Department of Radiology, The University of Chicago, Chicago, IL 60637, USA.
Med Phys. 2011 Oct;38(10):5303-6. doi: 10.1118/1.3633905.
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.
Burgess 等人已经表明，乳腺组织的功率谱密度 P(f) 遵循幂律，P(f)=c∕f(β)。(1)由于乳腺解剖结构的复杂性，乳腺体模通常利用幂律背景来近似乳腺图像的不规则纹理。然而，目前估计幂律系数的方法假设乳腺结构是各向同性的。本函的目的是证明乳腺解剖结构不是各向同性的，而是具有一个优先取向。此外，我们提出了一种形式来估计β和 c 的幂律系数，同时考虑了乳腺感兴趣区（ROI）中的组织取向。然后，我们展示了结构取向对β和 c 以及模拟幂律背景外观的影响。
当乳腺组织表现出优先取向时，相关功率谱中的径向对称被打破。新的对称性通过椭圆模型拟合。椭圆倾斜角和轴比在幂律拟合中得到了考虑。
平均而言，乳腺结构被发现指向乳头：在 MLO 视图中的平均取向为 22.5°，而在 CC 视图中为 5°，左乳的平均取向为负，而右乳的平均取向为正。对于幂律幅度和指数，平均差异具有统计学意义（<Δβ>=-0.096，<Δlog(c)>=-0.192）。
提供了一种量化乳腺结构和结构取向的形式。当考虑取向时，幂律系数估计的差异具有统计学意义。统计定义背景的示例表明，当考虑结构取向时，乳腺结构的模拟更接近。
