ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

pre-load within the plate (compression screws are inserted off-centre in plate holes
which forces the bone towards the fracture gap). Preloads have been included in
previous numerical studies, often represented using concentrated loads or applied
displacements [2, 3], however, the effect produced by them is not always realistic; for
example, an applied displacement to the bottom of a screw does not induce loads akin to
screw fastening as the bottom threads will carry most load. This study attempts to model
the mechanical environment in dynamic compression plate fixation in a more realistic
manner. The results are compared with those for a locking plate. Of particular interest is
the local strain environment around screw holes, the mechanical stimulus produced at
the fracture gap and the load sharing between plate and bone.
3. METHODS
Two reference tibial cross-sections with a cross-sectional areas 319 mm 2 and 265 mm 2
with an average unicortical thickness of 5.1 mm and 3.64 mm [4] were considered for
healthy and osteoporotic bone. These tibial cross-sections were extruded longitudinally
for three dimensional FE modelling. We considered a single fracture of the tibial
midshaft and assumed symmetry on either side of the fracture. The plate was fully
restrained of at the plane of symmetry.
For both compression plating and locked plating, models were developed to represent a
fracture gap scenario and a fully reduced fracture. Both plating systems and fracture gap
scenarios were modelled for healthy and osteoporotic bone using appropriate crosssectional
geometry and material properties.
The bone-plate construct was assumed to be symmetric about the fracture gap. As
locking plates are generally used with an offset between the plate and the bone, we
assumed no interaction between these two components in the locking plate models. The
intention of these boundary conditions was to highlight the differences caused by the
various plating systems without influence from further constraints such as muscles.
As the study examined the tibial diaphysis, only the cortical bone was included in the
models. Callus was not included in any of the models. The implant dimensions were
based on typical industry standard: locking plates with a cross-section 3.6x12 mm; hole
spacing of 20 mm; and locking screws with an external diameter of 4.5 mm and a core
diameter of 3.84 mm. Threads, with a spacing of 1.4 mm, were modelled as idealised
rings rather than helical, an approach also used by Karunratanakul et al. [5]. This
assumption eased meshing and was thought to be unlikely to affect the results. For
simplification only the threads in contact with the bone were modelled.
Screws were placed in the second and fourth holes from the fracture gap. The models
used approximately 220,000 linear tetrahedral elements with refinement around screw
holes. In the region around screw holes the average element edge length was 0.3mm. A
mesh convergence study was performed and the results showed that doubling mesh
density around screw holes resulted in change of displacement by less than 0.1%.
Similarly, the variation of maximum compressive strain was less than 5% at matching
locations around the screw hole. The analysis was conducted using Abaqus 6.10
(Simulia, Providence, RI, USA).
The material properties of bone were linear, orthotropic and heterogeneous (through the