The study protocol was reviewed and approved by the Biomedical Research Ethics Committee of our hospital (IRB #2024–724). Before initiating the research, we used Gpower software (Heinrich Heine Universitat Düsseldorf, Germany) to calculate and determined that the minimum sample size required for this study protocol was 8 (α = 0.05, β = 0.2, f = 0.42). Considering the reproducibility of the FEA model and the representativeness of the clinical data, the study included computed tomography data from the healthy femurs of 10 patients diagnosed with IFN-SF at our institution (Supplementary Table S1). None of the patients had osteoarthritis, bone tumors, or other metabolic diseases at the time of CT scanning. Given the retrospective nature of the study, the Ethics Committee waived the requirement for written informed consent.

In accordance with the research protocol described by Peng et al. (2020), the Mimics software (Materialise Group, Leuven, Belgium) was employed to process the CT data of the healthy-side femurs of ten patients participating in the study, generating patient-specific three-dimensional models of both cortical and cancellous bone. Subsequently, the femur models were imported into Geomagic software (Geomagic, United States) for additional refinement. Then, the models were imported into SolidWorks 2021 (Dassault, France) to create models of IFN-SFs. As indicated by Marins et al. (2021), in instances of IFN-SFs, the FNFs predominantly exhibit type B2 characteristics, and the most prevalent types of FSFs are classified as A3, B, and C. Most biomechanical studies utilize the Pauwels classification to quantify the biomechanical loading characteristics on FNFs (Zeng et al., 2020; Xia et al., 2021). In this study, we employed SolidWorks software to generate ten patient-specific femur models representing Pauwels type I, II, and III FNFs. Furthermore, to investigate the impact of FSF type, we developed transverse, wedge, and comminuted FSF models (Figure 1). These fracture models were then grouped into nine categories, resulting in a total of 90 fracture models: Pauwels type I FNF and transverse FSF (I-T), Pauwels type I FNF and wedge-shaped FSF (I-W), Pauwels type I FNF and comminuted FSF (I-C), Pauwels type II FNF and transverse FSF (II-T), Pauwels type II FNF and wedge-shaped FSF (II-W), Pauwels type II FNF and comminuted FSF (II-C), Pauwels type III FNF and transverse FSF (III-T), Pauwels type III FNF and wedge-shaped FSF (III-W), and Pauwels type III FNF and comminuted FSF (III-C).

The biomechanical study conducted by Wu and Tai (2009) suggested that incorporating a cannulated screw into reconstruction nail fixation could improve the stability of IFN-SF fixation. Therefore, based on the dimensions provided by manufacture, we used Solidworks software to developed three-dimensional solid models of the reconstruction nail and cannulated screw. The reconstruction nail had a diameter of 12 mm, with its length customized based on the femur length of patients. The cannulated screw design featured 7 mm diameter partially threaded screws, with simplified threads to mitigate stress concentration errors. Subsequently, fixation and assembly procedures were carried out following established surgical protocols. The cannulated screw model was placed in the anterior third of the femoral neck, while the reconstruction nail was positioned in the piriform fossa at the posterior third of the proximal femur (Spitler et al., 2020). The length of the implant and the fixation angle were customized for each femur model in the sample.

All models were assumed to be linearly elastic materials. Using the Mimics software, the elastic moduli of cortical and cancellous bone for each femur sample were determined by applying a formula that relies on the CT Hounsfield Unit (HU) values of the femurs from the ten patients (Jian-Qiao Peng et al., 2020): E B   MPa = 0.004   131 – 1.067 HU 2.01

EB is the elastic modulus of bone, and the Poisson’s ratio (ν) of bone was set to 0.3. All screw and reconstruction nail models were defined as titanium alloy (Ti - 6AL - 7Nb) materials, with a Young’s modulus of 110 GPa and a Poisson’s ratio of 0.3 (Huang et al., 2021).

The models were meshed using quadratic tetrahedral elements (C3D10) in Ansys Workbench 202R2. Mesh convergence analysis established the optimal mesh size for calculations (Huang et al., 2023). Increasing the number of mesh elements and nodes had a negligible effect on the Von Mises stress (VMS) values of the implant and femur, staying within a 5% variation (Supplementary Table S2; Supplementary Figure S1). Therefore, mesh sizes of 2 mm were designated for model meshing. The quantity of mesh elements (856,333 to 863,502) and nodes (561,888 to 566,405) varied among different solid models.

