Finite Element Analysis of the Optimal Con guration of Bridging Combined Internal Fixation System in The Treatment of Vancouver B1 Periprosthetic Femoral Fractures

Long Zhang Yan an Hospital A liated to Kunming Medical University https://orcid.org/0000-0001-9956-214X Md Ariful Haque Yan an Hospital A liated to Kunming Medical University Ying Xiong Yan an Hospital A liated to Kunming Medical University Jing Qin Yan an Hospital A liated to Kunming Medical University Luyun Liu Yan an Hospital A liated to Kunming Medical University Yingjie Zhang Yunnan University of Traditional Chinese Medicine Jiayu Xiao (  346721374@qq.com ) Yunnan University of Traditional Chinese Medicine


Introduction
As life expectancy increases, the incidence of falls and osteoporosis increases year by year. At the same time, the improvement of people's requirements for quality of life and the progress of surgical technology makes the application of hip arthroplasty more and more. As a result, Total hip arthroplasty (THA) demand is expected to increase by 174% to 572,000 procedures by 2030 1 . Unfortunately, there has been an increase in post-THA problems, including Periprosthetic fracture (PPF) 2 . Abdel M P et al. reviewed 32,644 patients undergoing primary total hip arthroplasty and found that the incidence of intraoperative femoral fractures was 1.7% and that postoperative periprosthetic fracture was 3.5% 3

. A prediction model
shows that the number of periprosthetic fractures will increase by an average of 4.6% per decade from 2015 to 2060 4 ,with a high clinical and economic burden 5 .
Treatment of periprosthetic fractures is complex due to the presence of arti cial hip prostheses and the poor essential physical condition of patients with periprosthetic fractures 6 . The treatment is varied.
Accurate classi cation is signi cant for managing periprosthetic fractures of the arti cial hip, and the Vancouver classi cation is currently the most commonly used 7 . Vancouver type B1 fracture is a stable prosthetic fracture with no loss of bone mass and is treated with internal xation as the preferred treatment 8-10 . Tanvir Khan reviewed 6,131 patients with PFF and found a high risk of death, with a 5-year mortality rate of 60% in the highest risk group 11 . The plate series is the standard treatment method, which can be combined with the ring ligation, and has achieved a particular effect [12][13][14][15] . The advantages of using a locking compression plate in the treatment of periprosthetic fractures are direct exposure and reduction of the fracture. The disadvantages are soft tissue dissection and the di culty of obtaining bicortical screw xation due to intramedullary prosthesis occlusion. Locking compression plate can be combined with Minimally invasive plate osteosynthesis (MIPO) to treat periprosthetic fractures and maintain bone vitality 16 . Some scholars suggest additional methods such as allogeneic bone plates and xation of at least 10 cortices [17][18][19][20] . The most common complications of existing internal xation methods included xation failure and nonunion, with rates of 4.4% and 3.9%, respectively 21 .
The bridged combined internal xation system(Ortho-bridge System, OBS) is a composite structure composed of the xed block, xed rod, and screw. The selected blocks include single side single hole, single side double hole, double rod single hole, double rod double hole, and special-shaped blocks adapted to different anatomical positions; Fixed rod includes unequal diameter; The screws include locking screws and standard screws (see Fig. 1). Its design concept advocates individualization, diversi cation and systematization of orthopedic internal xation, with the advantages of individualized shaping, free combination, three-dimensional xation, elastic xation, etc. In this study, the biomechanical properties of different varieties of bridging combined internal xation systems in the treatment of periprosthetic fractures were analyzed by nite element analysis to determine the optimal con guration of nails, rods, and blocks.

