Abstract
Background:
Despite efforts to improve mechanical stability and reduce complications after medial closed-wedge distal femoral osteotomy (MCDFO), the role of plate positioning in determining mechanical stability remains unclear.
Purpose:
To determine the biomechanically optimal plate position during MCDFO using finite element analysis (FEA).
Study Design:
Descriptive laboratory study.
Methods:
Five distinct 3-dimensional finite element models of the distal femur and implant (TomoFix Medial Distal Femur Plate and screws) were developed from computed tomography data, and a virtual MCDFO was performed. To identify the biomechanically optimal implant positioning, nine unique configurations were created by systematically varying the plate height (proximal-distal) and depth (anterior-posterior) in 5 mm increments. Physiological loading conditions were simulated by applying joint loads at 0°, 30°, and 90° of knee flexion. Biomechanical stability of the bone-implant construct, including the osteotomy site, was evaluated based on the following parameters: (1) micromotion at the osteotomy site, (2) mean stress applied to the bone and implant, (3) mean stress in the lateral hinge of the distal femur, and (4) peak von Mises stress (PVMS) on the plate and each screw.
Results:
A total of 30 analyses were conducted by performing 6 simulations for each model to meet the sample size requirement determined by a priori power analysis. Micromotion at the osteotomy site was significantly reduced with posterior and proximal plate positioning, a trend consistent across all knee flexion angles. The mean stress in the bone and implant showed no clear directional trend with plate position, whereas stress at the lateral hinge of the distal femur was lowest with posterior-middle placement and remained consistent across all flexion angles. PVMS revealed that anterior-distal placement tended to produce the highest stresses across the plate and screws—occasionally exceeding the titanium alloy's yield strength—while posterior-proximal repositioning progressively reduced them.
Conclusion:
Posterior plate positioning without distal placement was associated with improved biomechanical stability of the bone-implant construct during MCDFO in this FEA.
Clinical Relevance:
Because plate position can be readily adjusted during MCDFO, the present findings provide practical biomechanical guidance for implant placement and may help reduce mechanical complications associated with the procedure.
Keywords: distal femoral osteotomy, finite element analysis, micromotion, plate position, stability
Medial closing-wedge distal femoral osteotomy (MCDFO) has been regarded as an effective surgical treatment for lateral compartment osteoarthritis of the knee associated with valgus malalignment.3,20 By redistributing the load applied to the knee joint, this procedure can alleviate symptoms, relieve pain, and potentially delay or reduce the need for arthroplasty.3,11,18,20 The 10-year survival rate of MCDFO has been reported to be as high as 89.9%, supporting its efficacy in long-term joint preservation. 21 A similar surgical technique, lateral opening-wedge distal femoral osteotomy, has demonstrated comparable clinical outcomes. However, MCDFO has been shown to be relatively superior in terms of bone healing and mechanical stability.5,8,20
Nonetheless, despite the aforementioned potential benefits, challenges associated with bone-implant stability during MCDFO persist. Lateral hinge fractures continue to occur at a considerable rate, and complications related to mechanical stability, such as delayed union, nonunion, and loss of correction, have also been reported.5,20,24 Various studies have been conducted to minimize the incidence of such perioperative complications, suggesting that adjustment of factors such as lateral hinge position, hinge width, and osteotomy gap may reduce the associated risks.9,14,17,23 However, to date, no investigation has focused on determining the ideal plate position during MCDFO. The positioning of implants in fracture or osteotomy fixation can directly influence mechanical stability, load distribution, and bone healing.2,12,16,22 Since plate positioning can be readily adjusted intraoperatively, investigating this factor may contribute to enhancing the mechanical stability of MCDFO, thereby improving surgical outcomes.
Therefore, the present study aimed to determine the biomechanically optimal plate position during MCDFO through finite element (FE) analysis. It was hypothesized that a posterior plate position would provide optimal mechanical stability.
Methods
Three-Dimensional Modeling of the Distal Femur and Implants
Computed tomography (CT) data from 5 individuals without radiographic evidence of lower-limb malalignment, osteoarthritic changes, previous surgical intervention, or other structural abnormalities were used to reconstruct 3-dimensional (3D) models of the distal femur using Mimics software (Version 17; Materialise Ltd). CT data acquisition was performed with a 256-slice dual-source CT scanner (SOMATOM Definition Flash 256, Siemens Healthcare), with tube voltages ranging from 80 to 140 kVp and currents between 140 and 280 mA. Each scan was obtained with a slice thickness of 0.75 mm, a 512 × 512 acquisition matrix, and a field of view spanning 140 to 350 mm. The distal femoral geometries were accurately segmented and reconstructed in Mimics software, after which the models were imported into 3-Matic software (Version 18; Materialise).
To simulate implant fixation, a computer-aided design (CAD) model of the TomoFix Medial Distal Femur Plate and its corresponding locking screws (DePuy Synthes), a fixation system commonly used in MCDFO to stabilize the medial closing gap, was employed. The locking screw lengths were determined by the intended fixation strategy. Screws inserted through holes A, B, C, and D were designed to terminate approximately 10 mm short of the far cortex to achieve unicortical fixation, while screws at holes 1, 2, and 3 were configured to protrude about 5 mm beyond the far cortex to achieve bicortical fixation. 9 The screw at hole 4 was also set to stop approximately 10 mm from the far cortex. 4 For modeling simplicity, screw threads were omitted, and the screws were configured to engage securely with the plate.