The boundary conditions were set based on the methodology employed in prior research (Figure 2). The interface between the implant and bone was specified as a bonded contact, whereas the contact between the fracture surfaces was defined as a frictional contact with a friction coefficient of 0.3 (Yuan et al., 2022). To replicate the peak load encountered by the hip joint during walking, the degrees of freedom of the distal femur were restricted, and a load equal to 300% of the individual’s body weight was exerted on the femoral head along the mechanical axis of the femur (Jung et al., 2022).

Based on prior research, we evaluated nine biomechanical parameters related to fracture fixation stability (Samsami et al., 2019; Peng et al., 2020; Xia et al., 2021; Jung et al., 2022). These parameters comprised stiffness (load divided by displacement), the maximum implant von Mises stress (MIVMS), the maximum implant displacement (MID), the maximum proximal femur von Mises stress (MPFVMS), the maximum distal femur von Mises stress (MDFVMS), the maximum femur displacement (MFD), the maximum femoral neck von Mises stress (MFNVMS), the maximum femoral head-neck interfragmentary motion (MFHNIM), and the maximum proximal-distal femur interfragmentary motion (MPDFIM). The femoral head-neck interfragmentary motion (Figure 3A) was calculated using following Equation (Samsami et al., 2019): M F H N I M = HN X 2 + HN Y 2 + HN Z 2

HN_X, HN_Y, and HN_Z denote the relative displacements of the femoral head in the X, Y, and Z directions, respectively, concerning the femoral neck. The PDFIM represents the relative displacement between the proximal and distal femurs along the vertical axis (Figure 3B).

Statistical analyses were conducted using SPSS 22 (IBM Corp., Armonk, NY, United States) and GraphPad Prism 10.4 (GraphPad Software, San Diego, CA, United States). FEA results were reported as mean ± standard deviation. Normality and homogeneity of variance were assessed using Shapiro-Wilk and Levene’s tests, respectively. A two-way repeated measures ANOVA was employed to assess the impact of the interaction between FNF and FSF types on biomechanical parameters. Subsequently, the entropy method was used to rank the results of various biomechanical parameters. A p-value <0.05 was considered statistically significant.

Table 1 demonstrates that the type of FNF had a significant impact on the outcomes of MIVMS, MID, MPFVMS, MFNVMS, and MFHNIM (p < 0.01). FSF significantly influenced the results of MIVMS, MPFVMS, MDFVMS, and MPDFIM (p < 0.01). The interaction between the two fracture types primarily affected MIVMS, MPFVMS, and MDFVMS (p < 0.01).

The results of the two-way repeated measures ANOVA revealed a significant influence of both fracture type and its combination on key parameters, including MIVMS, MPFVMS, and MDFVMS (Table 1; Figures 4A–C). Specifically, MIVMS was predominantly concentrated at the fracture line of the femoral shaft under a single-leg standing load, with the III-C group exhibiting the highest value (283.4 ± 2.2 MPa) and the II-T group showing the lowest value (134.1 ± 25. MPa) (Figure 5). The reduction in MIVMS in the II-T group compared to the III-C group was 52.7%. MPFVMS was primarily concentrated below the femoral neck (Figure 6), while MDFVMS was focused at the interface between the locking screw and bone (Figure 7). The MPFVMS and MDFVMS of the III-C group were significantly high at 74.6 ± 4.8 MPa and 79.1 ± 2.7 MPa, respectively. Particularly, the MPFVMS showed a notable increase compared to the transverse and wedge FSF groups within all comminuted FSF groups, focusing specifically on the bone-nail interface of the femoral shaft fracture.

The MFNVMS and MFHNIM were additional parameters influenced by the type of femoral neck fracture (Table 1; Figures 4D,E, 8). The highest and lowest MFNVMS values were observed in the III-C (39.3 ± 2.4 MPa) and I-W (25.9 ± 3.6 MPa) groups, respectively, indicating a 34.1% lower stress on the neck fracture surface in the I-W group compared to the III-C group. Similarly, the highest and lowest MFHNIM values were found in the III-C (0.200 ± 0.020 mm) and I-T (0.110 ± 0.012 mm) groups, respectively, with a 45.0% reduction in MFHNIM in the I-W group compared to the III-C group.