Veri cation of scheme validity
The same bone condition was used to simulate a femoral shaft fracture at the same site, and xation was performed with a plate (see Fig. 2). The comparison results with OBS are shown in Table 1. In OBS treatment of periprosthetic fractures, the stress at the fracture end was lower than that of simple femoral shaft fractures xed with steel plate, which proved that the xation was effective. Optimal third rod position The analysis results were shown in Table 2. With the downward movement of the third rod, the femoral displacement generally showed a decreasing trend, while the maximum Von Mises stress of OBS showed an increasing trend. Thus, the comprehensive analysis showed that the femoral displacement and the maximum Von Mises stress of OBS were the minimum at the downward movement of the third rod 35mm. Optimal cross Angle of proximal screw The analysis results were shown in Fig. 3. When the spatial Angle between the proximal third rod screw and the rst and second rod xation screws was 71.92°, the femoral displacement and the maximum Von Mises stress of OBS were the minimum in the comprehensive analysis.
Optimal connection rod diameter The results are shown in Table 3. Femoral displacement and the maximum Von Mises stress of OBS are both smaller when using a 6mm diameter connecting rod than when using a 5mm connecting rod. Optimum screws number scheme The results were shown in Table 4. Again, scheme F had the most signi cant number of screws, and both femoral displacement and the maximum Von Mises stress of OBS were the smallest.

Discussion
There are various methods of internal xation for fractures around the Vancouver type B1 prosthesis.
Still, due to the presence of the intramedullary prosthesis, the double cortical xation cannot be achieved, the holding power of the internal xation is reduced, and the conventional internal xation often fails to achieve a strong xation, leading to reoperation 19,22 . The unique locking structure of OBS consists of a pin, rod, and block, which are freely matched to form a plurality of internal xation complexes. Different from the single position and direction of plate series screws, the position and direction of OBS screws can be adjusted and controlled at will according to the situation, providing wider operability and applicability for the treatment of periprosthetic fractures and well making up for the shortcomings of other internal xation devices. The multi-rod xation mode and cross-screw xation of OBS can achieve threedimensional xation and further improve the xation strength. The rod-block combination can better disperse stress, avoid stress concentration and reduce the fracture risk of the internal xator 23 . In addition, intraoperative soft tissue dissection is too much; the blood supply is reduced and can easily make the fracture heal. Therefore, the application of OBS can achieve minimally invasive or limited incision operation, with minimal damage to soft tissue and periosteum. Bridging xation does not directly compress the periosteum and fracture site, which has little impact on the blood supply of the fracture area and protects the biological environment of the fracture area 24 . An animal experiment also showed that OBS could effectively reduce the disruption of blood supply at the fracture site and provide a rm xation 25 . The OBS connection block can slide axially to achieve compression and has the function of a "reset device," which can be xed by changing the reduction edge during surgical operation 26 .
The use of OBS in the treatment of Vancouver B1 periprosthetic fracture of the femur has been proven to be solid and reliable with satisfactory clinical results 27 . Due to the exibility of the OBS combination mode, this experiment was designed to explore the optimal combination mode. The OBS rod-block structure allows the screw position to be adjusted freely according to the speci c situation, and the pressure hole or lock hole can be selected freely. The angular screws have better pull-out resistance and xed strength 15 . The three-dimensional xation of OBS can be achieved well when the three-rod xation is used. The third rod is about 20mm below the lateral concave of the femur, and the femoral displacement and the maximum Von Mises stress of OBS are both the maximum. The failure possibility of internal xation is the highest when the third rod is placed there. The lower 35mm femoral deformation and OBS stress are minimal, which is the best third-rod placement position. The intersection Angle of the proximal screw on the femoral displacement and the maximum Von Mises stress of OBS is generally gentle. Still, there are two trough points; namely, the intersection Angle is about 71° and 84°, respectively. We believe that both of these two cases are feasible. To x the strength, it is recommended to choose a 6mm connecting rod with low femoral displacement and the maximum Von Mises stress of OBS.
Although the number of screws was the most stable, considering the complexity of the clinical operation, we believed that the plan D with little difference was the best plan for the number of screws.
Our study has its limitations. The study included subjects that did not re ect actual bone mass in patients with periprosthetic fractures. In addition, due to the stress shielding effect, the proximal femur bone mineral density will decrease, and the Gruen7 area has the greatest decrease 28,29 . However, bone loss was not considered in this experiment. Muscle and other soft tissues were not considered in this study, and only biomechanical evaluation under the same bone and the same load was performed.

