Effect of radiation dose reduction on texture measures of trabecular bone microstructure: an in vitro study

Abstract

Osteoporosis is characterized by bone loss and degradation of bone microstructure leading to fracture particularly in elderly people. Osteoporotic bone degeneration and fracture risk can be assessed by bone mineral density and trabecular bone score from 2D projection dual-energy X-ray absorptiometry images. However, multidetector computed tomography image based quantification of trabecular bone microstructure showed significant improvement in prediction of fracture risk beyond that from bone mineral density and trabecular bone score; however, high radiation exposure limits its use in routine clinical in vivo examinations. Hence, this study investigated reduction of radiation dose and its effects on image quality of thoracic midvertebral specimens. Twenty-four texture features were extracted to quantify the image quality from multidetector computed tomography images of 11 thoracic midvertebral specimens, by means of statistical moments, the gray-level co-occurrence matrix, and the gray-level run-length matrix, and were analyzed by an independent sample t-test to observe differences in image texture with respect to radiation doses of 80, 150, 220, and 500 mAs. The results showed that three features—namely, global variance, energy, and run percentage, were not statistically significant ($p>0.05$) for low doses with respect to 500 mAs. Hence, it is evident that these three dose-independent features can be used for disease monitoring with a low-dose imaging protocol.

Appendix

$$\begin{aligned} \text {HG1: Global-Variance}=\frac{\sum _{x=1}^{M}\sum _{y=1}^{N}\{f(x,y)-\mu \}^2}{M \times N} \end{aligned}$$

(4)

$$\begin{aligned} \text {HG2: Global-Skewness}=\frac{1}{M \times N}\frac{\sum _{x=1}^{M}\sum _{y=1}^{N}\{f(x,y)-\mu \}^3}{\sigma ^3} \end{aligned}$$

(5)

$$\begin{aligned} \text {HG3: Global-Kurtosis}=\frac{1}{M \times N}\frac{\sum _{x=1}^{M}\sum _{y=1}^{N}\{f(x,y)-\mu \}^4}{\sigma ^4} \end{aligned}$$

(6)

$$\begin{aligned} \text {GL1: Energy}=\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1}p(l,m)^2 \end{aligned}$$

(7)

$$\begin{aligned} \text {GL2: Contrast}=\sum _{n=0}^{N_{g}-1} n^{2}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{g}}p(l,m)},|l-m |=n \end{aligned}$$

(8)

$$\begin{aligned} \text {GL3: Correlation}=\frac{\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1}\{l\times m\}\times p(l,m)-\{\mu _{l}\times \mu _{m}\}}{\sigma _{l}\sigma _{m}} \end{aligned}$$

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$$\begin{aligned} \text {GL4: Homogeneity}=\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1}\frac{1}{1+(l-m)^2}p(l,m) \end{aligned}$$

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$$\begin{aligned} \text {GL5: Dissimilarity}=\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1} |l-m |p(l,m) \end{aligned}$$

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$$\begin{aligned} \text {GL6: Entropy}=-\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1}p(l,m) \times log (p(l,m)) \end{aligned}$$

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$$\begin{aligned} \text {GL7: Variance}=\sum _{l=2}^{2N_{g}}(l-S_{E})^2p_{x+y}(l), S_{E}=-\sum _{l=2}^{2N_{g}}p_{x+y}(l)log\{p_{x+y}(l)\} \end{aligned}$$

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$$\begin{aligned} \text {GL8: Sum Average}=\sum _{l=2}^{2N_{g}}lp_{x+y}(l) \end{aligned}$$

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$$\begin{aligned} \text {GR1: SRE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} \frac{p(l,m)}{m^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR2: LRE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}m^2p(l,m)}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR3: GLN}=\frac{\sum _{l=1}^{N_{g}} \left( \sum _{m=1}^{N_{r}}p(l,m)\right) ^2}{\sum _{l=1}^{N_{g}} \sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR4: RLN}=\frac{\sum _{m=1}^{N_{r}} \left( \sum _{l=1}^{N_{g}}p(l,m)\right) ^2}{\sum _{l=1}^{N_{g}} \sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR5: RP}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)}{P} \end{aligned}$$

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$$\begin{aligned} \text {GR6: LGLRE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}\frac{p(l,m)}{l^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR7: HGLRE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)\cdot {l^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR8: SRLGE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} \frac{p(l,m)}{{l^2}\cdot {m^2}}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR9: SRHGE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} \frac{p(l,m)\cdot {l^2}}{m^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR10: LRLGE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} \frac{p(l,m)\cdot {m^2}}{l^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR11: LRHGE}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m) \cdot {m^2}\cdot {l^2}}{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}p(l,m)} \end{aligned}$$

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$$\begin{aligned} \text {GR12: GLV}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} (l \times p(l,m)- \mu _{N_{g}})^2}{N_{g} \times N_{r}}, \mu _{N_{g}}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}l\times p(l,m)}{N_{g} \times N_{r}} \end{aligned}$$

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$$\begin{aligned} \text {GR13: RLV}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}} (m \times p(l,m)- \mu _{N_{r}})^2}{N_{g} \times N_{r}}, \mu _{N_{r}}=\frac{\sum _{l=1}^{N_{g}}\sum _{m=1}^{N_{r}}m\times p(l,m)}{N_{g} \times N_{r}} \end{aligned}$$

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where M and N denote the number of rows and columns in the gray-level image, f(x, y) is the voxel intensity information in the x and y directions, $\mu$ is the mean gray levels, p(l, m) represents the normalized gray-tone spatial dependence matrix, $N_{g}$ denotes the number of gray levels in the quantized image, $N_{r}$ denotes the number of different run lengths in the GLCM, $\mu _{l}$, $\mu _{m}$, $\sigma _{l}$, and $\sigma _{m}$ denote the mean and standard deviation of $p_{l}$ and $p_{m}$, i and j denote the gray-level range and run length, $p_{x}(l)=\sum _{m=0}^{N_{g}-1 }p(l,m)$, $p_{y}(m)=\sum _{l=0}^{N_{g}-1 }p(l,m)$, $\mu _{x}=\sum _{l=0}^{N_{g}-1} l p_{x}(l)$, $\mu _{y}=\sum _{m=0}^{N_{g}-1} m p_{y}(m)$, $p_{x+y}(n)=\sum _{l=0}^{N_{g}-1}\sum _{m=0}^{N_{g}-1} p(l,m),l+m=n$, and P denotes the number of gray tones in the GLCM.