Enhancing fixation stability in proximal humerus fractures: screw orientation optimization in PHILOS plates through finite element analysis and biomechanical testing | Scientific Reports

Scientific Reports volume 14, Article number: 27064 (2024) Cite this article

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The optimal treatment strategy for proximal humerus fractures (PHFs) is debatable owing to the relatively high failure rate of locking plates. Optimizing implants may enhance the fixation stability of PHFs and reduce the rate of mechanical failures. We developed a finite element (FE) model to simulate the treatment of PHFs with Proximal Humerus Internal Locking System (PHILOS) plates. The model evaluated the average bone strain around the screw tips under vertical loading (as an alternative to the risk of cyclic screw cutout failure verified through biomechanical testing) to minimize this strain and maximize predicted fixation stability. After determining the optimal screw configuration, further FE analysis and in vitro biomechanical testing were conducted on both standard and optimized PHILOS screw orientation to assess whether the optimized plates have biomechanical advantages over the standard plates. The FE-based optimized configuration exhibited significantly lower bone strain around the implant than the standard PHILOS screw orientation (− 17.24%, p < 0.001). In both FE analysis and in vitro biomechanical testing, the optimized PHILOS plates achieved significantly lower average bone strain around the screws (p < 0.05), more uniform stress distribution, and greater structural stiffness (p < 0.05) than the standard PHILOS screw orientation. Our results show that biomechanical performance of the PHILOS plates can be improved by altering the orientation of the locking screws. This approach may be useful for future patient-specific design optimization of implants for other fractures.

Proximal humerus fractures (PHFs) account for 5–6% of all fractures and are the third-most frequent fracture among older adults1,2,3. PHFs primarily occur in older women with osteoporosis, accounting for 17.5% of all osteoporotic fractures in post-menopausal women aged > 50 years4. Bone loss and complex fracture instability makes joint-preserving surgery for PHFs in older adults a continued challenge. The introduction of locking plates has significantly improved surgical outcomes for patients with poor bone quality, becoming one of the most frequently utilized joint-preserving surgical treatments5,6. However, even with advanced locking plates, the mechanical fixation failure rate remains high, ranging from 15 to 35%5,7,8,9,10.

Although many finite element (FE)-based parameter optimization studies exist, there are very few on PHFs. Improving the biomechanical performance of internal implants by optimizing the angle of screws may consequently reduce the clinical failure rate of mechanical fixation. Jabran et al.11 developed an FE model to optimize the screw angle of the spatial subchondral support proximal humerus plate, wherein the displacement of fracture gap of the optimized plate was 4.686% lower than that of the manufacturer’s standard plate. Chader et al.12 and Mischler et al.13 used FE analysis to optimize the orientations of the six proximal screws of the Proximal Humerus Internal Locking System (PHILOS) plate. However, during the optimization process, the angle variation was limited to a small range of only 10°, and the step size for screw angle changes was too large, with a step size of 5°. This approach may have missed the optimal combination of screw parameters.

Therefore, the primary objectives of this study are as follows: (1) to optimize the PHILOS plate design by changing the orientation of its proximal two screws; and (2) to compare the biomechanical properties of the optimized PHILOS screw orientation and the standard PHILOS screw orientation by using FE analysis and in vitro biomechanical experiments. The optimization process used a larger range of screw angle variations (40°) and smaller step sizes (2°). Additionally, we developed a Python script to calculate all feasible combinations of screw angles. Through FE analysis, we computed the average principal compressive strain in the cylindrical bone region around the screws for each configuration, thereby determining the optimal angle combination.

This study was performed in accordance with the Declaration of Helsinki and the study was approved by The Research Ethics Committee of The Second Hospital of Jilin University (IRB no. 2023043 and IRB no.2024236). All volunteers provided informed consent. Computed tomography (CT) scans recorded data from a 50-year-old female volunteer. The process of FE analysis is shown in Fig. 114. The CT data were imported into Mimics v21.0 (Materialise, Leuven, Belgium) in Digital Imaging and Communications in Medicine (DICOM) format to reconstruct the geometry of the humerus model. The surface geometry of the humerus was then processed using Geomagic v21.0 (3D Systems, Rock Hill, SC, USA) and converted into a 3D solid model. A PHILOS plate (Synthes, West Chester, PA, USA) was scanned using laser scanner (ATOS5X, GOM, Stuttgart, Germany). The humerus and PHILOS plate were assembled in Solidworks v2017 (Dassault Systemes, Massachusetts, USA) according to the technical guidelines of the manufacturer. To simulate a two-part fracture of the proximal humerus, the humerus was resected 210 mm from the tip of the head and the bone segment between 50 and 60 mm from the head apex was removed15. The screw was idealized as an unthreaded cylinder with a diameter of 3.5 mm16. The creation of the cylindrical Regions Of Interest (ROI) in SolidWorks was accomplished after the successful establishment of the fracture model and its assembly with the implant. Initially, the ROI was defined at the head end of the screw (the end furthest from the plate) using the “Extruded Boss” feature. Subsequently, the "Combine-Delete " command was employed to remove the regions of interference between the ROI and the screw. Further, the "Combine-Delete " command is utilized to eliminate the ROI from the humerus. Ultimately, a model was generated in which the humerus, implant, and ROI do not interfere with one another.

The process of finite element (FE) analysis14.

