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Analysis of the helical plate for bone fracture fixation
Injury, Int. J. Care Injured (2008) 39, 1421—1436
www.elsevier.com/locate/injury
Analysis of the helical plate for bone fracture fixation Kotlanka Rama Krishna 1, Idapalapati Sridhar *, Dhanjoo N. Ghista 2 School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Accepted 17 April 2008
KEYWORDS Bone fracture; Stiffness; Helical plate; Screw orientation; Finite-element analysis; Fracture-gap movement
Summary The improvements in oblique fracture fixation by means of the hemihelical plate (HHP) to provide the bone—plate-screw assembly with enhanced holding capacity are discussed. The HHP is designed to provide stable fixation for helical cracks caused by torsional loading, such that the bone interfaces at the crack are brought into apposition and compressive strains are applied at the cracked interfaces. The HHP wraps around the bone, and hence is also suited for fixation of comminuted fractures. This is because, instead of employing multiple screws across the cracks, the HHP holds the bone fragments together. First, we illustrate through experiments the special capabilities of the HHP with respect to its fracture-holding capability, in comparison with straight-plate fixation with different screw orientations (convergent, divergent, alternately convergent and divergent, and perpendicular). Second, the finite-element (FE) analysis of the HHP is described, to elucidate the efficacy of fracture-gap movement and closure, and the flexibility of the fixation under compressive, bending moment and torsional loads. # 2008 Elsevier Ltd. All rights reserved.
Introduction Long bone, subjected to a combination of axial, bending and torsional loads in vivo, fractures in a variety of competing modes when the applied load exceeds the sustainable limit. Axial compressive * Corresponding author. Tel.: +65 6790 4784; fax: +65 6791 1859. E-mail address: [email protected] (Idapalapati Sridhar). 1 Currently with MEMS Program, Institute of Microelectronics, 11 Singapore Science Park II, Singapore 117685, Singapore. 2 Present Address as: Parkway Education College, 168 Japan Bukit Mehra, Singapore 150168, Singapore.
loads can cause oblique fracture due to shear failure; under axial tensile loading, maximum stresses are generated in a plane perpendicular to the loading direction, leading to transverse fractures; and when the bone is subjected to bending forces, both tensile and compressive stresses are generated. As bone is more susceptible to failure in tension than in compression, the crack initiates on the tension side and progresses across the bone, creating a butterfly type fracture. Torsion on a long bone results in a long spiral fracture, with the fracture line orientated at about 458 to the axis about which torque is applied.29,19
0020–1383/$ — see front matter # 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.injury.2008.04.013
1422 Fractured bones can be fixed by external immobilisation and fixation techniques such as plaster casting and multiple percutaneous transcortical pins,3,5,9,16 or by internal fixation using intramedullary rods1,30 and/or plates with screws.17,22,27,28 The choice of fixation and surgical technique is based on a range of factors, including bone quality, fracture type, anatomical location and, to some extent, on surgeons’ preferences. Particularly with oblique and helical cracks, fixation of fractured bone (or of healed bone to regain its pre-fracture stiffness and strength) continues to pose immense osteosynthesis challenges. Spiral fractures have generally been fixed by using three or more lag screws; the important parameters considered while fixing are spacing between the screws and stability, i.e. least micromovement at the fracture interface, referring to the gap strain theory of Perren.22 Too many screws will weaken the bone, as screw holes act as stress raisers; on the other hand, fewer screws will lead to instability at the fracture site. Other means of fixing spiral fractures include intramedullary rods and/or plating on the tension side. Intramedullary rods provide better stability than fixation by lag screws alone.25 When fixed by the conventional straight plate, the stability of fracture fixation is weak, as tensile forces are generated during torsion at 458 to the axis of the bone and do not act along the axis of the plate4; the straight plate is unable to handle tensile forces diagonal to the axis of the bone—plate assembly. Fernandez11,12 was the first surgeon to clinically moot the idea of fracture fixation using internal helical bone—plates. In particular, his anatomical study postulated the advantage of helical plates for treating fractures of the humerus. Clinical applications of the helical plate have been described by Apivatthakakul et al.2, Gardner et al.15 and Yang,31 as well as by us through computational biomechanical analysis.23 This paper addresses in detail the unique features of hemi-helical plate (HHP) internal bone fracture fixation, wherein screws are used to anchor a hemi-helical plate onto the fractured bone. In general, screws provide a bridge transferring forces between the plate and the fractured bone. Consequently, screws may be subjected to relatively large shear stresses during movement of the fractured limb. In addition, the bone surface adjacent to screws can be subjected to trauma at insertion, which may cause some temporary bone necrosis. These factors can lead to loosening and subsequent pulling out of screws, thereby destabilising the entire fracture-fixation assembly.1,6,7,8,20 Such a phenomenon is commonly observed in straight-plate fixation, where the screws are orientated normal to
K.R. Krishna et al. the plate in the same plane; angling of the screws is considered a possible solution, to mitigate loosening of fracture fixation (Fig. 1).22 In addition, the straight plate also induces undue stress-shielding of the fractured bone. This is because the straight-plate fixture is fastened onto the tensile surface of the fractured bone (thereby destressing the bone beneath the plate), and the plate material Young’s modulus (which is 200 GPa for 316 L stainless steel) is typically an order of magnitude higher than that of bone (which is about 20 GPa). In order to reduce the mismatch of the material properties of plate and bone, carbon fibre-reinforced polymer matrix composite materials and stiffness graded plates have been recommended.13,14,24
Helical-plate fixation: biomechanical justification, clinical applications and scope of our biomechanical studies Helical-plate fixation avoids some of the complications arising from the use of straight-plate fixation, particularly for oblique and spiral fractures resulting from torsion of long bones. In the first place, from a biomechanical view point, spiral fractures are generated by tensile stress acting diagonally to the axis of the bone, as illustrated in Fig. 1. Hence, a helical plate needs to be applied and orientated orthogonally to the spiral fracture, in order to absorb these tensile stresses. Second, because of the helical orientation of the plate, the screws anchoring the HHP to the fractured bone are inclined at different angles to the axis of the bone. This minimises the possibility of loosening of screws (associated with straight-plate fixation) under loading, and provides for more secure fixation of the plate to the bone, as has been demonstrated by our experimental studies elaborated in ‘Methods’. Third, when a plate—bone assembly using a straight plate is subjected to bending, the neutral axis (NA) of the composite plate—bone structure is located very close to the external surface of the
Figure 1 Diagram of fractured bone fixed by 1808 helical plate, under torsion.
Analysis of the helical plate for bone fracture fixation bone or even inside the plate, because the elastic modulus of the plate is much greater than that of the bone. This causes stress-shielding of the bone segments away from the fracture site, and weakening of these segments. However, because the helical plate is anchored in a spiral orientation to the bone, the plate—bone cross-sections at different locations away from the fracture site will also have the plate attached to the bone at varying orientations with respect to the plane of the bone (in which bending is applied.) This will induce tensile stresses in the bone portion of the plate—bone cross-sections, thereby alleviating the problem of stress-shielding of the bone away from the fracture site. Fourth, because the helical plate is fastened and wrapped around the fractured bone along its length, it enables reduction of the fracture gap in the axial direction along the entire fracture surface of the bone. This is clearly demonstrated in computational simulations of the fractured bone—plate assembly’s response to loadings (in finite-element (FE) analysis). These are some of the biomechanical factors contributing to better clinical outcomes of helical-plate fixation of oblique and spiral fractures. In addition, the helical plate permits more freedom in choice of entry point, and allows for positioning of the plate on different segments of the bone (such as laterally in the proximal part of the bone and anteriorly in the distal part of the bone) to avoid damage to nerves and vascular and musculocutaneous structures.15,17,31 There is consensus among orthopaedic surgeons that, whereas the ideal treatment of fractures (for example of the humerus) has not been definitively agreed, helical-plate fixation solves many problems. Yang31 indicated that plate fixation of comminuted fractures of the proximal and middle humerus requires a long plate to be applied from the lateral aspect of the greater tuberosity to the humerus shaft. Since this required dissection of the deltoid muscle insertion, these workers twisted the long plate and fixed it from the lateral aspect of the greater tuberosity to the anterior of the distal shaft of the humerus, and thereby were able to preserve deltoid muscle insertion. Fig. 2 illustrates how a straight plate can be pre-contoured in a helical fashion to fit the proximal and middle thirds of the humerus, using a skeleton as a template; herein, the proximal part of the helical plate is attached to the lateral aspect of the greater tuberosity, and its distal part is fixed to the anterior aspect of the humeral shaft.31 Fig. 3 illustrates a clinical application of the helical plate for proximal fracture of the humerus extending to the greater tuberosity.31 In
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Figure 2 Long plate precontoured helically to fit proximal and middle thirds of humerus, using skeleton as template. Anterior placement of distal part of helical plate can preserve deltoid muscle insertion. (A) Deltoid muscle insertion; (B) lesser tuberosity; (C) greater tuberosity.31.
fact, several cases have been reported as involving the technique of helical plating of proximal humeral fractures, where the proximal plate was placed laterally on the greater tuberosity and spiralled 908 distally to lie on the anterior surface of the humeral shaft. This technique avoids the danger zone of musculocutaneous nerve crossing for placement of screws.12,31 Fig. 4 schematically illustrates this mode of effective helical-plate fixation.15 Helical plating is also feasible for application to the femur, as reported by Fernandez.12 Helical-plate fixation has thus been innovatively employed for plating femoral and humeral shaft fractures. In order to provide biomechanical confirmation of the clinical efficiency of helical-plate bone fracture fixation, we carried out extensive experimental mechanical studies of this technique in relation to straight-plate fixation, to demonstrate superior plate attachment to bone and plate—bone strength-to-failure, and delineate camoative factors.