Virtual Implementation of MCDFO
The distal femur models were imported into commercial CAD software (SolidWorks 2021, SP5.0; Dassault Systèmes) for virtual MCDFO. A standardized geometric protocol was applied to ensure consistency across all models. To implement the osteotomy, the femurs were oriented such that both femoral condyles were completely superimposed in the sagittal plane and their distal ends were positioned parallel to the ground in the coronal plane, with the medial femoral condyle facing forward on the screen. The long axis of each distal femur (central diaphyseal axis) was aligned perpendicular to the ground to establish a consistent anatomical reference. Subsequently, the femurs were rotated 90° around the longitudinal axis so that the posterior condyles faced anteriorly, allowing visualization in the coronal plane. Transverse osteotomies were then created. Each horizontal cut was made parallel to the ground in the sagittal plane and started 40 mm proximal to the medial epicondyle in the coronal plane. 9 After this, an ascending osteotomy was performed. An oblique cut was created at one-quarter of the anteroposterior diameter of the femur, measured at the level of the transverse osteotomy. This ascending cut formed a 110° angle with the transverse cut and extended approximately 30 to 40 mm. 9 The hinge point was defined as the region immediately distal to the superior border of the lateral condyle. 17 A 5-mm bone bridge was preserved at the lateral cortex to maintain hinge integrity during wedge closure. Each osteotomy wedge base was set to a width of 10 mm. 14 After virtual wedge closure, a 1-mm residual gap was intentionally retained at the osteotomy site to simulate incomplete cortical contact that may occur because of saw blade thickness or biological variability9,14 (Figure 1). This approach was also adopted to allow more sensitive evaluation of interfragmentary micromotion and construct stability across different plate configurations by avoiding artificially rigid contact conditions at the osteotomy site.
Figure 1.
Virtual modeling of the MCDFO procedure, shown in the (A) coronal and (B) sagittal planes. A transverse osteotomy (first osteotomy line) was performed approximately 40 mm proximal to the medial epicondyle, followed by an ascending osteotomy (second osteotomy line) forming a 110° angle relative to the transverse cut in the sagittal plane. A 1-mm residual gap was intentionally preserved at the osteotomy site to simulate incomplete contact. The lateral hinge was located just distal to the superior border of the lateral femoral condyle, with a 5-mm bone bridge maintained to preserve hinge integrity. MCDFO, medial closing-wedge distal femoral osteotomy.
FE Model Construction and Loading Conditions
The FE models were generated using HyperMesh 11.0 (Altair Engineering, Inc) and analyzed using Abaqus (Version 6.11; Simula). FE meshing was performed using quadratic tetrahedral elements of type C3D10 for both the bone and implant components. Mesh convergence was achieved by progressively refining the mesh until the changes in peak von Mises stress (PVMS) and interface micromotion were <5%. The final mesh consisted of approximately 350,000 elements.
Each femur model was divided into 2 material domains: an outer cortical shell and an inner cancellous core. All materials were assumed to be linear elastic, homogeneous, and isotropic. The cortical and cancellous bone were assigned Young's moduli of 15,250 MPa and 449 MPa, respectively, with a Poisson's ratio of 0.3 for both.10,25 The implant components—including the TomoFix Medial Distal Femur Plate and screws—were modeled using titanium alloy, with a Young's modulus of 110,000 MPa and a Poisson's ratio 10 of 0.3. The screw-plate and bone-implant interfaces were defined as tie constraints to simulate rigid fixation, whereas the screw-bone interfaces were modeled using a frictional contact with a coefficient of 0.3. 19
To simulate physiological loading on the bone-implant construct under various clinical conditions, loads corresponding to 0°, 30°, and 90° of knee flexion were applied (Figure 2). These flexion angles were selected to represent clinically relevant knee positions during daily activities, including full extension, moderate flexion, and deep flexion. At 0° and 30° of flexion, a total axial load of 2200 N was applied, while at 90°, a reduced load of 1000 N was used to reflect decreased weightbearing in deep flexion. 1 The loads were applied as 2 concentrated forces at reference nodes representing the medial and lateral regions of the tibial plateau to simulate physiologic femorotibial load transmission. The medial-to-lateral load distribution ratio was set to approximately 60:40, representing typical medial-to-lateral load transmission under physiological conditions. 15 The proximal ends of the femoral condyles, corresponding to the hip joint centers, were fully constrained to prevent rigid body motion, while all translational and rotational degrees of freedom at the distal tibia were constrained to simulate a single-leg stance.
Figure 2.
Boundary and loading conditions used in the finite element analysis to simulate single-leg stance at different knee flexion angles: (A) 0°, (B) 30°, and (C) 90°. A total axial load of 2200 N was applied at 0° and 30° of flexion, and a reduced load of 1000 N was applied at 90° of flexion to reflect decreased weightbearing in deep flexion. The proximal ends of the femoral condyles were fully constrained to prevent rigid-body motion, and all degrees of freedom at the distal tibia were restricted to simulate a physiological single-leg stance.