All the FE models were discretized in Hypermesh v2020 (Altair Engineering, Troy, MI, USA), and the models were divided into a four-node tetrahedral mesh (C3D4). Then, the grid model is exported in the inp format from Hypermesh. Subsequently, the inp file (including ROI) were imported into Mimics. According to the gray value of CT in Mimics, the humerus was defined as a 3D model with inhomogeneous material properties (Fig. 2a–c). According to previous studies, the material properties of the humerus were calculated according to the following formulae17:

(a–c) Material assignment of the humerus. The humerus model is automatically divided into 10 materials in Mimics, and the material properties are shown in panel a. Panel b shows the number of meshes for the 10 materials. Panel c shows that the humerus model is automatically divided into 10 parts, and the heterogeneous model of the humerus is established. (d) Displays the partitioning and numbering of screws. (e) Visualizes the horizontal angles (θh) and vertical angles (θv). (f) Shows the bone around the screws (cylindrical regions of interest, ROIs). (g) Indicates the placement of strain gauges. (h) Shows the numbering of strain gauges.

where ρ is bone density, GV is the gray value of bone in CT data, and E is the elastic modulus. The material of the steel plate was Ti6Al4V, the elastic modulus is 110,000 MPa, and the Poisson’s ratio was 0.3; and material of the screws is 316L, the elastic modulus is 20,000 MPa, and the Poisson’s ratio was 0.318,19,20.

In this study, mesh convergence tests were performed to verify the effect of mesh refinement on FE model predictions. The model size was set to four different sizes for comparative analysis (Table 1). The element sizes of the FE model were set to 0.4, 0.6, 0.8, and 1.0 mm in the four cases, respectively. By comparing the predicted peak von-Mises stress values of the reference case, the corresponding values of case A, B, and C were considered accurate within 5% of the reference conditions. It is worth noting that case A shows higher accuracy than other cases.

Fletcher et al.21 determined the effect of screw configuration of the PHILOS plate on the fixation stability of PHFs through FE analysis. They found that row B screws (Fig. 2d) had the minimal effect on plate stability. This result makes row B screws an ideal focus for optimization research. The orientation of row B screws (screws 3 and 4, screw numbers shown in Fig. 2d) can be expressed in terms of horizontal angles (θh) and vertical angles (θv), which are the angles formed by the screws relative to the midline of the sagittal and frontal planes (Fig. 2e), respectively. Proximal screws. It has been demonstrated that bone strain around the screws (ROIs) is an even better predictor of construct failure (Fig. 2f)16,22 These regions of interest (ROIs) have a diameter of 8.5 mm and a length of 20 mm, with 5 mm inside the thread tip and 15 mm towards the screw head16,22. The bone elements of each screw’s ROIs were pooled, and the average of the principal compressive strains of these elements was calculated. In this study, the change in average principal compressive strain of ROIs before and after loading was defined as ΔS. Therefore, the main goal of design optimization was to find a feasible combination of horizontal and vertical angles of screws 3 and 4 to yield the minimum ΔS in the FE analysis.

In this study, an automated Python script was used to identify all feasible combinations of θh and θv from a large pool of candidate configurations. This not only saved computational time but also ensured each combination was viable. The ranges for θh and θv were set from 0° to 40° with a step size of 2° (Fig. 3). This was because screws at angles beyond this range were too far from the humeral head. Cases where screws were completely outside the humeral head or in contact with the contours of other screws were excluded. This script simplifies the screws into line segments. One end of the line segment in contact with the plate was fixed, while the position of the other end varied with changes in angle, automatically updated by the Python script. Collisions between screws were determined by the distance between line segments, with a screw diameter of 3.5 mm. Therefore, line segments with a distance ≤ 3.5 mm indicated screw collision and were excluded.

Illustration of screw orientation parameter optimization in the finite element model. By altering the tip positions of Screws 3 and 4 while maintaining the head positions constant, the direction of each proximal screw in the PHILOS plate can be changed. The diagram shows the grid of orientation changes, i.e., the parameter space used for optimization. For a given screw, 0° corresponds to the standard PHILOS plate screw orientation. The orientation varies within a 40° range in both the sagittal and horizontal planes in 2° increments. (a) for Screw 3, (b) for Screw 4.

Ultimately, 2290 feasible combinations of θh and θv were determined by the Python script. Considering the computational effort required for constructing FE models, it was impractical to reconstruct and solve 2290 models. Therefore, the one-factor-at-a-time (OFAT) approach was employed, assuming each screw as an independent factor. This allowed for the individual study of the effect of each screw while keeping the other screws in their original PHILOS configuration, reducing the number of theoretically feasible configurations to 102 (Screw 3: 53; Screw 4: 49). Finally, the results of the two screws’ variations in terms of orientation were combined to determine favorable configurations. The OFAT method has been successfully used in studies optimizing configurations and has proven effective13. Given the inconsistency of the model, we performed reconstruction and FE analysis of the humerus in 20 healthy volunteers. We then evaluated the effectiveness of the superposition principle by comparing the estimated strain reduction based on the combined individual screw variation results with actual strain reduction observed in the actual configuration. This comparison was performed for each model under the following three loading conditions (0° axial, + 20° abduction, and − 20° adduction).

All components were imported into Ansys in the CBD format. The interfaces of plate/screws, screws/bone, ROIs/screws, ROIs/bone were modeled as bonded23,24. During the configuration optimization process, the distal end of the humerus was constrained in all directions, and an axial compressive load of 200N was applied to the articular surface25. For each configuration, the average principal bone strain of the ROIs was computed.

