Breast Density Analysis Using Digital Breast Tomosynthesis

Abstract

We evaluated an automated percentage of breast density (BD) technique (PD_a) with digital breast tomosynthesis (DBT) data. The approach is based on the wavelet expansion followed by analyzing signal dependent noise. Several measures were investigated as risk factors: normalized volumetric; total dense volume; average of the DBT slices (slice-mean); a two-dimensional (2D) metric applied to the synthetic images; and the mean and standard deviations of the pixel values. Volumetric measures were derived theoretically, and PD_a was modeled as a function of compressed breast thickness. An alternative method for constructing synthetic 2D mammograms was investigated using the volume results. A matched case-control study (n = 426 pairs) was analyzed. Conditional logistic regression modeling, controlling body mass index and ethnicity, was used to estimate odds ratios (ORs) for each measure with 95% confidence intervals provided parenthetically. There were several significant findings: volumetric measure [OR = 1.43 (1.18, 1.72)], which produced an identical OR as the slice-mean measure as predicted; [OR =1.44 (1.18, 1.75)] when applied to the synthetic images; and mean of the pixel values (volume or 2D synthetic) [ORs ~ 1.31 (1.09, 1.57)]. PD_a was modeled as 2^nd degree polynomial (concave-down): its maximum value occurred at 0.41×(compressed breast thickness), which was similar across case-control groups, and was significant from this position [OR = 1.47 (1.21, 1.78)]. A standardized 2D synthetic image was produced, where each pixel value represents the percentage of BD above its location. The significant findings indicate the validity of the technique. Derivations supported by empirical analyses produced a new synthetic 2D standardized image technique. Ancillary to the objectives, the results provide evidence for understanding the percentage of BD measure applied to 2D mammograms. Notwithstanding the findings, the study design provides a template for investigating other measures such as texture.

Figure 1.

Image Illustrations: in the top row (a) C-View image for illustration-1; (b) respective central slice image; (c) C-View image for illustration-2; and (d) respective central slice image. Outlines in the top-row images are the largest rectangles that fit within the breast areas. These regions are shown in the second row with the same ordering for illustration purposes. The regions in the third row show the respective noise multiplication from Eq. [4]. Illustration-1 has 89m pixel spacing and illustration-2 has 107m pixel spacing. Breast areas for illustration-1 are (a) C-View-78 cm² and rectangle-34 cm²; (b) central slice-78 cm² and rectangle-33.cm²; Breast areas for illustration-2 are: (c) C-View-173 cm² and rectangle-77 cm²; (d) slice-170.cm² and rectangle-75.cm².

Figure 2.

Wavelet Expansion Component Illustrations: these show the wavelet expansion components corresponding to the regions in the second row of Figure 1 excised from the illustration images. The top row shows the ${\text{d}}_1(\text{x},\text{y})$ components from Eq. [1]: (a) derived from the C-View image for illustration-1; (b) respective central slice image; (c) derived from the C-View image for illustration-2; and (d) respective central slice image. In the same order, the bottom row shows the respective ${\text{e}}_1(\text{x},\text{y})$ components (from the third row of Figure 1) derived from noise multiplication in Eq. [4].

Figure 3.

Wavelet Expansion of Random Noise: we use this as a control experiment to show the variances from the wavelet expansion images from Eq. [2] for noise and to describe what we have termed chatter: (a) $\text{g}(\text{x},\text{y})$, random noise image; (b) ${\text{d}}_1(\text{x},\text{y})$, high pass expansion image (uniform chatter); (c) ${\mathrm{f}}_1\left(\mathrm{x},\mathrm{y}\right)$, low pass expansion image.

Figure 4.

Signal Dependent Noise Plots: the top row shows the plots resulting from Eq. [1] (without noise multiplication) for the illustration images: top row, (a) derived from the C-view of illustration-1; (b) derived from the respective central slice image; (c) derived from the C-view illustration-2; and (d) derived from the respective central slice. The bottom row shows the respective plots derived from Eq. [4] (with noise multiplication) using the same ordering.

Figure 5.

Variance Image Illustrations: these show the variance images for the regions shown in Figure 1, respectively. The top row results from Eq. [1] (without noise multiplication) and the bottom row from Eq. [4] (with noise multiplication): top row, (a) derived from the C-view of illustration-1; (b) derived from the respective central slice image; (c) derived from C-view of illustration 2; and (d) derived from the central slice. The bottom row is ordered as the top row. Window levels and widths are the same for all illustrations: set with the cumulative frequencies, where the lower 10% of the pixel values were set to the 10^th % value and the upper 10^th % percent of the pixel values were set to 90^th % value.

Figure 6.

Breast Density Detection: the top row shows the detection resulting from Eq. [1] (without noise multiplication) in the top row, (a) C-view, illustration-1; (b) respective central slice image; (c) C-view, illustration-2; and (d) the respective central slice. The respective detection images resulting from Eq. [4] (with noise multiplication) are shown in the bottom row with the same ordering.

Figure 7.

Projected Standardized Synthetic Breast Density Images: these show the standardized, s(x,y), images for illustration-1 (left) and illustration-2 (right) resulting from Eq. [4]. Pixel values represent the percentage of dense tissue above their locations.

Figure 8.

Regression analysis with PD_v as a function of PD_m This shows the scatter plot between the two measures (points) and regression line (solid red), The analysis gave: slope ≈ 1.002, intercept ≈ −0.0201, and linear correlation ≈ 1.0.

Figure 9.

PD_s slice Profiles: this shows PD_s (y-axis) by slice number using the normalized distance (p) from the breast support surface (p on the x-axis) for illustration-1 (left) and illustration-2 (right). PD_s values per slice number (points) were fitted with a second-degree polynomial (solid). The slice distance increases as the distance increases from the breast support surface (left side of each plot).

Figure 10.

DBT Volume Slice 2^nd Degree Polynomial Coefficient Histograms: these show the normalized histograms for the fit-coefficients, (a,b,c), separated by cases (top-row) and controls (bottom-row).

Figure 11.

Regression analysis with PD_v as a function of PD_syn: This shows the scatter plot between the two measures (points) and regression line (red-solid), The analysis gave: slope ≈ 0.92 with standard error ≈ 0.01, intercept ≈ −1.4 and R ≈ 0.93.