Abstract
Objectives:
To evaluate the influence of the level of three micro-CT reconstruction tools: beam-hardening correction (BHC), smoothing filter (SF), and ring artefact correction (RAC) on the fractal dimension (FD) analysis of trabecular bone.
Methods:
Five Wistar rats’ maxillae were individually scanned in a SkyScan 1174 micro-CT device, under the following settings: 50 kV, 800 µA, 10.2 µm voxel size, 0.5 mm Al filter, rotation step 0.5°, two frames average, 180° rotation and scan time of 35 min. The raw images were reconstructed under the standard protocol (SP) recommended by the manufacturer, a protocol without any artefact correction tools (P0) and 35 additional protocols with different combinations of SF, RAC and BHC levels. The same volume of interest was established in all reconstructions for each maxilla and the FD was calculated using the Kolmogorov (box counting) method. One-way ANOVA with Dunnet’s post-hoc test was used to compare the FD of each reconstruction protocol (P0–P35) with the SP (α = 5%). Multiple linear regression verified the dependency of reconstruction tools in FD.
Results:
Overall, FD values are not dependent on RAC (p = 0.965), but increased significantly when the level of BHC and SF increased (p < 0.001). FD values from protocols with BHC at 45% combined with SF of 2, and BHC at 30% combined with SF of 4 or 6 had no statistical difference compared to SP.
Conclusions:
BHC and SF tools affect the FD values of micro-CT images of the trabecular bone. Therefore, these reconstruction parameters should be standardized when the FD is analyzed.
Keywords: Fractals, Microcomputed Tomography, 3 D Imaging, X-Ray
Introduction
Fractal is a term introduced to describe structures with irregular formats and self-similarity. This concept has become increasingly applied to analyze structures that do not present regular formats, such as trabecular bone, which is characterized by a complex architecture composed of irregularly arranged trabeculae and medullary space.1,2 Fractal dimension (FD) is a measure of structural complexity based on fractal analysis. Higher FD values mean higher structural complexity, i.e. higher irregularity and number of trabeculae, and smaller spaces between them.
Fractal analysis has been widely applied in the evaluation of bone structure. Its clinical relevance and ability to assist in the diagnostic processes have been demonstrated in studies related to osteoporosis, temporomandibular joint disorders, diabetes, and thalassemia.3–7 FD may be calculated from conventional two-dimensional dental imaging. However, it is important to consider that in those exams, the complexity of the bone is assessed from overlapped images of anatomical structures. Three-dimensional exams, such as micro-CT and cone beam CT (CBCT), provide sectional information and, therefore, FD of the bone may be calculated with greater accuracy. However, CBCT used in clinical practice, exhibit a lower spatial resolution when compared to the micro-CT, and there is no standardization in the greyscale values, which may cause an unreliable representation of the bone structure.8,9
Micro-CT is a non-destructive and non-invasive sectional imaging method used mainly for scientific research purposes. It provides high-resolution structural analysis of bone tissue in micrometric scale, allowing reliable quantitative and qualitative analyses.8,10,11
Although the micro-CT can present artifacts that interfere in image quality, there are correction tools that can be used during the reconstruction process to overcome this limitation, such as smoothing filter, ring artefact correction, beam-hardening correction.12 Different levels of each of these tools can be applied, which characterizes the reconstruction parameters. The influence of the artefact reduction tools on FD values has not been demonstrated previously. Our null hypothesis was that different levels of artefact correction tools applied in the reconstruction of micro-CT images do not influence the FD values.
Therefore, the aim of the present study was to evaluate the impact of the reconstruction parameters of micro-CT images in the FD analysis of the trabecular bone.
Methods and Materials
Sample and micro-CT acquisition
The local Ethics Committee on Animal Research exempted this study from reviewing since the sample was derived from a previously approved study (protocol #3344-1/2014). Five Wistar rats’ maxillae were individually scanned in a SkyScan 1174 (Bruker, Kontich, Belgium) micro-CT device. For image acquisition, each sample was positioned with the long axis perpendicular to the horizontal plane and wrapped in wet paper. The following exposure settings were used: 50 kV, 800 µA, 10.2 µm voxel size, 0.5 mm Al filter, rotation step 0.5°, two frames average, 180° rotation, and scan time of 35 min.
