ABSTRACT
Introduction: Numerical modeling of the intervertebral disc (IVD) is challenging due to its complex and heterogeneous structure, requiring careful selection of constitutive models and material properties. A critical aspect of such modeling is the representation of annulus fibers, which significantly impact IVD biomechanics. This study presents a comparative analysis of different methods for fiber reinforcement in the annulus fibrosus of a finite element (FE) model of the human IVD. Methods: We utilized a reconstructed L4-L5 IVD geometry to compare three fiber modeling approaches: the anisotropic Holzapfel-Gasser-Ogden (HGO) model (HGO fiber model) and two sets of structural rebar elements with linear-elastic (linear rebar model) and hyperelastic (nonlinear rebar model) material definitions, respectively. Prior to calibration, we conducted a sensitivity analysis to identify the most important model parameters to be calibrated and improve the efficiency of the calibration. Calibration was performed using a genetic algorithm and in vitro range of motion (RoM) data from a published study with eight specimens tested under four loading scenarios. For validation, intradiscal pressure (IDP) measurements from the same study were used, along with additional RoM data from a separate publication involving five specimens subjected to four different loading conditions. Results: The sensitivity analysis revealed that most parameters, except for the Poisson ratio of the annulus fibers and C01 from the nucleus, significantly affected the RoM and IDP outcomes. Upon calibration, the HGO fiber model demonstrated the highest accuracy (R2 = 0.95), followed by the linear (R2 = 0.89) and nonlinear rebar models (R2 = 0.87). During the validation phase, the HGO fiber model maintained its high accuracy (RoM R2 = 0.85; IDP R2 = 0.87), while the linear and nonlinear rebar models had lower validation scores (RoM R2 = 0.71 and 0.69; IDP R2 = 0.86 and 0.8, respectively). Discussion: The results of the study demonstrate a successful calibration process that established good agreement with experimental data. Based on our findings, the HGO fiber model appears to be a more suitable option for accurate IVD FE modeling considering its higher fidelity in simulation results and computational efficiency.
ABSTRACT
The two aims of this study were to generate data for a more accurate calibration of finite element models including the L5-S1 segment, and to find mechanical differences between the L4-L5 and L5-S1 segments. Then, the range of motion (ROM) and facet forces for the L4-S1 segment were measured using the stepwise reduction method. This consists of sequentially testing and reducing each segment in nine stages by cutting the ligaments, facet capsules, and removing the nucleus. Five L4-S1 human segments (median: 65 years, range: 53-84 years, SD=11.0 years) were loaded under a maximum pure moment of 8Nm. The ROM was measured using stereo-photogrammetry via tracking of three markers and the facet contact forces (CF) were measured using a Tekscan system. The ROM for the L4-L5 segment and all stages showed good agreement with published data. The major differences in ROM between the L4-L5 and L5-S1 segments were found for lateral bending and all stages, for which the L4-L5 ROM was about 1.5-3 times higher than that of the L5-S1 segment, consistent with L5-S1 facet CF about 1.3 to 4 times higher than those measured for the L4-L5 segment. For the other movements and few stages, the L4-L5 ROM was significantly lower that of the L5-S1 segment. ROM and CF provide important baseline data for more accurate calibration of FE models and to understand the role that their structures play in lower lumbar spine mechanics.
