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

CONSTITUTIVE MODELLING OF THE ANNULUS FIBROSUS:
NUMERICAL IMPLEMENTATION AND NUMERICAL ANALYSIS
1. ABSTRACT
C. Lopes 1 , J.L. Alves 2
The biomechanics of the intervertebral discs is of an enormous complexity, on a large
extent due to the huge anatomical complexity of the annulus fibrosus (AF). The present
work aims to contribute to the development of a new constitutive modeling of the AF,
by taking into account the circumferential evolution of fibers’ angles, from AF ventral
to dorsal regions, and the evolutionary mechanical properties of the AF fibers, both
circumferentially and radially. The FE implementation and numerical simulations are
being carried out on a home-developed FE solver. The preliminary results of a
compressive load of the IVD seem to be in a very good agreement with the publish
ones, both in terms of compressive force and intradiscal pressure.
2. INTRODUCTION
The spine in general and the intervertebral discs (IVDs) in particular have an essential
role in Human mobility. The two most relevant tissues of a IVD are the nucleus
pulposus (NP), a very soft gel-like structure, and the AF, with a much stiffer lamellar
structure (Fig. 1). A closer observation reveals that AF lamellae consist of a fibrous
structure running helically around the NP. Karajan (2009) observed that when the
outermost lamella of the AF is dissected, the next lamella appears to have an opposite
fibers alignment (Fig. 1b). This alternation takes place until the NP is reached, yielding
a total of 15 to 25 distinct layers (Fig. 1a). Both Marchand and Ahmed (1990) and
Holzapfel et al. (2005) described that the fiber angle inside each lamellae varies
significantly from ventral to dorsal regions.
a) b)
Figure 1 Structural organization of
the IVD: (a) N is the nucleus and A
is the annulus fibrosus with a
lamellar structure; (b) Alternate
orientation of the connective tissue
of the annulus fibrosus (font
Kapandji, 2000, pp. 31).
The in-vivo study of the biomechanics of the IVDs is of a huge complexity, with a high
degree of uncertainty due to the intricate internal connections and electro-chemical
dependencies, complex loadings, geometry and anatomy, as well deep location in an
area of difficult access. Urban & Roberts (2003) referred that, despite the
aforementioned difficulties, most of the scientific information obtained about the IVD is
still obtained from studies with Humans. Example of this are the works of Marchand
and Ahmed (1990) and Holzapfel et al. (2005), which characterized the anatomic
constitution and the mechanical behavior of the two major tissues of the IVD, i.e., the
AF and the NP, and the work of Sato et al. (1999) which studied the in-vivo intradiscal
pressure. Finally, one should emphasize the important role of the IVDs in terms of both
1 PhD Student, CT2M – Center of Mechanical and Materials Technologies, Minho University, Azurém
Campus, 4800-058 Guimarães, Portugal (claracavalcanti@dem.uminho.pt)
2 Assistant Professor, CT2M – Center of Mechanical and Materials Technologies, Minho University.