In the comparative analysis of the optimized PHILOS screw orientation (OPSO) and standard PHILOS screw orientation (SPSO), the distal humerus was also constrained in all directions, and a 200N vertical compression load was applied to the articular surface in three positions (0° axial, + 20° abduction, and − 20° adduction). Additionally, a 3.5 Nm torque was applied to the humeral head surface to simulate the shoulder joint rotation26. The output parameters included the average principal compressive strain of ROIs and the maximum Von Mises stress of the plate. The stiffness of the FE model was compared with previously published data to verify the model’s effectiveness.

The axial testing conditions was adopted based on the fundamental test setup described by Lescheid et al.27 The abduction testing conditions was chosen to simulate shear loading across the proximal fracture site, which is typically experienced during activities such as rising from a chair or bearing weight on crutches27,28. The adduction setup was oriented around the findings from in vivo load transmission studies conducted by Bergmann et al. and Westerhoff et al.29,30.

In this study, selective laser melting (SLM) technology was used to fabricate 3D-printed implants. The STL files for the OPSO and SPSO were imported into a Platinum A320 3D printer (BLT Additive Manufacturing Co., Ltd., Xian, China). Titanium alloy (TI6Al4V) powder was used as the raw material, with the laser power set to 500W and a layer thickness of 40 μm. The printing process involved several steps: preheating the base plate to 200 °C, spreading the powder, scanning with an infrared laser beam, completing the print, heat treatment, cooling to room temperature, wire cutting of the model, and ultrasonic cleaning. The material of the screw is 316L (Fig. 4a). Twenty artificial synthetic humeri (LD 5030 Humerus; Synbone, Malans, Switzerland) were randomly divided into two groups: specimens fixed with SPSO were the control group, and specimens fixed with OPSO were the experimental group. Previous comparative studies have demonstrated that these synthetic bones are good substitutes for cadaveric bones in biomechanical analysis27. The humerus was cut 210 mm from the head tip to facilitate fixation of the distal end. A custom 3D-printed jig was made to accurately replicate two-part PHFs with a 10-mm bone defect, 50 mm from the head tip in the surgical neck for all specimens (Fig. 4b). The X-ray film after the plate was implanted into the fracture model as shown in Fig. 4c-d. The surface of the plates where strain gauges (SG) need to be attached were cross-sanded using sandpaper. The surfaces were then cleaned with ethanol and acetone and left to air dry naturally. The SGs were fixed in their designated positions using cyanoacrylate adhesive (T-1, Beihua Chemical Works, Beijing, China). The location and number of SGs are shown in Fig. 2g-h. The SG cables were connected to the multi-channel strainmeter (DH5981, Donghua Test Technology Co., Ltd., Jiangsu, China), using a quarter-bridge wiring configuration.

(a) 3D-printed SPSO (left) and OPSO (right), with the printing material being Ti6Al4V. (b) Custom osteotomy tool for biomimetic bone. The jig had two 2.5-mm K-wire channels for precise positioning of the Philos plate. The placement of these two K-wire channels was determined according to the manufacturer’s technical guidelines, allowing for accurate and repeatable placement of the plate in the same position: 6 mm distal to the superior aspect of the greater tubercle and 2–4-mm posterior to the bicipital groove. (c, d) X-rays of the fracture models implanted with the standard Philos plate (c) and the optimized Philos plate (d), respectively.

Vertical load tests were performed using material testing machine (MTS, 55,100, Shakopee, MN, USA) with a capacity of 100.0KN. The load was transmitted through a load sensor, and displacement was measured using a laser displacement sensor (HG-C1100, LingGuang Automation Technology Limited, Hefei, China) with a measuring range of 100 mm and a measuring accuracy of 0.01 (Fig. 5). The displacement sensor measured the relative displacement between the fracture fragments under the load. This method was chosen over vertical displacement, because vertical displacement represents the overall displacement of the model rather than the relative displacement of the fracture fragments.

Fixation of the distal humeral axis. Axial load (a), adduction load (b), abduction load (c), and torsional load (d) were applied to the humeral head. Angle θ is 20°, *Laser displacement sensor.

The machine applied vertical loads (load rate, 2 mm/min; preload, 50 N; maximum load, 200 N) to the apex of the humeral head in three postures (0° axial, 20° abduction, and 20° adduction), and the multi-channel strainmeter recorded the strain values of all SGs during the entire loading process.

Axial, abduction, and adduction stiffness were tested in three positions (0° axial, 20° abduction, and 20° adduction) at a displacement rate of 5 mm/min. The vertical compression load started at 50N and stopped at 200N, and axial stiffness was calculated using the slope of the load–displacement curve in the linear elastic region (average linear coefficient R2 > 0.99)31,32.

Torsional stiffness was measured with the proximal and distal ends of the specimen fixed without contacting the fracture site, articular surface, plate, or screws. The specimen was connected to the testing machine with the humeral axis placed horizontally. The torsion test was performed using a torsion testing machine at a constant speed of 2°/s until the torque reached 7.5 Nm.

Stiffness were calculated according to the slope of the load–displacement curve and torque-angulation curve (average linear coefficient R2 > 0.99).

Like the stiffness test, the cyclic loading test was also conducted in four positions. Axial cyclic load: Cyclic sinusoidal compression loading was performed at 2 Hz for 5000 cycles. The preload was 50N and the load was increased continuously at a rate of 0.03N/cycle throughout the test. This resulted in a maximum load of 200N after 5000 cycles. Displacement data were recorded every 500 load cycles.

