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

were modeled with identical geometry of the one used in the experimental validation
tests and the steel was modeled as a linear elastic isotropic material (Young
modulus=97.5GPa, Poisson ratio=0.3).
Simulations were run using the commercial code ABAQUS/Standard 6.10 (Dassault
Systèmes Ri. Simulia, USA) by imposing a vertical load of 2000 N to the S1 model
(results at a more physiological load of 500N were also extrapolated) while S2 model
was loaded as S1 with additional simulations imposing a 10Nm moment in flexion,
extension and torsion. For each simulation, the location of the most critical points in the
rods subjected to traction and the value of Von Mises stresses VM in those points have
been extrapolated.
3.2 Experimental validation
In order to validate the numerical predictions for the two models above described, two
experimental setups have been built according to ISO and ASTM standards (Figure 1).
On each of the two bars of the spinal fixators, one uniaxial linear strain gage (KGF–02-
120-C1-11; Kyowa Electronic Instruments Co. Ltd, Tokyo, Japan) was glued with its
long axis aligned with the longitudinal axis of the rod. In order to compensate
temperature effects, each strain gage was connected in a half-bridge Wheatstone
configuration to an identical transducer mounted on a dummy specimen. The bridge was
alimented and conditioned trough a HBM Spider 8 amplifier system.
The constructs were then mounted on a servohydraulic MTS 858 (MTS Systems,
Minneapolis, MN, USA) testing machine equipped with a 15 kN load cell and subjected
to six cycles under compression of loading and unloading between 30 and 300 N for the
ASTM configuration and between 600 and 2000 N for the ISO configuration. Signals
from the strain gages were registered and stored at a frequency of 20Hz; mean value and
standard deviation of the maximum strain measured during the tests were calculated.
Such values were then compared to those calculated in the FE models in an area
corresponding to the one where the strain gage was glued.
3.3 FE model of the instrumented lumbar spine
The FE model of the spinal fixator was then virtually mounted in a previously validated
model of L2-L4 lumbar spine [1] comprehensive of bony structures, discs and
ligaments.
The screws of the fixator were virtually inserted through the pedicles of the vertebras: in
order to allow for a correct positioning, both the angle between the two screws and the
orientation of the rods with respect to the vertical axis have been slightly modified with
respect to the configuration prescribed by the standards.
The link between the screws and the bone was described using the embedding elements
method: only the threaded part of each screw was embedded in a portion of bony
structures of the vertebras which acted as a host volume.
Three different models were built: (i) M1 model, a complete model of the L2-L4 lumbar
segment fixed with screws and rods; (ii) M2 model, a model of L2-L4 segment in which
vertebrectomy of L3 was performed, fixed with screws and rods, (iii) M3 model, the
same M2 model with a spring of 7280 N/mm stiffness interposed between L2 and L4,
simulating an anterior Titanium cage, usually clinically used to obtain fusion when
vertebrectomy is performed. All the models are reported in Figure 2.