Validation of a method for measuring the volumetric breast density from digital mammograms

Abstract

The purpose of this study was to evaluate the performance of an algorithm used to measure the volumetric breast density (VBD) from digital mammograms. The algorithm is based on the calibration of the detector signal versus the thickness and composition of breast-equivalent phantoms. The baseline error in the density from the algorithm was found to be 1.25 +/- 2.3% VBD units (PVBD) when tested against a set of calibration phantoms, of thicknesses 3-8 cm, with compositions equivalent to fibroglandular content (breast density) between 0% and 100% and under x-ray beams between 26 kVp and 32 kVp with a Rh/Rh anode/filter. The algorithm was also tested against images from a dedicated breast computed tomography (CT) scanner acquired on 26 volunteers. The CT images were segmented into regions representing adipose, fibroglandular and skin tissues, and then deformed using a finite-element algorithm to simulate the effects of compression in mammography. The mean volume, VBD and thickness of the compressed breast for these deformed images were respectively 558 cm(3), 23.6% and 62 mm. The displaced CT images were then used to generate simulated digital mammograms, considering the effects of the polychromatic x-ray spectrum, the primary and scattered energy transmitted through the breast, the anti-scatter grid and the detector efficiency. The simulated mammograms were analyzed with the VBD algorithm and compared with the deformed CT volumes. With the Rh/Rh anode filter, the root mean square difference between the VBD from CT and from the algorithm was 2.6 PVBD, and a linear regression between the two gave a slope of 0.992 with an intercept of -1.4 PVBD and a correlation with R(2) = 0.963. The results with the Mo/Mo and Mo/Rh anode/filter were similar.

Figure 1

Flowchart summary of the validation process. From top to bottom: sagittal slice from a segmented CT volume, sagittal slice from the displaced volume, negative logarithm of the simulated digital mammogram and calculated density map of the mammogram.

Figure 2

Illustration of segmentation on a coronal CT slice. Left: original slice in units of the effective linear attenuation coefficient (cm⁻¹) displayed with a narrow window; right: segmented slice.

Figure 3

Illustration of the finite-element model (FEM) deformation process. U represents the magnitude of the displacement in cm.

Figure 4

Projection geometry. Left: side view; right, top view.

Figure 5

Sample image of the ‘plug’ phantom with surrounding ‘padding’.

Figure 6

Illustration of the finite-element deformation and cropping (white vertical line). Left: original segmented CT; right: displaced fractional density volume. From top to bottom, sagittal, transverse and coronal slices.

Figure 7

Distribution of ADU/mAs values on simulated and experimental images of a breast equivalent phantom of thickness 5 cm (a) and 7 cm (b), imaged at 28 kVp (a) and 30 kVp (b), with a Rh/Rh anode/filter. The dashed line is the simulated image and the solid line is the experimental image. The distributions are computed over an area of approximately 107 cm² of the projected area of the phantom.

Figure 8

(a) Comparison between the means of the experimental (full lines) and simulated (dashed lines) phantom images. The open circles, squares and disk represent the 3 cm, 5 cm and 7 cm images, respectively. Marker size is representative of the error in the values. (b) Corresponding difference ΔM in PVBD between experiment and simulation.

Figure 9

Histogram of the VBD difference between the density on the plug phantoms and the calculated density from the phantoms using Cumulus.

Figure 10

Comparison between VBD from CT and Cumulus V for the set of images with a Rh/Rh anode/filter combination. Open circles denote the VBD with skin and crosses the VBD_NSk. Dashed line is the identity function.

Figure 11

Comparison between VBD from CT and Cumulus V for the set of images with a Mo/Rh anode/filter (a) and a Mo/Mo anode/filter (b). Open circles denote the VBD with skin and crosses the VBD_NSk. Dashed line is the identity function.