## 1 Introduction  
Nowadays, the endo-osseous screw dental implant is the most implanted medical device, for which success relies on osseointegration at the bone-implant interface. This biochemical reaction between the metallic part and the bone is achieved by titanium biocompatibility, highlighted for the first time by Pr. [PERSON] [1]. Its surgical procedure is completely controlled, ensuring a success rate exceeding 90% [2]. Dental implants placing configuration mainly depend on the geometrical configuration and placement choices of clinicians. It takes into account a lot of criteria. The prosthetic project and the anatomy of the patient appear to be the most essential ones. However, mechanical criteria are rarely considered. They have to be developed to increase the success rate of implantation especially in complex physiological configurations. The numerical mechanic allows, especially through the Finite Element (FE) method, determining loading levels in considered materials. Over the past two decades, numerous numerical studies have investigated the impact of an endo-osseous dental implant on the surrounding peri-implant bone. Each study focuses on particular parameters under different numerical assumptions by observing different types of results. Certain parameters are commonly used, especially those that describe the geometry of the implant, such as its diameter [3], length [4], taper [5] or threads [6]. General trends can be identified. The diameter and the length, which are the most studied variables, both strongly impact the mechanical environment of the peri-implant bone. It has been shown that a larger length reduces stress in the bone but not as much as a larger diameter [7]. The placement of the implant in the bone is also frequently studied, and some papers have considered its insertion depth [8] or inclination in the bone [9]. For example, it has been found that, the deeper the implant insertion, the more the peri-implant cortical bone is loaded and could be damaged. Bone anatomy is also a parameter often taken into account in numerical models through different modelling approaches. The geometry of the bone and its resorption can be determined from a CT scan [10; 11], but the comparison between these studies is limited since they deal with different cases of atrophy. The other widely used approach is to model several thicknesses of cortical bone corresponding to different levels of resorption [12]. Their results converge and lead to the same conclusion that the peri-implant bone is considerably more solicited with a thin cortical thickness. This variable is commonly combined with the characteristics of the bone material, where different moduli of elasticity of cortical or cancellous bone are considered, representative of atrophy levels [13]. These studies showed that the maximum stress in the peri-implant bone increases when the bone Young's modulus decreases. More rarely, the material of the dental implant is studied. The two most commonly used materials are Ti-6 Al-4V alloy [14] and zirconia [15]. Finally, other parameters that relate to numerical modelling assumptions have also been considered in the literature. Interactions and contacts between the different subparts of the models allow, for example, consideration of levels of osseointegration between the implant and the bone [16]. Regardless of the method used to model the interaction, reinforced contact results in better homogeneity and reduced stress in the bone. A more exhaustive list of studies on this topic is presented in Table 1, ordered by type of parameter studied. In general, papers focusing on similar variables lead to similar conclusions. To our knowledge, only a few studies compare the influence of several parameters. Thus, the results are not meaningful if all variables are not taken into consideration. The present study proposes to build a parametrized model to consider several variable parameters and to compare their influences following the same framework.