Minkowski Functionals: Quantitative Classification of Breast Parenchymal Density

A recent study was conducted to test the hypothesis that spatial distribution of x-ray attenuation values in digital mammograms can be analyzed quantitatively by using topologic techniques based on Minkowski functionals.

Minkowski functionals are described as a set of topographic descriptors used in an algorithm for quantitative imaging processors.

The study concluded that Minkowski functionals are a novel reproducible approach to quantitatively classify breast parenchymal density.

The Study

Digital mammograms of 100 women performed over a 1-year period at a single institution were randomly chosen. Those that had prior breast surgery, known malignant disease, or breast implants were excluded.

Methodology
A 512- x 512-pixel region of interest was drawn on each of the mammograms in an area of the breast where the density pattern was homogeneous.

Subsequently, 2 experienced radiologists classified the parenchymal pattern within these regions of interest as normal, involution atrophy, or fibrosis based on predetermined qualitative definitions for each category.

Subsequently, quantitative density measurements were performed by first using mean, median, and 20th percentile values of gray-level intensity.

Subsequently, mathematic topology using Minkowski functional spectra analysis as described in a prior publication by Michielsen et al was used. Both quantitative methods were compared with the predetermined radiologist classifications as the standard.

Results
Minkowski functionals are a novel reproducible approach to quantitatively classify breast parenchymal density.

Mean, median, and 20th percentile gray-level intensity for normal breast tissue was 90 ± 9, 91 ± 8, and 68 ± 18, respectively. The mean, median, and 20th percentile gray-level intensity for involution was 84±7, 83 ± 7, and 75 ± 6, respectively, and for fibrosis, the mean, median, and 20th percentile gray-level intensity was 90 ± 8, 89 ± 9, and 73 ± 10, respectively.

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Using the qualitative classification as a standard, with the parameters obtained from gray-level histograms, only 37% to 66% of cases were classified correctly.

Comparatively, discriminant models of the spectral information of the Minkowski functionals exhibited a rate of correct classification of 76% to 83%.

Reviewer’s Comments
The heavy use of statistical analysis and technical descriptors in this study belie the potential this may have on the future of breast imaging by way of computer-aided detection.

We may see this kind of information resurface at a later date, when this approach to categorizing the density of breast tissue trickles down the industry path.

Author: Basil Hubbi, MD

Reference:

Boehm HF, Schneider T, et al. Automated Classification of Breast Parenchymal Density: Topologic Analysis of X-Ray Attenuation Patterns Depicted With Digital Mammography. AJR; 2008;191 (December): W275-W282

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