Med Biol Eng Comput (2012) 50:411–417 DOI 10.1007/s11517-012-0892-x
ORIGINAL ARTICLE
The effects of femoral neck cut, cable tension, and muscles forces on the greater trochanter fixation Yvan Petit • Luc P. Cloutier • Kajsa Duke G. Yves Laflamme
•
Received: 18 August 2011 / Accepted: 1 March 2012 / Published online: 9 March 2012 Ó International Federation for Medical and Biological Engineering 2012
Abstract Greater trochanter (GT) stabilization techniques following a fracture or an osteotomy are still showing high levels of postoperative complications. Understanding the effect of femoral neck cut placement, cable tension and muscles forces on GT fragment displacements could help surgeons optimize their techniques. A 3D finite element model has been developed to evaluate, through a statistical experimental design, the impact of the above variables on the GT fragment gap and sliding displacements. Muscles forces were simulating typical daily activities. Stresses were also investigated. The femoral neck cut placement had the most significant effect on the fragment displacement. Lowering it by 5 mm increased the gap and sliding fragment displacements by 288 and 128 %, respectively. Excessive cable tightening provided no significant reduction in fragment displacement. Muscle activities increased the gap and the sliding displacements for all muscle configurations. The maximum total displacement of 0.41 mm was present with a 10 mm femoral neck cut, a cable tension of 178 N, and stair climbing. Caution must be used not to over tighten the cables as the potential damage caused by the increased stress is more significant than any reduction in fragment displacement. Furthermore, preservation of the contact area is important for GT stabilization.
Y. Petit (&) L. P. Cloutier Department of Mechanical Engineering, E´cole de Technologie Supe´rieure, 1100, rue Notre-Dame Ouest, Montreal, QC H3C 1K3, Canada e-mail:
[email protected] Y. Petit L. P. Cloutier K. Duke G. Y. Laflamme Laboratoire d’Imagerie et d’Orthope´die, Hoˆpital du Sacre´-Cœur, Research Center, Montreal, QC, Canada
Keywords Greater trochanter Finite element analysis Cable Fixation device Trochanteric osteotomy
1 Introduction Reattachment of the greater trochanter (GT) following a fracture or an osteotomy during revision of a total hip arthroplasty requires a system achieving rigid fixation. Despite numerous methods for fixation of the GT have been described, a high rate of non-union (9–31 %) is still reported [1, 12], suggesting that this remains an unresolved problem. In the 1970s clinical studies evaluating monofilament wiring techniques were reporting displacement of GT in 2.7–19.4 % of the cases and wire breakage from 17.2 to 32 % [6]. The Dall–Miles multifilament trochanter cable grip system [7], introduced in the 1980s, incorporated an H-shaped plate system that attached only to the GT fragment. This system was seen as an improvement to monofilament wiring but many cases of failure were still reported [16]. Even the second-generation trochanteric system (incorporating improved filament bundle pattern, plates and provisional fixation with retightening) report disappointing rates of non-union (14.6 %) and cable breakage (19 %) [1]. Mechanisms of failure associated with all these greater trochanter reattachment (GTR) devices are still poorly understood. During hip surgeries, surgeons can only directly act on few parameters such as the femoral neck cut placement and the cable tension. It is therefore important for them to have a better understanding of their subsequent effects. Furthermore, a lack of comprehension of the muscles forces on the GT during daily routine activities such as walking and stair climbing might lead to complications if not properly translated into rehabilitation advises for the patients.
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The objective of this study is to further investigate on the biomechanics of GT reattachment in determining the effect of the placement of the femoral neck cut and the cable tension on the GT fragment displacement under different typical daily activity muscle forces.
