The research was performed using the databases: PubMed, ResearchGate, and Google Scholar, covering data before June 2022. PRISMA P guidelines (PRISMA-P, 2022) were followed to build this systematic review, focusing on the published studies of mechanical stability in osseointegrated prostheses for transfemoral amputations (Figure 1). The search strategy was as follow: (Osseointegrated prosthesis OR bone-anchored OR implant OR prosthesis) AND (lower limb OR transfemoral OR distal femur OR femur) AND (primary stability OR stress-shielding OR stress-concentration OR mechanical stability) AND (in vitro test OR mechanical test OR FE model OR numerical simulation). Results were limited to full-text articles in English. Articles were not restricted based on publication status or date.

To be included in the final review, the screened papers had to satisfy the following criteria:

• The first inclusion criterion was the presence of at least one of the search key words in the title and/or in the abstract. The second inclusion criterion was the use of in vitro mechanical test or FE models to evaluate the primary stability, the stress-shielding, or the stress concentration, and the failure mode of the osseointegrated transfemoral prostheses.

The authors independently selected and reviewed the article title, key words and abstracts based on the inclusion and exclusion criteria. After the first screening (first exclusion criteria) the authors reviewed the full text articles. The articles that passed the first selection were then fully read. Any disagreements were solved between the reviewers and if something was unclear, the authors of the studies were contacted. The articles found in different databases were included only once. To further expand the research, citations of the papers and related articles were also tracked.

This systematic review aimed to summarize, evaluate, and discuss the different in vitro and in silico methods used for the biomechanical assessment of an osseointegrated transfemoral prosthesis (Figure 1). Thus, the next paragraphs are organized to present the methods related to the main three modes of biomechanical failure described in the Introduction: the lack of implant stability (Section 3.1), the strain/stress shielding (Section 3.2) and the strain/stress concentration (Section 3.3). Each of these topics will be analyzed and discussed in a similar by evaluating:

• The loading scenarios used to test each mode of failure, in terms of the loading conditions simulated either in the experimental test, or in the in silico model.

Primary stability is defined as the biomechanical stability upon implant insertion, and it is crucial to achieve the long-term stability. Primary stability is mainly achieved when interface micromotion does not exceed the threshold for granting bone ingrowth and osseointegration. There is a general consensus about a range of micromotions that can be tolerated: between 20 and 150 μm (Pilliar, Lee, and Maniatopoulos, 1986; Kohli, Stoddart, and van Arkel, 2021). In fact, an excessive interface micromotion can interfere with the process of osseointegration, leading to formation of a fibrous tissue layer at the implant-bone interface. Thus, this negative self-sustained loop can lead to aseptic loosening (i.e., loss of primary stability of the implant within the bone, with no sign of sepsis) (Cameron, Pilliar, and Macnab, 1973; Pilliar, Lee, and Maniatopoulos, 1986; Fukuoka, Yoshida, and Yamano, 2000; Duyck et al., 2006; Winter, Klein, and Karl, 2012). Since micromotion can interfere with the process of osseointegration (Winter, Klein, and Karl, 2012), the mechanical test evaluating micromotion is crucial to assess the osseointegration process. Micromotion can be classified as permanent migrations and inducible micromotions:

• Permanent migrations are defined as the non-reversible implant motion that is accumulated cycle after cycle, that remains even after removing the load. Permanent migrations do not necessarily prevent implant stability, in case they settle over time. The main shortcoming of permanent migrations (if not accompanied by excessive inducible micromotions, see below) is that they may result in a final implant position different from the intended one.

Primary stability can be assessed with different methods, such as measuring the extraction force (pull-out or push-out tests) or the micromotions at the interface between the implant and the host bone. Since a standard procedure to test and assess the primary stability of osseointegrated prostheses does not exist, different methods were developed to measure the pull-out or push-out load and the micromotion.

Experimental in vitro pull-out and push-out tests were performed at the time of in vitro implantation (Welke et al., 2013; Jeyapalina et al., 2014; Barnes et al., 2019) and after 3-6-9-12 months ex vivo on sheep (Jeyapalina et al., 2014). Micromotions were investigated both in vitro at the time of implantation (Barnes et al., 2019), and through in silico simulated rehabilitation exercises (Prochor and Anna Mierzejewska, 2019).

Stress shielding is a phenomenon that causes adaptive changes in bone morphology, and in bone tissue strength and stiffness in response to the altered mechanical environment caused by the presence of metal implants. Adverse bone remodelling leads to a lack of bone stock in case of surgery revision, weakens the bone, and contributes to implant loosening (Kagan et al., 2017; L Cristofolini et al., 2009). To the authors’ knowledge, only few in vitro studies were performed to evaluate the load distribution and the subsequent strain shielding of an osseointegrated transfemoral prosthesis (Cristofolini et al., 1998; Tomaszewski et al., 2013; Ahmed et al., 2020). In fact, the stress and strain of the bone surrounding the implant are difficult to measure in vitro and nearly impossible to measure in vivo. Therefore, in silico finite element models can advantageously be used to generate these information (Xu et al., 2006; Tomaszewski et al., 2010; Tomaszewski et al., 2012a; Tomaszewski, et al., 2012b; Newcombe et al., 2013; Tomaszewski et al., 2013; Stenlund et al., 2017; Prochor and Sajewicz, 2018; Prochor and Anna Mierzejewska, 2019).

