Damage-Based Assessment of the Risk of Cut-Out in Trochanteric Fractures for Different Proximal Femoral Nail Anti-Rotation (PFNA) Blade Positions

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This study coupled three-dimensional finite element models of two femora with unstable trochanteric fractures and a bone damage model to investigate the risk of cut-out for different superior–inferior and medial–lateral blade positions. By including a computational model to simulate bone damage progression and an unstable trochanteric fracture that is more severe than those simulated in the literature, this study advances the body of knowledge on the risk of cut-out in trochanteric fractures of the hip.

Abstract

Cut-out of the hip blade of fracture fixation implants, defined as the perforation of the femoral head by the blade due to the collapse of the neck-shaft angle into varus, is the most relevant mechanical complication in the treatment of trochanteric fractures. Among the factors that contribute to cut-out, the blade positioning in the femoral head is reported as one of the most relevant. Since the optimal blade position in the superior–inferior and medial–lateral directions is unknown, the goal of this work was to investigate the impact of blade positioning in these directions, using three-dimensional finite element models of two femora with an unstable trochanteric fracture (31-A2.2 in the Müller AO classification system with an intrusion distance of 95% of the fracture line length). The finite element models developed were coupled with a stiffness-adaptive damage model for the evaluation of the risk of cut-out. The Proximal Femoral Nail Anti-rotation (PFNA) blade was placed in each model at four discrete distances from the femoral head surface in central and inferior positions. The damage distribution in bone resulting from a gait loading condition was visually and quantitatively assessed to compare the performance of the eight positions and predict the relative risk of cut-out for each. The results suggest that the closer the tip of the blade to the femoral head surface, the lower the risk of cut-out. In the superior–inferior direction, contradicting findings were obtained for the modelled femora. The depth of placement of the blade in the medial–lateral direction and its superior–inferior position were shown to have great influence in the risk of cut-out, with the medial–lateral position being the most relevant predictor. The optimal blade positioning may be subject-specific, depending on bone geometry and density distribution.

1. Introduction

Screw or blade cut-out is the most relevant mechanical complication following proximal femoral fracture fixation [1,2,3,4,5]. Amongst the factors that may affect the risk of cut-out, the blade position is reportedly one of the most relevant [4]. Many clinical studies have evaluated the blade position immediately after surgery and after a follow-up period to identify statistical relations between the post-surgical position and the risk of cut-out [6,7,8,9,10]. Computational studies using the finite element method have also been used to find which blade positions lead to less bone damage [5,11,12,13,14,15,16]. Considering static analyses of stress or strain, and maximum principal stress or strain criteria as a measure of the risk of cut-out, Arias-Blanco et al. [5,16], Goffin et al. [11], Celik et al. [12], and Lee et al. [13] investigated the influence of different anterior–posterior and superior–inferior blade positions on the risk of cut-out. Two primary factors set these studies apart: the implants considered, which included the Proximal Femoral Nail Anti-rotation (PFNA) implant by Synthes (Oberdof, Switzerland) [5,16], the Omega3 Compression Hip Screw by Stryker Osteosynthesis (Schoenkirchen, Germany) [11], the Dynamic Hip Screw by Tipsan Tibbi Aletler (Bornova, Turkey) [12], and the Asia Anatomic Anteversion Hip Nail by A Plus Biotechnology (New Taipei City, Taiwan) [13]; and the fractures considered, which included a stable fracture classified as 31-A1 in the Müller AO classification system [5,13,16] and an unstable 31-A2 fracture, with an intrusion distance of 30% [11,12]. In addition to different superior–inferior positions, Liang et al. [14] and Quental et al. [15] also considered different medial–lateral positions, set by blade length, to investigate their influence on the risk of cut-out in the treatment of a stable 31-A1 fracture and an unstable 31-A2 fracture, with an intrusion distance of 30%, respectively, using the PFNA implant. While the central placement of the hip blade in the anterior–posterior direction is accepted to be less prone to cut-out in both clinical and computational studies, findings about the placement in the other directions are either limited or inconsistent. In the superior–inferior direction, literature conclusions are divided between central [5,6,16,17] and inferior [12,13,14] positions. In the medial–lateral direction, a deep placement of the hip blade, with the tip positioned near the surface of the femoral head surface, is suggested to reduce the risk of cut-out [14,15]; however, limited data exist on this direction when compared to the anterior–posterior and superior–inferior directions. Despite the debate in the literature, no clear consensus exists yet about the optimal position to reduce the risk of cut-out [3,16].