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Figure 3 (A) Preoperative and (B) final radiographs. Proximal fracture extended to greater tuberosity (arrow). Fractures fixed with four lag screws and 12-hole pre-bent helical thin narrow plate.31.
We then carried out comprehensive computational biomechanical studies by finite-element analysis of helical-plate fixation of simulated oblique fractures of bone (in comparison with straight-plate fixation) under compression, bending and torsional loadings. Clinical studies2,11,12,15,31 on helical-plate fixation primarily emphasise facilitation of surgical insertion of the fixation plate and the means by
which the fractured bone can be plated along its different aspects (lateral, anterior and medial) so as to provide better fixation-stability to the fractured bone and also preserve muscular insertions and vascular and neural structures. However, our biomechanical studies demonstrated some additional advantages of helical-plate fixation compared with straight-plate fixation, such as superior plate fixation to the bone by screws and
Analysis of the helical plate for bone fracture fixation
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Experimental studies of hemi-helical plate versus straight-plate bone fracture-fixation Materials and methods
Figure 4 Precontouring helical plate so that proximal limb lies on greater tuberosity laterally, distal limb rotates 908 to lie on anterior surface of humerus; 99% confidence interval of position of nerve crossing anterior humerus was 12.2—14.8 cm (shaded area). Flatow EL, Bigliani LU, April EW. An anatomic study of the musculocutaneous nerve and its relationship to the coracoid process. Clin Orthop 1989;166—71.
reduced stress-shielding, as mentioned above. Hence our studies aimed to elucidate the biomechanical basis of the advantages of helical-plate fixation over straight-plate fixation for oblique fractures of bone, in support of the relevant clinical studies. In this context, two specific issues pertaining to internal bone fracture fixation were addressed. First, the concept of HHP fixation was demonstrated, by providing the results of pull-out experiments with the aim of comparing the holding strengths of straight and hemi-helical plates for various screw configurations. Second, we performed FE analyses for three fracture fixation configurations (i.e. straight plate, 908 helical plate and 1808 helical plate) under uniaxial compression as well as for bending and torsional loadings, to compare the overall stiffness of the various assemblies and fracture-gap movement.
Fig. 5a is a diagrammatic description of a helical plate. The axis is defined as a straight line along the length of the bone at its centre, and the geometric radius is defined as the distance from the axis to the outer surface of the bone (at mid shaft). The effective length is the distance between the ends of the plate along the axis of the bone, and the pitch is the degree of rotation (or twist) of the plate. For example, 1-pitch represents a 3608 twist of the plate, 1/ 2-pitch represents a 1808 twist of the plate and 1/4pitch represents a 908 twist of the plate. Fig. 5b portrays helical-plate contour direction defined by a thumb rule; for example in a right-handed helical plate, the right-hand thumb shows the direction of the femoral head and the closed fingers show the direction of the helical-plate’s contours. Bone fracture fixation using a 3608 or 2708 helical plates is not used, because of clinical constraints. Hence, only 1808 and 908 helical plates were considered in the present investigation. In the current experiments, a twelve-hole Zimmer Dual Compression Contourable Plate, with 4.5 mm cortical screws, was fixed onto a Synthes femoral bone specimen (Mathys) by screws located at the 1st, 4th, 9th and 12th positions. Experiments were conducted to determine the axial pull-out strengths of both hemi-helical and straight bone—plates with perpendicular (PSO), convergent (CSO), divergent (DSO) and alternating (ASO) screw orientations as indicated in Fig. 6, in accordance with ASTM F1691-96. The experimental set-up for the pull-out experiments is shown in Fig. 7a. Special grips were designed and built to hold the ends of the femoral bone specimens and to comply with ASTM F1691-96 test techniques. Each bone— plate fracture fixation assembly was loaded by a 5 kN Instron testing machine, under displacement control at a loading rate of 5 mm/min. The experiments were confined to one sample of each configuration (i.e. PSO, ASO, CSO, DSO and hemi-helical fixation assembly) because of limited bone specimens; saw bones are not reusable, as they fracture after the test although the plates may remain elastic.
Results and discussion Fig. 8 shows the load—displacement responses for the hemi-helical and straight plates (with four different screw orientations) during pull-out testing
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Figure 5 (a) Side view shows 1/2 pitch of helical plate. (b) Thumb points to femoral head and fingers to direction of helical-plate contouring.
Figure 6 Pull-out tests. Inclined screw orientations. Straight-plate fixation with (a) perpendicular (PSO), (b) convergent (CSO), (c) divergent (DSO) and (d) alternating (ASO) screw orientations all in longitudinal plane. Helical plating with (e) hemi-helix 1808, screws oriented in different planes.
which enabled assessment of the holding capacity of the plate and screws on the fractured bone. Four distinct peaks were observed in the load—displacement curves of straight plates (with various screw orientations). These peaks reflect sequential screw pull-out, wherein the screws located at the 4th hole loosened initially; this was followed by progressive loosening at the 9th, 1st and 12th holes (Figs. 6 and 7b). In contrast, no sequential screw pull-out was observed in the hemi-helical fixation (Fig. 7c and d). It is also noteworthy that the holding strength of the hemi-helical fixation was higher than that of the straight plate with either PSO, CSO, DSO or ASO configurations; no screw loosening was observed with the HHP. The initial slopes of these load—displacement curves (Fig. 8) indicated that the straight plates with ASO and DSO configurations offered, respectively, the greatest and least stiffness for the fracture fixation assembly under bending loading. CSO and PSO straight-plate screw configurations as well as HHPs resulted in similar intermediate
Analysis of the helical plate for bone fracture fixation
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Figure 7 (a) Experimental set-up for pull-out test of 1808 helical plate and bone fixation held by four cortical screws with newly designed grippers holding assembly. (b) Sequential pull-out of straight plate with perpendicular, convergent, divergent and alternating configurations. (c) Holding power of hemi-helical plate is high, sequential screw pull-out not observed. (d) However, bone failed before screw pull-out, indicating that fixation stiff enough to prevent screw loosening.
levels of stiffness (as listed in Table 1). The areas under the respective load—displacement curves indicated that the hemi-helical and straight plates (with DSO configurations) resulted, respectively, in the greatest and least energy-to-fracture (or toughness) for the fixation assembly. The PSO, ASO and CSO screw configurations for straight-plate fixation yielded similar intermediate levels of energy-to-fracture. The HHP also conferred the highest pull-out strength in the fixation assembly, compared with straight-plate configurations with any of the four different screw orientations. In addition, as shown in Fig. 7b, there was the risk of loosening and sequential screw pull-out in straight plates, since the axes of the screws were all in the same plane (as seen from cross-sectional views along the longitudinal plane of the fixation assembly, Fig. 6a—d). In contrast, the axes of the screws in the hemi-helical fixation assembly were all in different planes (intersecting one another, as shown in Fig. 6e), thus eliminating or minimising the problem of loosening and progressive sequential pull-out of screws. The photographs in Fig. 7(c and d) illustrate the higher
load-carrying capacity of a helical-plate assembly. Overall, these results suggested that HHP fixation provided the optimal combination of strength, stiffness and toughness compared with straight plates with any screw orientation.
