Aims

The “2 to 10% strain rule” for fracture healing has been widely interpreted to mean that interfragmentary strain greater than 10% predisposes a fracture to nonunion. This interpretation focuses on the gap-closing strain (axial micromotion divided by gap size), ignoring the region around the gap where osteogenesis typically initiates. The aim of this study was to measure gap-closing and 3D interfragmentary strains in plated ovine osteotomies and associate local strain conditions with callus mineralization.

This work was motivated by the need to capture the spectrum of anatomical shape variability rather than relying on analyses of single bones. A novel tool was developed that combines image-based modelling with statistical shape analysis to automatically generate new femur geometries and measure anatomical parameters to capture the variability across the population. To demonstrate the feasibility of the approach, the study used data from 62 Caucasian subjects (31 female and 31 male) aged between 43 and 106 years, with CT voxel size ranging 0.488 × 0.488 × 1.5 mm to 0.7422 × 0.7422 × 0.97 mm. The scans were divided into female and male subgroups and high-quality subject-specific tetrahedral finite element (FE) meshes resulting from segmented femurs formed the so-called training samples. A source mesh of a segmented femur (25580 nodes, 51156 triangles) from the Visible Human dataset [Spitzer, 1996] was used for elastic surface registration of each considered target male and female subjects, followed by applying a mesh morphing strategy. To represent the variations in bone morphology across the population, gender-based Statistical Shape Models (SSM) were developed, using Principal Component Analysis. These were then sampled using the principal components required to capture 95% of the variance in each training dataset to generate 1000 new anatomical shapes [Bryan, 2010; Blanc, 2012] and to automatically measure key anatomical parameters known to critically influence the biomechanics after hip replacement (Figure 1). Analysis of the female and male training datasets revealed the following data for the five considered anatomical parameters: anteversion angle (12.6 ± 6.4° vs. 6.2 ± 7.5°), CCD angle (124.8 ± 4.7° vs. 126.3 ± 4.6°), femoral neck length (48.7 ± 3.8 mm vs. 52 ± 5 mm), femoral head radius (21.5 ± 1.3 mm vs. 24.9 ± 1.5 mm) and femur length (431.0 ± 17.6 mm vs. 474.5 ± 26.3 mm). However, using the SSM generated pool of 1000 femurs, the following data were computed for females against males: anteversion angle (10.5 ± 14.3° vs. 7.6 ± 7.2°), CCD angle (123.9 ± 5.8° vs. 126.7 ± 4°), femoral neck length (46.7 ± 7.7 mm vs. 51.5 ± 4.4 mm), femoral head radius (21.4 ± 1.2 mm vs. 24.9 ± 1.4 mm) and femur length (430.2 ± 16.1 mm vs. 473.9 ± 25.9 mm). The highest variability was found in the anteversion of the females where the standard deviation in the SSM-based sample was increased to 14.3° from 6.4° in the original training dataset (Figures 2 & 3). The mean values for both females (10.5°) and males (7.6 °) were found close to the values of 10° and 7° reported in [Mishra, 2009] in 31 females and 112 males with a [2°, 25°] and [2°, 35°] range, respectively. Femoral neck length of the female (male) subjects was 47.3 ± 6.2 mm (51.8 ± 4.1 mm) compared to 48.7 ± 3.8 mm (52 ± 5 mm) in the training dataset and 63.65 ± 5.15 mm in [Blanc, 2012] with n = 142, 54% female, 46% male and a [50.32–75.50 mm] range. For the measured CCD angle in both female (123.9 ± 5.8°) and male (126.7 ± 4°) subjects, a good correlation was found with reported values of 128.4 ± 4.75° [Atilla, 2007], 124.7 ± 7.4° [Noble, 1988] and 129.82 + 5.37° [Blanc, 2012]. In conclusion, the present study demonstrates that the proposed methodology based on gender-specific statistical shape modelling can be a valuable tool for automatically generating a large specific population of femurs to support implant design and planning of femoral reconstructive surgery

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