Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis

PURPOSE

A probabilistic finite element (FE) analysis of the L4-L5 and L5-S1 human annulus fibrosus (AF) was conducted to obtain a better understanding of the biomechanics of the AF and to quantify its influence on the range of motion (ROM) of the L4-L5 and L5-S1 segments.

METHODS

The FE models were composed of the AF and the upper and lower endplates. The AF was represented as a continuous material composed of a hyperelastic isotropic Yeoh matrix reinforced with two families of fibers described with an exponential energy function. The caudal endplate was fully restricted and 8 Nm pure moment was applied to the cranial endplate in flexion, extension, lateral flexion and axial rotation. The mechanical constants were determined randomly based on a normal distribution and average values reported.

RESULTS

Results of the 576 models show that the ROM was more sensitive to the initial stiffness of the fibers rather than to the stiffening coefficient represented in the exponential function. The ROM was more sensitive to the input variables in extension, flexion, axial rotation and lateral bending. The analysis showed an increased probability for the L5-S1 ROM to be higher in flexion, extension and axial rotation, and smaller in lateral flexion, with respect to the L4-L5 ROM.

CONCLUSIONS

An equation was proposed to obtain the ROM as a function of the elastic constants of the fibers and it may be used to facilitate the calibration process of the human spine segments and to understand the influence of each elastic constant on the ROM.

A finite element model of the L4-L5-S1 human spine segment including the heterogeneity and anisotropy of the discs

With the aim to study disc degeneration and the risk of injury during occupational activities, a new finite element (FE) model of the L4-L5-S1 segment of the human spine was developed based on the anthropometry of a typical Colombian worker. Beginning with medical images, the programs CATIA and SOLIDWORKS were used to generate and assemble the vertebrae and create the soft structures of the segment. The software ABAQUS was used to run the analyses, which included a detailed model calibration using the experimental step-wise reduction data for the L4-L5 component, while the L5-S1 segment was calibrated in the intact condition. The range of motion curves, the intradiscal pressure and the lateral bulging under pure moments were considered for the calibration. As opposed to other FE models that include the L5-S1 disc, the model developed in this study considered the regional variations and anisotropy of the annulus as well as a realistic description of the nucleus geometry, which allowed an improved representation of experimental data during the validation process. Hence, the model can be used to analyze the stress and strain distributions in the L4-L5 and L5-S1 discs of workers performing activities such as lifting and carrying tasks.