How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis

Abstract

The annulus fibrosus has substantial variations in its geometrical properties (among individuals and between levels), and plays an important role in the biomechanics of the spine. Few works have studied the influence of the geometrical properties including annulus area, anterior / posterior disc height, and over the range of motion, but in general these properties have not been reported in the finite element models. This paper presents a probabilistic finite element analyses (Abaqus 6.14.2) intended to assess the effects of the average disc height ( h p) and the area ( A) of the annulus fibrosus on the biomechanics of the lumbar spine. The annulus model was loaded under flexion, extension, lateral bending, and axial rotation and analyzed for different combinations of h p and A in order to obtain their effects over the range of motion. A set of 50 combinations of h p (mean = 18.1 mm, SD = 3.5 mm) and A (mean = 49.8%, SD = 4.6%) were determined randomly according to a normal distribution. A Yeoh energy function was used for the matrix and an exponential function for the fibers. The range of motion was more sensitive to h p than to A. With regard to the range of motion the segment was more sensitive in the following order: flexion, axial rotation, extension, and lateral bending. An increase of the h p produces an increase of the range of motion, but this decreases when A increases. Comparing the range of motion with the experimental data, on average, 56.0% and 73.0% of the total of data were within the experimental range for the L4–L5 and L5–S1 segments, respectively. Further, an analytic equation was derived to obtain the range of motion as a function of the h p and A. This equation can be used to calibrate a finite element model of the spine segment, and also to understand the influence of each geometrical parameter on the range of motion.