## 1 Introduction  
The osseointegration (OI) process is widely used as a long-term anchoring method for several applications, such as in maxillofacial reconstruction, arthroplasty, or dental applications [1]. In the last 30 years, OI was adopted to treat limb amputation by providing a stable fixation between the stump and the prosthetic limb. Recently, new implant solutions have been developed by exploiting OI to allow the connection between the residual bone of an amputee limb and the external prosthetic components [2, 3, 4, 5]. The OI phenomenon consists of bone ingrowth around the implant; the effectiveness of bone augmentation guarantees the achievement of good long-term stability (secondary stability) [2, 4, 5, 6, 7, 8, 9]. Primary stability could be defined as a short-term condition and is achievedthrough the mechanical connection between the prosthesis and the bone [4; 6; 10]. More recently, press-fit implants have been developed, for which the primary stability relies on the geometric interference [2; 5; 8; 11; 12]. However, excessive interference could lead to adverse events such as periprosthetic fracture and implant failure [7; 13; 14]. Conversely, an unstable press-fit condition could involve an elevated risk of mobilization in the short or long term [7; 8; 12; 15; 16; 17; 18; 19]. In the literature, the effectiveness of primary stability is evaluated by assessing the relative micromotion between the prosthetic implant and the surrounding bone [10; 13; 15; 17]. Micromotion at the bone-implant interface is a critical biomechanical factor influencing the success of osseointegration. It is well established that the type of new tissue formed at the bone-implant interface is directly influenced by the level of micromotions. Specifically, elevated micromotions exceeding 50 \(\upmu\)m are known to promote the development of fibrous tissue rather than desirable bone tissue, resulting in suboptimal long-term stability [15; 20; 21; 22]. The range from 50 to 150 \(\upmu\)m is considered the threshold of acceptable micromotions for achieving favorable osseointegration [13; 14; 17; 20]. For this reason, the morphological matching between the stem and medullary canal plays a fundamental role in obtaining good stability [13; 14; 23]. In this perspective, the hypothesis that a description of the geometry closer to the real shape of the medullary canal could lead to better surface matching between the stem and the bone and to reduced relative micromotion immediately post-surgery is considered in this study. Several studies investigated the primary stability at the bone-implant interface through experimental, radiological, and clinical assessments, supplying after-surgery evaluations [10; 13; 24; 25; 26]. Both short- and long-term evaluations could be achieved by computational studies and are widely used to quantify the relative motion that may occur at the bone-implant interface, providing valuable information for preclinical evaluations and new prosthesis designs [2; 6; 13; 15; 16; 17; 20; 27; 28]. Only a few computational models have been developed to investigate the press-fitted transfemoral osseointegrated implants [6; 29; 30; 31; 32]. Moreover, most of them approximate the interface between the bone and the implant as totally or partially bonded, simulating the various conditions of OI and not considering the relative micromotion [18; 29; 30; 31; 33; 34; 35; 36]. [PERSON] et al. have assessed the micromotion at the bone-implant interface, investigating the influence of the geometry (length and diameter) on the primary stability, but considering only a straight profile, without assessing the influence of the anatomical shape of the medullary canal [6]. The main goal of this study is to determine if a patient-specific implant design enhances immediate post-operative primary stability. We therefore compared two implants customized on the basis of medullary canal morphology with a standard straight implant as the reference.