Conclusion
The personalized and diversi ed xation mode of OBS is well adapted to the characteristics of periprosthetic fracture and provides an effective means for the treatment of periprosthetic femoral fracture.

Finite element model establishment
The bone model was derived from a 48-year-old healthy male volunteer whose CT data were collected. He had no skeletal lesions, no previous surgery history, no tumor history, and no drugs affecting bone metabolism in recent years. According to the size parameters of the femoral prosthesis and OBS, the three-dimensional models of the femoral prosthesis and OBS were established and assembled, and the fracture line was simulated at the distal end of the femoral prosthesis stem (see Fig. 4). For the material properties of cortical bone, elastic modulus Ex = Ey = 7.00GPa,Ez = 11.50GPa, shear modulus Gxy = 2.60GPa,Gyz = Gxz = 3.50GPa, and Poisson's ratio was 0.4. The elastic modulus of cancellous bone was 0.40GPa, and the Poisson's ratio was 0.3. The femoral stem, connecting rod, and screw were made of titanium alloy with an elastic modulus of 110.00GPa and a Poisson's ratio of 0.3. The connecting block comprises cobalt-chromium molybdenum alloy with an elastic modulus of 210.00GPa and a Poisson's ratio of 0.3 30 . Tetrahedral 10-node units were used to mesh the above structures. The mesh size of cortical bone was 3mm, the mesh size of cancellous bone and the femoral stalk was 2mm, and the mesh size of connecting rods, screws, and connecting blocks was 1.5mm. There were 249,285 mesh units and 390,122 nodes in total. The binding contract between the screw and cortical bone, screw and joint block, joint block and rod, and femoral stem and bone was set, and there was no frictional contact between the broken ends of the fracture. A force of Fx = 300N, Fz =-600N was applied to the top of the femoral head and the distal femur was xed with 6 degrees of freedom set to 0. The evaluation criteria included femoral displacement and the maximum Von Mises (equivalent) stress of OBS.

Optimal three-rod position relationship
The arc of the third rod was assembled near the great trochanter. Then, starting from the lateral recess of the femur, the mechanical properties of the third rod moving down 0mm, 10mm, 20mm, 25mm, 30mm, 35mm, and 50mm were analyzed, respectively, and the optimal position of the third rod was analyzed (see Fig. 5).

Optimal cross Angle of proximal screw
According to the optimal position of the third rod and the exibility of the proximal connecting block ( ) of the third rod, the direction of the proximal screw was adjusted accordingly. According to the position in Fig. 6, the optimal intersection Angle of the proximal screw was analyzed by gradient analysis at a spatial Angle of 3°.
Optimal diameter of connecting rod OBS connecting rod has two speci cations: 5mm and 6mm. Two xing models of connecting rods are used respectively to analyze the optimal diameter of connecting rod.

Optimal screw number scheme
According to the optimal position of the third rod and the optimal intersection Angle of proximal screws analyzed in the previous two steps, the xation model with the different number of screws was used to analyze the optimal number of screws. (Fig. 7) Declarations Ethical Approval: Approved by Yan'an Hospital A liated to Kunming Medical University Ethical Committee.
Con ict of interest statement : We declare that we have no nancial and personal relationships with other people or organizations that can inappropriately in uence our work, there is no professional or other personal interest of any nature or kind in any product, service or company that could be construed as in uencing the position presented in the manuscript entitled"Finite element analysis of the optimal con guration of bridging combined internal xation system in the treatment of Vancouver B1 periprosthetic femoral fractures".
Data Availability : The data sets used and analyzed during the current study are available from the corresponding author on reasonable request.