; 21; 22; 23; 24; 25] (clinical protocol 158/2 April 2018) assessing the proper finite elements method and boundary conditions to investigate the biomechanical behavior of dental tissues during orthodontic movements and various bone loss levels. Here, we ran 486 numerical simulations for FEA, analyzing 81 lower premolar models from nine patients (mean age 29.81 \(\pm\) 1.45 years, 4 males, 5 females, oral informed consent). Our sample size was nine, more than the above-mentioned FEA studies that used a sample size of one (since numerical studies require only a small sample size). The including criteria were a complete mandibular dental arch in the region of interest, with no malposition and intact teeth (no endodontic treatment, no filling or crown) in the analyzed region, no advanced bone loss, non-inflamed periodontitis, orthodontic treatment indication, and proper oral hygiene. The non-suitable patients were rated as such due to their incomplete mandibular arch, malposition, or non-intact teeth, in the region of interest. From the patients that were included in the study, other exclusion criteria were considered to be less common root geometry (e.g., non-fused double rooted, angulated root, root extreme curvature etc. ), an abnormal shape of the crown, deciduous teeth, abnormal root surface defects (e.g., external root resorption) or bone shape (various types of bone defects radiological visible), an abnormal pulp chamber (internal resorption, radiologically identified), bone loss of more than 2-3 mm, any signs of inflamed periodontium or bad oral hygiene after the acceptance in the study. The region of interest was the mandibular lateral region with the two molars and premolars, which was analyzed by means of CBCT (cone beam computed tomography, ProMax 3 DS, Planmeca, Helsinki, Finland, 0.075 mm voxel size). The reconstruction software was Amira 5.4.0 (Visage Imaging Inc. 300 Brickstone Square, Suite 201 Andover, MA, USA). The reconstruction was manually performed, since the automated process did not identify and separate the various shapes of grey anatomical tissues on DICOM slices. The analyzed model included the second lower premolar, with the surrounding bone, PDL, and NVB, while the alveolar sockets of the other three teeth were filled with cortical and trabecular bone. The manual reconstruction process identified and reconstructed all dental tissue components, including enamel, dentine, dental pulp, NVB, cortical bone, and trabecular bone. The cementum component failed to be clearly separated from the dentine component; thus, it was reconstructed as dentine, due to their similar physical properties (Table 1). All components were assembled into a single 3D mesh model (Figure 1). The PDL has a variable thickness of 0.15-0.225 mm, with NVB included in the apical third. On the vestibular side of the crown (enamel surface), the base of a stainless-steel bracket was reconstructed. For each of the nine patients, a mesh model with limited various bone loss levels (limited to the cervical third) was obtained. The nine second premolar models included seven that were single-rooted and three that were fused and double-rooted. The missing bone and PDL were manually reconstructed to obtain a mesh model with intact periodontium. The mesh models had 5.06-6.05 million C3D4 tetrahedral elements, 0.97-1.07 million nodes, and a global element size of 0.08-0.116 mm (i.e., a high level of anatomical accuracy, when compared with the above-mentioned FEA studies). The manual reconstruction displayed a limited number of surface irregularities in all models, located in non-essential areas (i.e., quasi-continuous stress areas) (Figure 2). All internal quality control checking algorithms were successfully passed, with no element errors, and with only a limited number of element warnings (e.g., the maximum number of elements warnings was 264 [0.0043%] for a total number of 6.05 million elements).