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

y exposure to interstitial fluid shear (Wang et al, 2010). Poroelastic simulations would
allow the further exploration of such complex mechanobiological processes, as well as
they are already used to assess the mechanically coupled nutrition of IVD cells
(Malandrino et al, 2011).
However, Stokes et al. (2010) reported recently that tissue poroelastic models may
become instable when physiological rapid loading are simulated. Such an issue would
largely hinder the mechanobiological explorations of the IVD in silico. Thus, this study
aims to evaluate whether the numerical convergence of an IVD poroelastic model is
reached under physiological load rates, and to find optimal mesh conditions for proper
convergence. Moreover, it was hypothesized that material property discontinuities
would be a preferential site for poromechanical instabilities.
3. MATERIALS AND METHODS
An anatomical IVD model including the annulus fibrosus, the nucleus pulposus, and the
endplates was used with four different mesh sizes: ∆h= 3.04 mm (Model 1), ∆h= 2.76
mm (model 2), ∆h= 1.72 mm (model 3), and ∆h= 0.83 mm (Model 4). The collagen
fibers in the annulus were not modeled in order to minimize the computational cost.
Material properties were taken from the literature (Table 1), and a strain-dependent
permeability was implemented (Eq. 1) (Argoubi and Shirazi-Adl, 1996):
(Eq. 1)
Physiological extension and axial rotation motions were simulated as pure rotations
corresponding to the intersegmental motions generated by 7.5 Nm moments in a lumbar
spine model for which range of motion predictions were validated (Noailly et al, 2007).
Loads were applied in 1s. External pore pressure was nil. Strain energy density (SED)
and fluid velocity (FV) were calculated along (1) mid-sagittal plane (Fig. 1), (2) disc
circumference, and (3) posterior and (4) anterior disc height node paths. SED results
were used to assess general model convergence, but the presence of possible numerical
instabilities related to the poromechanical predictions was explored, and different
strategies were tested to stabilize the predictions:
(a) Local mesh refinements based on Vermeer and Verruijt criterion, that relates the
mesh size (∆h) with the load application time (∆t) through the material Young’s
modulus, E, and permeability, K to avoid numerical pore pressure oscillations (Stokes et
al, 2010):
(Eq. 2)
(b) Material property transition area at the boundary AF-NP, using different types of
interpolations for the parameter values and applying local refinements to the AF area on
one hand, and to NP area on the other hand.
Since the application of these strategies will require many simulation runs, the
implementation will be done on one model or another depending on the computational
cost. Thereafter, modifications to achieve final mesh convergence were undertaken
when necessary.
The numerical stability of the poromechanical results was additionally explored along a
stress relaxation period of 1h, with and without swelling. Swelling application consisted
in a previous step of free swelling due to a NP osmotic pressure of 0.15 MPa until pore
pressure was stabilized in the IVD center.