## 2 Materials and Methods
### Procedures  
Static Load Test  
The bed for an in vitro implant lodging was formedinto a poly-methyl methacrylate (PMMA) piece (Plexiglas(r), Rohm GmbH, Darmstadt, Germany). to simulate, as far as possible in vivo conditions, following themanufacturers' recommendations Implants were positioned with a torque up to 100 Ncm, allowing a coronal portion of the implant to protrude through the opening of the PMMA exactly 0.3 \(\pm\) 0.05 cm below the abutment  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Configuration**} & \multirow{2}{*}{**Filtrure**} & \multirow{2}{*}{**Abutment**} & \multicolumn{3}{c}{**Ultimate Failure**} & \multirow{2}{*}{**Bending Moment,**} \\  & & & & **Load** & & **(BM in [N-cm])** \\ \hline C\({}_{1}\) & A-ZT-330-130 & A-MD-330-2 & CP-Ti grade 4 & 324.5 \(\pm\) 5.5 & 178.50 \(\pm\) 3.04 & deformation \\ C\({}_{2}\) & A-ZT-380-130 & A-MD-380-2 & CP-Ti grade 4 & 396.3 \(\pm\) 5.6 & 217.95 \(\pm\) 3.09 & deformation \\ C\({}_{3}\) & LA-ZT-380-130 & A-ABU-330-1 & CP-Ti grade 4 & 421.6 \(\pm\) 12.5 & 231.88 \(\pm\) 6.87 & deformation \\ \hline \hline \end{tabular}
\end{table}
Table 1: Implants and equipment employed in the study with UFL, BMs, and failure eventsfor the statical performance test. (A) c1: 0.33 cm subcrestal abutment-level finishing line with a cylindrical-shaped coronal emergence profile. (B) c2: 0.38 cm subcrestal abutment-level finishing line with a cylindrical-shaped coronal emergence profile. (C) c3: 0.33 cm abutment-level finishing line on diameter of cylindrical endosseous shape and transmucosal convergent neck with hyperbolic geometry.  
Figure 2: View of displacement curves for (**A–C**) c1; (**D–F**) c2; (**G–I**) c3 with permanent deformations to the right sides of the graphs.  
implant interface. The standardized experimental analysis established a lever arm size of 0.8 \(\pm\) 0.05 cm from the abutment-implant junction to the center of the hemisphere.  
Three repeated samples for each of the configurations were submitted to static fatigue overstress by a fatigue test machine (Instron ElectroPuls(r) E10000, Instron Industrial Products, Bucks, UK) with the following set-up: 30 \(\pm\) 2 stress-angle degrees between the axis of the dental implant and the direction of the loading device, and 2 mm/min load rate with the application of a preload force of 20 N.  
In this context, it was important to emphasize that the standard protocol ISO14801:2016 was used for in silico studies, with angles of inclination from 30 to 45 degrees [11; 12; 13]. That value of 30\({}^{\circ}\) was chosen because tilted implants in some clinical studies were positioned with an inclination ranging between 10 and 30 degrees [14; 15]. The increasing load was applied to the static sample until it was fractured or displaced.  
Tests for cyclical performance to fracture followed ISO guidelines. Two samples were submitted to dynamic fatigue overstress with the required mean value of the UFL by the same fatigue test machine. The setting used in the static loading tests for the two samples in each of the configurations were submitted to the dynamic fatigue overstress test with the required mean value of the UFL by the same fatigue test device and setting geometry used in the static loading tests (Figure 1).  
The test was run with the following UFL percentages decreasing in 10% increments from: 80% to zero. The frequency of the applied loading was 15 Hz. An individual dental implant survived the loading test if it reached 5 million cycles; otherwise, it was a failure. The number of cycles was registered.