Finite-element analysis of hemi-helical plate versus straight-plate bone fracture fixation It can be concluded from the above that helical plating has an improved load-holding capacity, which is necessary to avoid implant loosening (which is more prominent in osteoporotic bones). It is also necessary to study the fracture-gap movement characteristics and stiffness of the assembly of fixed fractured bone and plate, comparing helical and straight plating. For this purpose, FE analyses were carried out for fixations of an oblique fracture (angled 458 to the axis of the bone) fixed with a straight plate, a 908 helical plate and a 1808 helical plate under compression, bending and torsion loadings, using the ABAQUS program for FE analysis.
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Figure 8 Pull-out tests; load vs. extension curves for all configurations in Fig. 7. Insert depicts peaks in curve representing pull-out for convergent (CSO), perpendicular (PSO), alternating (ASO) and divergent (DSO) screw configurations. Stiffness of assembly is slope of load vs. extension curve and area under load vs. extension curve until initiation of pull-out represents energy to pull-out.
Modelling of bone fracture fixation FE analyses of the bone—plate-screws assembly were carried out with: screw holes modelled as hollow cylinders (outer diameter 24 mm, inner diameter 16 mm, length 170 mm, 8 screw holes); Table 1 Stiffness and energy to initiate pull-out and peak pull-out for perpendicular (PSO), convergent (CSO), divergent (DSO) and alternating (ASO) screw orientations and hemi-helical configurations in plate fixation Orientation
Stiffness (kN/m)
Energy to pull-out (J)
Peak pullout load (N)
PSO ASO CSO DSO Hemi-helical
55.1 58.0 49.3 44.7 55.4
7.17 9.67 10.12 6.88 10.83
796 900 924 679 1000
the 8 screws as cylinders 3.5 mm in diameter (in order to reduce the number of elements required for screws meshing, as screw threads require finer elements for meshing); different plate configurations (i.e. straight plate, 908 helical plate and 1808 helical plate). The plates were 12 mm wide, 4 mm thick and 140 mm in effective length, and the radius of the helix was 12 mm. In order to produce a helical plate, a straight plate was curved so that it exactly fitted the outer diameter of the bone. The distances between the screw holes were equal in all plate configurations. All three configurations of fixation (i.e. straight plate, 908 helical plate and 1808 helical plate) were modelled by commercial computer-aided design software UNIGRAPHICS. The FE models are depicted in Fig. 9a—d. The modelled parts (i.e. plate, bone and screws) were imported to the commercial FE analysis software ABAQUS from UNIGRAPHICS through STEP format. The bone was then modified to incorporate an oblique fracture
Analysis of the helical plate for bone fracture fixation
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Figure 9 Finite-element models in ABAQUS. (a) Straight-plate model. (b) 908 helical-plate model. (c) 1808 helical-plate model. (d) Oblique fracture fixed by helical plate. Bone axis is along coordinate 3.
gap of 2 mm at its mid span, angled 458 to the axis of bone (as shown in Fig. 9d). The screws were positioned such that they were always perpendicular to the top surface of the plate; in this way, the screws were in different planes incorporating the bone axis. The bone was modelled as a transversely isotropic material, with moduli and Poisson’s ratio of E1 = 14.5 (GPa), E2 = 14.5 (GPa), E3 = 19.7 (GPa), G12 = 7.0 (GPa), G13 = 7.0 (GPa), G23 = 5.28 (GPa), y12 = 0.285, y13 = 0.285 and y23 = 0.26515 GPa (the directions 1, 2, 3 are shown in Fig. 9).10 The plate and screws materials were assumed to be in an elastic state for the applied loading, and assigned 200 GPa Young’s modulus (316 L stainless steel) and 0.3 Poisson’s ratio values. In order to simulate the locking-screw mechanism during analysis, the screw head and the contoured surface of the plate were tied together by means of a contact option available in ABAQUS. Similar contact conditions were assigned for cylindrical screws and bone, so that the screws held the bone during loading. A coefficient of friction of 0.37 was assigned between bone and plate contacts, and a value of 1.0 between the broken bone fragments (i.e. at fracture interfaces). The computations were carried out for finite strain, by prescribing the non-linear geometry (NLGM) option in the ABAQUS program.
Loading and boundary conditions imposed on bone fractures after fixation Compressive, torsion and bending loadings were applied to obliquely fractured bones fixed by straight plating, 908 helical plating or 1808 helical plating. In order to apply a compressive load of 150 N, one end of the fracture-fixed bone was fully constrained and a compressive force of 150 N applied in the axial (U3) direction on a reference plane at the free end (as shown in Fig. 10a). In order to simulate torsional loading, a displacement of UR3 = 0.05 radians was applied to the reference plane at the free end, while the boundary conditions of the fixed end were maintained (Fig. 10c). A four-point bending loading was simulated, by applying the boundary condition (U1 = U2 = U3 = 0) to one half of the edge of the bone ends and a displacement of U2 = 0.15 mm at 10 mm from the bone ends, as shown in Fig. 10b.
Mesh sensitivity Tetrahedron (C3D4) elements were used for discretising the geometry of the bone—plate assembly. We had determined the variations of the deflection (for an applied axial compressive force, bending moment for an applied deflection and torque for
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Figure 10 Loading and boundary conditions applied to1808 helical-plate fixation on simulated fractured bone with 458 oblique fracture. (a) Compressive load. (b) Bending load. (c) Torsional load. Similar loading conditions are applied to straight-plate and 908 helical-plate fixations. U, displacement; UR, rotation; numbers in suffix, direction of loading.
an applied twist) with the number of elements used in the analyses. When the number of elements used in straight-plate fixation for compression, bending moment and torsion were 55,463, 55,762 and 55,463, respectively, the solution converged; the convergence to these numbers of elements was based on the variations in the results being less than 0.33% with the increase in the number of elements. Likewise, in 908 helical-plate fixation, we converged to 60,823, 61,218 and 60,823 elements for compression, bending moment and torsion loads. Similarly, in 1808 helical-plate fixation, we converged to 61,291, 61,812 and 61,291 elements for compression, bending moment and torsion loads. The mesh was graded such that finer mesh was chosen at regions of higher strain concentrations.
Results and discussion Stiffness of the assembly In both compression and bending, it was observed that the stiffness of the fracture fixation (slope of the load deflection curves for the fracture-fixed assembly) was lowest for the 1808 helical plate, second lowest for the 908 helical plate and highest for straight plate, as shown in Fig. 11(a and b). In torsion, the stiffness was lowest for straight plate, second lowest for the 908 helical plate and highest for the 1808 helical plate, as indicated in Fig. 11c. This means that with the increase in the degree of contouring in helical plating, compression and flexural stiffnesses reduced, where as torsional
Analysis of the helical plate for bone fracture fixation
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Figure 11 Comparison of stiffness of bone—plate assembly: (a) Compressive load vs. deflection of the reference plane (depicted in the figure). (b) Bending moment vs. deflection at the mid span of the top surface of the plate. (c) Torsion vs. rotation of the reference plane (depicted in the figure). Helical plate fixations offer less stiffness than the straight plate fixation in compression and bending loadings. In torsional loading helical plate fixation provides maximum stiffness. Oblique fractures produced by torsion have been a big concern for fixation by straight plates. Our helical plate provides a solution for this long-standing problem.
stiffness increased. Thus, helical-plate fixation made the assembly flexible in axial and bending loading conditions, while providing maximum torsional stiffness.
Relative fracture-gap movement The inset in Fig. 12 illustrates the bone cross-section at the fracture site. From the FE analysis, we com-
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Figure 12 Relative movement along axis 3 at A, B, C and D location on the fracture gap. (a) For compressive load. (b) For bending moment. (c) For torsional load. Fracture gap closure is maximum in the 1808 helical plate. It is seen that the fracture gap closes for all the plates, in compression and bending loadings. However, in the case of torsion, the fracture gap closes for the helical plate only and opens up for the straight plate. + displacement means gap closure, displacement means opening up.
puted the relative axial movements (i.e. the combined movements of both fracture fragments) at the fracture gap along axis 3 at locations A, B, C and D, for bone—plate fracture-fixation (with straight plating, 908 helical plating and 1808 helical plating)
under axial, bending and torsion loadings, as depicted in Fig. 12. It was observed that fracture-gap movement (or closure) along axis 3 (at locations A, B, C and D) was maximum for 1808 helical-plate fixation, followed
Analysis of the helical plate for bone fracture fixation
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Table 2 Stresses (MPa) at centre of plate (at fracture site) and extreme end of plate (furthest from the fracture site) Load at Centre Far end
Straight plate
Helical plate (908)
Helical plate (1808)
Compression
Bending
Torsion
Compression
Bending
Torsion
Compression
Bending
Torsion
192.41 27.82
381.29 46.46
364.37 48.52
189.49 23.04
350.96 49.29
369.74 43.41
180.31 23.07
340.56 43.03
372.43 52.39
by 908 helical plating and then by straight plating in compression and bending (Fig. 12). Hence, it was perceived that enhanced gap closure along the fracture site could be achieved by means of helical plating, which also enhanced bone healing.30 Further, it was noted that gap closure became more uniform with increasing contouring of the
helical plate, under all the loading conditions considered in this study, i.e. axial compression at the fracture gap (along axis 3) was greatest with the helical plate, and increased with the degree of contouring. According to fracture-gap movement for oblique fractures, helical-plate fixation offers gap movements that are more conducive to healing
Figure 13 Locations of neutral axis (NA) on bone cross-section at different points along length of bone for straightplate, 908 helical-plate and 1808 helical-plate fixations, subjected to bending moment. Change of colour from grey to black represents NA. (a) Locations considered for NA along length of the bone. (b) Cross-sections of bone showing NA at different locations along length of bone fixed by straight plate, (c) 908 helical plate and (d) 1808 helical plate.