Reconstruction protocols
The basis images of each maxilla were exported to NRecon software (Bruker, Kontich, Belgium). This software allows the adjustment the level of three reconstruction tools: smoothing filter (SF), ring artefact correction (RAC) and BHC (Table 1). First, the raw images were reconstructed under the standard protocol (SP) recommended by the manufacturer regarding the levels of artifacts reduction tools: two for SF, five for RAC, and 45% for BHC. Afterwards, a protocol without any artefact correction tools application was obtained (P0). Finally, 35 additional protocols were achieved by different combinations of these reconstruction parameters based on the available range for each tool and subjective image quality perception, totalizing 37 reconstructions for each maxilla (Table 2).
Table 1.
Reconstruction tools by NRecon software
| Reconstruction tools (range) | Description |
|---|---|
| Smoothing filter (0–10) | Smoothies images and removes noise |
| Ring artefact reduction (0–20) | Corrects for the defect of pixels due to its nonlinear behavior causing ring artifacts |
| Beam-hardening correction (0–100%) | Corrects for the absorption of lower-energy X-ray on the outside of the specimen |
Table 2.
Mean FD and SD from different micro-CT reconstruction protocols (SP and P0 to P35)
| Protocols | Smoothing filter | Ring artefact correction | Beam-hardening correction |
Fractal dimension | p-valuea | |
|---|---|---|---|---|---|---|
| Mean | SD | |||||
| SP | 2 | 5 | 45 | 2.68 | 0.018 | |
| P0 | 0 | 0 | 0 | 2.45 | 0.029 | 0.001a |
| P1 | 2 | 5 | 15 | 2.62 | 0.032 | 0.002a |
| P2 | 2 | 5 | 30 | 2.66 | 0.024 | 0.077 |
| P3 | 2 | 10 | 60 | 2.68 | 0.017 | 0.003a |
| P4 | 2 | 10 | 15 | 2.62 | 0.032 | 0.002a |
| P5 | 2 | 10 | 30 | 2.66 | 0.024 | 0.074 |
| P6 | 2 | 10 | 45 | 2.68 | 0.020 | 0.799 |
| P7 | 2 | 10 | 60 | 2.68 | 0.017 | 0.003a |
| P8 | 2 | 15 | 15 | 2.62 | 0.030 | 0.002a |
| P9 | 2 | 15 | 30 | 2.66 | 0.024 | 0.083 |
| P10 | 2 | 15 | 45 | 2.68 | 0.020 | 1 |
| P11 | 2 | 15 | 60 | 2.69 | 0.016 | 0.002a |
| P12 | 4 | 5 | 15 | 2.63 | 0.037 | 0.076 |
| P13 | 4 | 5 | 30 | 2.67 | 0.024 | 0.765 |
| P14 | 4 | 5 | 45 | 2.69 | 0.020 | 0.072 |
| P15 | 4 | 5 | 60 | 2.69 | 0.017 | 0.001a |
| P16 | 4 | 10 | 15 | 2.63 | 0.037 | 0.075 |
| P17 | 4 | 10 | 30 | 2.67 | 0.024 | 0.201 |
| P18 | 4 | 10 | 45 | 2.69 | 0.020 | 0.015a |
| P19 | 4 | 10 | 60 | 2.69 | 0.017 | 0.007a |
| P20 | 4 | 15 | 15 | 2.63 | 0.037 | 0.080 |
| P21 | 4 | 15 | 30 | 2.67 | 0.024 | 0.817 |
| P22 | 4 | 15 | 45 | 2.69 | 0.020 | 0.002a |
| P23 | 4 | 15 | 60 | 2.69 | 0.017 | 0.001a |
| P24 | 6 | 5 | 15 | 2.64 | 0.041 | 0.185 |
| P25 | 6 | 5 | 30 | 2.68 | 0.026 | 0.344 |
| P26 | 6 | 5 | 45 | 2.69 | 0.019 | 0.003a |
| P27 | 6 | 5 | 60 | 2.70 | 0.015 | 0.004a |
| P28 | 6 | 10 | 15 | 2.64 | 0.040 | 0.027 |
| P29 | 6 | 10 | 30 | 2.68 | 0.026 | 0.033 |
| P30 | 6 | 10 | 45 | 2.69 | 0.019 | 0.003a |
| P31 | 6 | 10 | 60 | 2.70 | 0.015 | 0.004a |
| P32 | 6 | 15 | 15 | 2.64 | 0.040 | 0.192 |
| P33 | 6 | 15 | 30 | 2.68 | 0.026 | 0.333 |
| P34 | 6 | 15 | 45 | 2.69 | 0.019 | 0.003a |
| P35 | 6 | 15 | 60 | 2.70 | 0.016 | 0.004a |
FD, fractal dimension; SD, standard deviation; SP, standard protocol.
p-values regarding comparison to SP according to one-way ANOVA and Dunnet post-hoc test.
