Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Abstract

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.