## 2 Materials and Methods
### Experimental Setup  
Experimental tests were performed on a dental implant model provided by BTI (Biotechnology Institute, Vitoria, Spain). The purpose of these tests was to validate the methodology presented in Figure 3. The dental implant assembly under study is composed by a BTI INTERNA(r) IIPUCA3313 implant with a 3.3 mm body diameter and a 4.1 mm Universal Platform with a four-lobe anti-rotation connection, a BTI INPPTU44 titanium abutment (used for direct restorations) and an INTTUH retaining screw with TiBlack(r) coating (see Figure 4). The half-angle of the thread profile is \(\alpha=30^{\circ}\) and the helix angle is \(\beta=5.75^{\circ}\) (0.35 mm pitch). The screw head and thread effective radii are \(r_{h}=1.115\) mm and \(r_{t}=0.810\) mm. The friction coefficients are \(\mu_{t}=\mu_{h}=0.17\) for the screw contacts and 0.21 for the implant-abutment contact, as measured in a MicroTest SMT-A/0200 pin-on-disk tribometer (Microtest S.A., Madrid, Spain) in a previous work by the authors (see Figure 5) [36]. The experimental tests were carried out by applying a cyclic load on the implant by means of an INSTRON 8801 servo-hydraulic direct stress test bench (Instron, Barcelona, Spain). Force control was used to apply the load cycles using a DYNACLLTM 2527-129 load cell (\(\pm 2\) kN load range). The dental implant was attached to the specimen holder hole by using Loctite 401, which is an embedding material that meets the specifications of [37]. Figure 3: Methodology to estimate screw self-loosening in dental implants. Using the predictions obtained from the methodology of Figure 3, the preliminary experimental tests confirmed that, under moderate external load F applied at 30\({}^{\circ}\)[37], the tightening torque recommended by the manufacturer (35 Ncm) is sufficient to avoid self-loosening. Extreme values of \(F\) that may structurally harm the dental implant are not of interest. As the aim of this work is to present and validate the screw self-loosening methodology, some modifications were introduced in order to promote the self-loosening phenomenon in the dental implant under study. Firstly, the screw tightening torque was reduced to 10, 15 and 20 Ncm. Secondly, the thickness of the lower part of the abutment was reduced 0.19 mm in diameter to allow bigger lateral movements of the abutment (see Figure 6). Finally, the cyclic external load \(F\) was applied in both directions (pure alternating sinusoidal force) at a frequency of 1 Hz on the bottom of the abutment perpendicular to the axis of the dental implant (i.e., with an inclination of 90\({}^{\circ}\)). For this purpose, a special loading jig was designed and manufactured to hold the dental implant and transmit the cyclic external load \(F\) to the bottom of the abutment as shown in Figure 7. A steel ring is installed around the abutment outside surface near the junction with the implant post to ensure a point load application on the bottom of the abutment. Under these deliberately unfavorable conditions, screw self-loosening takes place with reasonable external load magnitudes, and thus the methodology can be experimentally validated. Figure 4: Dental implant under study: (**a**) implant, (**b**) screw, (**c**) abutment, and (**d**) assembly. Figure 5: Pin-on-disk tribometer: (**a**) general view, (**b**) detail view [36]. Figure 6: Implant abutment connection: (**a**) original, (**b**) modified. Figure 7: Experimental test: (**a**) test bench, (**b**) detail of the designed loading jig for tests, (**c**) drawing of the loading jig, (**d**) section view. In order to validate the methodology under specific test conditions, three different screw tightening torques \(T_{T}\) were applied: 10, 15 and 20 Ncm by means of a TOHNICHI BTG60 CN-S torque gauge (2% accuracy). According to the methodology summarized in Figure 3, screw self-loosening under transverse loading occurs when \(T_{L}\leq 0\) in Equation (8). Experimentally, loosening is usually detected and quantified by measuring the change of force in the screw [38].