Torsional cyclic load: Cyclic sinusoidal compression loading was performed at 2 Hz for 3000 cycles. The preload was 1 Nm and the load was increased continuously at a rate of 0.002 Nm/cycle throughout the test. This resulted in a maximum load of 7.5 Nm after 3000 cycles. The angle data were recorded every 500 load cycles.

The axial stiffness and torsional stiffness were calculated according to the slope of the load–displacement curve and torque-angulation curve (average linear coefficient R2 > 0.99).

Statistical analyses were performed using the SPSS software package 24 (IBM SPSS Statistics, Armonk, NY, USA). The Kolmogorov–Smirnov test or Shapiro–Wilk test was used to assess continuous variables for normal distribution. If the data conformed to normal distribution, the independent two-sample t-test was used to compare whether significant differences existed between the two groups of data; if the data did not conform to normal distribution, the Mann–Whitney U test was used. To evaluate the validity of the superposition principle in optimizing configuration, Pearson’s correlation coefficient was calculated, and the average strain reduction estimated by superimposed single screw changes was compared with the actual strain reduction of the combined configuration. The significance level of all statistical tests was set at 0.05.

To validate the FE model of PHF, vertical compressive loads of 50N, 100N, 150N, and 200N were applied to the humerus’s articular surface while constraining the lower surface. The displacement of the fracture gap was measured and used to calculate the stiffness. The model’s stiffness was determined to be 189.38 N/mm, consistent with previous literature, indicating that the complete FE model of PHFs established in this study was effective33.

Figure 6 shows the percentage change in ΔS simulated by the 102 FE models relative to the baseline value across the feasible space of two design parameters (θh and θv). Figure 7 shows the SPSO and OPSO configurations. In the OPSO configuration, Screw 3 had a horizontal angle (θh) of 20° and an elevation angle (θv) of 10°, while Screw 4 had a θh of 16° and a θv of 6°. In the optimized configuration, the minimum average principal bone strain around the screws (212.95 ± 19.30 με) was achieved, significantly lower than the SPSO results (249.68 ± 247.72 με, p < 0.001) (Fig. 8a), corresponding to a relative strain reduction of 17.25%.

Contour plots show the percent change in mean bone strain (ΔS) around the screw for each of the 102 possible height and divergence angle combinations. The percentages are calculated relative to their baseline values for the standard model.

Frontal (a) and sagittal (b) views of the PHILOS plate (blue), original screws 3 and 4 are shown in green, while optimal screw configuration are shown in pink.

(a–e) Bone strain around screws: (a) axial load, (b) adduction load, (c) abduction load, (d) rotation load, (e) stretching load. (f–j) Stress distribution of the implant: (f) axial load, (g) adduction load, (h) abduction load, (i) torsional load, (j) tensile load.

In this study, the humeri of 20 volunteers was reconstructed, resulting in 20 PHF models. The demographic data of the 20 volunteers are shown in Table 2. Linear regression of the real and estimated values for six altered screw orientations corresponding to Configuration I (Fig. 5), based on 20 samples under three different anatomical loads (N = 60). Subsequently, a comparison of the 60 data sets was conducted, and the Pearson correlation coefficient for these 60 data points was calculated. These models were then fixated using either OPSO or SPSO. The analysis demonstrated a high correlation (R2 = 0.858) between the strain reduction obtained by superimposing individual screw strains and the results from FE simulations of the actual configuration.

As shown in Figs. 8a–d and 9a, the average equivalent compressive principal strain for the ROIs in the OPSO group under five loading conditions were 212.94 με, 168.51 με, 256.50 με, and 324.42 με, while for the ROIs in the SPSO group were 249.67 με, 197.18 με, 294.75 με, and 340.87 με. The OPSO exhibited significantly lower compressive principal strains than the SPSO (p < 0.001).

Average strain of ROIs and maximum stress of the implant: (a) Equivalent bone strain around screws, (b) Maximum von-Mises stress of the implant. *p < 0.05, statistical significance.

Under the four loading conditions, the primary stress distribution in both groups was concentrated around the connection between the calcar screws and plates, as shown in Fig. 8e–h and Fig. 9b. In the OPSO, the implant stress was lower than in the SPSO under vertical and abduction conditions (231.95 MPa vs. 253.1 MPa; 352.40 MPa vs. 387.37 MPa). However, there was little difference between the two groups under adduction and torsion conditions (108.42 MPa vs. 112.77 MPa; 266.59 MPa vs. 267.03 MPa).

Based on previous studies and using Hooke’s law (σ = Eε), stress values for each measurement point were calculated. The elastic modulus of Ti6Al4V was 110,000. The strain-load curve is shown in Fig. 10a–f. The stress comparison between the two groups is shown in Fig. 10g–i. Under different conditions, the variation trend of strain is similar with the increase of load. In both groups, stress was concentrated at measurement points 5 and 6. Additionally, smaller stress concentrations were found at points 3, 4, 7, and 8 for both groups. Stress at points 1 and 2 was very small. This is similar to the stress distribution of implants in the FE analysis. Under vertical and valgus loads, the stress values at points 3, 4, 5, 6, 7, and 8 of the OPSO were smaller than those of the SPSO, with the difference being statistically significant (p < 0.05). However, under varus load, there was no statistically significant difference in stress between the two groups. Under the three loads, the maximum stress of both steel plates was much smaller than the yield strength of the Ti6Al4V material (795 MPa)34.

(a–f) Load-strain curves of the eight measurement points. (h–j) Stress of 8 measurement.