Implant Placement Configurations and Quantitative Biomechanical Metrics
To determine the biomechanically optimal placement of the implant, 9 distinct configurations were defined. At the sagittal plane of complete overlap of the femoral condyles, the plate and screw assembly—including the corresponding screw length for each position—was translated in 5 mm increments along the proximal-distal and anterior-posterior axes. These configurations encompassed the clinically relevant range from anterior-distal to posterior-proximal orientations while maintaining anatomical conformity to the cortical surface of the distal femur throughout the 3D positioning process, resulting in plate fixation at 9 unique locations (Figure 3).
Figure 3.
Schematic illustration of the 9 unique plate configurations used to evaluate the biomechanically optimal fixation position. The plate and screw construct was translated in 5-mm increments along the proximal-distal and anterior-posterior axes in the sagittal plane, where the femoral condyles completely overlapped. Screw lengths were individually adjusted for each configuration to ensure proper cortical engagement.
To evaluate the biomechanical performance of each plate configuration, 4 outcome measures related to the biomechanical stability of the distal femur and fixation construct were assessed. First, interfragmentary micromotion at the osteotomy gap was quantified as the relative displacement between 2 markers positioned at the maximal opening of the osteotomy site (Figure 4A). Second, the mean stress in both the bone and implant structures was calculated under the applied loading conditions (Figure 4B). Third, the lateral hinge region—defined as the cortical area at the tip of the distal femoral osteotomy where hinge fractures most frequently occur—was designated as a region of interest, and the mean stress imparted to this zone was analyzed under the applied loading conditions (Figure 4C). 14 Finally, PVMS was recorded for the plate and each individual screw and subsequently compared with the 880 MPa yield strength of the titanium alloy to evaluate the risk of mechanical failure. These parameters were evaluated within the femoral model because this study focused on the local biomechanical effects of plate positioning on the osteotomy site, lateral hinge, and femur-implant construct after MCDFO.
Figure 4.
Finite element evaluation of biomechanical performance across plate configurations. (A) Interfragmentary micromotion was defined as the relative displacement between opposing cortical surfaces at the maximal osteotomy gap. (B) The mean stress was assessed in both the bone and the implant under simulated loading conditions. (C) Stress distribution at the lateral hinge region (red circle), defined as the cortical area at the tip of the MCDFO, was also evaluated. MCDFO, medial closing-wedge distal femoral osteotomy.
Statistical Analysis
Before the analyses, a sample size calculation was performed using G*Power Version 3.1.9.7 (Heinrich Heine University Düsseldorf). Repeated-measures analysis of variance (RMANOVA) was selected as the statistical method for the power analysis, with parameters set as follows: a significance level (α) of .05, statistical power (1–β) of 0.80, and a medium effect size (Cohen’s f) of 0.3. The number of repeated measurements was set to 9, corresponding to the total number of plate positions evaluated. Based on these parameters, the minimum required sample size was calculated to be 27 subjects.
Statistical analyses were conducted using IBM SPSS Statistics for Windows (Version 26.0; IBM Corp). Changes in biomechanical parameters across different plate positions were assessed using RMANOVA. P < .05 was considered statistically significant. When significant differences were observed, post hoc pairwise comparisons were performed using paired t tests, with P values adjusted using the Bonferroni correction method. The intraobserver reliability of the measurements was assessed using intraclass correlation coefficients (ICCs), with corresponding 95% CIs.
Results
A total of 5 distal femur models were available for analysis; however, an a priori power analysis indicated that at least 27 subjects would be required. Consequently, 6 independent simulations were conducted for each model to ensure that analyses were performed for 30 specimens in total. Measurement reliability for the evaluated metrics was deemed excellent, as reflected by ICC values ≥0.999 with 95% CIs.
Interfragmentary Micromotion at the Osteotomy Site
Interfragmentary micromotion at the osteotomy site decreased significantly as the plate was positioned more posteriorly and more proximally, respectively (P < .05 for all comparisons across every flexion angle) (Figure 5A; Supplementary Material 1). Post hoc pairwise comparisons confirmed statistically significant differences between all position combinations (Supplementary Material 2). Notably, the smallest micromotion was observed at the posterior-proximal position, a finding that was consistent across all knee flexion angles.
Figure 5.
Graphical comparison of biomechanical parameters across plate configurations and knee flexion angles. (A) Interfragmentary micromotion at the osteotomy site. (B) The mean stress in the distal femoral bone. (C) The mean stress in the implant. (D) The mean stress in the lateral hinge region of the distal femur.
Mean Stress in Bone and Implant
The mean stress values in both the bone and implant assembly demonstrated significant variation in response to alterations in plate depth and height (P < .05 for all comparisons across every flexion angle for bone and implant measures, respectively) (Figure 5, B and C; Supplementary Materials 3, 4, 5, and 6). Nevertheless, when assessed across all flexion angles and plate configurations, these stress responses did not conform to a single, uniform pattern; instead, they exhibited heterogeneous, configuration-specific trajectories.
