AUTHOR=Gruber Gabriel , Nicolini Luis Fernando , Ribeiro Marx , Lerchl Tanja , Wilke Hans-Joachim , Jaramillo Héctor Enrique , Senner Veit , Kirschke Jan S. , Nispel Kati 

TITLE=Comparative FEM study on intervertebral disc modeling: Holzapfel-Gasser-Ogden vs. structural rebars

JOURNAL=Frontiers in Bioengineering and Biotechnology

VOLUME=12

YEAR=2024

URL=https://www.frontiersin.org/journals/bioengineering-and-biotechnology/articles/10.3389/fbioe.2024.1391957

DOI=10.3389/fbioe.2024.1391957

ISSN=2296-4185

ABSTRACT=<p><bold>Introduction:</bold> 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.</p><p><bold>Methods:</bold> 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 <italic>in vitro</italic> 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.</p><p><bold>Results:</bold> The sensitivity analysis revealed that most parameters, except for the Poisson ratio of the annulus fibers and C<sub>01</sub> from the nucleus, significantly affected the RoM and IDP outcomes. Upon calibration, the HGO fiber model demonstrated the highest accuracy (R<sup>2</sup> = 0.95), followed by the linear (R<sup>2</sup> = 0.89) and nonlinear rebar models (R<sup>2</sup> = 0.87). During the validation phase, the HGO fiber model maintained its high accuracy (RoM R<sup>2</sup> = 0.85; IDP R<sup>2</sup> = 0.87), while the linear and nonlinear rebar models had lower validation scores (RoM R<sup>2</sup> = 0.71 and 0.69; IDP R<sup>2</sup> = 0.86 and 0.8, respectively).</p><p><bold>Discussion:</bold> 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.</p>