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Table 3 Location of neutral axis (NA) at different sites along length of bone Fixation type
Computed value (for bone) of NA location
At fracture site
At crosssection at first screw
At crosssection at second screw
At crosssection at third screw
At crosssection at fourth screw
Straight plate
NA from top of bone (mm) NA from top of bone (mm) NA from top of bone (mm)
Inside plate
1.5
2
2
2.5
Inside plate
2
2.6
3.2
4
Inside plate
2.8
4.3
5.5
6.8
908 helical plate 1808 helical plate
(for compression, bending and torsional loadings), when compared with straight-plate fixation. This means that the callus formed during the healing phase will be subjected to beneficial compression stresses for helical-plate fixation, which will induce consolidation of callus into bone and later aid remodelling of the bone. As regards lateral displacements at the fracture gap, these correspond to shear motion. Whereas compression is definitely conducive to bone healing, studies on the role of shear at the fracture gap are somewhat controversial.18,21,26
Stresses on the plate and screws The FE contours of Von-Mises stress in the plate reveal that, in all the loading conditions, the plate is highly stressed near the screw hole at the fracture site (stressed approximately eight times more than the stresses at the extreme ends of the plate; typical results are summarised in Table 2). Hence, the plate failure (if it initiates) can be expected to take place at the screw hole near the fracture site. Stress-shielding The location of the neutral axis (NA) for bending moment loading indicates the stress-shielding offered by the plate to the bone. As discussed earlier, optimal fracture fixation does not allow the fracture site to be in tension, i.e. the NA should at most be at the plate—bone interface. On the other hand, away from the fracture interface, the NA should be located within the bone, so that the bone also bears tensile stress. Fig. 13 depicts the locations of the NA (also tabulated in Table 3) on the bone cross-section at the fracture site, and at the sites of the first, second, third and fourth screws for straight-plate, 908 helical-plate and 1808 helicalplate fixations; it was noted that the NA shift (away from the fracture interface) into the bone for helical-plate fixation was more than that for the straight plate. Further, the amount of the shift in NA axis is also a function of the degree of contouring of helical
plate. Thus, the helical plate provides reduced stress-shielding. Remarks on helical-plate fixation The advantages offered by helical-plate fixation were as follows. Fracture-gap closure was greater (than for straight-plate fixation) at the fracture interface for all the loading conditions, and the uniformity of fracture-gap closure improved with increased contouring of the plate, i.e. increase of pitch. In bending-moment loading, the NA was located inside the plate at the fracture site (as with the straight plate). Away from the fracture site, because of the helical shape of the plate, the NA shifted into the bone (as shown in Fig. 13) and could hence allow the bone to take on both normal tensile and compressive stresses; thereby reducing stressshielding. In torsional loading, the bone elements were subjected to tensile stresses on the long diagonal planes. Because the axis of the helical plate was parallel to the orientation of the tensile stress (as schematically shown in Fig. 1), the helical plate absorbed the tensile stresses caused by torsional loading; this was not the case with straight-plate fixation, where the tensile stresses opened up the fracture gap obliquely. Thus, the helical plate can be most useful in the treatment of spiral fractures. The screw-holding power with helical-plate fixation was higher than with straight plating, as the screws were inclined at different orientations (as indicated in Table 1), thus avoiding sequential screw loosening. From the clinical point of view, according to Fernandez,11 helical plates have freedom at the entry point during minimally invasive surgery. Also, the helical plate is able to wrap around fractured bone on its different interfaces (as illustrated in Figs. 2—4), and thereby enhance the stiffness and stability of the fractured bone. Further, as indicated earlier, adroit positioning of the helical plate along the anterior, posterior and lateral segments of the fractured bone avoids damage to the vascular and nerve structures as well helping to preserve the muscle insertions.
Analysis of the helical plate for bone fracture fixation However, helical plates are not commercially available. Thus, currently, we need to contour a straight plate into a helical plate, as a temporary solution. However, during contouring, excessive screw-hole deformation can take place and hamper insertion during surgery. The situation is even worse if the locking compression plate is contoured, because the locking mechanism will be damaged by the excessive deformation. Residual stresses can also develop in the helical plate while contouring, and this can have an impact on the fatigue properties of the plate. Similarly, an excessively deformed screw hole acts as a stress raiser, and the plate will tend to fail at the screw hole during contouring. Hence, contouring straight plates should be replaced by the manufacture of helical plates to near net shape. Thus, our experimental and FE analyses have perhaps opened up a new arena for study and clinical practice in modern fracture fixation, using helical plates.
Acknowledgements K.R.K. thanks Nanyang Technological University for financial assistance in the form of a graduate scholarship. D.N.G. thanks Dr. K. Yang for his helpful suggestions. Authors thank Dr. S. Sivashanker for helping with the femurs and Dr. K. S. Khong for many useful clinical discussions.
Conflict of interest The authors certify that in this work there are no conflicts of interest with other persons or organisations. Certain commercial software, equipment, instruments and materials are identified in this paper in order to adequately specify the experimental and computational procedure. Such identification does not imply recommendation or endorsement by the authors, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
References 1. Albright JA, Johnson TR, Saha S. Principles of internal fixation. In: Ghista DN, Roaf R, editors. Orthopaedic mechanics: procedures and devices. New York: Academic Press; 1978. p. 123—229. 2. Apivatthakakul T, Arpornchayanon O, Bavornratanavech B. Minimally invasive plate osteosynthesis (MIPO) of the humeral shaft fracture. Is it possible? A cadaveric study and preliminary report. Injury 2002;36:530—8.
1435 3. Aro HT, Chao EY. Biomechanics and biology of fracture repair under external fixation. Hand Clin 1993;9:531—42. 4. Brooks DB, Burstein AH, Frankel VH. The biomechanics of torsional fractures: the stress concentration effect of a drill hole. J Bone Joint Surg Am 1970;52:507—14. 5. Chao EY, Aro HT, Lewallen DG, Kelly PJ. The effect of rigidity on fracture healing in external fixation. Clin Orthop 1989;241: 24—35. 6. Cordey J, Borgeaud M, Perren SM. Force transfer between the plate and the bone: relative importance of the bending stiffness of the screws and the friction between plate and bone. Injury 2000;31:21—8. 7. David MN, Perren SM. Force measurements in screw fixation. J Biomech 1976;9:669—75. 8. Deluca PA, Lindsey RW, Ruwe PA. Refracture of bones of the forearm after the removal of compression plates. J Bone Joint Surg 1988;70:1372—6. 9. Duda GN, Kassi JP, Hoffmann JE, et al. Mechanical behavior of Ilizarov ring fixators. Effect of frame parameters on stiffness and consequences for clinical use. Unfallchirurg 2000;103: 839—45. 10. Ferguson SJ, Wyss UP, Pichora DR. Finite element stress analysis of a hybrid fracture fixation plate. Med Eng Phys 1996;18:241—50. 11. Fernandez AAD. The principle of helical implants: unusual ideas worth considering. Injury 2002;33:1—27. 12. Fernandez AAD. Case-studies: the principle of helical implants: unusual ideas worth considering. Injury 2002;33: 29—40. 13. Fujihara K, Haung Z, Ramakrishna S, et al. Performance study of braided carbon/PEEK composite compression bone plates. J Biomater Appl 2003;24:2661—7. 14. Ganesh VK, Ramakrishna K, Ghista DN. Biomechanics of bone-fracture fixation by stiffness-graded plates in comparison with stainless-steel plates. J Biomed Eng 2005;4:46 [e-pub]. 15. Gardner MJ, Griffith MH, Loris DG. Helical plating of the proximal humerus. Injury 2005;6:1197—200. 16. Gardner TN, Evans M, Kenwright J. A biomechanical study on five unilateral external fracture fixation devices. Clin Biomech 1997;12:87—96. 17. John AH, Edward JC, Wilson CH. Biomechanics of fractures. In: Browner BD, Jupiter J, Levine A, Trafton P, editors. Skeletal trauma: fractures, dislocations, ligamentous injuries. Philadelphia, PA: Saunders; 1992 . p. 95—125. 18. Lutz EC, Christa AH, Cornelia NW, et al. Effects of mechanical factors on the fracture healing process. Clin Orthop 1998; 355:132—47. 19. Muller ME, Allgower M, Schneider R, Willengger H. Manual of internal fixation. Techniques recommended by the AO-ASIF Group. London: Springer—Verlag; 1991. 20. Panagiotopoulos E, Fortis AP, Millis Z, et al. Pattern of screw loosening in fractures fixed with conventional and functional plates. Injury 1994;25:515—7. 21. Park SH, Kim C, Harry M, Augusto S. The influence of active shear or compressive motion on fracture healing. J Bone Joint Surg Am 1998;80:868—78. 22. Perren SM. Evolution of the internal fixation of long bone fractures: the scientific basis of biological internal fixation; choosing a new balance between stability and biology. J Bone Joint Surg Br 2002;84:1093—110. 23. Ramakrishna K, Sivashanker S, Sridhar I, et al. Biomechanics of helical plate. In: Proceeding of Third Conference on Biomechanics organised by the International Association of Science and Technology for Development (IASTED), Spain. 2005. p. 220—3.