Among the described computational studies addressing the risk of cut-out [5,11,12,13,14,15,16], no study considered damage progression, which could also be an important contributing factor in its occurrence. Considering three-dimensional finite element models of two femora with unstable trochanteric fractures coupled with a bone damage model to simulate damage progression, the aim of this study was to advance the computational modelling of cut-out and investigate the risk of cut-out for different superior–inferior and medial–lateral positions of the PFNA implant. To simulate a severe scenario, an unstable 31-A2 fracture with an intrusion distance of 95% was modelled. The influence of the loading intensity on the risk of cut-out was also evaluated.

2. Materials and Methods

2.1. Damage Model

A quasi-brittle damage model based on continuum damage mechanics was used in this study. This model, based on Hambli [18], uses an isotropic behaviour law coupled with a quasi-brittle damage law to describe the bone damage evolution and its influence on the structural stiffness reduction. Considering a damage variable D that acts as a stiffness reduction factor, and ranges between 0 (no damage, no loss of stiffness) and 1 (total damage, total loss of stiffness), the effective Young’s modulus E is given as a function of the Young’s modulus E₀ of the undamaged material:

$$E=\left(1-D\right)E_0.$$

(1)

The damage parameter is computed according to the following damage law:

$$D=\left\{\begin{array}{c}0, {\epsilon }_{eq}\le {\epsilon }_0\\ D_c{\left(\frac{{\epsilon }_{eq}}{{\epsilon }_f}\right)}^n, {\epsilon }_0<{\epsilon }_{eq}<{\epsilon }_f\\ D_c, {\epsilon }_{eq}\ge {\epsilon }_f\end{array}\right.,$$

(2)

where ${\epsilon }_0$ is the yield strain; ${\epsilon }_{eq}$ is the equivalent strain; ${\epsilon }_f$ is the fracture strain; $D_c$ is the critical damage value at which the material loses all stiffness; and n is the damage law exponent, set to 2 based on the experimental results of Wolfram et al. [19]. The equivalent strain ${\epsilon }_{eq}$ is computed from the strain components ${\epsilon }_{ij}$ by

$${\epsilon }_{eq}=\sqrt{\frac{2}{3}{\epsilon }_{ij}{\epsilon }_{ij}}.$$

(3)

Damage growth is controlled by strain history, through a condition that prevents damage from decreasing [18].

The implemented damage model handled tension and compression differently, as detailed in

Table 1. Damage model parameters. D_c, ${\epsilon }_0$, and ${\epsilon }_f$ represent the critical damage, yield strain, and strain at fracture, respectively.

	Tension	Compression	Source
$D_C$	0.95	0.50	[18]
${\epsilon }_0$	0.70%	1.04%	[20]
${\epsilon }_f$	2.50%	4.00%	[18]

[18,20]. The differentiation was based on the hydrostatic stress: if the hydrostatic stress was positive, tensile conditions were considered; otherwise, compressive conditions were considered.