2 Methods A finite element model (FEM) of a femur was used in order to simulate a GT osteotomy with the femoral component of a hip prosthesis and a four cable GTR system (CableReadyÒ, Zimmer, Warsaw, IN) (Fig. 1). The femur geometry was obtained from the work of Cheung et al. [5], and represents a SawbonesÒ (Pacific Research Laboratories Inc., Vashon, WA) third-generation composite femur model. This geometrical model has been used by others to perform finite element analyses (FEA) [20]. The mechanical properties of cancellous (E = 137 MPa) and cortical (E = 1.7 GPa) bones were defined in the FEM according to the company’s specifications. Previous biomechanical testing has demonstrated that the third-generation Sawbones femur approximates the structural stiffness of human bones but with smaller variability [8]. An osteotomy of the GT was then simulated on the geometric model by cutting a 30° plane. A femoral stem implant CAD model was created from digital caliper measurements of a VerSys Fiber Metal Taper Hip Prosthesis (Zimmer, Warsaw, IN). The femoral stem implant was then inserted into the osteotomized femur model. Similarly, the plate implant modeled was the Zimmer Integral Long GTR Device with four cables (Zimmer, Warsaw, IN). The cables were modeled as a circular profile extruded along a path tangent to the surface of the femoral shaft geometry (Figs. 1, 2). Stainless steel mechanical properties (E = 200 GPa) were applied to the stem, plate, and cable implants. All material properties of this FEM
Fig. 1 3D models of the FEM femur, femoral stem at two different femoral neck cut placements (15 mm and 10 mm), GT fragment (osteotomy at 30°) and implants
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Fig. 2 FEM coarse and refined meshing, contact regions (dark dense zones) and five loads derived from Heller et al. [9] and detailed in Table 1
were considered as linear elastic, homogeneous, and isotropic with a Poisson’s ratio of 0.3. The finite element model consisted of an assembly of the following listed ten total parts connected with various contact elements: femoral cancellous and cortical bone, trochanteric cancellous and cortical bone, femoral stem, GTR device, and the four cables. The cortical and cancellous bone of the femur, the GT fragment as well as the femoral stem were rigidly fixed at their common interface. Contact between the femur and the GT fragment allowed the fragment to slide and separate away from the femur. Similar connectors were used to join the GTR device to the femur with the exception of anchoring the implant’s lower teeth to the femur. For the cables, one end was rigidly fixed to the GTR device. The other end was secured with a joint allowing free translation between the cables and the GT device. Cable tensioning was modeled by directly applying the target force to the cable extremity that was free to translate relative to the GT device. Finally, contacts allowed the cables to slide along the surface of the femur. Recommendations from Polgar et al. [14] and Viceconti et al. [18, 19] were applied in the model concerning element type and size. Extensive mesh refinement was also performed based on a convergence study in order to provide a satisfactory balance between accuracy and computing resources. In total, the FEM mesh was comprised of over 60,000 elements, and over 6,000 contact elements. Tetrahedral elements with 10 nodes were used to mesh cortical bone (18,516 elements for the femur and 25,659 elements for the GT), femoral stem (5,204 elements) and cables (1,894 elements). Tetrahedral elements with four nodes were used to mesh cancellous bone (1,078 elements for the femur and 957 elements for the GT) and the Zimmer plate (11,664 elements). Regions such as the cancellous femur were meshed with coarse element with a characteristic
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Table 1 Muscles forces (N) applied in the FEM (derived from Heller et al. [9]) Walking (N) x Hip contact
Stair Climbing (N) y
z
Total
x
y
z
Total
-519
-381
-2,570
2,649
-612
-750
-2,595
485
36
723
871
594
244
719
964
Tensor fascia latae and iliotibial tract
56
91
-48
117
109
58
-64
139
Vastus lateralis
-8
155
-777
792
-19
190
-1,144
1,160
Vastus medialis
0
0
0
0
-75
335
-2,262
2,288
Abductors (six muscles)