1436 24. Ramakrishna K, Sridhar I, Sivashanker S, et al. Design of fracture fixation plate for necessary and sufficient bone stress shielding. Jpn Soc Mech Eng 2004;47:1086—94. 25. Richard RT, Donald AW. The mechanics and biology of intramedullary fracture fixation. Clin Orthop 1986;212: 10—7. 26. Schell H, Epari DR, Kassi JP, et al. The course of bone healing is influenced by the initial shear fixation stability. J Orthop Res 2005;3:1022—8. 27. Stoffel K, Dieter U, Stachowiak G, et al. Biomechanical testing of the LCP–—how can stability in locked internal fixators be controlled? Injury 2003;34:11—9.
K.R. Krishna et al. 28. Stoffel K, Klaue K, Perren SM. Functional load of plates in fracture fixation in vivo and its correlate in bone healing. Injury 2000;31:7—50. 29. Tencer AF, Johnson KD. Biomechanics in orthopaedic trauma, bone fracture and fixation. London: Martin Dunitz; 1994. 30. Tong GO, Bavonratanavech S. Manual of fracture management, minimally invasive plate osteosynthesis–—MIPO. New York: Thieme; 2007. 31. Yang K. Helical plate fixation for treatment of comminuted fractures of the proximal and middle one third of the humerus. Injury 2005;36:75—80.
www.elsevier.com/locate/injury
Analysis of the helical plate for bone fracture fixation Kotlanka Rama Krishna 1, Idapalapati Sridhar *, Dhanjoo N. Ghista 2 School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Accepted 17 April 2008
KEYWORDS Bone fracture; Stiffness; Helical plate; Screw orientation; Finite-element analysis; Fracture-gap movement
Summary The improvements in oblique fracture fixation by means of the hemihelical plate (HHP) to provide the bone—plate-screw assembly with enhanced holding capacity are discussed. The HHP is designed to provide stable fixation for helical cracks caused by torsional loading, such that the bone interfaces at the crack are brought into apposition and compressive strains are applied at the cracked interfaces. The HHP wraps around the bone, and hence is also suited for fixation of comminuted fractures. This is because, instead of employing multiple screws across the cracks, the HHP holds the bone fragments together. First, we illustrate through experiments the special capabilities of the HHP with respect to its fracture-holding capability, in comparison with straight-plate fixation with different screw orientations (convergent, divergent, alternately convergent and divergent, and perpendicular). Second, the finite-element (FE) analysis of the HHP is described, to elucidate the efficacy of fracture-gap movement and closure, and the flexibility of the fixation under compressive, bending moment and torsional loads. # 2008 Elsevier Ltd. All rights reserved.
Introduction Long bone, subjected to a combination of axial, bending and torsional loads in vivo, fractures in a variety of competing modes when the applied load exceeds the sustainable limit. Axial compressive * Corresponding author. Tel.: +65 6790 4784; fax: +65 6791 1859. E-mail address: [email protected] (Idapalapati Sridhar). 1 Currently with MEMS Program, Institute of Microelectronics, 11 Singapore Science Park II, Singapore 117685, Singapore. 2 Present Address as: Parkway Education College, 168 Japan Bukit Mehra, Singapore 150168, Singapore.
loads can cause oblique fracture due to shear failure; under axial tensile loading, maximum stresses are generated in a plane perpendicular to the loading direction, leading to transverse fractures; and when the bone is subjected to bending forces, both tensile and compressive stresses are generated. As bone is more susceptible to failure in tension than in compression, the crack initiates on the tension side and progresses across the bone, creating a butterfly type fracture. Torsion on a long bone results in a long spiral fracture, with the fracture line orientated at about 458 to the axis about which torque is applied.29,19
0020–1383/$ — see front matter # 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.injury.2008.04.013
1422 Fractured bones can be fixed by external immobilisation and fixation techniques such as plaster casting and multiple percutaneous transcortical pins,3,5,9,16 or by internal fixation using intramedullary rods1,30 and/or plates with screws.17,22,27,28 The choice of fixation and surgical technique is based on a range of factors, including bone quality, fracture type, anatomical location and, to some extent, on surgeons’ preferences. Particularly with oblique and helical cracks, fixation of fractured bone (or of healed bone to regain its pre-fracture stiffness and strength) continues to pose immense osteosynthesis challenges. Spiral fractures have generally been fixed by using three or more lag screws; the important parameters considered while fixing are spacing between the screws and stability, i.e. least micromovement at the fracture interface, referring to the gap strain theory of Perren.22 Too many screws will weaken the bone, as screw holes act as stress raisers; on the other hand, fewer screws will lead to instability at the fracture site. Other means of fixing spiral fractures include intramedullary rods and/or plating on the tension side. Intramedullary rods provide better stability than fixation by lag screws alone.25 When fixed by the conventional straight plate, the stability of fracture fixation is weak, as tensile forces are generated during torsion at 458 to the axis of the bone and do not act along the axis of the plate4; the straight plate is unable to handle tensile forces diagonal to the axis of the bone—plate assembly. Fernandez11,12 was the first surgeon to clinically moot the idea of fracture fixation using internal helical bone—plates. In particular, his anatomical study postulated the advantage of helical plates for treating fractures of the humerus. Clinical applications of the helical plate have been described by Apivatthakakul et al.2, Gardner et al.15 and Yang,31 as well as by us through computational biomechanical analysis.23 This paper addresses in detail the unique features of hemi-helical plate (HHP) internal bone fracture fixation, wherein screws are used to anchor a hemi-helical plate onto the fractured bone. In general, screws provide a bridge transferring forces between the plate and the fractured bone. Consequently, screws may be subjected to relatively large shear stresses during movement of the fractured limb. In addition, the bone surface adjacent to screws can be subjected to trauma at insertion, which may cause some temporary bone necrosis. These factors can lead to loosening and subsequent pulling out of screws, thereby destabilising the entire fracture-fixation assembly.1,6,7,8,20 Such a phenomenon is commonly observed in straight-plate fixation, where the screws are orientated normal to
K.R. Krishna et al. the plate in the same plane; angling of the screws is considered a possible solution, to mitigate loosening of fracture fixation (Fig. 1).22 In addition, the straight plate also induces undue stress-shielding of the fractured bone. This is because the straight-plate fixture is fastened onto the tensile surface of the fractured bone (thereby destressing the bone beneath the plate), and the plate material Young’s modulus (which is 200 GPa for 316 L stainless steel) is typically an order of magnitude higher than that of bone (which is about 20 GPa). In order to reduce the mismatch of the material properties of plate and bone, carbon fibre-reinforced polymer matrix composite materials and stiffness graded plates have been recommended.13,14,24
Helical-plate fixation: biomechanical justification, clinical applications and scope of our biomechanical studies Helical-plate fixation avoids some of the complications arising from the use of straight-plate fixation, particularly for oblique and spiral fractures resulting from torsion of long bones. In the first place, from a biomechanical view point, spiral fractures are generated by tensile stress acting diagonally to the axis of the bone, as illustrated in Fig. 1. Hence, a helical plate needs to be applied and orientated orthogonally to the spiral fracture, in order to absorb these tensile stresses. Second, because of the helical orientation of the plate, the screws anchoring the HHP to the fractured bone are inclined at different angles to the axis of the bone. This minimises the possibility of loosening of screws (associated with straight-plate fixation) under loading, and provides for more secure fixation of the plate to the bone, as has been demonstrated by our experimental studies elaborated in ‘Methods’. Third, when a plate—bone assembly using a straight plate is subjected to bending, the neutral axis (NA) of the composite plate—bone structure is located very close to the external surface of the
Figure 1 Diagram of fractured bone fixed by 1808 helical plate, under torsion.