Post-operative periprosthetic fractures are most often caused by stress concentrations and occur when the patient abruptly changes the walking speed during gait (Juhnke et al., 2015; Al Muderis et al., 2016; Örgel et al., 2021; R; Brånemark et al., 2014). For this reason, the stress concentration tests focused on the ultimate load of the implanted femur (Welke et al., 2013) and on the stress concentration around the implant during daily activities (Ming, Xiang, and Yubo, 2005; Xu et al., 2006; Lee, et al., 2008b; Helgason et al., 2009; Tomaszewski et al., 2013; 2010; Tomaszewski et al., 2012b; Newcombe et al., 2013).

The primary stability of the implant has been evaluated in vitro either measuring the extraction force, or the micromotions at the interface between the implant and the host bone. The extraction force was evaluated in the literature with two different methods: either with a pull-out or a push-out test. The pull-out test allows to evaluate the extraction force preserving the natural anatomy of the implanted femur (Welke et al., 2013; Jeyapalina et al., 2014). Conversely, the push-out test is usually performed on short segments resected from the femur, and is suitable if a short implant must be tested (Barnes et al., 2019). The push-out test allows to evaluate the extraction force of different stems on the same specimen in different osteotomy levels. However, the pull-out and push-out tests, which are used when a fast and reproducible test is needed, do not represent a common failure scenario for osseointegrated prostheses. In fact, the load is applied with a monotonic axial ramp until the exit of the prosthesis or the fracture of the specimen. However, the pull-out test is often used in other prosthetic devices as an FDA test (U.S. Department of Health and Human Services et al., 2003).

As aseptic loosening of osseointegrated prostheses is mainly driven by excessive micromotions under cyclic loading, a more representative pre-clinical assessment should quantify permanent migrations and/or inducible micromotions. The in vitro evaluation of the micromotion of the prosthesis was performed only by Barnes et al. using displacement transducers (LVDT) (Barnes et al., 2019). Nevertheless, a single LVDT allows to measure the displacement only in one direction. This limitation can be partially overcome, using multiple LVDTs to detect three-dimensional motions; however also in this case measurement errors may arise due to misalignment of the transducers. A further improvement is provided by DIC, which allows a full-field three-dimensional displacement analysis. In the literature it is possible to find similar studies with DIC on different devices (Morosato et al., 2020).

The micromotion can also be investigated with numerical models. In fact, once an in silico model has been developed and validated, it can be advantageously used to simulate and evaluate several complex loading scenarios and motor tasks, to compare different conditions such as different degrees of osseointegration, or modified bone quality (Martelli et al., 2011). In fact, numerical models give the opportunity to simulate experimental tests and repeat the same experiment a limitless number of times on the same models for an almost infinite variation of parameters (Romero et al., 2007; Martelli et al., 2011). Prochor et al. exploited the advantages of numerical models to explore the effect of different parameters such as implant length, implant diameter and interface bonding on the micromotions in a simplified load condition (Prochor and Anna Mierzejewska, 2019). A very important caveat is that numerical models should not be trusted if they are not thoroughly verified and validated, especially when making clinically relevant decisions (Cristofolini et al., 2010; ASME V&V 40, 2018; Oefner et al., 2021).

As bone remodelling is driven by frequently recurring cyclic loads, a commonly used method to evaluate the strain-stress shielding is simulating daily motor task. In vitro methodologies allow to apply controlled loading components. The strain on the surface of the specimens were evaluated using strain gauges, obtaining precise and accurate measurements on selected points (Cristofolini et al., 1998; Tomaszewski et al., 2013; Ahmed et al., 2020). DIC provides a full field strain analysis on the surface of the specimens and has already been used in literature (Palanca, Tozzi, and Cristofolini, 2016; Palanca et al., 2018).

