Biomechanical analysis of the placement of fixation lag screw in different intertrochanteric hip fracture angles

The common surgical method for fracture fixation in the femoral neck and intertrochanteric region is the implantation a dynamic lag screw into the femoral head. However, failure rates of this fixation are high due to a cut-out of the lag screw from the femoral head. It is unclear if the lag screw positions will affect the stabilisation of the intertrochanteric fracture with different fracture angles. This study aimed to examine the influence of lag screw placement in the fixation of hip fractures with different fracture angles in healthy and osteoporotic femurs using three-dimensional finite element analysis. Two screw positions at the centre and inferior–posterior (IP) of the femoral head with three fracture angles (30°, 45°, 60°) were studied. The results showed that varying fracture angles and the onset of disease (osteoporosis) have influenced the optimal placement of the lag screw. The lag screw in the IP position in the healthy femur with 30° and 45° fracture angles and osteoporotic femur with 30° fracture angle induced lower periprosthetic bone strains. For a healthy femur with 60° fracture angle and osteoporotic bone with 45° and 60° fracture angles, a centralised placement of the lag screw in the femoral neck was preferred.


Introduction
There is an increase of hip fractures worldwide, with the peak number of hip fractures occurring in patients between 75 and 79 years of age for both genders [1]. This may be primarily due to the onset of osteoporosis in the elderly population. Although most hip fractures are not directly associated with death, the elderly usually do not fully recover from the fractures and instead face a compromise in their quality of life. With a growing elderly population in the world, the occurrence of hip fractures is projected to increase from 1.66 million in 1990 to 6.26 million in 2050 [2]. Fracture of a hip usually occurs in the upper third of the femur, and is categorised into three different types of intracapsular, intertrochanteric and subtrochanteric fractures depending on the complexity and mode of fracture. The intertrochanteric and intracapsular fractures have the largest incident rate, with both occurring in approximately the same frequency in patients between the age of 65 and 99 years old [3]. The occurrence of these fractures is rare in younger individuals. However, the risk factor of intertrochanteric fracture increases as a person ages, and if the person has osteoporotic bone, the risk of fragility fracture increases drastically. It was reported that more than 8.9 million osteoporotic fractures occur annually, amounting in an osteoporotic fracture every 3 s [1].
Treatment of intertrochanteric fractures usually includes surgical interventions as there is a need to reduce the movement of the fractured components and ensure a good fit to promote bone healing. Such interventions utilise implants that secured the fractured parts in place by using a dynamic hip screw (DHS) system. The DHS system consists of a lag screw that is coupled to a metal plate or sleeve that is fixated onto the femoral shaft. The screw is allowed to slide freely within the cancellous bone of the femoral head through the metal sleeve. When the patient walks or the hip subjects to loading, the fractured proximal femur is impacted onto the distal fractured bone producing dynamic compression of the fracture. However, the cut-out rate of the DHS from the femoral head was high, contributing to 80% of the hip fracture implants failure observed [4]. Studies have been conducted to determine an optimal insertion point of the lag screw of the DHS system in the femoral head. These studies were based mainly on radiographic follow-ups of patients with the hip implant [5][6][7][8][9] and computational modelling of the hip fractures with lag screw fixation [10,11]. Baumgaertner et al. [5] suggested the use of the tip apex distance (TAD) as an indicator of optimal placement of the lag screw relative to the femoral head. The TAD is a measure of how close the top of the lag screw lies relative to the femoral head and the average value was 24 mm for successfully treated fractures based on data of 193 patients. In a computational finite element (FE) study by Goffin et al. [11], they found that the DHS was preferred to be placed in the centre and inferior-posterior (IP) positions of the femoral head.
From the limited radiographic and computational studies performed on the DHS system, it was noticed the effect of disease, in particular, osteoporosis on the influence of the position of a DHS system in the femoral head was not studied. The reported studies had mainly focused on a single fracture angle. In actual hip fractures, the femur may fracture at different regions of the bone at different angles. The objectives of this study were to investigate the effects of different fracture angles and the onset of osteoporosis on the optimal placement of the DHS system in the femoral head using FE analysis (FEA). The study also aimed to evaluate the optimal positions of the lag screw in different femur fracture configurations. The effect of the lag screw on the strain change in the femoral head region was studied.