Mean Stress in the Lateral Hinge of the Distal Femur
The mean stress confined to the lateral hinge of the distal femur decreased progressively from anterior to posterior plate positions. It was consistently lowest at the mid-height configuration (P < .05 for all comparisons). These trends persisted across all knee flexion angles, and post hoc pairwise comparisons revealed statistically significant differences between all pairs of positions (Figure 5D; Supplementary Materials 7 and 8).
PVMS in Plate and Screw Components
To assess the potential for implant failure, PVMS were evaluated for the plate and each screw. Anterior-distal plate placement produced the greatest PVMS across all components—occasionally exceeding the plate's 880 MPa yield strength <90° flexion—whereas systematic repositioning toward the posterior-proximal orientation tended to yield progressively lower PVMS (Figure 6).
Figure 6.
PVMS values were recorded at the plate and each screw across all plate configurations and knee flexion angles (0°, 30°, and 90°). Each bar represents the PVMS for the plate or a specific screw (screw1–4, screwA–D) under a given positional setting. The horizontal dashed red line indicates the yield strength of the titanium alloy plate (880 MPa). PVMS, peak von Mises stress.
Discussion
The principal finding of this study is that positioning the plate more posteriorly and avoiding distal placement during MCDFO represents the biomechanically optimal strategy. In terms of interfragmentary micromotion at the osteotomy site and the PVMS generated in the plate and screws, the most favorable outcomes were identified when the plate was placed in the most posterior and proximal position, with respect to mean stress at the lateral hinge of the distal femur; a posterior and mid-height position was found to be advantageous. Collectively, these results suggest that during MCDFO, positioning the plate as posteriorly as possible while avoiding anterior placement may enhance the stability of the bone-implant construct.
Surgical failure remains a considerable concern for orthopaedic surgeons performing MCDFO.5,20,24 Hinge fracture, nonunion, malunion, correction loss, and implant breakage are not uncommon and may necessitate additional surgical intervention, resulting in persistent pain, prolonged rehabilitation, and a substantial clinical burden for patients. 20 Despite ongoing research and clinical efforts to mitigate these complications, the biomechanically optimal position for implant fixation during MCDFO has not yet been investigated. Accordingly, this study was conducted to determine the optimal implant fixation position to minimize surgical failure after MCDFO, using finite element analysis (FEA) to evaluate the stability of the bone-implant construct under physiological loading at various knee flexion angles.
In the present study, interfragmentary micromotion at the osteotomy site decreased consistently as the plate was positioned more posteriorly and more proximally across all tested knee flexion angles. Two primary biomechanical mechanisms can explain this pattern. First, placing the plate more posteriorly reduces the bending lever arm relative to the shaft's neutral axis in the sagittal plane, thereby diminishing the bending moment generated under physiological loading.6,7 As a result, the plate can more effectively resist gap opening and closing forces, minimizing relative displacement at the osteotomy site. Second, positioning the plate more proximally effectively increased the fixation span across the osteotomy site and allowed screws to be distributed over a larger segment of the femoral shaft. This configuration provided a more balanced force transfer and greater bending stiffness, thereby contributing to the observed reduction in interfragmentary micromotion. 13 The combination of a shorter bending lever arm and a longer fixation span explains why the posterior-proximal configuration consistently exhibited the lowest micromotion, indicating its biomechanical advantage in maintaining osteotomy stability and promoting favorable healing conditions. Consistent with the aforementioned findings on micromotion, PVMS in the plate and screws decreased progressively as the plate was positioned more posteriorly and more proximally. This trend indicates that posterior-proximal placement not only minimizes interfragmentary motion but also reduces the risk of implant stress concentration, thereby lowering the likelihood of implant failure under physiological loading conditions. These findings are consistent with previous finite element analyses of high tibial osteotomy, which reported improved construct stability with more posterior plate positioning.16,22 Collectively, these results demonstrate that positioning the plate more posteriorly and proximally provides clear biomechanical benefits by enhancing osteotomy site stability and ensuring safer stress distribution within the implant construct.
However, the mean stresses observed in the bone and the implant did not display a consistent trend. This can be attributed to the mean bone stress reflecting an average across both cortical and cancellous regions, diluting localized stress variations induced by changes in plate position. Similarly, the mean implant stress represents an average over the entire plate and screw construct, which masks local stress concentrations and redistributions.
Nevertheless, the mean stress confined specifically to the lateral hinge of the distal femur exhibited a clearer pattern, decreasing progressively with more posterior plate placement and reaching its minimum at the mid-height configuration. This finding highlights the unique biomechanical behavior of the lateral hinge, which serves as a localized stress concentration area that is highly sensitive to the direct alignment of the plate–screw force path with the hinge zone. A mid-level plate position appears to provide the most favorable force transfer pathway, as it aligns the plate-screw construct more directly with the hinge zone, thereby ensuring more efficient load sharing across the lateral cortex. This configuration facilitates more uniform stress distribution and lowers the risk of excessive stress at this critical site. This trend differs from interfragmentary micromotion and PVMS because these global parameters are predominantly governed by overall bending stiffness and construct stability, which are consistently enhanced by increasing the fixation span and decreasing the bending lever arm through more posterior and proximal plate positioning. This explains why the mean stress pattern at the hinge does not entirely mirror the global trends observed for micromotion and PVMS, underscoring the importance of balancing local hinge protection with overall construct stability when selecting the optimal plate position.