The mean stiffness and standard deviation for all groups and test modes are shown in Table 3 and Fig. 11a,c. The stiffness of the OPSO under vertical, varus, valgus, and torsion loads were 123.30 ± 16.77 N/mm, 215.29 ± 36.50 N/mm, 68.51 ± 16.39 N/mm, and 0.708 ± 0.19 Nm/degree, respectively. The stiffness of the OPSO was 141.59 ± 24.58 N/mm, 247.38 ± 36.68 N/mm, 66.50 ± 16.39 N/mm, and 0.95 ± 0.30 Nm/degree, respectively. Under vertical, varus, and torsion loads, the stiffness of the OPSO was greater than that of the SPSO (p < 0.05). However, under valgus loads, the difference was not statistically significant (p > 0.05).

Stiffness of SPSO and OPSO. (a) Stiffness in static stress; (b) Stiffness in cyclic loading experiments; (c) Torsional load; (d–f) Cycle-displacement curves; (g) Cycle-degree curves. *p < 0.05, statistical significance.

The cyclic-displacement curves under vertical, varus, and valgus loads are shown in Fig. 11d–g. The average stiffness of the two groups under vertical, varus, and valgus cyclic loading were 107.88 ± 18.62 N/mm vs. 123.00 ± 28.58 N/mm (p = 0.028), 180.59 ± 36.11 N/mm vs. 220.97 ± 48.21 N/mm (p = 0.029), and 48.33 ± 10.16 N/mm vs. 62.66 ± 18.12 N/mm (p = 0.025). Under the three loads, the stiffness of the optimized plate increased by 18.64%, 22.22%, and 29.6%, respectively, compared with the SPSO (Fig. 11b,c). The cycle-angle curves and stiffness under torsional load are shown in Fig. 11c,g and Table 3. Under torsional load, the stiffness is higher than that of the SPSO (0.64 ± 0.14 Nm/degree, p = 0.021).

Joint-preserving surgical treatment of PHFs remains challenging despite state-of-the-art locking plate fixation owing to high failure rate7,9,35. Improved implant designs offer promise in reducing mechanical fixation failures in PHFs. This study suggests that optimizing the orientation of proximal screws in the PHILOS plate can mitigate the risk of mechanical fixation failure in PHFs.

The optimized configuration exhibited significantly lower strains in the bone surrounding the implant compared to the SPSO. It reduced strains by 12% in the vertical direction, 14% in internal rotation, 25% in external rotation, 10% in torsion, and 12% in tension. The main changes in the optimized configuration—providing biomechanical advantages—were increased height and dispersion of the screw tips. This finding is consistent with previous computer optimization studies11,13. A recent study by Jabran et al.11 conducted an optimization of the Spatial Subchondral Support plate for PHFs. Unlike our approach, their main objective was to minimize the displacement of fragments, thereby maximizing the structural stiffness of the PHFs model. In our study, the optimization aimed to reduce bone strains around the screws, as previous research has shown that these strains can predict the mechanical fixation failure of locking plates in PHFs16. It can serve as an alternative estimate for structural stability under cyclic loading and is more relevant than stiffness for failure risk analysis13. Smaller strains around the screws lower the probability of mechanical fixation failure, thereby reduces the risk of mechanical fixation failure. This is likely because structural failure is primarily caused by the fracture of the trabecular bone surrounding the screws36. Mischler et al.13 optimized the PHILOS plate design by altering the screw orientation. However, the angle optimization range for the screws was limited to − 10° to 10°, with a step size of 5°. This narrow range and large step size may have overlooked optimal configuration combinations. In our study, optimization focused on Screws 3 and 4 in the PHILOS plate, which have the least stability effect, to enhance their function21. The optimization angle range was set to 40° with a step size of only 2°. A Python script automatically searched tens of thousands of combinations to identify feasible configurations, minimizing the possibility of missing the optimal one. Although some plates incorporated a variable-angle locking design, the orientation of intrahumeral head screws was chosen intuitively by the surgeon, which may not be reliable, repeatable, or achieve the highest stability37,38. Methods like FE analysis, once further developed for clinical application and high automation, could aid in selecting subject-specific screw trajectories.

In FE studies, stress distribution is often used to assess fixation failure risk, with von Mises stress being a key indicator. This study indicates that OPSO generates lower stresses than SPSO. Under vertical and varus loading conditions, the maximum von Mises stress in the OPSO was significantly lower than in the standard PHILOS plate, with reductions of 7.75% and 8.4%, respectively. Under valgus loading conditions, the reduction was 3.6%. Under torsional loading conditions, the reduction remained consistent. The maximum stress of SPSO and OPSO is much less than the yield strength of Ti6Al4V material (795 MPa)34. This suggests that the optimized PHILOS plate can reduce peak von Mises stresses and improve stress distribution. Stress is primarily concentrated at the interface between the screws and the plate, consistent with findings by Tilton et al.39 and Li et al.40 It should also be noted that under valgus loading conditions, the maximum von Mises stress in the implant and the average strain in the ROIs are highest. Therefore, postoperative management of PHFs should avoid forces that can cause valgus loading of the shoulder joint.

In this study, the results of strain electrical measurements show that stresses in both plates are mainly concentrated where Screws 8 and 9 connect to the plate (points 5 and 6), while stresses at points 1 and 2 are relatively small. This is similar to the stress distribution in FE analysis. Additionally, changing screw configuration affects plate stress distribution. Under vertical and valgus loads, the stress of OPSO at points 3, 4, 5, 6, 7, and 8 was lower than that of SPSO, with statistical significance. In addition, we compared the stresses on the plate surface in the FE analysis with the results of the strain electrical measurements. The stress distribution in the strain electrical measurements is similar to that in the FE analysis. And, the magnitude of the stress values is also similar. Therefore, OPSO produces a more uniform stress distribution than SPSO, hence offering an advantage in biomechanical compatibility.

