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

AN ALGORITHM FOR MODELING THE FIBRE DISTRIBUTION OF
THE ANNULUS FIBROSUS WITHIN ARBITRARILY-ALIGNED
MESHES
1. ABSTRACT
G. Marini 1 , I. Koh 1 , H. Studer 2 and S. J. Ferguson 1
The continuous evolution of numerical techniques in computational biomechanics has
driven the field ever closer to patient-specific models for both research and clinical
applications. The study of spine-related pathologies is particularly relevant. Although
algorithms exist for the semi-automatic extraction and reconstruction of vertebral
models from medical images, the description of the intervertebral disc, with its
anisotropic multilayer structure, remains a challenge. We have developed an algorithm
for the automatic inclusion of fibre reinforcement, given only the external and internal
geometry of the annulus. A continuum description of fibre reinforcement has been
developed. To support automatic meshing algorithms, which employ irregular
tetrahedral elements, the algorithm was refined to describe an anatomical fibre
alignment within arbitrarily-aligned tetrahedral elements. We investigated and
compared the results provided by a semi-elliptical disc model meshed with either brick
or tetrahedral elements. A nonlinear hyperelastic formulation has been used for the
material model of the nucleus pulposus and annulus fibrosus. A pre-stress technique has
been applied to simulate swelling pressure in the initial state. Loading cases included
axial compression, flexion, axial and lateral torque. The simulations showed that
collagen fibre reinforcement of a tetrahedral mesh with irregularly sized and aligned
elements can be achieved with an automated algorithm. This allows the automated
generation of patient-specific models of the intervertebral disc. Depending on mesh
size, element type and integration scheme, the method provides a similar response to a
model with a regular hexahedral mesh, for the investigated loads, with a maximum error
of approximately 3% for an equivalent mesh seed. However, the convergence of the
tetrahedral model towards the hexahedral reference highlights the importance of
appropriate mesh refinement.
2. INTRODUCTION
The efforts to analyse the mechanics of the spine segment through computational
methods have been growing exponentially in the past decade. New numerical
techniques and theories within the domain of Finite Elements (FE) methods have been
developed to better estimate stresses and strains experienced by the human spinal
segments through daily activities [1, 2, 3, 4, 5]. However, studies of the mechanics of
spinal segments still demonstrate ambiguities due to the high efforts involved in
creating adequate patient specific FE models. Although algorithms exist to semiautomatically
[6, 7, 8, 9, 10, 11], and automatically [12] segment medical images to
create FE models of vertebrae, the description of the intervertebral discs remain as a
1 Institute for Biomechanics, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, CH
2 Institute for Surgical Techn. and Biomech., University of Bern, Stauffacherstrasse 78, 3014 Bern,CH