Several limitations should be acknowledged in this study. First, although 30 analyses were performed in this study, they were based on only 5 models, which may not have adequately captured the full spectrum of anatomical variation and bone density observed in actual patients. Consequently, the magnitude of the biomechanical advantages associated with different plate positions may vary with individual femoral morphology and bone quality, potentially limiting the generalizability of the present findings. Second, although the biomechanical stability of the bone-implant construct was evaluated under various knee flexion angles, dynamic loading conditions, such as walking and squatting, could not be replicated. Third, because the analyses relied solely on bone models, the influence of surrounding soft tissues was not accounted for, potentially limiting the simulations’ ability to fully reproduce physiologic joint mechanics and force distribution. Fourth, because the present FEA was conducted using a single plating system (TomoFix Medial Distal Femur Plate and screws), the results should not be interpreted as universally applicable to all fixation devices used in MCDFO. Differences in plate geometry, stiffness, and screw configuration among implant systems may influence biomechanical behavior and construct stability. Fifth, all materials were assumed to be linear elastic, homogeneous, and isotropic. Although cortical bone exhibits transversely isotropic behavior, identical material properties were applied to all models to allow consistent comparative evaluation among plate positions. Therefore, the absolute stress values should be interpreted with caution. Lastly, because this study was conducted as a descriptive laboratory investigation using FEA, discrepancies from actual clinical conditions are inevitable. Factors such as soft tissue interactions and the use of surgical instruments, which were not included in the simulation, may limit the generalizability of these findings to clinical practice.
Although various factors must be considered during the surgical procedure of MCDFO, the plate position remains one of the few modifiable factors that can be readily adjusted intraoperatively. If adjusting the implant fixation position can improve the stability of the bone-implant construct during MCDFO, there would be little reason to hesitate to apply this strategy in clinical practice. Indeed, this study demonstrated that positioning the implant as posteriorly as possible and avoiding distal placement can yield biomechanical advantages, providing an evidence-based strategy for optimizing the surgical technique. Consequently, the findings of the present study may help minimize technique-related complications and contribute to improved clinical outcomes in MCDFO.
Conclusion
Posterior plate positioning without distal placement was associated with improved biomechanical stability of the bone-implant construct during MCDFO in this FEA.
Supplementary Material 1.
Interfragmentary Micromotion at the Osteotomy Site Under Varying Plate Positions and Knee Flexion Angles a
| At 0° Flexion | ||||
|---|---|---|---|---|
| Height | Distal, μm | Middle, μm | Proximal, μm | P b |
| Depth | ||||
| Anterior, μm | 78 ± 3 | 76.2 ± 3 | 71.8 ± 2.9 | <.05 |
| Center, μm | 62 ± 2.2 | 57.2 ± 2.1 | 51.4 ± 1.9 | <.05 |
| Posterior, μm | 61.5 ± 2.1 | 49.1 ± 1.8 | 44.8 ± 1.6 | <.05 |
| P c | <.05 | <.05 | <.05 | - |
| At 30° Flexion | ||||
| Height | Distal, μm | Middle, μm | Proximal, μm | P b |
| Depth | ||||
| Anterior, μm | 102.2 ± 4.5 | 100 ± 4.3 | 97.5 ± 4.3 | <.05 |
| Center, μm | 88.1 ± 3.8 | 86.6 ± 3.7 | 86 ± 3.7 | <.05 |
| Posterior, μm | 82.8 ± 3. 6 | 81.3 ± 3.5 | 79.4 ± 3.4 | <.05 |
| P c | <.05 | <.05 | <.05 | |
| At 90° Flexion | ||||
| Height | Distal, μm | Middle, μm | Proximal, μm | P b |
| Depth | ||||
| Anterior, μm | 21.8 ± 1.3 | 21.5 ± 1.3 | 21.1 ± 1.3 | <.05 |
| Center, μm | 21.5 ± 1.2 | 21.4 ± 1.1 | 20.9 ± 1.1 | <.05 |
| Posterior, μm | 20.9 ± 1.1 | 20.7 ± 1 | 20.5 ± 1.1 | <.05 |
| P c | <.05 | <.05 | <.05 | |
A repeated-measures analysis of variance was performed to evaluate changes in inter-fragmentary micromotion at the osteotomy site according to variations in plate position with respect to both height and depth.
P value for comparing different plate depths.
P value for comparing different plate heights.
Supplementary Material 2.
Post Hoc Pairwise Comparisons of Interfragmentary Micromotion According to Plate Position and Flexion Angle a
| Fixed Plate Height at 0° Flexion | |||
|---|---|---|---|
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Height at 30° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Height at 90° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs Posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 0° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 30° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <0.001 | <.001 | <.001 |
| Fixed Plate Depth at 90° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
The values are given as adjusted P values obtained by Bonferroni correction.
Supplementary Material 3.
