Synchrotron Tomography-Based Inversion Pipeline for Estimating Elastic Properties of Rat Vertebral Endplate Finite Element Models

Abstract

Lower back pain is linked to vertebral biomechanics, with vertebral endplates (VEPs) playing a key role. Finite element modelling (FEM) is a powerful tool for studying VEP biomechanics but relies on accurate material property inputs, which remain difficult to obtain. Synchrotron computed tomography (sCT) allows for detailed visualisation of the microstructure of intact VEPs under near-physiological loads and, when coupled with digital volume correlation (DVC), can be used to quantify three-dimensional (3D) strain fields, providing experimental reference data for FEM validation. We developed an inversion pipeline to spatially couple DVC data with an image-based FE model, and thus to estimate the elastic properties of rat VEPs. On the first rat lumbar FEM, the pipeline estimated a VEP elastic modulus of 129 MPa and a Poissons ratio of 0.24. Welchs ANOVA revealed statistically significant differences between FEM and DVC strain distributions (p < 0.001) but with small effect sizes ({superscript 2} = 0.1%-0.6%), indicating high practical similarity. Its efficacy was further validated using Bland-Altman analysis, demonstrating over 95% spatial agreement between the FEM-predicted strains and the DVC measurements across multiple loading steps. The pipelines consistency was further evaluated across multiple rat lumbar FE models (n = 3), yielding an estimated VEP elastic modulus = 145 {+/-} 18 MPa and a Poissons ratio = 0.28 {+/-} 0.04. Statistically significant regional variations of strain distribution in VEPs were also identified (p < 0.05 to p < 0.001, {superscript 2} up to 41.8%). This study highlighted the efficacy of the developed pipeline in estimating the isotropic elastic modulus and Poissons ratio of VEP FEMs in a physiologically relevant, complex load transfer system. Our pipeline may be used in estimating properties of VEP in larger animals and humans.