Goodsitt M M, Chan H P, Liu B, Guru S V, Morton A R, Keshavmurthy S, Petrick N
Department of Radiology, University of Michigan Hospital, Ann Arbor 48109, USA.
Med Phys. 1998 Jun;25(6):937-48. doi: 10.1118/1.598272.
We are developing an external filter method for equalizing the x-ray exposure in mammography. Each filter is specially designed to match the shape of the compressed breast border and to preferentially attenuate the x-ray beam in the peripheral region of the breast. To be practical, this method should require the use of only a limited number of custom built filters. It is hypothesized that this would be possible if compressed breasts can be classified into a finite number of shapes. A study was performed to determine the number of shapes. Based on the parabolic appearance of the outer borders of compressed breasts in mammograms, the borders were fit with the polynomial equations y = ax2 + bx3 and y = ax2 + bx3 + cx4. The goodness-of-fit of these equations was compared. The a,b and a,b,c coefficients were employed in a K-Means clustering procedure to classify 470 CC-view and 484 MLO-view borders into 2-10 clusters. The mean coefficients of the borders within a given cluster defined the "filter" shape, and the individual borders were translated and rotated to best match that filter shape. The average rms differences between the individual borders and the "filter" were computed as were the standard deviations of those differences. The optimally shifted and rotated borders were refit with the above polynomial equations, and plotted for visual evaluation of clustering success. Both polynomial fits were adequate with rms errors of about 2 mm for the 2-coefficient equation, and about 1 mm for the 3-coefficient equation. Although the fits to the original borders were superior for the 3-coefficient equation, the matches to the "filter" borders determined by clustering were not significantly improved. A variety of modified clustering methods were developed and utilized, but none produced major improvements in clustering. Results indicate that 3 or 4 filter shapes may be adequate for each mammographic projection (CC- and MLO-view). To account for the wide variations in exposures observed at the peripheral regions of breasts classified to be of a particular shape, it may be necessary to employ different filters for thin, medium and thick breasts. Even with this added requirement, it should be possible to use a small number of filters as desired.
我们正在开发一种用于均衡乳腺摄影中X射线曝光的外部滤过方法。每个滤过器都经过特殊设计，以匹配压缩乳房边界的形状，并优先衰减乳房周边区域的X射线束。为了切实可行，该方法应仅需使用有限数量的定制滤过器。据推测，如果可以将压缩乳房分类为有限数量的形状，这将是可行的。进行了一项研究以确定形状的数量。基于乳腺造影片中压缩乳房外边界的抛物线外观，边界用多项式方程y = ax² + bx³和y = ax² + bx³ + cx⁴拟合。比较了这些方程的拟合优度。a、b和a、b、c系数用于K均值聚类程序，将470张头尾位（CC）视图和484张内外斜位（MLO）视图的边界分类为2至10个聚类。给定聚类内边界的平均系数定义了“滤过器”形状，并且将各个边界进行平移和旋转以最佳匹配该滤过器形状。计算了各个边界与“滤过器”之间的平均均方根（rms）差异以及这些差异的标准差。将经过最佳平移和旋转的边界重新用上述多项式方程拟合，并绘制出来以便直观评估聚类的成功情况。两种多项式拟合都足够好，对于二系数方程，均方根误差约为2毫米，对于三系数方程，均方根误差约为1毫米。尽管对于三系数方程，对原始边界的拟合更好，但通过聚类确定的与“滤过器”边界的匹配并没有显著改善。开发并利用了多种改进的聚类方法，但没有一种方法在聚类方面产生重大改进。结果表明，对于每个乳腺摄影投照（CC视图和MLO视图），3或4种滤过器形状可能就足够了。为了考虑在分类为特定形状的乳房周边区域观察到的曝光的广泛变化，可能需要针对薄、中、厚乳房采用不同的滤过器。即使有了这个额外要求，按需使用少量滤过器应该也是可行的。
