Composite and Metal Bone Plate - Screw Fixation: A Numerical Comparison

Seckin Erden, Hasan Yildiz Ege University Izmir, TURKEY

Abstract: Although they cause some problems, metallic bone plates have been used widely in the healing of especially long bone fractures. As composites are less rigid, and their mechanical properties may be closer to that of bone, it seems possible to avoid these problems with their usage as alternative implant materials. The aim of this study was to compare theoretically the metallic and composite bone plates used in the healing of tibial fractures according to their effects on the bone and the fracture site, and their behaviours under the condition of compression, which is caused while the patient stands up. Also, the screws used for the fixation of the bone/plate system are compared for metallic and composite plate cases. A 3D finite element model was developed to analyse the problem. Results of the analyses were evaluated using the theory of strain energy density, and the calculated stress values. The results obtained for the fracture site showed that in the case of composite plates, an increase in bone density is obvious, ie. bone remodelling can be faster. Additionally, screws used in metallic plate cases were found to be more critical in failure.

Introduction: Orthopaedic surgeons have been using metallic bone plates commonly (Figure 1 (Reference 11)) especially for the fixation of long bone (diaphysial) fractures. However, it is obvious that metallic prostheses, which are generally made of stainless steel and titanium alloys, cause some problems like metal incompatibility, corrosion, magnetism effect, anode-cathode reactions, etc., and also decrease in bone mass (osteopenia), increase in bone porosity (osteoporosis), and delay in fracture healing (callus formation, ossification) as almost all loads are transferred through these rigid plates (stress shielding effect / stress protection atrophy) (Reference 4, 5, 10). Due to insufficient bone growth, refractures after the removal of the prostheses are also widely reported (Reference 4). It’s also found that the difference in elasticity of a metallic implant and bone may cause loosening of the implant (Reference 3). Also in composite plates the screw at the area of maximum bending moment was found to back out of the bone while it is rare in metal plates (Reference 4).

Figure 1 - Typical bone plates used in long bone fractures

Researches for seeking alternative implant materials have been widely carried out especially during the last decade in order to increase bone remodelling. Composite materials, which are less rigid than metals and

may have properties closer to bone mechanical properties, have been considered as alternatives. It was found that they help to avoid stress shielding and increase bone remodelling (Reference 1, 2). Finally, these researches led to the development of new alternative biomaterials known as biodegradable implants, which are thought to reduce operations and consequently hospital queues. Therefore, it seems like these upcoming events will be of great importance in the development of orthopaedics.

These new developments in alternative biomaterials, led us to this study, in which the metallic bone plates and composites, which are thought to be their alternatives, are compared theoretically, according to their effects on the bone and the fracture site. Additionally, the effects of the plate material on the screws used for the plate fixation are also investigated. A series of finite element analyses were performed to solve the problem, discretizing the geometric model with the use of three dimensional finite elements. The finite element analysis tool ANSYS Multiphysics / LS-DYNA was used for the solution. Static compression, which is caused while the patient stands up, was considered as the loading condition. In the case of metallic plates, the implants were assumed to be of stainless steel and Ti6Al4V titanium alloy, while composite plates were thought to be of graphite/epoxy and carbon/hydroxyapatite (HA). The cortical screws were considered as stainless steel (Figure 17 (Reference 11)). Additionally, mechanical properties of the bone and the fracture site were determined using the properties of tibia. Results of the analyses were evaluated using the theory of strain energy density (SED) which implies the exponential relationship between strain energy density and bone density, ie. bone growth. The comparison of the results obtained for several cross-sections in the fracture site showed that SED distributions in case of composite bone plates are much even. Consequently, it is obvious that there is a smoother load distribution in bone in the case of composite plates, unlike the regional overloading in the case of metallic plates. This leads us to the possibility of avoiding bone loss. Additionally, it can be stated that SED values increase along the bone. Thus, an increase in bone density is obvious, ie. a much suitable environment for bone growth can be established. Therefore, it can be stated that bone growth, or in other words, fracture healing can be faster.

Procedure

The geometric model: The following were assumed while forming the geometric model of the problem:

• Bone (tibia) and the fracture site were defined as smooth, hollow cylindrical geometric shapes having a definite tube thickness. This is because the bone marrow is thought not to carry any load.

• Plate was dimensioned using an eight-hole narrow dynamic compression plate (DCP), but the holes were drilled as in neutralization bone plates. This is because better results were obtained with the use of them in human cases (Reference 1). Also, although the reference plate was 3.5 mm in thickness, in order to ease the composite plate configurations, plate thickness in the model was taken as 4 mm. Thus, thirty-two 0.125 mm thick laminae were easily configured symmetrically to form the composite plates. Also, the plates were assumed to have a curvature to surround the outer surface of the bone.