2.2. Finite Element Models

The three-dimensional finite models of male and female right femora generated from the CT data of the Visible Human Project [21] by Quental et al. [15] were used as the basis for this work. These models were qualitatively validated by showing that their computational predictions of bone strain were consistent with experimental measurements performed on cadaveric femora [15,22]. Considering an anteroposterior view, an unstable fracture classified as 31-A2.2 in the Müller AO classification system was modelled in Solidworks (Dassault Systèmes, Waltham, MA, USA) with an angle of 43° between the fracture line and the femoral shaft axis [23], an opening angle of 6.5°, and an intrusion distance of 95% of the fracture line length to simulate a severe scenario based on clinical experience. The fracture divided the bone model into two parts: a superior part (SP), including the femoral neck and head, and an inferior part (IP), including the femoral shaft. The fracture fragments were not included in the model. To virtually treat the simulated trochanteric fracture, a PFNA implant was modelled in Solidworks, in accordance with a real sample. The assembly of the components followed the guidelines of the surgical technique guide, with the blade being placed in eight positions (Figure 1): in the superior–inferior direction, central and inferior positions were considered; and for each of these positions, four discrete positions were considered along the medial–lateral direction. The four central positions were defined by placing the tip of the blade 5 mm, 10 mm, 15 mm, and 20 mm away from the femoral head surface, using screw lengths of 105 mm, 100 mm, 95 mm, and 90 mm, respectively. The four inferior positions were defined through the inferior translation of the central positions by half the distance between the blade axis and the inferior surface of the femoral neck [15]. For all configurations, the blade was placed centrally in the anterior–posterior direction since it has been widely reported to reduce the risk of cut-out [6,7,8,9,10]. Henceforth, and for the sake of simplicity, each geometry is referred to by a code starting with “M” or “F” if it belongs to the male or female femur, respectively; followed by “Inf” or “Cent” if it corresponds to the inferior or central positions; and by the distance, in mm, from the tip of the blade to the external surface of the femoral head that was used to generate the model. For instance, the central position with a distance of 10 mm to the femoral head surface for the male model is referred to as “M-Cent-10”.

Isotropic, linear elastic material properties were assigned to all components [15]. The implant was made of a titanium alloy with a Young’s modulus E = 105 GPa and a Poisson’s ratio ν = 0.3. Bone was modelled as an inhomogeneous material, with its Young’s modulus as a function of density. The density distributions of the male and female femora were estimated assuming a linear relationship with the Hounsfield Units extracted from the CT images using Abaqus plug-in Bonemapy. The density was set to range between 0.01 g cm⁻³ and 1.32 g cm⁻³, which are typical density values for osteoporotic bones, as these fractures tend to occur mostly in the elderly population [15,24]. To reduce the impact of the partial volume effect on the definition of the bone material properties, two shells reproducing the external surfaces of the SP and IP were modelled, representing the external cortex. These shells were assigned a Young’s modulus of 10.37 GPa, corresponding to the Young’s modulus of the maximum bone density considered, and a thickness of 0.5 mm [25,26]. The relationship between Young’s modulus and bone density $\rho$ for each point of the bone was given by [27]:

$$E_0=6850 {\rho }^{1.49}.$$

(4)

Tie constraints and surface-to-surface contact interactions were used to describe interactions between parts. The outer cortical bone shells and the distal locking screw were tied to the bone. The bone–bone, bone–implant and implant–implant interactions were defined as surface-to-surface contacts with friction coefficients μ of 0.46 [1], 0.3 [1] and 0.2 [28], respectively.

The loading conditions simulated the forces acting on the femur during gait, according to Heller et al. [29]. Three forces representing the hip contact force, abductor and tensor fascia latae muscle forces, and the vastus lateralis muscle force were applied. These forces were applied at attachment points located at their corresponding anatomical sites, and were distributed to the bone surface, to avoid high punctual stresses, using coupling constraints. Forces in percentage of body weight were transformed to Newton considering a mass of 90.8 kg for the male subject, based on the Visible Human Project data [21]. For the female subject, a mass of 75.5 kg was assumed, based on average population weights reported in the literature [30], since no specific data were found. To prevent rigid body motion, the distal end of the bone was constrained using an encastre condition. Since cut-out may result from the damage accumulation of more demanding loading conditions than that considered here (gait), additional simulations were performed considering two times the forces considered for gait [29].

The 3D bone and implant geometries were discretized using quadratic tetrahedral elements (C3D10). The bidimensional shell parts were discretized with quadratic triangles (STRI65). Mesh sizes were defined following Quental et al. [15], who performed a convergence analysis to select a proper element size for the finite element meshes.

2.3. Damage Model and Finite Element Model Coupling

The developed finite element models were coupled with the damage model described in Section 2.1 in an iterative procedure implemented in Matlab (MathWorks, Natick, MA, USA). Briefly, considering an initial undamaged condition, stresses and strains are computed through a FE analysis, performed in Abaqus (Dassault Systèmes, Waltham, MA, USA), and the nodal damage distribution is computed in Matlab using Equations (1)–(3), leading to novel Young’s modulus for each bone node. According to the damage model, a node under critical damage conditions has a null Young’s modulus; however, as a way of avoiding numerical instabilities, a minimum Young’s modulus of 0.1 MPa was set [31]. After updating the nodal damage distribution, if convergence is not verified, a novel FE analysis is performed considering the novel damage condition and the described procedure is repeated until convergence.

