Initially, the developed fracture prediction tool was tested on samples of subjects with varying BMD distribution. This was done in order to verify the usability of the approach on oncological samples. This subsection describes data collection and retrospective use of the tool on historical data.
Fracture data and microCT images were pooled from previous studies where single vertebrae were experimentally tested to induce fracture. The collection criteria were defined thusly:
i. A single vertebra compression wedge fracture conducted on human samples
ii. Use of the same scanning protocol
iii. Use of the same compression testing procedure with comparable output in terms of strength estimation
More specifically, samples were collected from studies in which all specimens underwent testing based on a single vertebra model used by Oakland, Furtado et al. [3, 38]. In this protocol, samples were disarticulated and freed of soft tissue through sequential trimming of the processes but preserving the integrity of the spinal canal by keeping the neural arch intact. All samples underwent initial microCT scanning and were subsequently fractured.
Collected historical samples used for validation 3.1.2.5.1
Pooled samples consisted of three morphologically distinct pathologies: osteoporosis, bladder cancer and multiple myeloma cancer. All specimens used for this retrospective assessment were rendered anonymous and checked for eligibility for use in this study in terms of the ethical considerations (ethical approvals 09/H1306/1, 10/H1306/60 and 10/H1306/83).
The final dataset consisted specifically of forty-one osteoporotic samples (OP) from a total of eleven spines, twelve samples from one spine from a donor diagnosed with bladder cancer with metastases to spine (mets) and finally of forty-four samples from three spines diagnosed with multiple myeloma (MM).
Historical data - Scanning procedure 3.1.2.5.2
All collected samples underwent scanning in microCT (uCT80, Scanco Medical AG, Bassersdorf, CH). The osteoporotic and bladder cancer samples underwent the assessment at a resolution of 148x148x148 µm3
voxel size and scanned in air, whereas the multiple myeloma samples were scanned with a final voxel size of 70.8x70.8x70.8 µm3 and scanned while submerged in water without applying vacuum prior to the scan. Furthermore, in all three cases the scanning parameters remained unaltered: 250 projections were used (70kV, 114mA, and 300ms) and reconstruction took place with the use of an in-build 200mgHA/cm3 beam hardening correction provided by the manufacturer (Scanco Medical AG, Bassersdorf, CH). All images were then converted to ρBMD using Hydroxyapatite phantom.
Historical data - Wedge compression fracture 3.1.2.5.3
The first and second datasets (OP, mets) were fractured in a custom- built testing rig and subjected to compression in a single axis compression machine (AGS-10kNG, Shimadzu Corp.). The third dataset (MM) was tested using the enhanced rig developed as a part of this work as per testing protocol described in subsection: 3.2.2.4: “Single vertebra Wedge Compression Fracture rig”. In all cases the vertebral strength was taken from the first peak on the load-displacement curve (zero-slope).
Predicting historical data - beam theory and BMD-based 3.1.2.5.4
method
All collected microCT images were assessed using the beam theory fracture prediction tool discussed previously. Where necessary, given the complex nature of the deterioration, a manual correction of the detected boundary was undertaken, in which case every fifth slice was corrected.
For the purpose of developing the model, multiple material laws suggested in relevant studies [200, 204, 213] have been initially tested for comparison with the model proposed by Kaneko et al. [198, 214], obtained based on metastatic and osteoporotic cored samples. The initial test was performed on a smaller number of samples (training dataset) and extended to the full population once the model with the closest agreement had been chosen.
In addition, the metastatic samples were reanalysed afterwards excluding the extra-vertebral body formations from the fracture prediction modulus map. Figure 16 depicts one of the samples containing such formations, comparing the morphological imprint of the lytic and blastic tumours. To exclude these formations, a similar tool to the one used to manually define vertebral body outlines was used to define the body without the external lesions.
The theoretical background of this assessment is that the structure is firmly attached to the vertebral body, hence is assumed to contribute to vertebral strength. According to engineering principles the osteo-sclerotic nature of the structure and its anterior position suggest that the structure will be expected to support the loads. This assumption is supported by the fact that, if the yield of the healthy and osteo-sclerotic tissue remains the same, than the bending stiffness - a significant contributor to the strength of the vertebra (subsection “Composite theory approach”, eq. (1.3)) - is in fact a product of Young’s modulus (density dependent variable) and distance from the neutral axis squared (eq. (1.5)). However, in tools such as those using standalone BMD without accounting for density distribution, this sclerotised tissue would not be considered, hence the strength predictions would be hampered.