Apart from MIVMS, MPFVMS, and MDFVMS, the MPDFIM index is also influenced by the type of FSF (Table 1; Figure 4F). The MPDFIM value was most pronounced in the III-C group at 0.271 ± 0.025 mm, whereas it was least in the I-T group at 0.011 ± 0.001 mm, indicating a 95.9% decrease relative to the III-C group.

The entropy scoring method evaluated various biomechanical parameters to generate composite scores for IFN-SF models (Table 2). The MIVMS and MPDFIM were assigned the highest weights of 24.53% and 17.1%, respectively, underscoring their significance in evaluating the fixation stability of these fractures. The analysis of the composite scores revealed that the I-T group obtained the highest score of 0.79, whereas the III-C group received the lowest score of 0.22 (Figure 9).

The spatial characteristics of a fracture, rather than isolated damage at a single site, significantly influence the biomechanical stability of fracture fixation. Our findings demonstrate that type III-C fracture fixation constructs exhibit the lowest composite score, indicating the poorest stability compared to other fracture types. FEA results suggest that the FNF type significantly influences the overall fixation stability. In cases of type III-C fractures with a Pauwels angle exceeding 50°, the transmission of load from the femoral head through the calcar to the femoral shaft is inefficient, necessitating reliance on implant transmission. This leads to concentrated implant stress at the fracture line of the femoral shaft, aligning with the site of fixation failure observed in clinical practice (Zhang et al., 2021).

The types of FSFs work together to affect the overall stability of the fracture fixation. Transverse fractures provide a large contact area, maintaining the MPDFIM within the optimal range for bone healing. Wedge-shaped fractures maintain partial cortical contact and exhibit intermediate stability between transverse and comminuted fractures. Comminuted FSFs, however, pose a higher risk of nonunion due to elevated MPDFIM values. These observations align with the retrospective clinical analysis by Lin et al. (2014), which demonstrated a correlation between the fracture gap and bone healing. Their findings revealed that bone healing was approximately 3.6 times more likely in the low fracture gap group compared to the high fracture gap group at the 12-month postoperative mark.

The interaction of femoral neck and femoral shaft fractures increases the risk of deterioration of biomechanical stability of fixation constructs. The outcomes of two-way ANOVA showed that the types of IFN-SFs significantly affected the biomechanical parameters such as MIVMS, MPFVMS, and MDFVMS. Consequently, previous clinical studies suggesting no disparity in treatment efficacy between single and dual implants for IFN-SFs may have been influenced by confounding variables related to the type of fracture. In instances where a substantial number of I-T fractures are included in the analysis, distinctions in fixation techniques may be overshadowed by the inherent stability of the fracture itself.

The interaction outcomes of IFN-SF types underscore the necessity for a comprehensive evaluation of multiple fractures. Traditional studies commonly rely on stress, displacement, and stiffness indicators to assess the general stability of IFN-SFs (Xiao et al., 2025). However, it is crucial to recognize that various biomechanical parameters hold distinct implications for assessing the biomechanical stability across different fracture sites. Notably, MFHNIM and MPDFIM play pivotal roles in appraising the fixation stability of FNF and FSF. The EEM score offers a comprehensive evaluation of all biomechanical parameters to assess the overall effectiveness of fracture fixation (Zhan et al., 2021). This study employed EEM to objectively assign weights to nine commonly utilized biomechanical parameters for assessing IFN-SFs, thereby establishing a multi-parameter evaluation framework. The results revealed that the MIVMS (weight = 24.53%) and MPDFIM (weight = 17.1%) emerged as primary predictors of IFN-SF fixation stability. Nonetheless, specific biomechanical parameters of the femoral neck, such as the MFHNIM, require independent evaluation in conjunction with the fracture type.

The spatial distribution of implant stress and the load-conduction path are critical factors that directly influence the longevity of implants (Zhang et al., 2025). In all categories of comminuted FSFs, the Maximum Implant Von Mises Stress (MIVMS) was predominantly localized in the region of implant-bone interface distal to the fracture end of the femoral shaft. Owing to inadequate bone support in this specific region, the MIVMS exhibited a significant elevation compared to wedge-shaped and transverse FSFs, consequently increasing the risk of fixation failure. This finding is consistent with previous research conclusions (Jitprapaikulsarn et al., 2025). Hence, for such fractures, the implementation of supplementary fixation strategies like combined wire fixation may enhance the stability of fracture fixation (Wang et al., 2021).