Three-dimensional (3D) FE models
A 3D FE model of the femur was built from CT images of the Visible Human Project female right femur. The images were segmented using Mimics 17.0 (Materialise, Belgium). The proximal femur was saved as a point cloud file and imported into SolidWorks (Dassault Systemes, France) where the fracture geometry and implant insertion holes on the femoral stem and head were created to simulate the insertion path of the hip implant (Fig. 1).
Two different positions of the lag screw namely at the centre and IP relative to the femoral head were examined based on an earlier study of a DHS system in a femoral model with a 45°fracture angle [11]. Fracture lines were varied at different angles (30°, 45°a nd 60°). The holes modelled in the femur simulated the initial drill path of the lag screw. All holes created were perpendicular to the 45°fracture line regardless of the fracture angle. This was to assume the insertion angle of a lag screw was parallel to the femoral neck in all cases. The lag screw and the bone plate were modelled according to the Synthes DHS Standard System in SolidWorks. The barrel angle of the lag screw was modelled as 135°and in accordance with the most commonly used models of the Synthes DHS Standard System. In this study, the threads in the screw were not modelled. A macroscopic overview of the effect of the lag screw on the strain change of the femoral head region was studied. All the components were modelled using the Abaqus FEA software (Dassault Systemes, France) using linear tetrahedron C3D4 elements. Mesh refinement study was conducted to ensure that the predicted FE results were insensitive of the element size. The FE mesh was found to converge at the global element size of 2 mm with ∼180,000 elements. The convergence tolerance was set at <5% comparable to the earlier study conducted by Chong et al. [12].

Material and contact properties assignment
The heterogeneous properties of the bone were assigned by an element-by-element basis, with properties of each element defined by mapping the CT Hounsfield units to the elastic modulus (E). Elements with density (ρ) <1.03 g/cm 3 were assigned to trabecular bone properties and elements with density >1.03 g/cm 3 were assigned cortical bone properties [13] based on equations specified by Rho et al. [14] as listed below: The bone was assumed to be isotropic as a study by Baca et al. [15] suggested little difference between isotropic and anisotropic material behaviour in bigger scaled FE models. To account for the material properties of osteoporotic bone, a reduction in the elastic modulus of the original (healthy) bone model was performed. It was reported that osteoporotic bone has a 32 and 66% reduction in elastic modulus for cortical and cancellous bones, respectively [16][17][18][19][20]. A Poisson's ratio of 0.3 was assigned to both the healthy and osteoporotic bone models. The hip implant was made of stainless steel, and an elastic modulus of 195 GPa was assigned to both the lag screw and hip plate.
In this study, surface pair contacts were defined between three interacting parts, namely (i) bone-to-bone interaction with a coefficient of friction of 0.46, (ii) bone-to-implant interaction with a friction coefficient of 0.3, and (iii) implant-to-implant interaction with a friction coefficient of 0.23 [21]. The hip plate was tied to the femoral stem to simulate the screws were holding the hip plate in place.

Loading and boundary conditions
A hip loading force of 1866 N [22] was applied at the femoral head pointing laterally in the coronal place at an angle of 13°to the femoral axis and posteriorly at an angle of 8°to the femoral axis [23]. This force simulated the maximum load (approximately three times of body weight) that the femur experienced during a normal walking cycle. A hip abductor muscle force [24] was also incorporated in the FE model. The distal end of the femur was constrained in all directions of translation and rotation. The femoral head was constrained in the plane orthogonal to the loading vector to simulate the direct impact of the acetabulum onto the femoral head and eliminating sliding of the femoral head.