• Screws were taken as 4.5 mm cortical screws and modelled as completely fixed to the bone, ie. they were screwed to both of the cortical sections in the bone cross-section (Figure 2, 3).

Dimensions of the geometric model used in the analyses are as follows (for one side of the symmetry axis):

Bone:

Inner / outer diameter – length: 10.0 / 25.0 – 67.0 [mm]

Fracture site:

Inner / outer diameter – length: 10.0 / 25.0 – 1.0 [mm]

Plate:

Length – width – thickness: 68.0 – 12.0 – 4.0 [mm]

Screw:

Diameter – length – head diameter: 4.5 – 25.0 – 8.5 [mm]

Figure 2 - Geometric model of the problem

Figure 3 - Quarter symmetric model / loaded

The finite element model: The following assumptions were considered for the finite element model (Figure 4, 5):

• Bone/plate system was modelled as it was only subjected to compression, ie. the case of torsion was excluded. Therefore, it had been possible to consider just a quarter of the whole model geometry for the solution. Essential boundary conditions such as symmetry-displacement were applied (Figure 3).

• Compression, which was considered as the loading condition of the problem, was thought to be caused by the patient’s weight while standing up. For an 80 kg weighing patient, approximate load applied to the tibial cross-section was calculated as:

NkgfkgfF 400402

80≈==

( )[ ] 222 400334,41255,12 mmA ≈=−⋅= π

MPammN

AFp 1

400400

2 =≈=

• Fractured bone was assumed to be bonded to the intact bone. This was done by issuing VGLUE command to glue bone and fracture site volumes (Figure 5). Also, the elasticity values of fractured bone were taken much lower than the intact bone’s as it was subjected to plastic deformation (Table 2).

• Friction between the plate/bone and the screw/bone interfaces were omitted. Instead, a 0.1 mm gap was assumed between the plate and the bone, considering that the plate would not be able to cover the whole bone surface under it as the plate/bone interface is not a smooth surface. Also, the screws were assumed to be bonded to the bone and the plate seperately. This was again done by using VGLUE command to glue screw volumes to the bone volume and the plate volume seperately (Figure 5).

• As shell element types were used in case of composite plates, AGLUE was issued to glue screw areas to the coincident plate areas instead of VGLUE command. Composite plate had to be constructed of two areas with the upper one (according to z axis) coincident to the screw heads, and the lower one to the screw shafts (Figure 3).

Figure 4 - The finite element model

Figure 5 - The finite element model / detailed

Element types used in the finite element model were SOLID92 and SHELL99 (Table 1). SOLID92 was used in case of metallic bone plates while SHELL99 was chosen in case of composites. No mid-nodes option was turned on for SOLID92 element meshes in order to reduce the number of nodes to decrease model memory requirement and solution time. The layer stacking sequence for the angle-ply laminate configuration ([±45]8s) of the two layered elements 33296 and 33410, which were defined in the upper and lower plate areas respectively, are given in Figure 18.

Table 1. Element types used in the finite element model Volume Name Element Type

Bone – Intact SOLID92 Bone – Fractured SOLID92

Metal SOLID92 Bone Plate Composite SHELL99 Screws SOLID92

Materials: Tibia was considered for bone properties. Stainless steel and Ti6Al4V were considered for metallic plates, and graphite/epoxy and carbon/HA for composites. Screws were of stainless steel (Table 2). Carbon/HA properties were calculated considering 20% carbon and 80% HA in volume. Screw and metallic plate materials were taken as isotropic, composites, and intact and the fractured bone as orthotropic materials.

Table 2. Materials used in the analyses (Reference 5, 6, 7, 8, 9) Material Ex[MPa] Ey[MPa] Ez[MPa] νxy νyz νxz Gxy[MPa] Gyz[MPa] Gxz[MPa]

Stainless steel 200000 200000 200000 0.3 0.3 0.3 77000 77000 77000 Ti6Al4V 117240 117240 117240 0.3 0.3 0.3 45090 45090 45090 Gr/Epoxy 132400 10800 10800 0.24 0.49 0.24 5600 3600 5600 C/HA 78000 47900 47900 0.27 0.27 0.27 5800 5800 5800 Bone – Intact 18400 7000 8500 0.12 0.37 0.14 3600 2400 5000

Bone – Fractured 1840 700 850 - - - - - -

Analysis The finite element analyses were performed regarding the above assumptions. Composite plate analyses were first performed for four different laminate layups: Unidirectional, crossply, quasi-isotropic, and angle-ply. Among these, angle-ply laminate configuration was found to give the best results. Therefore, the analyses were continued using the angle-ply laminate configuration (Figure 18). Four plate material cases were considered then: Two for metals (stainless steel and Ti6Al4V), and two for composites (graphite/epoxy and carbon/HA). Global Stats for the composite and metal plate models are compared in Table 3 while the Run-Time Stats for the four plate cases are given in Table 4.