Analysis of the helical plate for bone fracture fixation bone or even inside the plate, because the elastic modulus of the plate is much greater than that of the bone. This causes stress-shielding of the bone segments away from the fracture site, and weakening of these segments. However, because the helical plate is anchored in a spiral orientation to the bone, the plate—bone cross-sections at different locations away from the fracture site will also have the plate attached to the bone at varying orientations with respect to the plane of the bone (in which bending is applied.) This will induce tensile stresses in the bone portion of the plate—bone cross-sections, thereby alleviating the problem of stress-shielding of the bone away from the fracture site. Fourth, because the helical plate is fastened and wrapped around the fractured bone along its length, it enables reduction of the fracture gap in the axial direction along the entire fracture surface of the bone. This is clearly demonstrated in computational simulations of the fractured bone—plate assembly’s response to loadings (in finite-element (FE) analysis). These are some of the biomechanical factors contributing to better clinical outcomes of helical-plate fixation of oblique and spiral fractures. In addition, the helical plate permits more freedom in choice of entry point, and allows for positioning of the plate on different segments of the bone (such as laterally in the proximal part of the bone and anteriorly in the distal part of the bone) to avoid damage to nerves and vascular and musculocutaneous structures.15,17,31 There is consensus among orthopaedic surgeons that, whereas the ideal treatment of fractures (for example of the humerus) has not been definitively agreed, helical-plate fixation solves many problems. Yang31 indicated that plate fixation of comminuted fractures of the proximal and middle humerus requires a long plate to be applied from the lateral aspect of the greater tuberosity to the humerus shaft. Since this required dissection of the deltoid muscle insertion, these workers twisted the long plate and fixed it from the lateral aspect of the greater tuberosity to the anterior of the distal shaft of the humerus, and thereby were able to preserve deltoid muscle insertion. Fig. 2 illustrates how a straight plate can be pre-contoured in a helical fashion to fit the proximal and middle thirds of the humerus, using a skeleton as a template; herein, the proximal part of the helical plate is attached to the lateral aspect of the greater tuberosity, and its distal part is fixed to the anterior aspect of the humeral shaft.31 Fig. 3 illustrates a clinical application of the helical plate for proximal fracture of the humerus extending to the greater tuberosity.31 In
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Figure 2 Long plate precontoured helically to fit proximal and middle thirds of humerus, using skeleton as template. Anterior placement of distal part of helical plate can preserve deltoid muscle insertion. (A) Deltoid muscle insertion; (B) lesser tuberosity; (C) greater tuberosity.31.
fact, several cases have been reported as involving the technique of helical plating of proximal humeral fractures, where the proximal plate was placed laterally on the greater tuberosity and spiralled 908 distally to lie on the anterior surface of the humeral shaft. This technique avoids the danger zone of musculocutaneous nerve crossing for placement of screws.12,31 Fig. 4 schematically illustrates this mode of effective helical-plate fixation.15 Helical plating is also feasible for application to the femur, as reported by Fernandez.12 Helical-plate fixation has thus been innovatively employed for plating femoral and humeral shaft fractures. In order to provide biomechanical confirmation of the clinical efficiency of helical-plate bone fracture fixation, we carried out extensive experimental mechanical studies of this technique in relation to straight-plate fixation, to demonstrate superior plate attachment to bone and plate—bone strength-to-failure, and delineate camoative factors.
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Figure 3 (A) Preoperative and (B) final radiographs. Proximal fracture extended to greater tuberosity (arrow). Fractures fixed with four lag screws and 12-hole pre-bent helical thin narrow plate.31.
We then carried out comprehensive computational biomechanical studies by finite-element analysis of helical-plate fixation of simulated oblique fractures of bone (in comparison with straight-plate fixation) under compression, bending and torsional loadings. Clinical studies2,11,12,15,31 on helical-plate fixation primarily emphasise facilitation of surgical insertion of the fixation plate and the means by
which the fractured bone can be plated along its different aspects (lateral, anterior and medial) so as to provide better fixation-stability to the fractured bone and also preserve muscular insertions and vascular and neural structures. However, our biomechanical studies demonstrated some additional advantages of helical-plate fixation compared with straight-plate fixation, such as superior plate fixation to the bone by screws and
Analysis of the helical plate for bone fracture fixation
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Experimental studies of hemi-helical plate versus straight-plate bone fracture-fixation Materials and methods
Figure 4 Precontouring helical plate so that proximal limb lies on greater tuberosity laterally, distal limb rotates 908 to lie on anterior surface of humerus; 99% confidence interval of position of nerve crossing anterior humerus was 12.2—14.8 cm (shaded area). Flatow EL, Bigliani LU, April EW. An anatomic study of the musculocutaneous nerve and its relationship to the coracoid process. Clin Orthop 1989;166—71.
reduced stress-shielding, as mentioned above. Hence our studies aimed to elucidate the biomechanical basis of the advantages of helical-plate fixation over straight-plate fixation for oblique fractures of bone, in support of the relevant clinical studies. In this context, two specific issues pertaining to internal bone fracture fixation were addressed. First, the concept of HHP fixation was demonstrated, by providing the results of pull-out experiments with the aim of comparing the holding strengths of straight and hemi-helical plates for various screw configurations. Second, we performed FE analyses for three fracture fixation configurations (i.e. straight plate, 908 helical plate and 1808 helical plate) under uniaxial compression as well as for bending and torsional loadings, to compare the overall stiffness of the various assemblies and fracture-gap movement.
Fig. 5a is a diagrammatic description of a helical plate. The axis is defined as a straight line along the length of the bone at its centre, and the geometric radius is defined as the distance from the axis to the outer surface of the bone (at mid shaft). The effective length is the distance between the ends of the plate along the axis of the bone, and the pitch is the degree of rotation (or twist) of the plate. For example, 1-pitch represents a 3608 twist of the plate, 1/ 2-pitch represents a 1808 twist of the plate and 1/4pitch represents a 908 twist of the plate. Fig. 5b portrays helical-plate contour direction defined by a thumb rule; for example in a right-handed helical plate, the right-hand thumb shows the direction of the femoral head and the closed fingers show the direction of the helical-plate’s contours. Bone fracture fixation using a 3608 or 2708 helical plates is not used, because of clinical constraints. Hence, only 1808 and 908 helical plates were considered in the present investigation. In the current experiments, a twelve-hole Zimmer Dual Compression Contourable Plate, with 4.5 mm cortical screws, was fixed onto a Synthes femoral bone specimen (Mathys) by screws located at the 1st, 4th, 9th and 12th positions. Experiments were conducted to determine the axial pull-out strengths of both hemi-helical and straight bone—plates with perpendicular (PSO), convergent (CSO), divergent (DSO) and alternating (ASO) screw orientations as indicated in Fig. 6, in accordance with ASTM F1691-96. The experimental set-up for the pull-out experiments is shown in Fig. 7a. Special grips were designed and built to hold the ends of the femoral bone specimens and to comply with ASTM F1691-96 test techniques. Each bone— plate fracture fixation assembly was loaded by a 5 kN Instron testing machine, under displacement control at a loading rate of 5 mm/min. The experiments were confined to one sample of each configuration (i.e. PSO, ASO, CSO, DSO and hemi-helical fixation assembly) because of limited bone specimens; saw bones are not reusable, as they fracture after the test although the plates may remain elastic.
Results and discussion Fig. 8 shows the load—displacement responses for the hemi-helical and straight plates (with four different screw orientations) during pull-out testing
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Figure 5 (a) Side view shows 1/2 pitch of helical plate. (b) Thumb points to femoral head and fingers to direction of helical-plate contouring.
