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

The aim of the present study was twofold. Firstly, to develop a parameterized FE model of the
human IVD that can be used to simulate the influence of different IVD geometries on the
mechanical response of the discs. Secondly, to use this model to identify a window of
mechanical properties that candidate implant materials would have to fit into to, to regenerate
a range of motion after implantation comparable to the in-vivo conditions for healthy discs.
3. MATERIALS AND METHODS
A pair of L4-L5 vertebrae from a bone bank was used to define generic disc shapes; this level
in the spine is prone to suffer from DDD. The vertebrae were modeled as rigid structures and
the facet joints were simplified by two parallel plain surfaces that represent the cartilage
layers. The shape of the disc in the disc plane was defined by eight landmarks that were
interpolated by spline curves which allowed for a parameterization of the disc shape. The
lordotic angle, disc height, endplate shape and disc bulge were also parameterized. The ratio
of nucleus area vs. disc area (0.43) was defined according to literature [2]. The model was
symmetric about the sagittal plane. The gap between the plane cartilage surfaces (0.5 mm),
which represent the facet joints, was defined according to Zander et al. [3]. A
parameterization of the disc mesh was coded in Python (Release 2.5.4) and implemented in
ABAQUS vers. 6.11. The annulus was meshed with 8-node hybrid elements (C3D8H) but the
nucleus was meshed with fluid elements (F3D4) to build a fluid cavity. The implementation
of an-isotropic annulus fiber orientation was taken from the literature [4] and is alternating in
each annulus layer. Ligaments were modeled with connector elements. The influence of
individual muscle forces was ignored. All loads were applied through a reference point in the
superior vertebra. The model was supported at the inferior disc level. FE mesh convergence
was investigated by monitoring a selected range of motion parameters. The FE model results
were found to be only weakly mesh dependent. The resulting FE model is illustrated in fig. 1.
Fig.1. Left: A Parameterized FE model of a L4-L5 intervertebral disc. Right: The nine
different vertebrae geometries investigated in this study. The vertebra body size was varied
from -1.5 to +1.5 standard deviations (SD) from the average geometry reported by Panjabi et
al. [5]. The disc height and lordotic angle were varied from -1.0 to +1.5 standard deviations
from the average of the values reported by Abuzayed et al. [6].
The annulus matrix was assumed to follow a Neo-Hookean material behavior in accordance
with the study of Rohlmann et al. [7], with: C10 = 0.3448 and D1 = 0.3. The fiber
reinforcement was defined in accordance with the study of Markert et al. [8], with the
coefficient μ = 0.1073 and = 25.8129 taken from the study of Studer et al. [9]. The material
behavior was implemented as a user subroutine (UMAT) in ABAQUS. The material
properties of the cartilage (E = 10 MPa, Poisson ratio = 0.4) were defined in accordance with