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

incorporation of the osmotic pressure at the nucleus also improved the FV results by
eliminating the oscillation in the posterior part of the disc, but the oscillation remained
in the anterior part (Fig. 6b).
a) b)
Fig. 6: FV behavior, a) after 1h of load relaxation, and b) incorporating of the osmotic
pressure at the nucleus
5. DISCUSSION
Simulations showed that material discontinuities in the nonlinear IVD model were
responsible for most of the numerical instabilities related to poroelasticity, i.e. FV
oscillations. This was confirmed through calculations by using one continuous material.
Poromechanical instabilities were not detectable by assessing mesh convergence with
simple elasticity-related computations.
Comparing fluid velocity instabilities with the spatial variations of the different terms of
Darcy’s Equation and of the pore pressure revealed that the spatial derivative pore
pressure was mostly responsible for these instabilities (Fig. 4). Such outcome was in
agreement with the result obtained by Stokes et al. (2010). Nonetheless, they also
predicted oscillations of the pore pressure at order zero which was not an issue in our
calculations.
Stoke et al (2010) showed that pore pressure numerical oscillations could be removed
by applying a mesh refinement based on the Vermeer and Verruijt criterion (Eq. 2)
within a one-material model. Our study showed that this criterion alone is inefficient to
cope with the FV oscillations at material discontinuities. The creation of a radial
material transition area at the AF-NP boundary with local mesh refinements and
material interpolation forms adapted to tissue consolidation led to significant
improvements, i.e. oscillations were reduced by 47% (Fig. 2b), and best results were
obtained with exponential interpolations.
Load relaxation results suggested that fluid velocities decreased below a materialdependent
critical value where calculations were not affected anymore by numerical
instabilities (Fig. 4a). The values obtained with the incorporation of the osmotic
pressure suggested that simulating swelling effects selectively attenuates the oscillation
of pore pressure gradient in the compressed areas of the disc (Fig. 4b).
6. CONCLUSION
The study performed showed that material discontinuities create oscillations in IVD
poroelastic models when physiological loads rates are applied. The creation of an AF-
NP transition zone, with a gradient of material properties and local mesh refinements,