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

3. MATERIALS AND METHODS
In order to drive FE models with muscle forces, two models were engaged: an inverse
static (IS) model which allows a determination of individual muscle forces based on a
certain posture [11], and a finite element model which allows a calculation of intradiscal
pressure (IDP) and intervertebral rotation (IVR) under different loads.
The spinal IS model used was developed in the AnyBody Modelling System and is
composed of eight rigid bony structures: the thoracic part, the five lumbar vertebrae, the
sacrum and the ilium. Ball-and-socket joints simulate intervertebral discs. Muscle
fascicles are fixed to anatomical attachment points. In order to provide passive
structures and to reduce the difference to the FE model, detailed ligaments with material
properties from the literature [12] were added, and stiffnesses for intervertebral discs
were included. The model was the validated with measured data taken from the
literature [13].
Similar to the IS model, the FEMSPC incorporated (Fig. 1) consists of the thoracic
spine including rib cage [14], lumbar spine [4, 15] and pelvis [16]. The
osteoligamentous lumbar spine has been previously described and validated in detail [4,
15]. In brief, the vertebral bodies of the lumbar spine consist of an isotropic cortical
shell, a transverse isotropic cancellous core and posterior bony structures. The nuclei
pulposi of the intervertebral discs were modelled as incompressible fluid-filled cavities
while the annuli fibrosi were modelled as fibre-reinforced hyperelastic composites. All
ligaments existing in the lumbar spine were included. The thoracic vertebrae with ribs
and sternum as well as the pelvic region were assumed to be rigid and are used to
provide bony structures for the attachment points of the muscles. The orientation and
height of the FEMSPC were adapted to the IS model.
The attachment points of the 233 muscle fascicles in the FEMSPC were obtained from
the literature [17] and simulated with connector elements in the finite element software
ABAQUS. Muscle forces were calculated in the IS model and transferred to the
connector elements. For the muscle fascicles which do not connect to the exiting bony
structures in the FEMSPC, individual muscle forces were replaced by a group of
resultant forces and moments acting in the centre of the related vertebral body. The
individual muscle forces as well as the resultant forces and moments were calculated in
the IS model for standing and flexion. The IVRs for the FEMSPC caused by the
transferred muscle forces were compared with the corresponding values of the IS model
for verification.
Additionally, simplified loads were applied to the FEMSPC. Upright standing was
simulated by applying a follower load of 500 N [9]. For simulating flexion, a follower
load of 1175 N and a flexion bending moment of 7.5 Nm were chosen [10]. The IDP in
the L4-L5 disc was calculated and compared with the FEMSPC with muscle forces. The
in vivo measured IDP data from Wilke at el. [18] was used for comparison.
2