Mean Stress in the Bone Under Varying Plate Positions and Knee Flexion Angles a
| At 0° Flexion | ||||
|---|---|---|---|---|
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Depth | ||||
| Anterior, MPa | 6.4 ± 0.5 | 6.8 ± 0.5 | 6.5 ± 0.5 | <.05 |
| Center, MPa | 6 ± 0.4 | 6.3 ± 0.4 | 6.2 ± 0.5 | <.05 |
| Posterior, MPa | 5.8 ± 0.4 | 6.1 ± 0.5 | 5.9 ± 0.3 | <.05 |
| P c | <.05 | <.05 | <.05 | - |
| At 30° Flexion | ||||
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Depth | ||||
| Anterior, MPa | 5.1 ± 0.4 | 5.3 ± 0.4 | 5.2 ± 0.4 | <.05 |
| Center, MPa | 5.5 ± 0.4 | 5.6 ± 0.4 | 5.4 ± 0.4 | <.05 |
| Posterior, MPa | 5.6 ± 0.4 | 5.8 ± 0.4 | 5.5 ± 0.4 | <.05 |
| P c | <.05 | <.05 | <.05 | |
| At 90° Flexion | ||||
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P a |
| Depth | ||||
| Anterior, MPa | 3.1 ± 0.3 | 3.2 ± 0.3 | 3 ± 0.3 | <.05 |
| Center, MPa | 3.3 ± 0.3 | 3.4 ± 0.3 | 3.3 ± 0.3 | <.05 |
| Posterior, MPa | 3.4 ± 0.3 | 3.5 ± 0.3 | 3.4 ± 0.3 | <.05 |
| P c | <.05 | <.05 | <.05 | |
A repeated-measures analysis of variance was performed to evaluate changes in mean stress on the bone according to variations in plate position with respect to both height and depth. MPa, megapascals.
P values for comparing different plate depths.
P values for comparing different plate heights.
Supplementary Material 4.
Post Hoc Pairwise Comparisons of Mean Stress in the Bone According to Plate Position and Flexion Angle
| Fixed Plate Height at 0° Flexion | |||
|---|---|---|---|
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Height at 30° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Height at 90° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 0° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 30° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 90° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
The values are given as adjusted P values obtained by Bonferroni correction.
Supplementary Material 5.
Mean Stress in the Implant (Plate and Screws) Under Varying Plate Positions and Knee Flexion Angles a
| At 0° Flexion | ||||
|---|---|---|---|---|
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Depth | ||||
| Anterior, MPa | 24.3 ± 3.5 | 25.3 ± 3.9 | 26 ± 3.6 | <.05 |
| Center, MPa | 22.6 ± 3.2 | 23.6 ± 3.4 | 24.3 ± 3.4 | <.05 |
| Posterior, MPa | 21.6 ± 3.1 | 22.3 ± 3.2 | 23.2 ± 3.1 | <.05 |
| P c | <.05 | <.05 | <.05 | - |
| At 30° Flexion | ||||
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Depth | ||||
| Anterior, MPa | 41.7 ± 2.5 | 38.4 ± 2.7 | 40.6 ± 2.6 | <.05 |
| Center, MPa | 36.6 ± 2.6 | 34.3 ± 2.9 | 37.6 ± 2.7 | <.05 |
| Posterior, MPa | 36.1 ± 3 | 32.6 ± 3 | 37.3 ± 2.8 | <.05 |
| P c | <.05 | <.05 | <.05 | |
| At 90° Flexion | ||||
| Height | Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Depth | ||||
| Anterior, MPa | 45.4 ± 2 | 44.4 ± 1.9 | 45.9 ± 2 | <.05 |
| Center, MPa | 42.6 ± 1.9 | 40.4 ± 1.9 | 40.8 ± 1.9 | <.05 |
| Posterior, MPa | 41.9 ± 1.9 | 38.6 ± 1.9 | 41.2 ± 1.9 | <.05 |
| P c | <.05 | <.05 | <.05 | |
A repeated-measures analysis of variance was performed to evaluate changes in mean stress in the implant (plate and screws) according to variations in plate position with respect to both height and depth. MPa, megapascals.
P value for comparing different plate depths
P value for comparing different plate heights
Supplementary Material 6.
Post Hoc Pairwise Comparisons of Mean Stress in the Implant (Plate and Screws) According to Plate Position and Flexion Angle
| Fixed Plate Height at 0° Flexion | |||
|---|---|---|---|
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | 0.011 | 0.01 | 0.011 |
| Anterior vs posterior | <0.001 | <0.001 | <0.001 |
| Center vs posterior | 0.044 | 0.037 | 0.04 |
| Fixed Plate Height at 30° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <0.001 | <0.001 | <0.001 |
| Anterior vs posterior | <0.001 | <0.001 | <0.001 |
| Center vs posterior | <0.001 | <0.001 | <0.001 |
| Fixed Plate Height at t 90° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <0.001 | <0.001 | <0.001 |
| Anterior vs posterior | <0.001 | <0.001 | <0.001 |
| Center vs posterior | 0.029 | <0.001 | 0.047 |
| Fixed Plate Depth at 0° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | .036 | .038 | .049 |
| Distal vs proximal | <.001 | <0.001 | <.001 |
| Middle vs proximal | .047 | .048 | .045 |
| Fixed Plate Depth at 30° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at 90° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | .043 | .042 | .024 |
| Middle vs proximal | <.001 | <.001 | <.001 |
The values are given as adjusted P values obtained by Bonferroni correction.
Supplementary Material 7.
