A Method for Evaluation the Fatigue Microcrack Propagation in Human Cortical Bone Using Differential X-ray Computed Tomography
Abstract
:1. Introduction
2. Material and Methods
2.1. Specimens
2.2. Mechanical Loading
2.3. Radiographical Imaging and Computed Tomography
2.4. Digital Volume Correlation
2.4.1. Analysis of Optimal Correlation Window Size
3. Results
4. Discussion
- It was possible to identify fatigue microcracks and their propagation in the entire volume of the investigated sample using the laboratory X-ray scanner and custom post-processing procedures. The ability to identify the system of microcracks is essential to understand the bone failure mechanisms on the microscopic level, particularly regarding the fact that the microscopic damage of the bone and the rate of its accumulation plays a significant role in the reduction of the bone bearing capacity in the post-yield regime. The fully volumetric analysis, in this case, also brings advantages over an investigation based on 2D slices, both in terms of the microcrack identification and quantification, which is given by their complex arbitrary shape in the microstructure of the bone.
- In all the cases, it was found out, at the achieved voxel size, that the existing or newly formed microcracks either originate from the stress concentrators in the microstructure of the bone or interconnect them. In the investigated samples, the stress concentrators can be divided into three groups comprising the microcracks present in the intact state, the cracks on the surface of the specimen created during the manufacturing of the sample, and the Haversian canals. Although this is an expected result conforming to the fundamentals of fracture mechanics, it is an important finding that the regions of stress concentration with the presence of a system of microcracks were clearly apparent in the displacement field of the full-affine DVC procedure. With respect to the 2 micron resolution achieved in the reconstructed 3D images of the bone, the statistics from the two perpendicular planes, where the full-affine DVC was evaluated, shows approximately a 50% probability that a microcrack is present at the strain concentration location. This is still, however, a valuable result since the automated identification of the microcracks can be limited only to the regions of interest determined from the DVC with implications on computational costs and a time reduction. Conversely, no microcracks in the regions of the uniform strain distribution were identified at this scale level limited by the micrometric voxel size.
- It is possible to perform the in situ fatigue loading of a cylindrical human cortical bone sample using a laboratory CT scanner at a resolution given by the geometry of the loading device influencing the achievable source-to-object distance, and thus the achievable geometrical magnification of the projections. This enabled us to identify the microcracks in both the intact sample and after the loading procedure, with the width of at least 2 voxels, i.e., . Due to the nature of the CT imaging, regarding the conclusions, the probable presence of microcracks with dimensions under the resolution limit of the imaging instrumentation is questionable. However, this factor does not necessarily decrease the impact of this study as the aim was to show the methodology based upon a laboratory CT scanner, where the DVC using full-affine transformation serves as a tool for the identification of the damage accumulation in the bone represented by a system of microcracks.
- However, it is necessary to take appropriate measures with laboratory CT scanners to achieve the sufficient quality of the resulting reconstructed 3D images. Thus, the achieved value of the geometrical magnification of the projections is only one of the parameters determining the overall quality of the radiographical imaging. To reduce the influence of various tomographical artifacts including ring artifacts and the beam hardening effect, appropriate corrections of the imaging detector and X-ray source characteristics have to be performed to sharpen the reconstructed 3D image and enable the reliable identification of the microscopic features in the bone. It can be seen in the projections that the beam hardening effect consists of a higher intensity in the vicinity of the surface as no particular treatment was applied to its reduction. However, since the evaluation near the surface of the sample was omitted due to the damage induced by the sample preparation, the beam hardening itself has only a negligible influence on the acquired results. Furthermore, we have shown in the FWHM comparison with the SEM imaging that a combination of projection-level corrections with the focal spot drift correction leads to a quality of the reconstructed 3D images comparable to the SE microscopy in terms of the crack thickness calculation and void-material interface identification.
- Since the aim of the study was to show the methodology combining in situ fatigue loading using a simulated gait cycle with a DVC based evaluation and differential tomography for the identification of the microcracks present in the microstructure of the bone, only one sample was subjected to the full evaluation procedure comprised of the discussed methods. Nevertheless, in total, six samples were tested using the in situ loading procedure, but the acquired results were unsatisfactory due to several reasons. During two tests, problems were encountered with the mechanical response of the sample resulting in its sudden disintegration during the loading procedure, presumably due to the thermal and mechanical damage inflicted during the sample preparation. Generally, due to the variability in the mechanical response of the samples, it was difficult to determine the number of required cycles to generate microcracks, but prevent the destruction of the sample. Additionally, the behavior of the microstructure may also result in the closing of the microcracks, which corresponds to the behavior of the bone in the human body, but such a process precludes a study of the crack formation using time-lapse radiographical imaging. Additionally, the long-term stability of the detector used for imaging has an influence on the noise in the reconstructed 3D images and their sharpness, where the achieved geometrical resolution with a reduced reconstruction quality may also prevent the evaluation of the experiment.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Abbreviations
API | Application Programming Interface |
CMOS | Complementary Metal Oxide Semiconductor |
CT | Computed Tomography |
DIC | Digital Image Correlation |
DVC | Digital Volume Correlation |
FBP | Filtered Back-Projection |
FDK | Feldkamp, Davis, and Kress (CT reconstruction algorithm) |
GOS | Gadolinium oxysulfide |
FWHM | Full-Width Half-Maximum |
MBE | Mean-Bias Error |
NCC | Normalized Cross-Correlation |
RMSE | Root-Mean Square Error |
SEM | Scanning Electron Microscopy |
VOI | Volume Of Interest |
XCT | X-ray (micro) Computed Tomography |
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Window Size | Elapsed Time | NaN | Mean | MBE | RMSE | |
---|---|---|---|---|---|---|
ine [px] | [s] | [nodes] | [px] | [px] | [-] | [-] |
ine 6 | 2674 | 159 | 24.38 | 3.9 | 3.9 | 6.73 |
8 | 2521 | 83 | 27.13 | 1.15 | 1.15 | 3.34 |
10 | 2627 | 47 | 27.92 | 0.37 | 0.37 | 1.72 |
12 | 3161 | 1 | 28.25 | 0.04 | 0.04 | 0.43 |
14 | 6915 | 0 | 28.28 | 0.15 | ||
16 | 6028 | 0 | 28.28 | |||
18 | 3423 | 0 | 28.28 | |||
20 | 4117 | 0 | 28.28 |
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Koudelka, P.; Kytyr, D.; Fila, T.; Sleichrt, J.; Rada, V.; Zlamal, P.; Benes, P.; Bendova, V.; Kumpova, I.; Vopalensky, M. A Method for Evaluation the Fatigue Microcrack Propagation in Human Cortical Bone Using Differential X-ray Computed Tomography. Materials 2021, 14, 1370. https://doi.org/10.3390/ma14061370
Koudelka P, Kytyr D, Fila T, Sleichrt J, Rada V, Zlamal P, Benes P, Bendova V, Kumpova I, Vopalensky M. A Method for Evaluation the Fatigue Microcrack Propagation in Human Cortical Bone Using Differential X-ray Computed Tomography. Materials. 2021; 14(6):1370. https://doi.org/10.3390/ma14061370
Chicago/Turabian StyleKoudelka, Petr, Daniel Kytyr, Tomas Fila, Jan Sleichrt, Vaclav Rada, Petr Zlamal, Pavel Benes, Vendula Bendova, Ivana Kumpova, and Michal Vopalensky. 2021. "A Method for Evaluation the Fatigue Microcrack Propagation in Human Cortical Bone Using Differential X-ray Computed Tomography" Materials 14, no. 6: 1370. https://doi.org/10.3390/ma14061370