Analysis of results
In the study by Goffin et al. [11], they identified that bone yielding and failure could be described by the minimum (compressive) and maximum (tensile) principal strains. And it was crucial to prevent straining of the bone beyond its yield strength in the region immediately superior of the lag screw to minimise the risk of cut-out failure. Hence in this study, comparisons between the healthy and osteoporotic bone models were made by analysing the maximum and minimum principal strains in the trabecular bone. To evaluate the risk of a cut-out of the lag screw, the percentage of bone elements with strain values exceeding the average maximum principal strain (AMaPS) and average minimum principal strain (AMiPS) of the respective bone models were computed. It was assumed in this approach that a higher percentage value would constitute a higher relative risk of the lag screw susceptible to cut-out. The displacement of the tip of the lag screw upon loading was also analysed between positioning the lag screw at the centre and IP of the femoral heads.

Results
The maximum and minimum principal strains distribution in the trabecular bone about the sagittal plane along the centre of the femoral head (where the lag screw was inserted) for both the healthy and osteoporotic bone models are shown in Figs. 2 and 3, respectively. The results indicated that regions of high bone strains were concentrated at the trabecular bone surrounding the tip of the lag screw and at the femoral neck.  (Fig. 4), 45 and 51% of the bone elements exceeded the AMaPS and AMiPS, respectively. However, when the lag screw was placed at the IP position, the percentages of the bone elements exceeded the AMaPS and AMiPS were reduced by 10.8 and 9.9%, respectively. For the 60°fracture angle, an opposite trend was notedthe lag screw in the IP position had resulted in greater percentages of bone elements exceeding the AMaPS (55.6% versus 40.8%) and AMiPS (52% versus 44.8%) as compared to the lag screw in the centre position. For the 45°fracture angle in the healthy bone, the percentages of the bone elements exceeded the AMaPS and AMiPS were comparable when the lag screw was placed in either the centre or IP position.
In an osteoporotic bone model with 30°fracture angle where the lag screw was placed centrally (Fig. 5), 43.4 and 49.6% of the bone elements exceeded the AMaPS and AMiPS, respectively. When the lag screw was placed at the IP position, the percentages of the bone elements exceeded the AMaPS and AMiPS were reduced by 11.6 and 11.2%, respectively. For the 45°and 60°F    The displacement of the tip of the lag screw from its original position upon loading was also analysed and presented in Table 1. An average tip displacement of 0.188 mm (0.168-0.199 mm) and 0.368 mm (0.343-0.387 mm) was predicted for the healthy and osteoporotic bone models, respectively. The variation of the tip displacement between different fracture angles within the healthy and osteoporotic bone models was of a minimal range of 0.03 and 0.04 mm, respectively.

Discussion
The main objective of this study was to investigate the effect of the onset of osteoporosis on the optimal placement of the DHS in the femoral head of different fracture angles by FEA. The effect of the lag screw on the strain change in the femoral head region was also examined. The principal bone strains were used to evaluate the risk of a cut-out of the lag screw from the femoral head. According to Goffin et al. [11], bone yielding and failure can be characterised by the maximum and minimum principal strains, respectively. Anchorage between the lag screw and the femoral head plays an important role in the stability of the implant, where it is important to prevent loading the bone beyond its yield point at the region superior to the tip or thread of the lag screw.
The validity of the FE model was referred to the cadaveric study of a femur conducted by Rohlmann et al. [25]. A femur FE model (healthy bone) was built in the current study and prescribed with similar loading conditions in Rohlmann et al.'s work. The maximum and minimum principal strains induced in the femoral cortex of the FE model were extracted (refer to Fig. 6) and compared with the measured strain values. Levels 6-11 corresponding to the levels where strain rosettes were attached to the femur bone surface in the experiment. The yellow, blue and green FE predicted strains corresponded to the circumference locations of ventrally, dorsomedially and dorsolaterally, respectively, at each level on the femoral shaft. The purpose of this comparison was to check that the strain predictions were realistic. The predicted and measured strains were in the range of 200-800 and 250-750 µɛ respectively, and the correlation of each strain location was within 60-80%. This indicated that the FE predicted strain values were reasonably in agreement with the measured strains. And the current FE model could be used to analyse the optimal placement of the DHS in the femoral head of different fracture angles.