Figure 6 Pull-out tests. Inclined screw orientations. Straight-plate fixation with (a) perpendicular (PSO), (b) convergent (CSO), (c) divergent (DSO) and (d) alternating (ASO) screw orientations all in longitudinal plane. Helical plating with (e) hemi-helix 1808, screws oriented in different planes.
which enabled assessment of the holding capacity of the plate and screws on the fractured bone. Four distinct peaks were observed in the load—displacement curves of straight plates (with various screw orientations). These peaks reflect sequential screw pull-out, wherein the screws located at the 4th hole loosened initially; this was followed by progressive loosening at the 9th, 1st and 12th holes (Figs. 6 and 7b). In contrast, no sequential screw pull-out was observed in the hemi-helical fixation (Fig. 7c and d). It is also noteworthy that the holding strength of the hemi-helical fixation was higher than that of the straight plate with either PSO, CSO, DSO or ASO configurations; no screw loosening was observed with the HHP. The initial slopes of these load—displacement curves (Fig. 8) indicated that the straight plates with ASO and DSO configurations offered, respectively, the greatest and least stiffness for the fracture fixation assembly under bending loading. CSO and PSO straight-plate screw configurations as well as HHPs resulted in similar intermediate
Analysis of the helical plate for bone fracture fixation
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Figure 7 (a) Experimental set-up for pull-out test of 1808 helical plate and bone fixation held by four cortical screws with newly designed grippers holding assembly. (b) Sequential pull-out of straight plate with perpendicular, convergent, divergent and alternating configurations. (c) Holding power of hemi-helical plate is high, sequential screw pull-out not observed. (d) However, bone failed before screw pull-out, indicating that fixation stiff enough to prevent screw loosening.
levels of stiffness (as listed in Table 1). The areas under the respective load—displacement curves indicated that the hemi-helical and straight plates (with DSO configurations) resulted, respectively, in the greatest and least energy-to-fracture (or toughness) for the fixation assembly. The PSO, ASO and CSO screw configurations for straight-plate fixation yielded similar intermediate levels of energy-to-fracture. The HHP also conferred the highest pull-out strength in the fixation assembly, compared with straight-plate configurations with any of the four different screw orientations. In addition, as shown in Fig. 7b, there was the risk of loosening and sequential screw pull-out in straight plates, since the axes of the screws were all in the same plane (as seen from cross-sectional views along the longitudinal plane of the fixation assembly, Fig. 6a—d). In contrast, the axes of the screws in the hemi-helical fixation assembly were all in different planes (intersecting one another, as shown in Fig. 6e), thus eliminating or minimising the problem of loosening and progressive sequential pull-out of screws. The photographs in Fig. 7(c and d) illustrate the higher
load-carrying capacity of a helical-plate assembly. Overall, these results suggested that HHP fixation provided the optimal combination of strength, stiffness and toughness compared with straight plates with any screw orientation.
Finite-element analysis of hemi-helical plate versus straight-plate bone fracture fixation It can be concluded from the above that helical plating has an improved load-holding capacity, which is necessary to avoid implant loosening (which is more prominent in osteoporotic bones). It is also necessary to study the fracture-gap movement characteristics and stiffness of the assembly of fixed fractured bone and plate, comparing helical and straight plating. For this purpose, FE analyses were carried out for fixations of an oblique fracture (angled 458 to the axis of the bone) fixed with a straight plate, a 908 helical plate and a 1808 helical plate under compression, bending and torsion loadings, using the ABAQUS program for FE analysis.
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Figure 8 Pull-out tests; load vs. extension curves for all configurations in Fig. 7. Insert depicts peaks in curve representing pull-out for convergent (CSO), perpendicular (PSO), alternating (ASO) and divergent (DSO) screw configurations. Stiffness of assembly is slope of load vs. extension curve and area under load vs. extension curve until initiation of pull-out represents energy to pull-out.
Modelling of bone fracture fixation FE analyses of the bone—plate-screws assembly were carried out with: screw holes modelled as hollow cylinders (outer diameter 24 mm, inner diameter 16 mm, length 170 mm, 8 screw holes); Table 1 Stiffness and energy to initiate pull-out and peak pull-out for perpendicular (PSO), convergent (CSO), divergent (DSO) and alternating (ASO) screw orientations and hemi-helical configurations in plate fixation Orientation
Stiffness (kN/m)
Energy to pull-out (J)
Peak pullout load (N)
PSO ASO CSO DSO Hemi-helical
55.1 58.0 49.3 44.7 55.4
7.17 9.67 10.12 6.88 10.83
796 900 924 679 1000
the 8 screws as cylinders 3.5 mm in diameter (in order to reduce the number of elements required for screws meshing, as screw threads require finer elements for meshing); different plate configurations (i.e. straight plate, 908 helical plate and 1808 helical plate). The plates were 12 mm wide, 4 mm thick and 140 mm in effective length, and the radius of the helix was 12 mm. In order to produce a helical plate, a straight plate was curved so that it exactly fitted the outer diameter of the bone. The distances between the screw holes were equal in all plate configurations. All three configurations of fixation (i.e. straight plate, 908 helical plate and 1808 helical plate) were modelled by commercial computer-aided design software UNIGRAPHICS. The FE models are depicted in Fig. 9a—d. The modelled parts (i.e. plate, bone and screws) were imported to the commercial FE analysis software ABAQUS from UNIGRAPHICS through STEP format. The bone was then modified to incorporate an oblique fracture
Analysis of the helical plate for bone fracture fixation
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Figure 9 Finite-element models in ABAQUS. (a) Straight-plate model. (b) 908 helical-plate model. (c) 1808 helical-plate model. (d) Oblique fracture fixed by helical plate. Bone axis is along coordinate 3.
gap of 2 mm at its mid span, angled 458 to the axis of bone (as shown in Fig. 9d). The screws were positioned such that they were always perpendicular to the top surface of the plate; in this way, the screws were in different planes incorporating the bone axis. The bone was modelled as a transversely isotropic material, with moduli and Poisson’s ratio of E1 = 14.5 (GPa), E2 = 14.5 (GPa), E3 = 19.7 (GPa), G12 = 7.0 (GPa), G13 = 7.0 (GPa), G23 = 5.28 (GPa), y12 = 0.285, y13 = 0.285 and y23 = 0.26515 GPa (the directions 1, 2, 3 are shown in Fig. 9).10 The plate and screws materials were assumed to be in an elastic state for the applied loading, and assigned 200 GPa Young’s modulus (316 L stainless steel) and 0.3 Poisson’s ratio values. In order to simulate the locking-screw mechanism during analysis, the screw head and the contoured surface of the plate were tied together by means of a contact option available in ABAQUS. Similar contact conditions were assigned for cylindrical screws and bone, so that the screws held the bone during loading. A coefficient of friction of 0.37 was assigned between bone and plate contacts, and a value of 1.0 between the broken bone fragments (i.e. at fracture interfaces). The computations were carried out for finite strain, by prescribing the non-linear geometry (NLGM) option in the ABAQUS program.
Loading and boundary conditions imposed on bone fractures after fixation Compressive, torsion and bending loadings were applied to obliquely fractured bones fixed by straight plating, 908 helical plating or 1808 helical plating. In order to apply a compressive load of 150 N, one end of the fracture-fixed bone was fully constrained and a compressive force of 150 N applied in the axial (U3) direction on a reference plane at the free end (as shown in Fig. 10a). In order to simulate torsional loading, a displacement of UR3 = 0.05 radians was applied to the reference plane at the free end, while the boundary conditions of the fixed end were maintained (Fig. 10c). A four-point bending loading was simulated, by applying the boundary condition (U1 = U2 = U3 = 0) to one half of the edge of the bone ends and a displacement of U2 = 0.15 mm at 10 mm from the bone ends, as shown in Fig. 10b.
Mesh sensitivity Tetrahedron (C3D4) elements were used for discretising the geometry of the bone—plate assembly. We had determined the variations of the deflection (for an applied axial compressive force, bending moment for an applied deflection and torque for
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Figure 10 Loading and boundary conditions applied to1808 helical-plate fixation on simulated fractured bone with 458 oblique fracture. (a) Compressive load. (b) Bending load. (c) Torsional load. Similar loading conditions are applied to straight-plate and 908 helical-plate fixations. U, displacement; UR, rotation; numbers in suffix, direction of loading.
an applied twist) with the number of elements used in the analyses. When the number of elements used in straight-plate fixation for compression, bending moment and torsion were 55,463, 55,762 and 55,463, respectively, the solution converged; the convergence to these numbers of elements was based on the variations in the results being less than 0.33% with the increase in the number of elements. Likewise, in 908 helical-plate fixation, we converged to 60,823, 61,218 and 60,823 elements for compression, bending moment and torsion loads. Similarly, in 1808 helical-plate fixation, we converged to 61,291, 61,812 and 61,291 elements for compression, bending moment and torsion loads. The mesh was graded such that finer mesh was chosen at regions of higher strain concentrations.