The convergence criterion was based on a measure of bone damage over the entire domain, hereafter referred to as “DVol”, and computed as:

$$DVol={\sum }_{e=1}^{n_{el}}{\sum }_{i=1}^{n_{IP}}{D}_i^{e}IVo{l}_i^e,$$

(5)

where $n_{el}$ is the number of elements of the bone mesh, $n_{IP}$ is the number of integration points per element, and IVol is the volume associated with each integration point. IVol was provided by Abaqus as an output of the FE analysis. The iterative procedure of damage simulation was considered complete when the relative deviation of DVol between consecutive iterations changed less than 5%.

2.4. Analysis of the Risk of Cut-Out

In this study, DVol, which quantifies bone damage over the bone domain (Equation (5)), was used as a measure of the risk of cut-out. To evaluate the influence of the superior–inferior and medial–lateral positions of the blade, simulations were performed for the eight configurations presented in Figure 1, for both the female and male models. In addition to computing DVol for the entire domain, DVol was also computed separately for the superior (DVol-SP) and inferior (DVol-IP) parts of the femora. Considering that cut-out depends on an adequate anchorage of the blade in the head and neck region [11], the relative risk of cut-out of the different configurations was primarily assessed through DVol-SP.

3. Results

Figure 2 presents the damage distribution resulting from the gait loading condition for all configurations of the female and male models. In both central and inferior positions, three main regions tended to be critical: at the tip of the blade; around the transition of the blade from a cylindrical to a helical shape; and at the vicinity of the fracture. Comparing the configurations along the medial–lateral direction, damage increased with the distance to the femoral head surface in the three mentioned regions.

Figure 3 presents the DVol for all configurations of the female and male models, including detailed information on SP and IP. For a given superior–inferior position, either central or inferior, deeper insertions of the blade led to lower DVols in both models. For a given medial–lateral position, contradicting findings were obtained for the male and female models regarding the superior–inferior direction: DVol-SP was lower in the male model for the central positioning of the blade, whereas in the female model it was lower for the inferior positioning.

The least and most risky positions for the female femur were F-Inf-5 and F-Cent-20, respectively. For these positions, increasing the applied forces by 100% led to an increase in damage in the previously identified critical regions, as well as to a propagation of damage to other femoral regions, as shown in Figure 4. DVol-SP increased from 207 mm³ (26.4% of the total DVol) to 4361 mm³ (57.5% of the total DVol) in the F-Inf-5 model, and from 1754 mm³ (63.6% of the total DVol) to 9093 mm³ (65.1% of the total DVol) in the F-Cent-20 model.

4. Discussion

Assuming the femoral head and neck region, identified here as SP, as the most critical region for cut-out [11], this study found contradicting results for the male and female femora in the superior–inferior direction: the inferior positioning of the blade was less prone to cut-out for the female model, whereas for the male model it was the central positioning. Regarding the insertion depth, the results were consistent for both models, showing that the closer the tip of the blade to the femoral head surface, the lower the risk of cut-out.

The best position of the PFNA blade in the superior–inferior direction is not consensual in the literature. Arias-Blanco et al. [5,16], Hsueh et al. [6] and Konya and Verim [17] defended that the blade should be placed centrally, while Lee et al. [13], Quental et al. [15] and Celik et al. [12] recommended an inferior position. Interestingly, this study also found contradicting results between its male and female models, which may be explained by differences in their bone density distributions. For the female model, the blade was always positioned in regions of low bone density (average density of 0.22 g cm⁻³ at the tip for central positions and of 0.18 g cm⁻³ for inferior positions), whereas for the male model, the central positioning of the blade placed it in a region of higher bone density than when placed inferiorly (average density of 0.35 g cm⁻³ at the tip for central positions and of 0.23 g cm⁻³ for the inferior positions). If the superior–inferior placement of the blade is density-dependent, its positioning should be adapted according to each patient’s density distribution. However, further investigation is necessary to assess the influence of bone density on the risk of cut-out.