Fracture displacement may relate to the stiffness of the fixation construct. Bone healing time is affected by fixation stability; higher fixation stiffness shortens healing time41. In vitro biomechanical experiments in this study showed that OPSO exhibits higher stability than SPSO. Under vertical, varus, and torsional loading, post-fixation displacement at the fracture site is smaller in OPSO than SPSO. Compared to SPSO, the stiffness of OPSO under vertical, varus, and torsion loads increased by 14.82%, 14.91%, and 33.47%, respectively. There were no significant differences between the two groups under valgus loading conditions. Stable fixation is crucial for fracture healing and early recovery, even in older patients with severe osteoporosis and comminuted fractures. The cyclic loading simulation represents long-term repetitive stress stimulation of the shoulder joint. The results of cyclic loading indicate that OPSO exhibits greater resistance to fracture fragment displacement than SPSO. After 5000 cycles of loading in five scenarios, displacement in OPSO was significantly smaller than that in SPSO. Mischler et al. also obtained similar results19. They conducted biomechanical experiments on their optimized PHILOS plates. They found that, compared to the original design, the optimized implants achieved a significantly greater number of cut-through failure cycles19. This finding is consistent with previous research that correlated the average principal strain around the screw and the number of cycles to failure34.

Given the differences in the processes of finite element modeling and analysis, we reconstructed the humeri of 20 volunteers to establish 20 PHF models, thereby validating the OFAT. We found that a high correlation (R2 = 0.858) between the strain reduction obtained by superimposing individual screw strains and the results from FE simulations of the actual configuration.

Several limitations must be considered in this study. First, this study focused on optimizing one specific normal humerus, so the results may not be generalizable to a larger population, such as individuals with osteoporosis. It remains unclear whether this humerus adequately represents the target patient population that would benefit most from improved treatments. Second, as mentioned earlier, the model only included one type of PHF, so the results may not be applicable to different fracture types. Third, the biomechanical testing and FE modeling in this study only involved a synthetic humerus. Testing on cadaveric humerus is needed to develop FE models that account for differences in cortical and trabecular microstructural regions, allowing more accurate calculations of stress and load. Fourth, the OFAT method simplifies the process of optimization, but it does not account for potential interactions between the two screws. Fifth, the plate might be optimized for a subset of potential clinically relevant load cases. Sixth, each humerus has undergone various loads, and subsequent loading experiments may result in fatigue or damage to the microstructure of the trabecular bone.

This study demonstrates the potential to improve fixation stability by altering the screw orientation of the PHILOS plate, thereby reducing the predicted risk of mechanical fixation failure. This study explored a wide range of optimization angles for the screws—up to 40°—the largest known range. While the final implant design cannot be declared as a new plate, it showcases the capability of computer simulations to effectively evaluate thousands of potential screw configurations and determine the optimal configuration based on validated output measurements. Furthermore, FE analysis and in vitro biomechanical experiments confirmed the enhanced biomechanical stability of OPSO compared to SPSO.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Court-Brown, C. M. & Caesar, B. Epidemiology of adult fractures: A review. Injury 37, 691–697. https://doi.org/10.1016/j.injury.2006.04.130 (2006).

Article PubMed Google Scholar

Roux, A. et al. Epidemiology of proximal humerus fractures managed in a trauma center. Orthop. Traumatol.: Surg. Res. 98, 715–719. https://doi.org/10.1016/j.otsr.2012.05.013 (2012).

Article CAS PubMed Google Scholar

Patel, A. H. et al. Trending a decade of proximal humerus fracture management in older adults. JSES Int. 6, 137–143. https://doi.org/10.1016/j.jseint.2021.08.006 (2022).

Article PubMed Google Scholar

Chu, S. P. et al. Risk factors for proximal humerus fracture. Am. J. Epidemiol. 160, 360–367. https://doi.org/10.1093/aje/kwh224 (2004).

Article PubMed Google Scholar

Oldrini, L. M. et al. PHILOS synthesis for proximal humerus fractures has high complications and reintervention rates: A systematic review and meta-analysis. Life https://doi.org/10.3390/life12020311 (2022).

Article PubMed PubMed Central Google Scholar

Hamandi, F., Laughlin, R. & Goswami, T. Failure analysis of PHILOS plate construct used for pantalar arthrodesis paper II—screws and FEM simulations. Metals https://doi.org/10.3390/met8040279 (2018).

Article Google Scholar

Südkamp, N. et al. Open reduction and internal fixation of proximal humeral fractures with use of the locking proximal humerus plate. Results of a prospective, multicenter, observational study. J. Bone Joint Surg. Am. 91, 1320–1328. https://doi.org/10.2106/jbjs.H.00006 (2009).

Article PubMed Google Scholar

Kralinger, F. et al. The influence of local bone density on the outcome of one hundred and fifty proximal humeral fractures treated with a locking plate. J. Bone Joint Surg. Am. 96, 1026–1032. https://doi.org/10.2106/jbjs.M.00028 (2014).

Article PubMed Google Scholar

Hengg, C. et al. Cement augmentation of the proximal humerus internal locking system in elderly patients: A multicenter randomized controlled trial. Arch. Orthop. Trauma Surg. 139, 927–942. https://doi.org/10.1007/s00402-019-03142-6 (2019).