The mechanical performance of FSF fixation is assessed by the MPDFIM, which plays a crucial role in clinical practice. Studies have shown that the ideal interfragmentary motion at the fracture end is between 0.2 and 1 mm (Han et al., 2020). Moderate axial movement between fracture fragments can stimulate the activity of osteoblasts, while excessive movement can inhibit callus formation and lead to the generation of fibrous connections (Elkins et al., 2016). Conversely, comminuted FSFs compromise the circumferential support structure of the diaphyseal cortical bone, resulting in a notable increase in displacement between femoral shaft fragments, surpassing the ideal threshold for callus formation (Claes et al., 1998). Consistent with previous research, high-gap fractures exhibit increased interfragmentary motion and reduced fixation stability (Abd Aziz et al., 2024). Our study reveals that axial movement of femoral shaft fragments in wedge-shaped and comminuted FSF categories exceeds the threshold for optimal callus formation, thereby diminishing fracture fixation stability compared to transverse FSF cases.

The mechanical stability of fracture fixation is closely related to the MFHNIM, which also impacts blood supply. Pauwels type III FNFs showed the highest MFHNIM values among all fracture models. Inadequate stability due to excessive shear displacement impedes callus formation at the end of the FNF, raising the likelihood of non-union and femoral head necrosis (Augat et al., 2003).

By comprehensively evaluating nine biomechanical parameters to assess the fixation stability of femoral neck and shaft fractures using the entropy method, the potential bias of relying on a single indicator is avoided. The MFNVMS in the I-C group was comparable to that in the I-T group. However, the MPDFIM in the I-C group exhibited a significant increase and was notably lower than that in the I-T group, highlighting the distinct risk associated with comminuted FSFs. This underscores the importance of employing a multi-parameter approach to assess overall stability, as reliance on a single biomechanical parameter may lead to misinterpretations.

The present study establishes a biomechanical foundation for enhancing the clinical outcomes of patients with IFN-SFs of varying fracture patterns. Through a quantitative analysis of the biomechanical stability across different fracture types, a system for assessing “fracture type-stability risk” in clinical settings has been developed. Clinical evidence reveals that in stable IFN-SFs, such as I-T type fractures, there was no significant disparity in healing rates between the single-implant and double-implant groups (Singh et al., 2008). This aligns with the current study’s results, indicating that the intrinsic stability of the fracture may mitigate differences arising from various fixation methods. Conversely, in unstable IFN-SFs, the healing rates of femoral neck and shaft fractures were notably higher in the double-implant group compared to the single-implant group (Ostrum et al., 2014). Hence, for such fractures, the selection of double implants, precise reduction achievement, and reinforcement of fixation during surgery are imperative strategies to reduce implant stress, minimize femoral head-neck interfragmentary motion, and enhance fracture fixation stability (Oh et al., 2021). Furthermore, in cases of comminuted FSFs, reducing the residual gap at the fracture site and restoring cortical continuity are critical for enhancing fixation stability. In instances where a substantial fracture gap persists following reduction, the consideration of artificial bone grafting or biodegradable three-dimensional printed support cages is warranted to enhance fracture stability and promote bone healing (Chou et al., 2017). Unstable IFN-SFs have shown to surpass the bone healing threshold under simulated single-leg weight-bearing loads, indicating the importance of avoiding such loading conditions postoperatively for these patients. For low-risk Type I-T fractures, stabilizing the fracture fixation can be achieved effectively by using a reconstruction nail in combination with cannulated screws. However, it is crucial to perform a pre-surgery hip MRI to identify any hidden FNFs (MacKinnon et al., 2022), which can be obscured by high-energy injuries such as shaft fractures. Despite the use of high-resolution CT scans in the initial evaluation of IFN-SFs, up to 30% of cases may overlook FNFs, leading to substantial medical challenges for patients (Tornetta et al., 2007). The varied biomechanical stability exhibited by different FNF types highlights the significance of promptly recognizing the fracture classification.

This study offers novel insights into the biomechanical characteristics of different types of IFN-SFs, but it has certain limitations. Firstly, despite efforts to enhance the sample size to mitigate the influence of material property variations within individual samples on the experimental outcomes, the number of patients included remains restricted. Consequently, the trends identified in this study may not be universally generalizable. Additionally, the analysis is restricted to assessing biomechanical outcomes under a single-leg standing load condition, neglecting dynamic activities like walking and stair climbing that may lead to distinct stress distributions. Thus, additional research is warranted to investigate these scenarios further.