## 2 Materials and Methods  
This numerical FEA analysis is part of a larger step-by-step research project [2; 3; 5; 6; 9; 10; 16; 48] (with clinical protocol no. 158/02.04.2018) investigating the FEA methodology to improve the accuracy of numerical study results and to assess the biomechanical behavioral changes in dental tissues produced by the periodontal breakdown. Herein, the study performed 810 numerical simulations on 81 models of the lower premolar from nine patients (with mean age 29.81 \(\pm\) 1.45 years, four males, five females, oral informed consent); thus, a sample size of nine. Nevertheless, it must be emphasized that all FEA numerical studies mentioned above used a sample size of one (one patient, one model, and a few numerical simulations). Thus, the sample size used here was found to be acceptable. Initially, more patients were examined, but only nine met the inclusion criteria (intact mandibular arch, intact teeth, no malposition, non-inflamed periodontitis, no advanced bone loss, orthodontic treatment indication, regular follow-up availability, good oral hygiene). The exclusion criteria were in opposition to the above. The mandibular region with two molars and premolars received a CBCT examination (cone beam computed tomography, ProMax 3 DS, Planmeca, FI-00880 Helsinki, Finland, 0.075 mm voxel size). The DICOM slices containing various shades of gray were loaded in Amira 5.4.0 (Visage Imaging Inc., 300 Brickstone Square, Suite 201, Andover, MA 01810, USA) reconstruction software. The reconstruction process was manual since the automated software function did not correctly identify all tissular components, thereby enhancing the anatomical accuracy of the models. Only the second lower premolar was reconstructed, while the alveolar bone socket of the other three teeth was filled with bone (cortical and trabecular). All dental tissue components were identified and reconstructed: enamel, dentine, dental pulp, neuro-vascular bundle (NVB), periodontal ligament (PDL), cortical and trabecular bone (Figure 1). Cementum could not be separated from dentine; thus, due to the similar physical properties, it was reconstructed as dentine. PDL had a variable thickness of 0.15-0.225 mm and included NVB in its apical third. The base of a stainless-steel bracket was reconstructed on the enamel component. Since the models had various but small levels of bone loss, limited to cervical third, the missing bone and PDL were reconstructed, thus obtaining nine models with intact periodontium of 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 (high anatomical accuracy, when compared with the above-mentioned numerical studies). Due to the manual reconstruction process, all models displayed a small number of surface irregularities in non-essential areas (the stressed areas were quasi-continuous). All internal mesh testing for verifying the algorithm base processes in both software resulted in no mesh/element errors, with only a limited number of element warnings (Figure 2, yellow dots). Thus, for one of the intact periodontium nine models from a total number of 5.06-6.05 million elements, there were only 264 element warnings (representing 0.0043%): 201 (0.0039%) of 5,117,355 bone structure elements, 63 (0.00677%) of 930,023 of tooth, bracket, and PDL elements, 39 (0.00586%) of 665,501 tooth and bracket elements, 26 (0.00459185%) of 566,221 radical dentine-cementum and coronal dentine elements, and 17 (0.0141469%) of 120,168 enamel and bracket elements (Figure 2). A gradual horizontal periodontal breakdown process (0-8 mm) was simulated by reducing the bone and PDL by 1 mm, thus obtaining eighty-one models. All numerical simulations were performed using Abaqus 6.13-1 software (Dassault Systemes Simulia Corp., Stationsplein 8-K, 6221 BT Maistricht, The Netherlands). The boundary conditions were isotropy, linear elasticity, and homogeneity (similar to the above-mentioned numerical studies, Table 1).