Article PubMed PubMed Central Google Scholar

Panagiotopoulou, V. C., Varga, P., Richards, R. G., Gueorguiev, B. & Giannoudis, P. V. Late screw-related complications in locking plating of proximal humerus fractures: A systematic review. Injury 50, 2176–2195. https://doi.org/10.1016/j.injury.2019.11.002 (2019).

Article PubMed Google Scholar

Jabran, A., Peach, C., Zou, Z. & Ren, L. Parametric design optimisation of proximal humerus plates based on finite element method. Ann. Biomed. Eng. 47, 601–614. https://doi.org/10.1007/s10439-018-02160-6 (2019).

Article PubMed Google Scholar

Schader, J. F. et al. One size may not fit all: patient-specific computational optimization of locking plates for improved proximal humerus fracture fixation. J. Shoulder Elb. Surg. 31, 192–200. https://doi.org/10.1016/j.jse.2021.06.012 (2022).

Article Google Scholar

Mischler, D., Windolf, M., Gueorguiev, B., Nijs, S. & Varga, P. Computational optimisation of screw orientations for improved locking plate fixation of proximal humerus fractures. J. Orthop. Trans. 25, 96–104. https://doi.org/10.1016/j.jot.2020.02.007 (2020).

Article Google Scholar

Varga, P., Inzana, J. A., Gueorguiev, B., Südkamp, N. P. & Windolf, M. Validated computational framework for efficient systematic evaluation of osteoporotic fracture fixation in the proximal humerus. Med. Eng. Phys. 57, 29–39. https://doi.org/10.1016/j.medengphy.2018.04.011 (2018).

Article PubMed Google Scholar

Le, L., Jabran, A., Peach, C. & Ren, L. Effect of screw thread length on stiffness of proximal humerus locking plate constructs: A finite element study. Med. Eng. Phys. 63, 79–87. https://doi.org/10.1016/j.medengphy.2018.12.004 (2019).

Article PubMed Google Scholar

Varga, P., Grünwald, L., Inzana, J. A. & Windolf, M. Fatigue failure of plated osteoporotic proximal humerus fractures is predicted by the strain around the proximal screws. J. Mech. Behav. Biomed. Mater. 75, 68–74. https://doi.org/10.1016/j.jmbbm.2017.07.004 (2017).

Article PubMed Google Scholar

Mo, F., Zhang, H., Zhao, S., Xiao, Z. & Liu, T. Coupling musculoskeletal dynamics and subject-specific finite element analysis of femoral cortical bone failure after endoprosthetic knee replacement. Appl. Bion. Biomech. 2019, 4650405. https://doi.org/10.1155/2019/4650405 (2019).

Article Google Scholar

Wee, H., Reid, J. S., Chinchilli, V. M. & Lewis, G. S. Finite element-derived surrogate models of locked plate fracture fixation biomechanics. Ann. Biomed. Eng. 45, 668–680. https://doi.org/10.1007/s10439-016-1714-3 (2017).

Article PubMed Google Scholar

Mischler, D. et al. Locking plates with computationally enhanced screw trajectories provide superior biomechanical fixation stability of complex proximal humerus fractures. Front. Bioeng. Biotechnol. 10, 919721. https://doi.org/10.3389/fbioe.2022.919721 (2022).

Article PubMed PubMed Central Google Scholar

Hamandi, F., Simon, G., Laughlin, R. & Goswami, T. Biomechanical behavior of a variable angle locked tibiotalocalcaneal construct. Bioengineering https://doi.org/10.3390/bioengineering7010027 (2020).

Article PubMed PubMed Central Google Scholar

Fletcher, J. W. A., Windolf, M., Richards, R. G., Gueorguiev, B. & Varga, P. Screw configuration in proximal humerus plating has a significant impact on fixation failure risk predicted by finite element models. J. Shoulder Elb. Surg. 28, 1816–1823. https://doi.org/10.1016/j.jse.2019.02.013 (2019).

Article Google Scholar

Varga, P., Grünwald, L. & Windolf, M. The prediction of cyclic proximal humerus fracture fixation failure by various bone density measures. J. Orthop. Res.: Off. Publ. Orthop. Res. Soc. https://doi.org/10.1002/jor.23879 (2018).

Article Google Scholar

Synek, A., Chevalier, Y., Baumbach, S. F. & Pahr, D. H. The influence of bone density and anisotropy in finite element models of distal radius fracture osteosynthesis: Evaluations and comparison to experiments. J. Biomech. 48, 4116–4123. https://doi.org/10.1016/j.jbiomech.2015.10.012 (2015).

Article CAS PubMed Google Scholar

Lee, J.-S., Kim, J. H., Kim, K. G., Yoon, Y.-C. & Gas, P. Effect of calcar screw in locking compression plate system for osteoporotic proximal humerus fracture: A finite element analysis study. BioMed Res. Int. 1–9, 2022. https://doi.org/10.1155/2022/1268774 (2022).

Article Google Scholar

Shin, M. J. et al. Role of inferomedial supporting screws for secondary varus deformity in non-osteoporotic proximal humerus fracture: A biomechanical study. Arch. Orthop. Trauma Surg. 141, 1517–1523. https://doi.org/10.1007/s00402-020-03627-9 (2021).

Article PubMed Google Scholar

Zhang, Y. K. et al. Biomechanical effect of the configuration of screw hole style on locking plate fixation in proximal humerus fracture with a simulated gap: A finite element analysis. Injury 47, 1191–1195. https://doi.org/10.1016/j.injury.2016.02.028 (2016).