Table 3. Comparison of Global Stats for composite and metal plate models COMPOSITE METALKeypoints 132 132Lines 238 242Areas 105 113Volumes 6 7Nodes 8445 8385Elements 31532 33286Element types 3 1Real constant sets 2 0Material property sets 4 4

Table 4. Comparison of Run-Time Stats for all of the cases Plate Material Est. total time [sec]

C/HA 823.92 G/Ep 823.92 Ti6Al4V 733.10 St 682.07

Analysis Results & Discussion Finite element analyses of bone plate-long bone assembly were conducted for above mentioned implant materials. The results were implemented in three important categories: SED, peak stresses, and deformations (Figure 7, 8, 9). The calculated values for the path shown in Figure 6 were compared in graphical plots (Figure 10, 11). The comparison of results showed that in the fracture area the load in the bone is distributed evenly for composite bone plates with proper fiber orientation ([±45]8s) and there are decreases in the local peak stress values (Figure 8). Changing the ply orientation of the composite bone plates could alter deformations positively in the plate (Figure 9). Additionally, Figure 7 and Figure 10 show that SED values of carbon/HA increase in the critical region of the fractured bone where the SED values are low for other cases. Therefore, it is expected that the adverse bone remodelling will slow down. Thus, the bone growth, in other words, fracture healing could be faster with the composite bone plates, and for this study especially with the use of carbon/HA plates.

Figure 6 - Path of calculations in fracture site

Figure 7 - SED distribution in the fracture site

Figure 8 - Peak stresses in plates - Fig8.jpg

Figure 9 - Maximum deformations in plates

Figure 10 - SED values along the path

Figure 11 - Stress values along the path

When the results for the screws were examined, it was seen that the maximum stress values for all plates occur in the proximal screws. When the stress values obtained for these screws were compared, it was found that the stress distributions are smoother for composites while they are more localised for metals (Figure 12, 13). Also, the peak stress chart (Figure 14), and the graphical plots (Figure 15) for the path at the screw axes (Figure 16) showed that the screws in case of composite plates are more advantageous. It’s obvious that stresses for metals are higher, and also the screw necks are much critical in failure.

Figure 12 - Stress values in the proximal screws

Figure 13 - Stress values in the proximal screws

Figure 14 - Peak stresses in screws

Figure 15 - Stress values along the path in screws

Figure 16 - Path of calculations in screw axes

Figure 17 - Typical cortical screws used in bone plate fixation

Figure 18 - Layer stacking sequence of angle-ply composite plates

Conclusion Results of the analyses shows that the bone growth, in other words, fracture healing could be faster with the composite bone plates, and that the screws in case of composite plates are more advantageous as the stresses for metals are higher. Therefore, screw necks are much critical in failure in case of metal plates.

References: 1) M.S. Ali, et al., Carbon Fibre Composite Bone Plates: Development, Evaluation and Early Clinical

Experience, J. Bone & Joint Surg. [Br], 72-B, 586-91, 1990

2) Baixauli, et al., Carbon Fibre Composite Bone Plates for Fixation of Forearm Fractures, J. Bone & Joint Surg. [Br], 77-B (2), 227, 1995

3) S. Blazewicz, et al., Experimental Study of Mechanical Properties of Composite Carbon Screws, Biomaterials, 18, 437-439, 1997

4) M. Zimmerman, and J.R. Parsons, The Design and Analysis of a Laminated Partially Degradable Composite Bone Plate for Fracture Fixation, Journal of Biomedical Material Research, 21(A3), 345-361, 1987

5) H. Yildiz, Composite Hip Prosthesis Design, Ph.D Thesis, Stanford University, 1993

6) E.J. Barbero, On A Generalized Laminate Theory With Application To Bending, Vibration, And Delamination Buckling In Composite Laminates, Ph.D Thesis, Virginia University, 1989

7) J.B. Park, R.S. Lakes, Biomaterials, Plenum Press, 1992, New York

8) S.C. Cowin, Bone Mechanics, CRC Press, 1989, Florida

9) S. Erden, H. Yildiz, An Advanced Structural Design For Bone Plate, ISB 2001, Zurich

10) K. Fujihara, Design of carbon / epoxy braided composite bone plate, National University of Singapore, http://iris14.cadcam.nus.edu.sg/~p81313a/phdwork.html

11) Sushrut Surgicals Pvt Ltd & Adler Mediequip Pvt Ltd, http://www.sushrut.com