The clinical uptake of minimally invasive interventions for intervertebral disc, such as nucleus augmentation, is currently hampered by the lack of robust pre-clinical testing methods that can take into account the large variation in the mechanical behaviour of the tissues. Using computational modelling to develop new interventions could be a way to test scenarios accounting for variation. However, such models need to have been validated for relevant mechanical function, e.g. compressive, torsional or flexional stiffness, and local disc deformations.

The aim of this work was to use a novel in-vitro imaging method to assess the validity of computational models of the disc that employed different degrees of sophistication in the anatomical representation of the nucleus.

Bovine caudal bone-disc-bone entities (N=6) were dissected and tested in uniaxial compression in a custom-made rig. Forty glass markers were placed on the surface of each disc. The specimens were scanned both with MRI and micro-CT before and during loading. Specimen-specific computational models were built from CT images to replicate the compression test. The anatomy of the nucleus was represented in three ways: assuming a standard diameter ratio, assuming a cylindrical shape with its volume matching that measured from MRI, and deriving the shape directly from MRI. The three types of models were calibrated for force-displacement. The radial displacement of the glass markers were then compared with their experimental displacement derived from CT images.

For a similar accuracy in modelling overall force-displacement, the mean error on the surface displacement was 35% for standard ratio nucleus, 38% for image-based cylindrical nucleus, and 32% for MRI-based nucleus geometry.

This work shows that, as long as consistency is kept to develop and calibrate image-based computational models, the complexity of the nucleus geometry does not influence the ability of a model to predict surface displacement in the intervertebral disc.

Purpose: Subject-specific computational models of anatomical components can now be generated from image data and used in the assessment of orthopaedic interventions. Whilst such models are becoming more commonplace, there are few studies that have investigated the effects of element size or the level of morphological detail that is required to model complex hierarchical structures such as trabecular bone [1,2]. The purpose of this study was to investigate the modelling of the mechanical properties of a trabecular-like material under compression, and in particular to evaluate the relationship between the grey-scale dependent density, determined from microCT, and the elastic modulus at different levels of mesh density.

Materials and Methods: A specific open cell rigid foam (pcf 7.5, Sawbone, Sweden), with a porosity over 95% and cell size between 1.5 and 2.5 mm, was chosen to represent human cancellous bone. Five cylindrical specimens (24 mm diameter, 19 mm height) were compressed under a maximum displacement of 0.35 mm in a materials testing machine. All the specimens were imaged by microCT (ƒÝCT80, Scanco Medical, Switzerland) before the test to provide the geometry and greyscale distribution. Corresponding finite element models of each specimen were generated using proprietary software (ScanFE, Simpleware, UK) with an element size of 1.5 mm. The elastic modulus of each element was based on the image greyscale using a conversion factor that was determined, through trial-and-error, by matching the predicted displacement with the experimental measurement in the linear region (> 0.2 mm). For each specimen, models of higher and lower mesh densities were constructed by down-sampling the microCT output to different levels. The smallest element size was limited to 0.5 mm due to computational restrictions, however a smaller 8 mm cube of the material was also analysed, with element sizes down to 0.25 mm.

Results: From the experimental tests, the mean apparent elastic modulus of the specimens was found to be 15 MPa, as compared with 18 MPa specified by the manufacturer. For the computational models, the predicted elastic modulus of the whole specimen models was found to decrease with decreasing element size. In particular, there was a large drop in the predicted values when the element size was of the same order as the cell size. With larger elements, the results indicated some convergence and there was reasonable agreement with the experimental results. For the cube model with smaller element sizes, the predicted moduli values again appeared to converge as the element size was reduced to 0.25 mm.

Conclusion: The results of this study show that the optimum conversion factor from an image greyscale value to an elastic modulus varies with element size. If the finite element method is to be used effectively to model bone, then the mesh size must either be sufficiently large to use a continuum approach or sufficiently small to capture the behaviour of the individual trabeculae. Different conversion factors will be required to determine the material properties from the image greyscale in each case.