length of 7 mm while areas of greater interest such as the cortical bone of the GT fragment were refined under 2 mm. Extensive mesh refinement, such as 1.4-mm element size at the interface with cables, was also performed in the contact areas (Fig. 2). All simulations were performed as non-linear quasi-static analyses using CATIA v5R17 Advanced Generative Structural Analysis Toolbox. The femur FEM had a total length of 25 cm with its distal end fixed. Hip contact resulting force was applied on the femoral stem. Specific regions were defined on the outer cortical surface of the femur model to simulate nine muscle insertions, six of them being used to simulate the abductors. They were considered to be the muscles acting directly on the GT fragment and include the six following muscles: piriformis, gemellus superior, gemellus inferior, obturator internus, gluteus medius, and gluteus minimus. Table 1 shows the resulting five muscles forces of Fig. 2 applied to the hip contact and the nine muscle insertions to simulate walking or stair climbing as described by Heller et al. [9]. All loads were applied based on the same coordinate system used by Heller et al. [9]. Three independent variables were varied in this model including femoral neck cut placement, cable tension and muscles forces. In order to evaluate the significant effects of the variables a Box, Hunter and Hunter [2] full factorial mixed two and three levels experimental design [13] consisting of 18 simulations was performed (Table 2). The placement of the femoral neck cut was simulated in two positions: 10 or 15 mm at a 30° angle above the lesser trochanter as shown in Fig. 1. Cable tightening of 356 N (80 lbs) was based on the manufacturer’s recommendation. In addition, tension of 178 N (40 lbs) and 534 N (120 lbs) were tested. Finally, muscles forces defined in Table 1 were maintained at zero for rest or applied to simulate walking or stair climbing. In order to evaluate the displacement of the fragment, a local coordinate system was defined with the x–y plane (sliding displacement) on the osteotomised surface of the femur and z-axis perpendicular (gap displacement). Displacements of the GT fragment were resolved at three points around the perimeter of the osteotomised surface: two at the top corners and one at the bottom. In addition,
2,770
Table 2 Levels defined in the experimental simulations for all independent variables Femoral neck cut (mm)
Cable tension (N)
Set of muscles forces
10
178
Rest
15
356
Walking
534
Stair climbing
overall maximum displacement gap and sliding components were resolved. As well as extracting information concerning the displacements of the model, von Mises stresses in the GTR device and the cortical bone were also obtained. To ensure consistent measurements, the von Mises stress observed in the GTR device was measured at approximately mid length in the thinnest part of the shaft. The maximum von Mises stress in the cortical bone was measured underneath the distal cables on the anterior medial side of the femoral shaft. All the results were analyzed with factorial ANOVA methods using Statistica (StatSoft, USA). Validation of this finite element model through an experimental setup has been published in another article [4]. Although the specific objective of this previous paper was to look at the effect of cable tensioning on the displacement of the GT, the methods were planned with the validation of this FEM study in mind. Two variables were tested instead of three. They were the cable tension and muscle forces representing walking. The femoral neck cut was fixed at 10 mm and stair climbing was not tested. Similar to the FEM study, osteotomy (30°), cable tension (178, 356, and 534 N), GTR device, number of cables (4) and loading orientation per Heller et al. [9] were used. Differences included the mechanical properties of the composite femur (fourth vs. third generation), lower loading magnitudes due to bench test limitations (2,340 N vs. 2,649 N on the stem head and 667 N vs. 871 N on the GT) and less number of muscles simulated due to the complexity of the setup (tensor fascia latae, iliotibial tract, and vastus lateralis were not present). This loading was applied three times to evaluate the effect of walking. The cycling
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Fig. 3 a FEM average gap displacement (mm) for one fixed variable (femoral neck cut, cable tension or muscles forces) and the variation of the remaining two others from their minimum to maximum levels. b FEM average sliding displacement (mm) for one fixed variable (femoral neck cut, cable tension or muscles forces) and the variation of the remaining two others from their minimum to maximum levels. c FEM average von Mises stress (MPa) in the plate for one fixed
variable (femoral neck cut, cable tension or muscles forces) and the variation of the remaining two others from their minimum to maximum levels. d FEM average von Mises stress (MPa) in the bone for one fixed variable (femoral neck cut, cable tension or muscles forces) and the variation of the remaining two others from their minimum to maximum levels
was repeated three times for a total of nine trials for each tightening tension. The Femur and GT displacement was measured with an Optotrak 3D camera system (Northern Digital inc., Canada). The x-, y-, and z-coordinates of two rigid bodies associated with the GT and the femur were recorded. Then GT displacements with respect to the femur were evaluated using similar measures to the FEM study: the maximum gap and sliding displacements. The gap and sliding were measured at the three peak loads. Comparison of the gap and sliding were done at the last peak using ANOVA and Student’s t test.
