Quantifying Variability in Lumbar L4-L5 Soft Tissue Properties for Use in Finite-Element Analysis

Abstract

Soft tissue structures of the L4-L5 level of the human lumbar spine are represented in finite-element (FE) models, which are used to evaluate spine biomechanics and implant performance. These models typically use average properties; however, experimental testing reports variation up to 40% in ligament stiffness and even greater variability for annulus fibrosis (AF) properties. Probabilistic approaches enable consideration of the impact of intersubject variability on model outputs. However, there are challenges in directly applying the variability in measured load–displacement response of structures to a finite-element model. Accordingly, the objectives of this study were to perform a comprehensive review of the properties of the L4-L5 structures and to develop a probabilistic representation to characterize variability in the stiffness of spinal ligaments and parameters of a Holzapfel–Gasser–Ogden constitutive material model of the disk. The probabilistic representation was determined based on direct mechanical test data as found in the literature. Monte Carlo simulations were used to determine the uncertainty of the Holzapfel–Gasser–Ogden constitutive model. A single stiffness parameter was defined to characterize each ligament, with the anterior longitudinal ligament (ALL) being the stiffest, while the posterior longitudinal ligament and interspinous ligament (ISL) had the greatest variation. The posterior portion of the annulus fibrosis had the greatest stiffness and greatest variation up to 300% in circumferential loading. The resulting probabilistic representation can be utilized to include intersubject variability in biomechanics evaluations.