A study of the progression of damage in an axially loaded Branta leucopsis femur using X-ray computed tomography and digital image correlation

Selection of vertebrate long bone

The characteristics of the test rig and scanning system placed some constraints on the size of bone and size of internal features under study. Simply stated, the bone cannot be longer than 70 mm so as to fit within the test rig (see Figs. 1 and 2) and only micro-structural features somewhat larger than one voxel can be captured. With respect to the latter, the high aspect ratio of long bones (long bones are significantly narrower than they are long) limits the resolution of scan that can be acquired.

Therefore, at the beginning of the study, a selection of bones from different species was identified as ‘test specimens’ on the basis of their lengths. The bones were individual femora from each of the following vertebrates: pigeon (Columba livia); partridge (Perdix perdix); Barnacle goose (B. leucopsis); Guinea fowl (Numida meleagris); pheasant (Phasianus colchicum) and rabbit (Oryctolagus cuniculus). These were sourced and prepared according to the procedure outlined in the next section.

A static X-ray tomography scan was carried out for each femur. Details of the scanning arrangements are given in the X-ray tomography section. The scans were reconstructed and the quality of each was assessed. In many of the specimens, micro-structural features in the cancellous bone were not captured as they were below the resolution of the scan. The goose bone produced a high-quality scan and the microstructure of the cancellous bone was very clearly defined. The goose was therefore selected for this study on the basis of its resolution and visibility of microstructure of the cancellous bone.

Sample preparation

The right and left femora were obtained from an adult Barnacle goose (B. leucopsis) with accession number SF320. Both femora were 59 mm long. The intact adult weighed 2.03 kg. All soft tissues were carefully removed using standard laboratory procedures such that the distal and proximal epiphyses remained intact.

The bones were then cleaned following methodology of Cauble (2010) and Nawrocki (1997). This methodology entails taking care of the preparation of specimens such that the procedure does not weaken the bones before carrying out the mechanical test (Boyle, 2010; Grygon, 2010; Onwuama et al., 2012). All bones (including those in the previous section) were first treated with 75% saline solution to avoid use of organic/chemical. These bones were then subjected to ‘supervised boiling’ in tap water with a small amount of basic detergent for 6 h. During boiling the water was replaced after every hour. This released most of the soft tissue on the surface and the fats held within the marrow. Bones were then kept for air drying for three to four weeks. Drying was considered complete when the weight of the bone stayed constant over a few days.

The right femur was used as a ‘test specimen’ to devise, evaluate and improve the experimental protocols before carrying out the final destructive axial loading test on the left femur. Safety assessment procedures and protocols were followed in compliance with the BIOCOSSH procedures set out by the Medical School at the University of Manchester, UK (University of Manchester, 2016).

X-ray tomography

A Nikon Custom Bay 320kV micro-CT scanner at the School of Materials, University of Manchester, UK (Fig. 1) was used for this study. The resolution acquired was 31.5 μm using 59 kV and 195 μA. The distance between the sample and the detector was 234 mm. In total, 2001 projections were collected over 360°. The acquisition time per scan was 50 min each. The number of pixels was 1,792 × 712 × 1,574. The pixel size was 0.0315 mm.

A specially designed mechanical loading rig was used with a scanner to carry out the axial loading. The rig has two adjustable steel platens, one on the top and the other on the base (see Fig. 1).

The left goose femur was mounted in the loading rig vertically along its axis. Epoxy resin disc spacers were specially manufactured and introduced between the bone and the steel platens at both the top and bottom of the loading rig. The purpose of the spacers was to avoid the steel platens casting a shadow on the tomography scans at the distal ends of the bone. Discs of abrasive paper of equal dimension to the epoxy resin were used between the bone and the resin in order to stop the bone moving laterally. Open cell phenolic foam (Smithers Oasis, Kent, OH, USA) was glued over the bottom epoxy resin disc, holding the bone upright. The foam is radio-transparent which avoids introducing any unwanted artefacts into the scan. The mounting protocols described were developed, tested and refined using other bone specimens. The loading rig and mounting of the specimen are shown in Fig. 2.

A 10,000 N load cell was used to load the bone through the upper platen. The lower platen was fixed. A compressive pre-load of 10 N was applied at the beginning of the experiment to take up any slack between the bone, the spacers and the rig. Once a stable force reading was reached (after ∼100–150 s), the load step was increased. In total 11 loading increments (using displacement control), numbered from 0 to 10 were applied at a rate of 0.5 mm/min. Loading was stopped when the bone had completely failed. The magnitudes of the displacements applied along with the corresponding loads are given in the results section. At the end of each displacement increment and when a stable force reading was acquired, a full 3D scan was carried out with the sample displacement fixed. The whole rig rotates on the X-ray instrument rotation table.

Image processing

The images were reconstructed using the commercial CT-Metris Pro software (Nikon Metrology, Tring, UK). The centre of rotation was determined and the noise levels were reduced. Later on, the level of beam hardening was chosen. Data were exported in unsigned 16-bit DICOM format (VG Studio Max v. 2.0; Volume Graphics, Heidelberg, Germany). They were then processed using Avizo 7 (http://www.fei.com/software/avizo3d/). First a median filter, with a kernel size of 3×3×3 pixels, was applied in order to reduce the effects of noise.

The bone was segmented from the background using an interactive threshold tool in the Simpleware Ltd. software ScanIP (http://simplewareinc.com/wordpress/training-manuals/). The optimum threshold parameters were selected manually. Virtual isosurface renderings were then created for selected exemplars of the various deformation features (cracking, necking) found in the scans. Isosurfaces for each scan captured through the loading sequence were generated using the same thresholding parameters. This allowed the evolution of the features of interest to be followed from one scan to the next. The number of times each type of feature was present in each scan was counted manually to see whether there was a pattern of feature growth or feature emergence as the bone progressed to failure.

