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

MATERIAL DISCONTINUITIES CREATE FLUID FLOW
INSTABILITIES IN INTERVERTEBRAL DISC POROELASTIC
FINITE ELEMENT MODELS
1. ABSTRACT
C. Ruiz 1 , J. Noailly 2 and D. Lacroix 2,3
Fluid flow predictions are important in intervertebral disc models to explore the
mechanobiology and biomechanics of the tissue. Poroelastic models are used in this
sense, but the results from applying physiological load rates may present instabilities.
Four IVD models including the annulus fibrosus, the nucleus pulposus, and the
endplates were used with different mesh sizes under physiological extension and axial
rotational loads. Simulations indicated that oscillations were caused by numerical
instability of the pore pressure derivation at material discontinuities. Applying local
refinement only was not enough to eliminate the instabilities. Indeed, mesh refinements
had to be local and material-dependent, and had to be supplemented by the creation of a
material transition zone, including exponentially interpolated material properties
between the nucleus and the annulus.
2. INTRODUCTION
The intervertebral disc (IVD) is a highly organized matrix laid down by relatively few
cells in a specific manner. The central gelatinous nucleus pulposus (NP) is confined by
the anulus fibrosus (AF) laterally and by the cartilage end plates inferiorly and
superiorly. This arrangement shapes the functional behaviour of the disc including a
controlled flexibility that largely provides the spine with a finely tuned mechanical
response in daily activities (Roberts et al., 2006).
The complex behaviour of the intervertebral disc as a multiphasic material can be
explored numerically through poroelastic finite element (FE) analyses. As such, several
poroelastic models of lumbar motion segments (or only IVD) have been published in
the literature, and partially validated against experimental data (Laible et al., 1993 and
Ferguson et al., 2004). These models have shown the link between the fluid flow within
the IVD and the mechanical response of the spinal segments as well as the relevance of
such link in disc degeneration.
Indeed, ageing and degeneration of the IVD have been related with changes in lumican
amount among other aspects. Lumican is small proteoflycan that plays a role in the
assembly and regulation of collagen fibers, and its expression was found to be regulated
1
PhD Student, Biomechanics and Mechanobioly, Institute for Bioengineering of Catalonia, Parc Científic,
C/ Baldiri Reixac, 4, Torre I, 10ª , 08028 Barcelona, Spain
2
Senior Researcher, Biomechanics and Mechanobioly, Institute for Bioengineering of Catalonia, Parc
Científic, C/ Baldiri Reixac, 4, Torre I, 10ª , 08028 Barcelona, Spain
3
Professor, Department of Mechanical Engineering, University of Sheffield, Mappin Street S1 3JD,
Sheffield, UK