Results and discussion Stiffness of the assembly In both compression and bending, it was observed that the stiffness of the fracture fixation (slope of the load deflection curves for the fracture-fixed assembly) was lowest for the 1808 helical plate, second lowest for the 908 helical plate and highest for straight plate, as shown in Fig. 11(a and b). In torsion, the stiffness was lowest for straight plate, second lowest for the 908 helical plate and highest for the 1808 helical plate, as indicated in Fig. 11c. This means that with the increase in the degree of contouring in helical plating, compression and flexural stiffnesses reduced, where as torsional
Analysis of the helical plate for bone fracture fixation
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Figure 11 Comparison of stiffness of bone—plate assembly: (a) Compressive load vs. deflection of the reference plane (depicted in the figure). (b) Bending moment vs. deflection at the mid span of the top surface of the plate. (c) Torsion vs. rotation of the reference plane (depicted in the figure). Helical plate fixations offer less stiffness than the straight plate fixation in compression and bending loadings. In torsional loading helical plate fixation provides maximum stiffness. Oblique fractures produced by torsion have been a big concern for fixation by straight plates. Our helical plate provides a solution for this long-standing problem.
stiffness increased. Thus, helical-plate fixation made the assembly flexible in axial and bending loading conditions, while providing maximum torsional stiffness.
Relative fracture-gap movement The inset in Fig. 12 illustrates the bone cross-section at the fracture site. From the FE analysis, we com-
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Figure 12 Relative movement along axis 3 at A, B, C and D location on the fracture gap. (a) For compressive load. (b) For bending moment. (c) For torsional load. Fracture gap closure is maximum in the 1808 helical plate. It is seen that the fracture gap closes for all the plates, in compression and bending loadings. However, in the case of torsion, the fracture gap closes for the helical plate only and opens up for the straight plate. + displacement means gap closure, displacement means opening up.
puted the relative axial movements (i.e. the combined movements of both fracture fragments) at the fracture gap along axis 3 at locations A, B, C and D, for bone—plate fracture-fixation (with straight plating, 908 helical plating and 1808 helical plating)
under axial, bending and torsion loadings, as depicted in Fig. 12. It was observed that fracture-gap movement (or closure) along axis 3 (at locations A, B, C and D) was maximum for 1808 helical-plate fixation, followed
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Table 2 Stresses (MPa) at centre of plate (at fracture site) and extreme end of plate (furthest from the fracture site) Load at Centre Far end
Straight plate
Helical plate (908)
Helical plate (1808)
Compression
Bending
Torsion
Compression
Bending
Torsion
Compression
Bending
Torsion
192.41 27.82
381.29 46.46
364.37 48.52
189.49 23.04
350.96 49.29
369.74 43.41
180.31 23.07
340.56 43.03
372.43 52.39
by 908 helical plating and then by straight plating in compression and bending (Fig. 12). Hence, it was perceived that enhanced gap closure along the fracture site could be achieved by means of helical plating, which also enhanced bone healing.30 Further, it was noted that gap closure became more uniform with increasing contouring of the
helical plate, under all the loading conditions considered in this study, i.e. axial compression at the fracture gap (along axis 3) was greatest with the helical plate, and increased with the degree of contouring. According to fracture-gap movement for oblique fractures, helical-plate fixation offers gap movements that are more conducive to healing
Figure 13 Locations of neutral axis (NA) on bone cross-section at different points along length of bone for straightplate, 908 helical-plate and 1808 helical-plate fixations, subjected to bending moment. Change of colour from grey to black represents NA. (a) Locations considered for NA along length of the bone. (b) Cross-sections of bone showing NA at different locations along length of bone fixed by straight plate, (c) 908 helical plate and (d) 1808 helical plate.
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Table 3 Location of neutral axis (NA) at different sites along length of bone Fixation type
Computed value (for bone) of NA location
At fracture site
At crosssection at first screw
At crosssection at second screw
At crosssection at third screw
At crosssection at fourth screw
Straight plate
NA from top of bone (mm) NA from top of bone (mm) NA from top of bone (mm)
Inside plate
1.5
2
2
2.5
Inside plate
2
2.6
3.2
4
Inside plate
2.8
4.3
5.5
6.8
908 helical plate 1808 helical plate
(for compression, bending and torsional loadings), when compared with straight-plate fixation. This means that the callus formed during the healing phase will be subjected to beneficial compression stresses for helical-plate fixation, which will induce consolidation of callus into bone and later aid remodelling of the bone. As regards lateral displacements at the fracture gap, these correspond to shear motion. Whereas compression is definitely conducive to bone healing, studies on the role of shear at the fracture gap are somewhat controversial.18,21,26
Stresses on the plate and screws The FE contours of Von-Mises stress in the plate reveal that, in all the loading conditions, the plate is highly stressed near the screw hole at the fracture site (stressed approximately eight times more than the stresses at the extreme ends of the plate; typical results are summarised in Table 2). Hence, the plate failure (if it initiates) can be expected to take place at the screw hole near the fracture site. Stress-shielding The location of the neutral axis (NA) for bending moment loading indicates the stress-shielding offered by the plate to the bone. As discussed earlier, optimal fracture fixation does not allow the fracture site to be in tension, i.e. the NA should at most be at the plate—bone interface. On the other hand, away from the fracture interface, the NA should be located within the bone, so that the bone also bears tensile stress. Fig. 13 depicts the locations of the NA (also tabulated in Table 3) on the bone cross-section at the fracture site, and at the sites of the first, second, third and fourth screws for straight-plate, 908 helical-plate and 1808 helicalplate fixations; it was noted that the NA shift (away from the fracture interface) into the bone for helical-plate fixation was more than that for the straight plate. Further, the amount of the shift in NA axis is also a function of the degree of contouring of helical
plate. Thus, the helical plate provides reduced stress-shielding. Remarks on helical-plate fixation The advantages offered by helical-plate fixation were as follows. Fracture-gap closure was greater (than for straight-plate fixation) at the fracture interface for all the loading conditions, and the uniformity of fracture-gap closure improved with increased contouring of the plate, i.e. increase of pitch. In bending-moment loading, the NA was located inside the plate at the fracture site (as with the straight plate). Away from the fracture site, because of the helical shape of the plate, the NA shifted into the bone (as shown in Fig. 13) and could hence allow the bone to take on both normal tensile and compressive stresses; thereby reducing stressshielding. In torsional loading, the bone elements were subjected to tensile stresses on the long diagonal planes. Because the axis of the helical plate was parallel to the orientation of the tensile stress (as schematically shown in Fig. 1), the helical plate absorbed the tensile stresses caused by torsional loading; this was not the case with straight-plate fixation, where the tensile stresses opened up the fracture gap obliquely. Thus, the helical plate can be most useful in the treatment of spiral fractures. The screw-holding power with helical-plate fixation was higher than with straight plating, as the screws were inclined at different orientations (as indicated in Table 1), thus avoiding sequential screw loosening. From the clinical point of view, according to Fernandez,11 helical plates have freedom at the entry point during minimally invasive surgery. Also, the helical plate is able to wrap around fractured bone on its different interfaces (as illustrated in Figs. 2—4), and thereby enhance the stiffness and stability of the fractured bone. Further, as indicated earlier, adroit positioning of the helical plate along the anterior, posterior and lateral segments of the fractured bone avoids damage to the vascular and nerve structures as well helping to preserve the muscle insertions.
Analysis of the helical plate for bone fracture fixation However, helical plates are not commercially available. Thus, currently, we need to contour a straight plate into a helical plate, as a temporary solution. However, during contouring, excessive screw-hole deformation can take place and hamper insertion during surgery. The situation is even worse if the locking compression plate is contoured, because the locking mechanism will be damaged by the excessive deformation. Residual stresses can also develop in the helical plate while contouring, and this can have an impact on the fatigue properties of the plate. Similarly, an excessively deformed screw hole acts as a stress raiser, and the plate will tend to fail at the screw hole during contouring. Hence, contouring straight plates should be replaced by the manufacture of helical plates to near net shape. Thus, our experimental and FE analyses have perhaps opened up a new arena for study and clinical practice in modern fracture fixation, using helical plates.
Acknowledgements K.R.K. thanks Nanyang Technological University for financial assistance in the form of a graduate scholarship. D.N.G. thanks Dr. K. Yang for his helpful suggestions. Authors thank Dr. S. Sivashanker for helping with the femurs and Dr. K. S. Khong for many useful clinical discussions.
Conflict of interest The authors certify that in this work there are no conflicts of interest with other persons or organisations. Certain commercial software, equipment, instruments and materials are identified in this paper in order to adequately specify the experimental and computational procedure. Such identification does not imply recommendation or endorsement by the authors, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
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