Fractal dimension analysis
A volume of interest (VOI) with 0.5 mm in diameter and thickness of 100 slices was established for each maxilla, using CTAn software (Bruker, Konitch, Belgium). The same VOI was applied in all reconstructions for each maxilla. Morphometric three-dimensional analysis was performed so that FD was calculated using the Kolmogorov (box counting) method. The VOI was divided into an array of cubes of the same size, and the number of cubes containing part of the trabecular surface was counted. The number of cubes containing surface was plotted against cube length in a log–log plot, and the FD was obtained from the slope of the log–log regression.13
Statistical analysis
Statistical analysis was performed using SPSS software (v.24.0, IBM Corp., Armonk, NY). Repeated measures one-way ANOVA, with Dunnet’s post-hoc test was used to compare the mean FD values and standard deviation (SD) from each reconstruction protocol (P0–P35) to those from the SP, with the level of significance set at p < 0.05 (α = 5%). The analysis of data yielded an effect size of 0.776 and a post-hoc observed power of 1. Multiple linear regression was calculated to confirm the dependence of FD in relation to micro-CT reconstruction tools (SF, RAC, and BHC).
Results
Table 2 shows the mean values of FD and SD, and the p-value for each protocol regarding the comparison to SP. The protocol P0 and protocols combining a SF of 2 & BHC of 15% or 60% (P1, P3, P4, P7, P8, and P11) were significantly different from the SP (p < 0.05) (Figure 1). Protocols combining a SF of 4 or 6 & BHC of 45% or 60% (P15, P18, P19, P22, P23, P26, P27, P30, P31, P34, and P35) were also statistically different from the SP (p < 0.05)(Figure 1), except for P14 (p > 0.05).
Figure 1.
Shadow projection and VOI binarized images of the SP and the reconstruction protocols that were statistically different from the SP. SP,standard protocol; VOI, volume of interest.
The multiple linear regression model demonstrated the dependence of the independent variables in FD values (F(3,176) = 51.77; p < 0.001) with an R² = 0.469. SF and BHC were significant predictors of FD (β = 0.203; p < 0.001 and β = 0.654; p < 0.001, respectively), while RAC was not significant (β = 0.002; p = 0.965) (Table 3). Indeed, when the BHC decreased to 30%, and the SF increased to 4 or 6, FD values also remained the same. These results show that the FD values were directly influenced by SF and BHC level. In all cases, the variation in RAC level did not influence FD values.
Table 3.
Multiple linear regression for dependent variable (FD) dependency to the independent variables (MicroCT reconstruction tools)
| Model | Unstandardized coefficients | t | β | p-value | |
|---|---|---|---|---|---|
| B | SE | ||||
| Constant | 2.605 | 0.008 | 334.01 | <0.001* | |
| SF | 0.004 | 0.001 | 3.695 | 0.203 | <0.001* |
| RAC | 2.000E-5 | 0.000 | 0.044 | 0.002 | 0.965 |
| BHC | 0.001 | 0.000 | 11.902 | 0.654 | <0.001* |
BHC: beam-hardening correction;FD, fractal dimension; RAC: ring artefact correction;SF: smoothing filter.