Digital image correlation

Digital image correlation was used to evaluate the evolution of a small crack feature. This crack was chosen to be used for DVC, among the several deformation features reported in this study. Displacements were calculated in the 2D plane. Methods that have been developed include least-squares approaches (Roux et al., 2008) and Bayesian probability methods (Clocksin, Quinta Da Fonseca & Withers, 2002). In this study, correlation was performed using an algorithm developed by LaVision, Göttingen (originally conceived for particle image velocimetry (PIV)), which is part of the Strainmaster™ software package. It uses fast Fourier transform (FFT) cross-correlation to compare small sub-regions of the images (Quinta Da Fonseca, Mummery & Withers, 2005). The method is based on generalised texture mapping functions and on the fact that, under suitable conditions, groups of particles or regions of image texture will retain similar appearances under small translations and deformations. The particles or textured regions can then be tracked as a group using a correlation function to perform pattern matching as a function of the displacement. The algorithms thus use the characteristic local intensity variation to identify a region before and after deformation and thereby estimate the associated displacements. The actual displacement is determined from the location of the maximum value of the correlation function, and is always done to sub-pixel accuracy, with a local curve fit of the correlation data. If the correlations are performed correctly, the maximum value represents the most likely displacement of the image in each interrogation window. Multiple iterations are used during which the search sub-region is iteratively translated and deformed, using interpolation, until the highest correlation possible is achieved with accuracies of 0.01 pixels.

All the scans were imported into ImageJ (http://imagej.nih.gov/ij/). Scan 0, which is unloaded and therefore undeformed was selected as a reference image. The background was cropped for each image. Boundary pixels near the shaft in each image were aligned with reference to the first scan. All the images were then exported as a set of ‘raww’ files. These were imported into Avizo 7 and accurately aligned with one another using the affine registration module. DIC was then performed on the sequence of sub-images containing the crack feature. Correlation was performed on a sub-region of decreasing size, from 32×32 pixels to 16×16 pixels and with a sub-region overlap of 25%. This was found to provide a good compromise between spatial resolution and displacement accuracy, giving an uncertainty in strain resolution of around 0.05%. Strains were calculated by measuring the change in length/displacement between the original and the deformed images. The output was a sequence of strain maps corresponding to the associated loading increments.

Macro-scale load–displacement response

The load–displacement response is shown in (Fig. 3); the consecutive numbers ‘0’ to ‘10’ mark the points at which loading was interrupted to carry out the tomography scans. Whilst the scans were taken (∼50 min each), the loads decreased, probably due to creep in the bone material. The load–displacement data are also presented in Table 1. The first data point ‘0’ corresponds to the first tomography scan. A displacement of around 2 mm was recorded for an insignificant load reading. This represents the load required for all the slack to be taken up in the testing rig and for the bone to be held firmly in position. The reconstructed volume for the unloaded scan 0 is shown in Fig. 4.

Based on the load–displacement curve, there appear to be four stages in the macro- scopic response to loading. These are identified as follows: (i) The part of the curve from scan 0 to 2 appears to show an approximately linear load–displacement response; (ii) Scans 2–4 (displacement range 3.5–4.5 mm) corresponds to a plateaux (∼200–250 N) in the loading curve; (iii) Scans 5–6 show an increase in load (to ∼343 N) for a small increase in displacement (∼0.5 mm).

This is matched by the macro-scopic observation of a visible crack in the greater trochanter region of the head of the femur. (iv) Finally, scans 7–10 show a reduction in load bearing capacity of the bone which corresponds with shear failure in the epiphyseal region of the femur.

Figure 5 shows the external surface view (the macro level) of the progression of the crack and Fig. 6 shows 2D slices of the tomography scan for the same set of features from scan 0 to 9. These results are similar to those described in Ritchie (1988).

Meso-scale deformation features

Five distinct types of deformation mechanism in the cancellous bone were identified from the reconstructed tomography data. Each of these appeared at specific points in the loading path. The evolution of these features could be followed to a certain degree at subsequent loading intervals. Both brittle and ductile mechanisms were observed, reflecting the varied influence of bone’s complex architecture. The mechanisms observed included (i) cracking (Fig. 7); (ii) thinning and (iii) tearing of cell walls and struts (Fig. 8); (iv) notch formation (Fig. 9) and (v) buckling of struts (Fig. 10). All these deformation features (Figs. 7–10) were located in the upper condoyle near the greater trochanter of the femoral head.

Buckling

An example of buckling is shown in Fig. 10 and is a classic mode of elastic deformation.

The number of occurrences of each of the meso-scale deformation features is plotted in Fig. 11 for the series of scans. The features rank from most to least dominant as follows: (1) thinning and tearing, (2) cracking, (3) necking, (4) bending and (5) notch formation.

Micro-scale deformation

It is not apparent from the first three scans of Fig. 12 that a crack is about to form. However, DIC enabled a more quantitative measure of the deformation process. A crack feature as shown in Fig. 12 was chosen for finer scale investigation using DIC (Fig. 13).

The crack feature appears in scan 7 (Fig. 12D) and DIC cannot therefore be used for scans 7–10. A black line in Fig. 13I shows where exactly the crack appeared in the successive scans.

The displacement vectors in (Figs. 13G–13I) show that the bottom half of this section of bone is being displaced to the right as the top half moves upwards. In the strain maps, the y-component increases up to a value of 6% strain (Fig. 13F) in the region where the crack occurs (Fig. 13D).