Mean Stress in the Lateral Hinge of the Distal Femur Under Varying Plate Positions and Knee Flexion Angles a
| At 0° Flexion | ||||
|---|---|---|---|---|
| Height Depth |
Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Anterior, MPa | 11.5 ± 1 | 10.7 ± 0.9 | 11 ± 0.9 | <.05 |
| Center, MPa | 10.5 ± 0.8 | 9.9 ± 0.8 | 10.1 ± 0.8 | <.05 |
| Posterior, MPa | 10.3 ± 0.4 | 9.6 ± 0.6 | 9.7 ± 0.4 | <.05 |
| P c | <.05 | <.05 | <.05 | - |
| At 30° Flexion | ||||
| Height Depth |
Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Anterior, MPa | 13.4 ± 0.9 | 12.5 ± 1 | 12.8 ± 1 | <.05 |
| Center, MPa | 12.3 ± 11.6 | 11.6 ± 0.9 | 12 ± 0.9 | <.05 |
| Posterior, MPa | 11 ± 0.9 | 10.2 ± 0.6 | 10.4 ± 0.6 | <.05 |
| P c | <.05 | <.05 | <.05 | |
| At 90° Flexion | ||||
| Height Depth |
Distal, MPa | Middle, MPa | Proximal, MPa | P b |
| Anterior, MPa | 6.9 ± 0.5 | 6.5 ± 0.5 | 6.7 ± 0.5 | <.05 |
| Center, MPa | 6.7 ± 0.5 | 6.5 ± 0.5 | 6.3 ± 0.4 | <.05 |
| Posterior, MPa | 6.2 ± 0.4 | 6.1 ± 0.5 | 6 ± 0.6 | <.05 |
| P c | <.05 | <.05 | <.05 | |
A repeated-measures analysis of variance was performed to evaluate changes in mean stress in the lateral hinge of the distal femur according to variations in plate position with respect to both height and depth. MPa, megapascals.
P value for comparing different plate depths.
P value for comparing different plate heights.
Supplementary Material 8.
Post Hoc Pairwise Comparisons of Mean in the Lateral Hinge of the Distal Femur According to Plate Position and Flexion Angle
| Fixed Plate Height at 0° Flexion | |||
|---|---|---|---|
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs Posterior | <.001 | <.001 | <.001 |
| Fixed Plate Height at 30° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | .013 | .007 | .007 |
| Fixed Plate Height at 90° Flexion | |||
| Pairwise Comparison a | Distal | Middle | Proximal |
| Anterior vs center | <.001 | <.001 | <.001 |
| Anterior vs posterior | <.001 | <.001 | <.001 |
| Center vs posterior | .013 | <.001 | <.001 |
| Fixed Plate Depth at 0° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at t 30° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | <.001 | <.001 | <.001 |
| Fixed Plate Depth at t 90° Flexion | |||
| Pairwise Comparison a | Anterior | Center | Posterior |
| Distal vs middle | <.001 | <.001 | <.001 |
| Distal vs proximal | <.001 | <.001 | <.001 |
| Middle vs proximal | .029 | <.001 | .037 |
The values are given as adjusted P values obtained by Bonferroni correction.
Footnotes
Final revision submitted June 10, 2026; accepted June 28, 2026.
The authors declared that they have no conflicts of interest in the authorship and publication of this contribution.
Ethical approval was obtained from the Institutional Review Board of Gangnam Severance Hospital (IRB No. 3-2025-0147).
ORCID iDs: Hyun-Soo Moon 
https://orcid.org/0000-0001-8678-2960
Min Jung https://orcid.org/0000-0002-7527-4802
Se-Han Jung https://orcid.org/0000-0001-8422-093X
Kyoung-Tak Kang https://orcid.org/0000-0002-6752-4576
Sung-Hwan Kim https://orcid.org/0000-0001-5743-6241
References
- 1. Burastero G, Pianigiani S, Zanvettor C, et al. Use of porous custom-made cones for meta-diaphyseal bone defects reconstruction in knee revision surgery: a clinical and biomechanical analysis. Arch Orthop Trauma Surg. 2020;140(12):2041-2055. [DOI] [PubMed] [Google Scholar]
- 2. Cao Y, Zhang Y, Huang L, Huang X. The impact of plate length, fibula integrity and plate placement on tibial shaft fixation stability: a finite element study. J Orthop Surg Res. 2019;14(1):52. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 3. Chahla J, Mitchell JJ, Liechti DJ, et al. Opening- and closing-wedge distal femoral osteotomy: a systematic review of outcomes for isolated lateral compartment osteoarthritis. Orthop J Sports Med. 2016;4(6):2325967116649901. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4. Davenport SR, Lindsey RW, Leggon R, Miclau T, Panjabi M. Dynamic compression plate fixation: a biomechanical comparison of unicortical vs bicortical distal screw fixation. J Orthop Trauma. 1988;2(2):146-150. [PubMed] [Google Scholar]
- 5. Diaz CC, Lavoie-Gagne OZ, Knapik DM, et al. Outcomes of distal femoral osteotomy for valgus malalignment: a systematic review and meta-analysis of closing wedge versus opening wedge techniques. Am J Sports Med. 2023;51(3):798-811. [DOI] [PubMed] [Google Scholar]
- 6. Evans A, Glyde M, Day R, Hosgood G. Effect of plate-bone distance and working length on 2.0-mm locking construct stiffness and plate strain in a diaphyseal fracture gap model: a biomechanical study. Vet Comp Orthop Traumatol. 2024;37(1):1-7. [DOI] [PubMed] [Google Scholar]