Moreover, excluding (masking) of the mineralised tissue from the modulus map will decrease both the axial and bending stiffness in the fracture prediction equation. The comparison before and after the masking of the tissue from the prediction with sequential comparison to the experimentally obtained value can be then used to investigate whether the tissue is more likely to be mechanically supporting the vertebra and hence enhancing the vertebral strength.
The results of predicted strength prior to and after alteration of the masks were compared to those obtained experimentally and will be discussed in the results subsection.
Figure 16: Example of microCT vertebral body assessment depicting severe metastatic infiltration. An axial slice obtained from microCT (above) shows a notable influence on the internal structure when mixed lesions are present. Beneath is a 3d representation of the infiltrated vertebra
Results in predicting historical data 3.1.3
3.1.3.1 Historical data – Collected osteoporotic samples
In total forty-one scans and experimental data of osteoporotic samples matching the criteria were collected for this retrospective analysis. Data from microCT scans were used to estimate fracture load based on a product of BMD and cross-sectional area and using a beam theory approach. The results of both methods were then compared to experimental compression test output. A typical output of the fracture prediction tool is shown in Figure 31, where the first slices clearly overestimate the strength due to the presence of the cortical wall. However, as the analysis takes into account only the weakest slice, an overemphasis on the strength of the bony endplates is irrelevant.
The dataset also consisted of 6 samples which showed unexpected strength (exceeding 3.9kN and up to 6.4kN). These samples were each treated in the same way in order not to bias the fracture prediction tool validation study.
With regards to the structural analysis compared to experimental data, the mean difference was -0.25kN, the limit of agreement was ±0.91kN (depicted in Figure 17) and the coefficient of determination R2 was 0.93 (p<0.001). In terms of accuracy, the mean difference was found to be sufficiently close to zero. The reason for discrepancy in the stronger samples originates in the nature of the location of high density bone, where the weight of each voxel of every pixel contributing to flexural rigidity is a product of density and distance from the bending axis squared. Sensitivity to any impairments of the density-to-modulus relationship or misalignment with bending rigidity is then overwhelmed by these osteophytes.
The results of the analysis based on the product of BMD and cross- sectional area proposed by Brinckmann [64] with the same apparatus show the adjusted linear interpolation coefficients (a=0.32 and b=0.00308; conducted by a former researcher from the University of Leeds using the same methodology and apparatuses [95]) to be significantly poorer in terms of both agreement and association (mean diff -0.7kN; limits of agreement ± 2.78kN; coefficient of determination R2 of 0.16 (p=0.011). The comparison of both methods in Figure 18 displays data from which a number of observations can be made.
Figure 17 Bland-Altman analysis of predicted and experimentally obtained fracture loads for collected osteoporotic samples. The difference between both datasets indicates modest limits of agreement lower than ± 1kN
Firstly, despite the high correlation in the structural analysis, the model tends to overestimate the failure load for small loads; nevertheless this is reversed for larger ones. The analysis based on Brickmann/Oakland’s prediction [64, 95] tends to overestimate the failure loads for all samples except those where osteophytes are present.
In an attempt to discern the reasons for the discrepancy between the two models, the presence of osteophytes was investigated. First, three samples with clearly enlarged osteophytes (strength exceeding 5kN) were excluded, which altered coefficients of determination from R2=0.93 to R2=0.83 for the beam theory based method and from R2=0.16 to R2=0.27 for the BMD based method. Bland-Altman’s mean difference and limits of agreement were found to be -0.31 ± 0.81 kN and -1.02 ± 1.7 kN for the beam theory and the BMD based method respectively.
Excluding additional stronger vertebrae (smaller osteophytes) altered the correlation, mean difference and limits of agreement to R2=0.75; -0.39 and ± 0.6 kN for the beam theory and R2=0.4; -1.2 and ± 1.14 for the BMD based method. It is interesting to note that despite the reduction in R2, the limits of agreement became narrower, which highlights that the use of R2 alone is an inappropriate measure of accuracy and/or precision.
Figure 18 Plot of the predicted versus experimentally determined failure load. Beam-theory method (red “o” marker) shows good agreement and correlation in comparison to the formerly used product of BMD and cross-sectional area (blue “Δ” marker), with the example in the bottom right corner depicting a sample reaching 6.03kN strength most probably due to the presence of extra-vertebral body formations. In fact, all samples in the red- dashed area contained similar osteophytes