Discriminating low-grade ductal carcinoma in situ (DCIS) from non-low-grade DCIS or DCIS upgraded to invasive carcinoma: effective texture features on ultrafast dynamic contrast-enhanced magnetic resonance imaging

Abstract

Purpose

To investigate effective model composed of features from ultrafast dynamic contrast-enhanced magnetic resonance imaging (UF-MRI) for distinguishing low- from non-low-grade ductal carcinoma in situ (DCIS) lesions or DCIS lesions upgraded to invasive carcinoma (upgrade DCIS lesions) among lesions diagnosed as DCIS on pre-operative biopsy.

Materials and methods

Eighty-six consecutive women with 86 DCIS lesions diagnosed by biopsy underwent UF-MRI including pre- and 18 post-contrast ultrafast scans (temporal resolution of 3 s/phase). The last phase of UF-MRI was used to perform 3D segmentation. The time point at 6 s after the aorta started to enhance was used to obtain subtracted images. From the 3D segmentation and subtracted images, enhancement, shape, and texture features were calculated and compared between low- and non-low-grade or upgrade DCIS lesions using univariate analysis. Feature selection by least absolute shrinkage and selection operator (LASSO) algorithm and k-fold cross-validation were performed to evaluate the diagnostic performance.

Results

Surgical specimens revealed 16 low-grade DCIS lesions, 37 non-low-grade lesions and 33 upgrade DCIS lesions. In univariate analysis, five shape and seven texture features were significantly different between low- and non-low-grade lesions or upgrade DCIS lesions, whereas enhancement features were not. The six features including surface/volume ratio, irregularity, diff variance, uniformity, sum average, and variance were selected using LASSO algorism and the mean area under the receiver operating characteristic curve for training and validation folds were 0.88 and 0.88, respectively.

Conclusion

The model with shape and texture features of UF-MRI could effectively distinguish low- from non-low-grade or upgrade DCIS lesions.

Appendix

Shape features

Volume is the volume of the lesion in mm³.

Surface area is the surface area of the lesion in mm².

$$\mathrm{Effective Radius},\mathrm{ R}eef=\sqrt[3]{(3\times \mathrm{Volume})/4\uppi },$$

(7)

$$\mathrm{Sphericity }=\frac{\mathrm{Volume of Lesion Inside Sphere of radius }{\mathrm{R}}_{eef}}{\mathrm{Total Lesion Volume}},$$

(8)

$$\text{Irregularity}=1-\frac{{4{\pi R}}_{eef}^{2}}{\text{Surface Area}}.$$

(9)

Texture features

The following mathematical expressions are used to calculate the GLCM-based texture

$${p}_{x}\left(i\right)=\sum_{j=1}^{G}p\left(i.j\right),$$

(10)

$${p}_{y}\left(j\right)=\sum_{i=1}^{G}p\left(i.j\right),$$

(11)

$${p}_{x+y}\left(k\right)=\sum_{i=1}^{G}\sum_{j=1}^{G}p\left(i.j\right),$$

(12)

$$k=i+j=\mathrm{2,3},\cdots 2G,$$

(13)

$${p}_{x-y}\left(k\right)=\sum_{i=1}^{G}\sum_{j=1}^{G}p\left(i.j\right),$$

(14)

$$k=\left|i\right.-\left.j\right|=\mathrm{0,1},2,\cdots G-1,$$

(15)

GLCM textures are calculated using the following equations:

$$\mathrm{Contrast}=\sum_{k=1}^{G-1}{k}^{2}{p}_{x-y}\left(k\right),$$

(16)

$$\mathrm{Correlation}=\frac{\sum_{i=1}^{G}\sum_{j=1}^{G}\left(i\bullet J\right)p\left(i,j\right)-{\mu }_{x}{\mu }_{y}}{{\sigma }_{x}{\sigma }_{y}},$$

(17)

$$\mathrm{Diff Entropy}=-\sum_{k=0}^{G-1}{p}_{x-y}\left(k\right)\mathrm{log}\left({p}_{x-y}\left(\mathrm{k}\right)\right),$$

(18)

$$\mathrm{Diff Variance}=\sum_{k=0}^{G-1}(k-{\mu }_{x-y}{)}^{2}{p}_{x-y}(k),$$

(19)

where ${\mu }_{x-y}$ is the mean of ${p}_{x-y}(k)$

$$\mathrm{Uniformity}=\sum_{i=1}^{G}{\sum_{j=1}^{G}p(i,j)}^{2},$$

(20)

$$\mathrm{Entropy}={f}_{9}=-\sum_{i=1}^{G}\sum_{j=1}^{G}p\left(i,J\right)\mathrm{log}\left(p\left(i,j\right)\right),$$

(21)

$$\mathrm{Homogeneity}=\sum_{i=1}^{G}\sum_{j=1}^{G}\frac{1}{1+{\left(i-j\right)}^{2}}p\left(i,j\right),$$

(22)

$$\mathrm{Sum Average}={f}_{6}=\sum_{k=2}^{2G}{kp}_{x+y}(k),$$

(23)

$$\mathrm{Sum Entropy}=-\sum_{k=2}^{2G}{p}_{x+y}\left(k\right)\mathrm{log}\left({p}_{x+y}\left(k\right)\right),$$

(24)

$$\mathrm{Sum Variance}=\sum_{k-2}^{G}(k-{f}_{6}{)}^{2}{p}_{x+y}\left(k\right),$$

(25)

$$\mathrm{Variance}=\sum_{i=1}^{G}(i-{\mu }_{x}{)}^{2}{p}_{x}(i),$$

(26)

$$\mathrm{Margin Sharpness}=\frac{{\widehat{G}}_{xyz}^{*}}{{\widehat{B}}^{*}\bullet {\Delta }_{xyz}},$$

(27)

where

$${\widehat{G}}_{xyz}^{*}=\sum \left\{{g}_{xyz}^{*}|{g}_{xyz}^{*}\in {g}_{xyz}^{*}(i,j,k)\right\}/{N}^{*},$$

(28)

$${\widehat{B}}^{*}=\sum \left\{b|b\in {B}^{*}(i,j,k)\right\}/{N}^{*},$$

(29)

where N* is the number of voxels in the border, B*, and Δ_xyz is the isotropic voxel size.

$$\mathrm{Variance of Margin Sharpness}=\frac{\sqrt{{{\widehat{{G}^{2}}}^{*}}_{xyz}-{\widehat{G}}_{xyz}^{*}}}{{\widehat{B}}^{*}\bullet {\Delta }_{xyz}},$$

(30)

Where

$${{\widehat{{ G}^{2}}}^{*}}_{xyz}=\frac{\sum \left\{{{g}_{xyz}^{*}}^{2}|{g}_{xyZ}^{*}\in {G}_{xyz}^{*}(i,j,k)\right\}}{{N}^{*}},$$

(31)

$$v\mathrm{RGH}=\sqrt{{\widehat{{RGH}^{2}}-\widehat{RGH}}^{2},}$$

(32)

were

$$\widehat{{RGH}^{2}}=\sum \left\{{rgh}^{2}|rgh\in RGH\right\}/(N\bullet {N}_{b}),$$

(33)

$$\widehat{RGH}=\sum \left\{rgh|rgh\in RGH\right\}/(N\bullet {N}_{b}).$$

(34)