Article PubMed Google Scholar

Lescheid, J., Zdero, R., Shah, S., Kuzyk, P. R. & Schemitsch, E. H. The biomechanics of locked plating for repairing proximal humerus fractures with or without medial cortical support. J. Trauma 69, 1235–1242. https://doi.org/10.1097/TA.0b013e3181beed96 (2010).

Article PubMed Google Scholar

Katthagen, J. C. et al. Biomechanical effects of calcar screws and bone block augmentation on medial support in locked plating of proximal humeral fractures. Clin. Biomech. (Bristol, Avon) 29, 735–741. https://doi.org/10.1016/j.clinbiomech.2014.06.008 (2014).

Article PubMed Google Scholar

Bergmann, G. et al. In vivo gleno-humeral joint loads during forward flexion and abduction. J. Biomech. 44, 1543–1552. https://doi.org/10.1016/j.jbiomech.2011.02.142 (2011).

Article CAS PubMed Google Scholar

Westerhoff, P. et al. In vivo measurement of shoulder joint loads during activities of daily living. J. Biomech. 42, 1840–1849. https://doi.org/10.1016/j.jbiomech.2009.05.035 (2009).

Article CAS PubMed Google Scholar

Zhang, W. et al. The mechanical benefit of medial support screws in locking plating of proximal humerus fractures. PLoS One 9, e103297. https://doi.org/10.1371/journal.pone.0103297 (2014).

Article ADS CAS PubMed PubMed Central Google Scholar

Katthagen, J. C. et al. Influence of plate material and screw design on stiffness and ultimate load of locked plating in osteoporotic proximal humeral fractures. Injury 47, 617–624. https://doi.org/10.1016/j.injury.2016.01.004 (2016).

Article PubMed Google Scholar

Gradl, G. et al. Locking plate fixation of humeral head fractures with a telescoping screw. A comparative biomechanical study versus a standard plate. Injury 43, 734–738. https://doi.org/10.1016/j.injury.2011.08.012 (2012).

Article PubMed Google Scholar

Tumulu, S. K. & Sarkar, D. Computer-aided design, finite element analysis and material-model optimisation of knee prosthesis. J. Aust. Ceram. Soc. 54, 429–438. https://doi.org/10.1007/s41779-017-0169-9 (2017).

Article CAS Google Scholar

Oldrini, L. M. et al. PHILOS synthesis for proximal humerus fractures has high complications and reintervention rates: A systematic review and meta-analysis. Life (Basel, Switzerland) https://doi.org/10.3390/life12020311 (2022).

Article PubMed Google Scholar

Steiner, J. A., Ferguson, S. J. & van Lenthe, G. H. Computational analysis of primary implant stability in trabecular bone. J. Biomech. 48, 807–815. https://doi.org/10.1016/j.jbiomech.2014.12.008 (2015).

Article PubMed Google Scholar

Voigt, C., Geisler, A., Hepp, P., Schulz, A. P. & Lill, H. Are polyaxially locked screws advantageous in the plate osteosynthesis of proximal humeral fractures in the elderly? A prospective randomized clinical observational study. J. Orthop. Trauma 25, 596–602. https://doi.org/10.1097/BOT.0b013e318206eb46 (2011).

Article PubMed Google Scholar

Ockert, B. et al. Monoaxial versus polyaxial screw insertion in angular stable plate fixation of proximal humeral fractures: Radiographic analysis of a prospective randomized study. J. Trauma 69, 1545–1551. https://doi.org/10.1097/TA.0b013e3181c9b8a7 (2010).

Article PubMed Google Scholar

Tilton, M. et al. Biomechanical testing of additive manufactured proximal humerus fracture fixation plates. Ann. Biomed. Eng. 48, 463–476. https://doi.org/10.1007/s10439-019-02365-3 (2020).

Article PubMed Google Scholar

Li, D. et al. Application of a lateral intertubercular sulcus plate in the treatment of proximal humeral fractures: A finite element analysis. BMC Surg. 22, 98. https://doi.org/10.1186/s12893-022-01557-4 (2022).

Article PubMed PubMed Central Google Scholar

Wehner, T., Claes, L., Niemeyer, F., Nolte, D. & Simon, U. Influence of the fixation stability on the healing time—a numerical study of a patient-specific fracture healing process. Clin. Biomech. 25, 606–612. https://doi.org/10.1016/j.clinbiomech.2010.03.003 (2010).

Article Google Scholar

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Department of Orthopedics, The Second Hospital of Jilin University, Changchun, Jilin Province, China

Jichao Liu, Ziyan Zhang & Chengdong Piao

Department of Engineering Mechanics, Jilin University, Changchun, Jilin Province, China

Peng Li

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J.L: Writing-original draft, Methodology, Investigation, Data collection and analysis. Z.Z: Methodology, Data collection. P.L: Methodology, Data collection. C.P: Writing-review & editing, Conceptualization. All authors reviewed and approved the final manuscript.

Correspondence to Chengdong Piao.

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Liu, J., Zhang, Z., Li, P. et al. Enhancing fixation stability in proximal humerus fractures: screw orientation optimization in PHILOS plates through finite element analysis and biomechanical testing. Sci Rep 14, 27064 (2024). https://doi.org/10.1038/s41598-024-78702-x

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Received: 23 July 2024

Accepted: 04 November 2024

Published: 07 November 2024

DOI: https://doi.org/10.1038/s41598-024-78702-x

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