Predictive mathematical modeling of biomechanical behavior in all-on-4 implants design: effects of distal implant and occlusal load angulation using RSM based on FEA

This study presents a predictive biomechanical modeling approach for optimizing distal implant placement in the All-on-4 treatment concept, with a focus on implant angulation and occlusal load direction. Finite Element Analysis (FEA) was integrated with Response Surface Methodology (RSM) to develop 15 simulation models based on a Central Composite Design, incorporating distal implant angulations of 15°, 30°, and 45°, and occlusal load directions in both sagittal and frontal planes (45°, 67.5°, and 90°). The maximum von Mises stress in cortical bone was selected as the response variable. Regression analysis revealed that the frontal load angle had the most significant effect on stress distribution, followed by implant angulation. The resulting second-order predictive model demonstrated a strong statistical fit (R 2 = 93.39%, adjusted R 2 = 81.49%). The lowest cortical stress (95.75 MPa) occurred at 15° implant angulation with 45° occlusal loading in both planes, whereas the highest stress (265.72 MPa) was recorded at 45° angulation with 90° frontal loading. Although reducing implant tilt generally decreases peri-implant stress, no universally optimal angle can be defined due to variability in biomechanical responses under different occlusal loading conditions. Clinically, optimizing cusp inclination and load direction in conjunction with implant positioning may enhance the biomechanical performance and long-term success of full-arch implant-supported prostheses.