Discussion
Micro-CT is primarily used for in vitro or ex vivo studies. However, the analyses based on this method can be applied directly in the clinical practice through evaluations of bone samples. Although further studies and refinement of the technique are necessary in order to differentiate bone alterations based on trabeculation and mineralization density, the future optimization of the micro-CT devices can make it possible to diagnose and/or follow-up bone pathologies through a bone biopsy of patients with suspected or diagnosed metabolic bone diseases.14 The FD analysis, in turn, can contribute in the diagnosis of some bone diseases, bringing information on microstructural bone complexity that is not visible to the naked eye.3,15 However, image characteristics, as spatial resolution, can influence the FD, resulting in different values when this parameter is altered.16 Changes in other image characteristics and their impact on FD analysis have not been tested before. In micro-CT imaging, although the manufacturer indicates an SP as a reference to the reconstruction tools level, there is a wide range of levels of application of these tools. In the present study, the FD values increased when the level of application of BHC and SF were increased. Such results show the influence of BHC and SF tools on the FD values. Therefore, considering that one of the clinical applications of FD is also to compare the complexity of an area of interest over different periods, we emphasize the need for standardization of these parameters when FD is analyzed in micro-CT images. Differently, RAC levels did not interfere in the FD values.
The FD is calculated through the box-counting method, which is characterized by the count of boxes required to cover all trabecular boundaries.17 As BHC equalizes the inhomogeneous grey values caused by the filtration of the polychromatic radiation beam,18 this may have changed the interface between bone trabeculae and medullary space and, therefore, affected the FD values when the bone trabeculae were counted. The increase in the FD values probably occurred because the bone trabeculae became more evident when the level of BHC application was increased. The same may have occurred with the SF application. Since the detection of the boundaries of the structures is imperative to calculate FD, and noise compromises edge detection,19 significantly higher FD values were obtained when the level of application of SF increased, confirming that FD is more sensitive to changes in texture in smoother images.20
Despite FD values increased significantly when the application level of BHC and SF increased, the FD values did not differ significantly when the combinations of BHC and SF remained the same as those from the SP (i.e. BHC of 45% and SF of 2). Interestingly, when the BHC decreased to 30%, and the SF increased to 4 or 6, FD values also remained the same. In other words, a small decrease in BHC was compensated by the increase in SF. Such result is understandable since both tools attempt to standardize the image, either by linearizing the histogram to remove cupping or by smoothing image differences through a Gaussian filter, which acts in each pixel in linear mode to remove noise.21
It has been previously stated that FD is sensitive to ring artifacts,20 but in the present study the RAC did not affect the FD values. This discrepancy probably occurred because ring artifacts were not very prominent in the images of the present study, even in P0, in which no RAC tool was applied. Also, some methods to remove image noise also help to remove ring artefact,19,21 as is the case of the Gaussian filter used in the SF tool of the present study, which may also have contributed to the noninfluence of the level of application of RAC on the FD values.
The choice of reconstruction tools levels was based on the manufacturer’s manual, and on its recommendation to adjust these tools visually. The voxel size used for image acquisition (10 µm) is adequate for FD analysis of rat bone, since their trabeculae are approximately 30–50 µm in width, and a voxel size of less than 20 µm has been recommended.11,22
Only the maxillary bone of rats was evaluated in the present study. Further studies should be developed to investigate if such results remain the same on different bones. In addition, although there was some knowledge that imaging parameters could influence the value of FD, such as spatial resolution or the method for calculating FD,6,16 there are no previous studies that aimed to evaluate the influence of artefact reduction tools on FD analysis. Based on the results found in the present study, it is pertinent to investigate the influence of other reconstruction parameters, and different micro-CT units should be tested.
As the FD analysis does not have a gold-standard, it is not possible to know which protocol provides an FD value closer to the actual complexity of the bone. Nevertheless, as the manufacturer suggests that the SP is the one that provides a more accurate image, it is recommended that this protocol should be used, so does the other protocols that did not significantly differ for FD assessment.
Conclusion
In conclusion, the BHC and SF tools affect the FD values of micro-CT images of the trabecular bone. Therefore, reconstruction parameters should be standardized when the fractal dimension is analyzed.
Footnotes
Acknowledgment: The authors declare no conflict of interest. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
Contributor Information
Hugo Gaêta-Araujo, Email: hugogaeta@hotmail.com.
Nicolly Oliveira-Santos, Email: nicolly.os@hotmail.com.
Danieli Moura Brasil, Email: danielibrasil@hotmail.com.
Eduarda Helena Leandro do Nascimento, Email: eduarda.hln@gmail.com.
Daniela Verardi Madlum, Email: danielaverardi@hotmail.com.
Francisco Haiter-Neto, Email: haiter@unicamp.br.
Christiano de Oliveira-Santos, Email: oliveirach@usp.br.
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