Biomechanical comparison of different screw-included angles in crossing screw fixation for transverse patellar fracture in level walking: a quasi-dynamic finite element study

A knee joint model containing the patella, distal femur, proximal tibia, and fibula was developed based on the computer tomographic images of a healthy man with a body weight of 70 kg and height of 170 cm. The images were obtained when the subject was lying supine; hence, the knee model was created in the full extension position. The areas of the cortical and cancellous bone in the images were isolated out by the higher gray values than the surrounding soft tissues. The 3D model of the bones was then developed by stacking the isolated bony areas. It was subsequently imported into the CAD software, SolidWorks 2019, to create the cartilage and meniscus. The thickness of the cartilage of the patella, distal femoral, and proximal tibia was set at 1 mm based on the literature [22]. The space between the cartilage was created as a meniscus. The transverse fracture type AO 34-C1 at the middle of the patella was used in this study (Fig. 1a). The transverse fracture was created by a virtual plane; hence, no gaps existed after the section. After the fracture was created, a 4.5 mm headless compression screw (HCS, DePuy Synthes, Raynham, MA, US) was used to fix the fractured patellar fragments (Fig. 1b).

To investigate the effect of the included angle of the screws in crossing fixations, three crossing angles were considered: 30°, 60°, and 90°. Furthermore, in the crossing screws, there are two different screw configurations: the anterior screw inward and anterior screw outward. In addition to cross-fixation, traditional parallel screw fixation was used for comparison. Two parallel screws were placed in the middle third of the patella in the front plane. The proximity of the screws was approximately half of the thickness of the patella. Additionally, the currently used anterior wire in a figure of eight with two parallel screws was used for validation. The diameter of the anterior wire was set at 1 mm. The length of the screws ranged from 35 to 40 mm, and the thread length was 12 mm. The thread was controlled to avoid passing through the fracture site; hence, compression and separation of the fractured patellar fragments under loading were allowed. In total, eight different configurations were used (Fig. 2): two parallel screws (Para), two parallel screws with anterior wire (Para&Wire), crossing 30°with the anterior screw inward (X30-AI), crossing 30°with the anterior screw outward (X30-AO), crossing 60°with the anterior screw inward (X60-AI), crossing 60°with the anterior screw outward (X60-AO), crossing 90°with the anterior screw inward (X90-AI), and crossing 90°with the anterior screw outward (X90-AO).

The model was imported into ANSYS Workbench 2022 for simulation. A quadratic tetrahedron element (solid 187) was used to mesh the complex model, including the bone, cartilage, screw, and wire. The ligaments of the knee joint were reconstructed using tension-only springs in the ANSYS Workbench. In total, five ligaments (Table 1), namely the patellar, medial collateral, lateral collateral, anterior cruciate, and posterior cruciate ligaments, were created in the FE model. The stiffness of the spring was defined based on literatures [23‐26]. The material properties of the bone, cartilage, and meniscus were set according to literature (Table 2) [27‐31]. The material properties of the metal were used based on the engineering database in the ANSYS Workbench. All the materials were as assumed to be linear elastic, isotropic, and homogeneous.

A convergence test was conducted with the Para model in the full extension position to confirm that the mesh status of the FE model was stable. The total number of elements was increased by globally reducing the edge length of the element to confirm the stability of the numerical model. The maximum gap distance between the fractured patella and contact area between the patellar fragments were used as indices. After convergence, to validate the present FE model, the rotational degree in the sagittal plane of the patellar fragment Para&Wire model was compared to the proposed result in a cadaveric study [32].

After validation and convergence, the motion of the knee joint during level walking was simulated by applying rotational degrees to the femur. Normalized displacement was applied to the superior surface of the femur, while the distal end of the tibia and fibula were completely fixed (Fig. 3). In total, 20 positions with a sequential increment of 5% in the walking cycle were used (Table 3). All internals were consistent, and the endpoint of the interval was the starting point of the following interval. Linear interpolation was used for each interval. In addition to the displacement, a quadriceps force parallel to the long axis of the femur was applied to the base surface of the fractured patella. The applied degree and force data were set based on a previous study [33]. During the late swing phase, quadriceps force was set to 1 N for solving.

The gap opening distances at the anterior, medial, and lateral sides of the fracture gap during walking were used as indices for comparison. Furthermore, the change in the contact area between the proximal and distal patellar fragments with different configurations during walking was plotted for comparison.

The difference in maximum gap opening distance at the anterior gap was 1.4% (from 0.72 to 0.71 mm) between 452 053 and 3 208 329 nodes. Additionally, the difference in the contact area between the patellar fragments was 1.4% (from 90.1 to 91.4 mm²) between 452 053 and 3 208 329 nodes (Fig. 4a and b). Furthermore, the rotational stiffness of the Para&Wire model was similar to that in a previous study [32]. The results of the rotational stiffness in the present and published studies were 453 N/degree and 510 (SD 362) N/degree, respectively (Fig. 4c).

The fractured patella separated at the anterior surface, and a large gap was developed, while the posterior aspect remained in contact with each other during walking (Fig. 5). Parallel screw fixation, regardless of whether the anterior wire was used, yielded a smaller gap opening distance than crossing screw fixation. Furthermore, the maximum gap opening distance during walking increased with an increase in the included angle in the crossed screws. In stance phase, the maximum gap opening distance of X90.AO was 1.25 (Fig. 6), 1.01 (Fig. 7) and 0.63 mm (Fig. 8) at anterior, medial, and lateral site of the gap, respectively, at 15% of the walking cycle. In swing phase, the maximum gap opening distance of X90.AO was 0.57, 0.4 and 0.16 mm at the anterior, medial, and lateral site of the gap, respectively, at 60% of the walking cycle. In general, the anterior gap opening distance was larger than the medial and lateral gaps during the walking cycle.

The contact area of the patellar fragments at the fracture site with parallel screw fixations was obviously larger than that with crossing screw fixations in the stance phase (5–30% of the walking cycle) (Fig. 9). The contact areas in the fracture patella with different fixations were similar during the swing phase. The maximum contact areas in the Para model were 176 mm² and 280 mm² in the stance phase and swing phase, respectively. The difference in contact area between parallel screw fixation with and without anterior fixation was very minor.