Validation of a CT-based Finite Element Model of human vertebral bodies in intact and lesion-affected conditions against experimental data from Digital Image Correlation

Despite about one-third of bone metastases affect vertebrae, compromising bone integrity, the most used clinical score to estimate the risk of instability or fracture of a metastatic spine, i.e. the Spinal Instability Neoplastic Score (SINS), does not consider vertebral biomechanics. This thesis is a part of a project of the Bioengineering and Computing Laboratory of Rizzoli Orthopedic Institute that aims to complement SINS by validated subject-specific finite elements models (SSFEMs) built from routinely collected CT images. The main object of this thesis was the computational part of the validation of SSFEM vertebral strains and displacements against experimental measurements. T8 vertebrae from two donors were tested in intact and lesion conditions; these latter were simulated with dome-shaped, endplate-centred holes of increasing size (d = 6, 10, 15, 20 mm) to represent a progressively worsening lytic lesion. An innovative loading setup applied a homogeneous pressure on the caudal endplate by pressurizing a fluid silicone, while constraining the cranial endplate in a low melting alloy. Superficial displacements and strains of anterolateral aspects in vertical and circumferential directions were measured through Digital Image Correlation (DIC), and caudal endplate deflection through an LVDT. SSFEMs of intact and lesion-affected vertebrae were created by: CT segmentation; cortical thickness and density estimation by the cortical bone mapping (CBM) algorithm, creating cortical and trabecular bone components; 10-node tetrahedral meshing; material properties mapping from CT according to density, and accounting for different transverse isotropy relationships in cortical and trabecular bone; simulations in Ansys, replicating experimental boundary conditions. SSFEMs results were compared to experimental ones after spatial registration of measurement areas. In intact vertebrae, SSFEMs and DIC displacements were correlated both in vertical (R2 ~ 0.90) and circumferential directions (R2 > 0.64), while median [IQR] SSFEMs strain errors with respect to DIC were -13% [-21%, -1%] (indicating a slight overestimation and a narrow scatter) for vertical strains and -10% [-30%, 14%] (larger scatter) for circumferential strains. Overall, SSFEMs validation results were similar or better (in circumferential direction) than those reported in an earlier published study on lumbar vertebrae (doi: 10.1016/j.jmbbm.2023.105706), confirming the reliability of the new experimental setup. In lesion-affected conditions, SSFEMs displacements were correlated not dissimilarly than in intact conditions with DIC measurements, both in longitudinal (R2 = 0.87) and circumferential direction (R2 = 0.83). SSFEMs median [IQR] strain errors were 5% [-23%, 29%] in vertical and 23% [11%, 35%] in circumferential direction, indicating a slight underestimation and a slightly larger scatter with respect to intact conditions. However, the primary finding was that caudal endplate displacements were accurately predicted by SSFEMs (6 mm offset for every lesion dimension, corresponding to a 3% overestimation for the 20mm hole (LVDT = 169mm; SSFEM = 175mm)), proving for the first time an accurate representation of the increased endplate compliance with increasing lesion dimensions. These results, to be confirmed in a larger sample, demonstrate the accuracy of SSFEMs in capturing vertebral biomechanical changes caused by metastatic lesions, representing a first step toward the integration of a quantitative stability assessment into SINS.