variation of the remaining two others from their minimum to maximum levels shown in Table 2. The P values from the ANOVA analysis are also given. Distinction between P \ 0.01 and P \ 0.05 is noted in order to see which parameter has a greater significant effect. Lowering the femoral neck cut by only 5 mm reduced the osteotomy contact surface area by 20 % and affected significantly the positional stability of the system. The gap and sliding displacements were significantly (P \ 0.01) increased by 288 % (0.210 ± 0.147 mm) and by 128 % (0.101 ± 0.050 mm) when the placement of the femoral neck cut was at 10 mm to the lesser trochanter compared to 15 mm. The von Mises stress in the GTR device also increased (P \ 0.01) by 139 % (62.18 ± 29.62 MPa). However, the femoral neck cut had no significant effect on the von Mises stress in the bone (P [ 0.05). The tightening of the cables had no significant effect on the gap and the sliding displacement (P [ 0.05). However, from a tension of 178–534 N, it significantly increased
3 Results The histograms of Fig. 3a–d show the effects of the three independent variables on the measured responses. All results shown represent the average for one fixed variable (femoral neck cut, cable tension, or muscles forces) and the
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(P \ 0.01) the von Mises stress in the GTR device by 51 % (30.93 ± 69.15 MPa) and in the bone by 219 % (17.65 ± 9.23 MPa). Muscle activity significantly increased the gap (P \ 0.01) and the sliding (P \ 0.05) displacements for all of the muscle configurations. In particular, gap and sliding displacement increased by 178 % (0.151 ± 0.217 mm) and by 35 % (0.038 ± 0.123 mm), respectively from rest to stair climbing. As expected, stair climbing produced the largest increase of von Mises stress in the bone from rest but walking produced the largest increase in the GTR device. For these conditions, significant effect on bone (P \ 0.05) and GTR device (P \ 0.01) von Mises stresses gave increments of 42 % (5.30 ± 18.34 MPa) and 15 % (10.45 ± 72.76 MPa), respectively. Of the 18 simulations, the maximum total displacement of 0.41 mm (0.38 mm gap and 0.17 mm sliding) was present with this combination: a 10 mm femoral neck cut, a 178 N cable tension and stair climbing. The greatest GTR device and bone von Mises stresses both occurred while the femoral neck cut was placed at 10 mm and with the cables tightened to 534 N. For the GTR device, the highest von Mises stress of 125 MPa was a result of muscle loading due to walking, while the greatest bone von Mises stress of 33 MPa was observed during stair climbing. The experimental validation of the FEM was performed comparing maximum gap and sliding displacements of both simulation methods and for the three cable tensions. All maximum gap and sliding displacements were higher for the experimental simulation versus the FEM. Gap displacements for cable tension ranging from 178 to 534 N varied from 7.9 to 27.1 and to 27.1 %, respectively (0.03, 0.12, and 0.11 mm). Inversely, sliding displacements varied from 81.8 to 22.3, and to 19.6 % (0.71, 0.05, and 0.05 mm) for cables tensioned at 178–534 N.
4 Discussion This finite element model demonstrates that femoral neck cut, cable tension, and muscles forces produce biomechanical effects on the GT fixation. The femoral neck cut was the variable with the most significant effect on fragment displacement. Lowering the femoral neck cut greatly reduced the contact surface area between the fragment and femur and hence resulted in instability that led to significantly greater fragment displacement. This supports that preservation of the contact surface area is important when performing a trochanteric osteotomy. Cable tension had the greatest effect on the von Mises stress generated in the GTR device and the bone but no significant effect on the stability of the trochanter.