The depth of the blade placement was found to greatly influence the decrease of the risk of cut-out. For both male and female models, the results showed that the higher the distance from the tip of the blade to the external surface of the femoral head, the higher the damage at the tip of the blade, the blade transition region, and the fracture region, which is consistent with the regions identified by Goffin et al. [11] and Quental et al. [15] as critical for the risk of cut-out. The influence of the blade insertion depth was observed regardless of the positioning in the superior–inferior direction, as also observed by Quental et al. [15]. Despite this result, the insertion depth of the PFNA blade must be considered with caution as other complications, such as medial perforations of the proximal femur [32], may arise if the PFNA blade is too close to the femoral head surface. In this study, the minimum distance considered between the tip of the PFNA blade and the femoral head surface was 5 mm based on the recommendations from the manufacturer [33]. Nevertheless, further investigation is necessary to identify the best balance between the risk of cut-out and the risk of proximal femoral perforation to help clinical decision-making.

The difference in the risk of cut-out for different insertion depths was higher than that for different superior–inferior positions—for instance, for the female model, a deep central position was less prone to cut-out than a less deep inferior position. This suggests that the insertion depth of the blade is a more relevant indicator for the risk of cut-out than the superior–inferior position of the blade.

Unlike previous biomechanical studies that assessed the risk of cut-out through the evaluation of minimum principal strains or stresses obtained from static analyses (e.g., [11,15]), this study considered the progressive propagation of bone damage through the application of a damage model, which enabled an enhanced assessment of the risk of cut-out [18]. The simulation of damage propagation highlighted a greater extent of concerning regions of bone damage, especially at the tip of the blade and around the transition of the blade from a cylindrical to a helical shape. As opposed to the results reported by Quental et al. [15], the male models presented a higher risk of cut-out, based on DVol, than the female models for the same blade positions.

The results for the simulations considering two times the forces applied for gait showed a substantial increase in the risk of cut-out: DVol-SP increased five and twenty-one times in the F-Cent-20 and F-Inf-5 models, respectively. Note that for the sake of briefness, these simulations, which intended to approximate patients’ incidents, such as slipping or tripping, were only performed for the least (F-Inf-5) and most (F-Cent-20) risky positions identified for the female femur. Despite not reflecting the actual loading conditions in such scenarios, the increasing of the force magnitudes allowed observing a large accumulation of damage above the entire length of the blade, indicating the propensity of the femoral head to move down relatively to the blade, leading to a higher risk of the blade to cut-out.

Despite its contributions, this work includes some limitations. Firstly, from a geometric point of view, only one female and one male femora were studied, with only one fracture geometry. The fracture modelled in this work stands out from fractures considered in previous studies by representing a poorer reduction, making the construction more unstable and at a higher risk of cut-out [2]. Additionally, although this study would have benefited from having more femur geometries, the analysed femora fall within typical geometries of the general population [15]. Regarding the loading conditions, only one loading case, representative of gait, was implemented in this work, limiting its generalization to everyday activities. Other studies implemented their damage model in Abaqus/Standard using a UMAT subroutine [18], while in this work a MATLAB routine was developed to couple the damage model and Abaqus. The implementation of a UMAT allows the damage model to be integrated into the constitutive laws, which likely allows a more refined simulation of bone damage progression than the methodology considered. Nonetheless, from a qualitative point of view, the differences in methodologies are expected to be negligible.

5. Conclusions

By coupling a quasi-brittle stiffness-adaptive damage model with 3D finite element models of two femora, this study evaluated the risk of cut-out of different Proximal Femoral Nail Anti-Rotation blade positions considering bone damage progression. Overall, the depth of placement of the blade in the medial–lateral direction and its superior–inferior position were shown to have great influence in the risk of cut-out, with the medial–lateral position being the most relevant predictor. The closer the tip of the blade to the femoral head surface, up to a minimum distance of 5 mm, the lower the risk of cut-out. The optimal blade positioning may be subject-specific, depending on bone geometry and density distribution.