## 2 Materials and Methods  
Numerical models were prepared using CAD tools (SolidWorks) to accommodate individual anatomical characteristics of the mandible. A spatial model of a computationally reconstructed mandible with average anatomical features was selected, from which a parametric model was derived (Figure 1). The mandibular model included a cortical bone plate, while trabecular bone behavior was approximated using a homogeneous internal structure. The model was constructed based on a reconstruction from a surface triangular mesh (STL) using B-spline curves, as automatic surface reconstruction methods failed despite mesh repair and achieving a continuous, defect-free STL mesh. No software was available to directly generate a finite element mesh from the STL. However, this approach offered the advantage of allowing control over the bone thickness dimensions in the region of the implant fixation screw. A resection area was designated, and a prosthetic model was designed (Figure 2), shown in assembly view with the mandible. Figure 1: CAD parametric model of the mandible: (**a**) without implant, (**b**) with implant. Fixation screws of 2 mm in diameter and 6 mm in length were assumed, simplified to cylindrical shapes without threads. Cylinders were introduced for the molars and incisors to allow proper occlusal support alignment with the bone surface, maintaining the occlusal plane distance. The resection area, implant model, and bone fixation region were designed in consultation with an oral and maxillofacial surgery specialist. Fixations were designed similarly to standard bone fixation plates to facilitate intraoperative manual adaptation by surgeons. Figure 3 presents the mandibular model with an implant, indicating joint support points and three occlusal support variants on the incisor (C), natural molar (D), and prosthetic molar on the mandibular prosthesis side (E). Muscle attachment areas and force vectors are also shown. Muscle force vectors and magnitudes (active forces) were activated in the model according to one of the three analyzed bite scenarios (support reaction enabled in simulation). Muscle force values were based on known physiological data and previous FEM studies to ensure identical oblique occlusal reaction forces across cases, reaching the maximum recorded human values [6; 7]. Pilot studies (Figure 4) determined joint and occlusal reaction forces under bite conditions on the left or right molar or incisor. Results indicated that unilateral lateral occlusal force (E) on the prosthesis side (left) rather than the natural mandible side (right) was critical. This load condition was adopted for further strength analysis. Figure 5 shows that joint reaction directions matched the physiological condylar pressure orientation within the articular fossa, while lateral oblique occlusal forces were identical regardless of whether joint support was included on the bite side or limited to the contralateral joint. Further comparative studies consistently applied an oblique force of 538 N generated by muscle activation. Figure 3: Mandibular model with implant, indicating muscle attachments and activated forces corresponding to physiological activity for one of the three analyzed bite scenarios (A—Left condyle, B—Right condyle, C—Incisor, D—Right molar, E—Left molar, F—Right deep masseter muscle, G—Right superficial maseeter muscle, H—Right anterior temporalis muscle, I—Right middle temporalis muscle, J—Right posterior temporalis muscle): (**a**) right-side view, (**b**) left-side view. Figure 4: Conditions of joint and occlusal support that, as a result of active muscular forces, generated joint and occlusal reaction forces: (**a**) left conde of the mandible, (**b**) right conde of the mandible, (**c**) left molar, (**d**) right molar, (**e**) incisor, (**f**) occlusal force with support in both joints, (**g**) occlusal force with support exclusively in the joint on the side opposite to the occlusion. Figure 5: Finite element division of the implant model in the fixation area with the bone.