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Increasing cable tension increased the von Mises stress in both the implant and bone. Even though absolute maximum stress value from a FEM requires experimental validation, in this model it tends to be below the yield strength of titanium alloy in the GTR device but is in the unsafe region in the bone. In practice, this could cause the cables to cut into the bone especially in the osteoporotic elderly patient. This suggests that excessive cable tightening may not provide additional stability to the GT. Caution must be used not to over tighten the cables above the manufacturer’s recommended tension as it may be done by surgeons trying to maximize stability. It is difficult to directly compare the results obtained with the proposed finite element model to the existing literature. The authors are not aware of any biomechanical experiments that analyze the effect of femoral neck cut and cable tension on GT cable plate fixation. However, Plausinis et al. [15] tested a short Dall–Miles cable system with compressive abductor loads. They observed GT displacement generally less than 0.5 mm. Markolf et al. [11] investigated different wiring techniques and observed as much as 6.9 mm displacement for a first load cycle while displacement was as low as 0.7 mm for functional displacement after the fragment had reached a stable position. Hersh et al. [10] compared wire cable and cable grip systems and found this last one to be the stiffest. The displacements recorded were up to 20 mm. Recently in 2008, Schwab et al. [17] compared two cables versus three for fixing an extended trochanter osteotomy. They reported an average transverse displacement of 0.2 ± 1.7 mm of the osteotomy fragment relative to the femoral shaft for the two cable configurations and found no statistical difference between the two groups. The results from our finite element model show a maximum relative displacement of 0.41 mm which falls within the range of displacement observed in biomechanical experimental tests. One limitation of the FEM was the absence of friction between the GT fragment and femur at the osteotomised plane x–y. Friction was neglected due to the absence of reliable data in the literature on the bone–implant and bone–bone interactions. This simplified the model and provided a worst case scenario, exacerbating the effect of cable tightening on GT displacements as compared to stresses in the bone or the implant. The cables were also represented as solid elements, which may have contributed to overestimate their internal stresses. However, this was not the purpose of the current study since the cables were essentially used to apply the tightening forces between the femur, the GT and the implant. Literature is also lacking reliable data of forces acting directly on the GT. Only the ones used from Heller et al. [9] have tentatively defined them for different daily activities. However, this FEA model has innovated by
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splitting the abductor forces to more acting points (6 vs. 1) on the GT than suggested by Heller et al. [9], thus representing a more realistic loading pattern (Fig. 2; Table 1). It has also innovated by considering these two musculoskeletal loads which are usually neglected in the literature: (1) compression effect on the GT (from the tensor of the fascia latae and the iliotibial tract) and (2) vastus lateralis for counteracting the abductor forces, although no direct connections exist between both. All simulations were performed in a quasi-static mode, thus underestimating the dynamic effect of these muscles. The finite element model is only concerned with the initial stability of the construct post op and is not able to analyze the long-term effects of cable loosening or how osteointegration may occur around the implant. As the cables were modeled as solid loops and projected directly onto the surface of the bone the initial condition was idealized. In a clinical setting it may be difficult to ensure that the bone is perfectly dissected and that there is no soft tissue between the cables and bone. Due to the solid nature of the simulated cables their rigidity is possibly more representative of wires than cables. Certain approximations are often used in finite element studies where comparative rather than absolute values are of interest [20]. In this study it was primarily the comparison between the different scenarios that was of the greatest interest. As mentioned the objective of this finite element model was to determine which of the three variables had the greatest effect on displacement and von Mises stresses. The results from this FEM will aid in the design of subsequent biomechanical testing of the modeled construct by allowing the researchers to limit the factors studied. The gap and sliding displacements were all higher when measured with the experimental bench test versus the FEM simulation. Although more muscles were simulated on the FEM study, they were not acting directly on the GT fragment, thus having little effects on the final displacements. Even though the magnitudes of the loads applied on the experimental bench test were lower due to limitations, the counter intuitive higher results could be explained in part by the simplifications inherent to the FEM approach. As for e.g., connections between screws, bone and plate (rigid contacts) are stiffer in the FEM than in experimentation. Bourgeois et al. [3]. have shown similar higher experimental displacements versus a FEM simulation while using lower loads as well. Finally, both higher cable tensions gave displacements variations in a similar 19–27 % range while at the lowest tension, the variation went from 8 to 82 %. One could suspect a systematic error occurring while the system is more restricted, i.e., at higher cable tension and suspect no control on displacements while the tension is well below the manufacturer’s recommendation.
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This FEA model suggests that care must be taken at surgery to preserve the contact surface area by limiting the femoral neck cut which will decrease both the sliding and gap GT fragment displacements. Also, caution must be used not to over tighten the cables as the potential damage caused by the increased stress in the bone and device is more significant than any reduction in GT fragment displacement.
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