- 7. Johnson F, Scarrow P, Waugh W. Assessment of loads in the knee joint. Med Biol Eng Comput. 1981;19(2):237-243. [DOI] [PubMed] [Google Scholar]
- 8. Kim YC, Yang JH, Kim HJ, et al. Distal femoral varus osteotomy for valgus arthritis of the knees: systematic review of open versus closed wedge osteotomy. Knee Surg Relat Res. 2018;30(1):3-16. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9. Kuwashima U, Itoh M, Itou J, Okazaki K. Impact of support instruments in medial closed-wedge distal femoral osteotomy: a finite element analysis. Arch Orthop Trauma Surg. 2024;144(3):1039-1045. [DOI] [PubMed] [Google Scholar]
- 10. Kwon HM, Hong HT, Kim I, et al. Biomechanical effects of stem extension of tibial components for medial tibial bone defects in total knee arthroplasty: a finite element study. J Knee Surg. 2024;37(13):879-886. [DOI] [PubMed] [Google Scholar]
- 11. Mabrouk A, Risebury M, Yasen S. Double-level knee valgization osteotomy has high survivorship and a low complication rate in a single-center series of 58 cases with a mean clinical follow-up of 10 years. Knee Surg Relat Res. 2025;37(1):22. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12. MacLeod AR, Serrancoli G, Fregly BJ, Toms AD, Gill HS. The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates: an experimental and finite element study. Bone Joint Res. 2018;7(12):639-649. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 13. Märdian S, Schaser KD, Duda GN, Heyland M. Working length of locking plates determines interfragmentary movement in distal femur fractures under physiological loading. Clin Biomech (Bristol). 2015;30(4):391-396. [DOI] [PubMed] [Google Scholar]
- 14. Meisterhans M, Flury A, Zindel C, et al. Finite element analysis of medial closing and lateral opening wedge osteotomies of the distal femur in relation to hinge fractures. J Exp Orthop. 2023;10(1):33. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15. Moewis P, Checa S, Kutzner I, Hommel H, Duda GN. Physiological joint line total knee arthroplasty designs are especially sensitive to rotational placement: finite element analysis. PLoS One. 2018;13(2):e0192225. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16. Moon HS, Youn JH, Lee SJ, et al. Optimal plate position for biomechanical stability in medial opening-wedge high tibial osteotomy: a finite element analysis. Clin Orthop Surg. 2025;17(4):622-630. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 17. Nha KW, Kim HS, Jin DU, et al. Predictive factors for lateral hinge fracture in medial closing wedge distal femoral osteotomy. Am J Sports Med. 2022;50(14):3819-3826. [DOI] [PubMed] [Google Scholar]
- 18. Park J, Chaar O, Narayanakurup J, et al. Do knee alignment patterns differ between Middle Eastern and East Asian populations? A propensity-matched analysis using artificial intelligence. Knee Surg Relat Res. 2025;37(1):11. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19. Raja Izaham RM, Abdul Kadir MR, Abdul Rashid AH, Hossain MG, Kamarul T. Finite element analysis of Puddu and Tomofix plate fixation for open wedge high tibial osteotomy. Injury. 2012;43(6):898-902. [DOI] [PubMed] [Google Scholar]
- 20. Sherman SL, Thompson SF, Clohisy JCF. Distal femoral varus osteotomy for the management of valgus deformity of the knee. J Am Acad Orthop Surg. 2018;26(9):313-324. [DOI] [PubMed] [Google Scholar]
- 21. Sternheim A, Garbedian S, Backstein D. Distal femoral varus osteotomy: unloading the lateral compartment: long-term follow-up of 45 medial closing wedge osteotomies. Orthopedics. 2011;34(9):e488-490. [DOI] [PubMed] [Google Scholar]
- 22. Takeuchi R, Woon-Hwa J, Ishikawa H, et al. Primary stability of different plate positions and the role of bone substitute in open wedge high tibial osteotomy. Knee. 2017;24(6):1299-1306. [DOI] [PubMed] [Google Scholar]
- 23. Tanaka A, Matsushita T, Nakatsuji T, et al. Setting hinge position distal to the proximal margin of the distal lateral femur reduces the maximum principal strains of the hinge area and risk of hinge fractures. J Exp Orthop. 2024;11(2):e12015. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 24. Wylie JD, Jones DL, Hartley MK, et al. Distal femoral osteotomy for the valgus knee: medial closing wedge versus lateral opening wedge: a systematic review. Arthroscopy. 2016;32(10):2141-2147. [DOI] [PubMed] [Google Scholar]
- 25. Yuan D, Wu Z, Luo S, et al. Impact of femoral neck cortical bone defect induced by core decompression on postoperative stability: a finite element analysis. Biomed Res Int. 2022;2022:3667891. [DOI] [PMC free article] [PubMed] [Google Scholar]