## 2 Materials and Methods
### Evaluations of the Osseeintegration Process  
#### 2.5.1 Bone-Implant Interface (BII) and Bone-Implant Contact (BIC)  
The osseointegration process of titanium (Ti) implants in the body begins with the oxidation of Ti on the implant periphery by biological fluids (blood and lymph). This oxidation results in the formation of a TiO\({}_{2}\) layer.  
This step is followed by the formation of a calcified (but not ossified) layer with a thickness of about a few nanometers. Such calcification occurs by adsorption on the oxidized metal by the mean of calcium (Ca) and phosphate ions present in the blood. This layer has been observed by [PERSON] et al. [21], [PERSON] [22], and [PERSON] et al. [23].  
Then, healing proceeds by the formation of an intermediate osteoid tissue, the woven or fibrous bone, in the empty spaces. Ossification takes place within this tissue. However, there remains an interface called the bone-interface implant (BII) between the metal and the bone. The surgical success of the integration and fixation of an implanted device in the human body depends on the stability of the implant. This stability is determined by the biomechanical properties of this BII. The BII is the weakest region in the bone-implant system, and most of the failures occur there. Good-quality osseointegration requires close contact between the bone and the implant over a significant proportion of the implant surface. The thickness of this BII is an important characteristic of the quality of osseointegration. A thickness of less than 10 \(\upmu\)m is recognized as an indicator of high quality [8; 21; 24].  
The fraction of the implant surface in contact with bone, i.e., the ratio of bone over metal in a given direction, is provided by the bone-implant contact (BIC), a metric that quantifies the stability and the durability of the implant. Classically, the BIC is evaluated by histomorphometry. In the present article, it was evaluated from the XCT images segmented by ML. According to [PERSON] et al. [25] in 2012, histomorphometry and 3D XCT provide similar results. For [PERSON] et al. [26] in 2011, the BICs evaluated from histomorphometric sections and those evaluated from 2D XCT sections also showed a strong correlation. Finally, [PERSON] et al. [27] in 2022 found the same correlation. Thus, the measurements performed on 2D slices extracted from 3D XCT images are justified.  
The advantages of evaluating the BIC from XCT images rather than from histomorphometry are (a) the non-invasive character of XCT, (b) the ability to perform multiple evaluations on different sections (in histomorphometry, the evaluation is performed on thin layers explicitly fabricated), and (c) the 3D approach. Thus, the evaluation of osseointegration of implants from XCT images seems relevant.  
In the present study, BICs with the side-closed cylinder open at its bottom were evaluated (8 mm of lattice for 10 mm in total) (Figure 1b). The measurements were performed on 1 mm high sagittal sections (see blue rectangle in Figure 10) corresponding to 150 pixels of 6.8 \(\upmu\)m (Figure 11).  
More precisely, the sections were located at different angular positions at the cylinder periphery: 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\) and 135\({}^{\circ}\) (Figure 12). On these sections, the number of pixels of osteoid tissue in contact with the metal was counted by visual examination.