Efficient probabilistic finite element analysis of a lumbar motion segment

Finite element models of the lumbar spine are useful in assessing biomechanics and performance of implants. Models are often developed using the anatomy of an individual subject. Average mechanical property values for the annulus and other soft tissue structures are typically utilized from the literature, as data for the same subject are not available. However, these properties can have significant variability. While probabilistic methods enable the impact of soft tissue property variability on spine mechanics to be assessed, they often require lengthy computation times. Accordingly, the objective of this study was to develop efficient methods to perform Monte Carlo simulations of a finite element model of the L4 L5 functional spinal unit considering variability in the properties of the soft tissue structures. Distributions for the soft tissue properties included the stiffness of spinal ligaments and parameters of a Holzapfel-Gasser-Ogden constitutive material model of the disc. Variance reduction sampling methods, including the Sobol and Descriptive sampling techniques, were assessed for efficiency and accuracy in comparison to traditional random Monte Carlo sampling. Comparisons were based on output torque-rotation curves at the 10th and 90th percentile for flexion, extension, axial rotation, and lateral bending. The Descriptive sampling technique best matched the random sampling technique, at the extremes of rotation, with a 3.6% mean difference. This was achieved with a 10× reduction in the number of iterations and computation time. Improvements in efficiency and maintained accuracy enable intersubject variability to be considered in a variety of biomechanical evaluations, including design-phase screening of orthopedic implants.