Effect of lag screw placement in different hip fracture angles
In this study, it was observed that none of the bone elements in the healthy bone models exceeded the yield strain of the trabecular bone at maximum (7800 µɛ) and minimum (−8400 µɛ) yield strains, respectively [26]. However, the osteoporotic FE models reported 0.1-4.4% of bone elements exceeding the yield strain values, effectively increasing the risk of a cut-out of the lag screw from the femoral head as compared to the healthy bone.
For the healthy bone model with 30°and 45°fracture angles, the lag screw placed in the IP position of the femoral head has resulted in a lower percentage of bone elements exceeding the AMaPS and AMiPS values, indicating a lower risk of cut-out failure as compared to the centralised screw position. This was in agreement with the study by Goffin et al. [11]. However, for a 60°fracture angle, a centralised placement of the lag screw in the femoral neck was preferred for a lower risk of cut-out failure. As for the osteoporotic bone models, the lag screw placed in the IP position of the femoral head was optimal for a fracture angle of 30°. With hip fracture angles of 45°and 60°in an osteoporotic bone, a centralised placement of the lag screw in the femoral neck was more favourable with higher cut-out resistance. It was further observed for both the healthy and osteoporotic bone models, the percentages of bone elements exceeding AMiPS were higher than the percentages of bone elements exceeding AMaPS for almost all configurations of screw positions and fracture angles (except for an IP position of the lag screw in the healthy bone with a fracture angle of 60°). This suggested that the bone would have a tendency to fail by compression rather than in a tensile mode.

Displacement of the tip of the lag screw
It was noted that displacement of the tip of the lag screw in the femoral head did not contribute greatly to the risk of cut-out failure with <0.4 mm displacement (max) in all healthy and osteoporotic bone models. It suggested that the current loading condition comprising of a joint load and a hip abductor muscle force may not be sufficient to displace the lag screw by a significant amount which could lead to implant failure. However, it was observed the lag screw in the osteoporotic bone models were displaced more in magnitude as compared to the healthy bone models regardless of the screw position. The healthy bone models had an average tip displacement of 0.188 mm while the tip of the lag screw was displaced by an average of 0.368 mm in the osteoporotic bone models. The increase of 95.4% in tip displacement could indicate a greater instability of the lag screw in the osteoporotic bone than in the healthy bone.
Also, it was found that the centralised screw placement resulted in a lower tip displacement in healthy and osteoporotic bone models with fracture angles of 45°and 60°. For a fracture angle of 30°, an IP screw placement was favourable for a lower tip displacement.
One limitation of this study was CT images of an osteoporotic bone not available at the time of the study. The current osteoporotic bone model was built based on a reduction in the elastic modulus of the healthy bone model with the loss of stiffness of the different regions of the bone and cortical thinning of the bone due to age and osteoporosis being accounted for. While a direct prediction of the lag screw failure in the osteoporotic bone was not possible, a relative comparison between the osteoporotic and healthy bone models would still be meaningful and representative based on the current study. Furthermore, the FE models and results obtained represented only three instances of simple two-part fractures, classified as 31-A1 in the Muller AO classification.

Conclusions
FEA was performed for the investigation of biomechanical responses of lag screw fixation in different intertrochanteric hip fracture angles. Based on the simulation results, varying fracture angles and the onset of osteoporosis did influence the optimal placement of the lag screw. The lag screw in the IP position in the healthy femur with 30°and 45°fracture angles and osteoporotic femur with 30°fracture angle induced lower periprosthetic bone strains. For a healthy femur with 60°fracture angle and osteoporotic bone with 45°and 60°f racture angles, a centralised placement of the lag screw in the femoral neck was preferred.