Poro-elastic Finite Element Model for Prediction of Progressive Failure of Lumbar Discs

ADINA is widely used in biomedical applications not only for its versatile multiphysics capabilities but also for the reliability and efficiency of its solution techniques.

In this News we present the finite element model of a lumbar disc subjected to cyclic loading. The aim is to study the progressive failure of the disc due to heavy loading cycles. Results of such studies can help prevent back injuries resulting from repetitive loading.

An intervertebral disc (shown in the blue color in the above animation), like many other biological materials, is a porous material consisting of a solid and a fluid phase. As such, to obtain a physiologically accurate model, one needs to take into account the changes in the water content within the disc and associated changes in the poro-elastic properties during loading cycles. To account for the coupling between the pore pressure and the deformation of the solid phase of the disc, the poro-elastic model in ADINA is used. To account for changes in the permeability of the disc during the loading cycles the model is further customized by using a "user supplied material model". The swelling caused by electro-chemical processes inside the disc is also taken into account using a "user supplied load" subroutine (see Ref.).

The finite element model of the disc and the surroundings are depicted in Figure 1.

Figure 1 Finite element model of the disc and its surroundings

To understand the initiation and progression of the disc failure, the aforementioned nonlinear finite element model was subjected to several cycles of the loading shown in Figure 2. The loading mimics the effect of a person’s weight and physical activities. Failure of the disc is modeled by reducing the elastic constants at those integration points in which the stress exceeds an assumed failure stress.

Figure 3 shows the effective stress plots in the disc for different load cycles.

Figure 2 Different components of load as a function of time (one cycle shown)

Figure 3 Effective stress contours in the disc in load cycles at
maximum load (a) 2^nd load cycle (b) 15^th load cycle

Figure 4 shows the volumetric percentage of the failed regions of the disc as a function of load cycles for different reduction factors of elastic modulus of the failed regions.

Figure 4 Volumetric percentage of the failed regions of the disc as a function of load cycles

In addition to the biomedical applications, the porous media formulation in ADINA can also be used in geotechnical engineering for modeling soil consolidation and in the oil and gas industry for modeling the deformations and stresses caused by drawdowns in oil fields.

Reference

• R.N. Natarajan, J.R. Williams, S.A. Lavender, and G.B.J. Andersson, "Poro-elastic finite element model to predict the failure progression in a lumbar disc due to cyclic loading", Computers & Structures, 85:1142-1151, 2007.

Keywords:
Poro-elastic, stress-diffusion coupling, multiphysics, cyclic load, lumbar disc, biomechanics, spine, user subroutine, soil consolidation

Courtesy of R.N. Natarajan, Department of Orthopedic Surgery, Rush University Medical Center