On the orientation of mammographic structure

Burgess et al. have shown that the power-spectral density of mammographic breast tissue P(f) follows a power-law, P(f) = c∕f(β).(1) Due to the complexity of the breast anatomy, breast phantoms often make use of power-law backgrounds to approximate the irregular texture of breast images. However, the current methodology of estimating power-law coefficients assumes that the breast structure is isotropic. The purpose of this letter is to demonstrate that breast anatomic structure is not isotropic, but in fact has a preferred orientation. Further, we present a formalism to estimate power-law coefficients β and c while accounting for tissue orientation in mammographic regions-of-interests (ROIs). We then show the effect of structure orientation on β and c, as well as on the appearance of simulated power-law backgrounds.

When breast tissue exhibits a preferred orientation, the radial symmetry in the associated power spectrum is broken. The new symmetry was fit by an ellipsoidal model. Ellipse tilt angle and axis ratio were accounted for in the power-law fit.

On average, breast structure was found to point toward the nipple: the average orientation in MLO views was 22.5 °, while it was 5 ° for CC views, and the mean orientation for left breasts was negative while it was positive for right breasts. For both power-law magnitude and exponent, the mean difference was statistically significant (<Δβ > = -0.096, <Δlog(c) > =-0.192).

A formalism for quantification of breast structure and structure orientation is provided. The difference in power-law coefficient estimates when accounting for orientation was found to be statistically significant. Examples of statistically defined backgrounds indicate that breast structure is mimicked more closely when structure orientation is accounted for.