However, in vitro mechanical tests allow to simulate only a limited set of loading conditions, while in silico methodologies allow to simulate different motor task and to investigate stress and strain at the interface between the prosthesis and the bone (Cristofolini et al., 2010). Moreover, the osseointegration between the prosthesis and the bone cannot be simulated in vitro, while with in silico models the different degree of osseointegration can be chosen, from unbonded with a given coefficient of friction (Tomaszewski et al., 2010; Prochor and Anna Mierzejewska, 2019; Ahmed et al., 2020) to fully bonded with a perfect osseointegration (Xu et al., 2006; Tomaszewski et al., 2012a; Tomaszewski et al., 2012b; Newcombe et al., 2013; Prochor and Sajewicz, 2018). All the numerical studies of this review are similar for what concerns the loading scenarios, while the quality of the bone tissue was represented with different degrees of detail. Indeed, some studies considered bone as isotropic (Tomaszewski et al., 2012a; Tomaszewski et al., 2012b; Prochor and Sajewicz, 2018; Prochor and Anna Mierzejewska, 2019), others anisotropic (Xu et al., 2006; Newcombe et al., 2013; Stenlund et al., 2017; Ahmed et al., 2020). In addition, some models considered the elastic modulus of the bone homogeneous (Xu et al., 2006; Newcombe et al., 2013; Stenlund et al., 2017; Prochor and Sajewicz, 2018; Prochor and Anna Mierzejewska, 2019; Ahmed et al., 2020), while others adapted the elastic modulus based on bone density (Tomaszewski et al., 2010; Tomaszewski et al. 2012a; Tomaszewski et al. 2012b). In a specific case, the bone was idealized with a cylindrical geometry (Stenlund et al., 2017) and with a generic geometry from standardized femur data (Prochor and Sajewicz, 2018), while in other cases the in silico model of the bone was based on computed tomography (CT) data of a femoral bone (Xu et al., 2006; Tomaszewski et al., 2010; Tomaszewski et al. 2012a; Tomaszewski et al. 2012b; Newcombe et al., 2013; Prochor and Anna Mierzejewska, 2019). However, bone density of some models was re-scaled to the typical young amputated patient since the CT images were of a cadaver old subject (Tomaszewski et al., 2010; Tomaszewski et al. 2012a; Tomaszewski et al. 2012b). Although different modelling strategies can be observed, comparable findings were obtained from different studies. This shows that the macro effects were captured by the models.

A limitation of these numerical studies is that in most cases the in silico models have not been experimentally validated. Indeed, Ahmed et al. and Tomaszewski et al. are among the few who used a validated model (Tomaszewski et al., 2013; Ahmed et al., 2020).

Evaluation of possible stress concentrations is crucial, as they can lead to bone fracture and subsequent implant failure. A commonly used method to evaluate the strain-stress concentration is simulating physiological loading, and the typical falling scenarios. Welke et al. (2013) aimed to investigate the ultimate load and the fracture modes with a simplified in vitro test. Typically, bending moment is the most critical loading scenario during normal daily activities, and a frequent cause for bone fractures. Thus, Welke et al. (2013) simulated the most critical condition by analyzing a highly repeatable loading scenario, i.e., the four-point-bending test. It must be noted that the four-point-bending test does not correspond to any realistic scenarios during the physiological conditions or falling. However, this testing condition may provide a first estimate of the load that can lead to a stress concentration and resulting in a bone fracture.

Subsequent studies evaluated the stress concentration around the implant using numerical simulations (Ming, Xiang, and Yubo, 2005; Xu et al., 2006; Lee, et al., 2008b; Helgason et al., 2009; Tomaszewski et al., 2010; Tomaszewski et al., 2012b; Newcombe et al., 2013). All the numerical models focusing on stress concentration are similar in loading strategies, while the quality of the bone tissue was represented with different degrees of detail. Indeed, some studies considered bone as isotropic (Helgason et al., 2009; Tomaszewski et al., 2010; Tomaszewski et al., 2012a), others anisotropic (Ming, Xiang, and Yubo, 2005; Xu et al., 2006; Lee, et al., 2008b; Newcombe et al., 2013). Some models applied homogeneous properties (Ming, Xiang, and Yubo, 2005; Xu et al., 2006; Lee, et al., 2008b; Helgason et al., 2009), while others modified the elastic modulus based on bone density (Tomaszewski et al., 2010; Tomaszewski et al., 2012b). In a specific case, the bone was idealized with a generic standardized geometry (Ming, Xiang, and Yubo, 2005), while in other cases the FE geometry of the bone was based on computed tomography (CT) scan of a femoral cadaveric bone (Xu et al., 2006; Helgason et al., 2009; Tomaszewski et al., 2010; Tomaszewski et al. 2012a; Tomaszewski et al. 2012b; Newcombe et al., 2013) or a femoral composite bone (Lee, et al., 2008b). However, as these models were based on a CT scan of an old subject, the bone density was re-scaled to the density that can be expected in amputees (typically young patients). Despite these different modelling strategies, comparable findings were obtained from the different studies showing that the macro effects were captured by the models.

In silico models estimating the risk of periprosthetic bone fractures mostly rely on the Von Mises stress criterion. The Von Mises criterion combines stress components and is applicable to ductile materials. Recent advances demonstrated that criteria based on the maximum principal strain are more accurate in predicting bone failure (Schileo et al., 2008; Miles et al., 2015).

Another limitation of many of these numerical studies is that in silico models have not been experimentally validated. To the authors’ knowledge, only Tomaszewski et al. reported a validated model (Tomaszewski et al., 2010; Tomaszewski et al., 2012a).