Modeling, definition and applications of histogram features based on DNA values weighed by sine functions

To model new DNA histogram features that weigh DNA values with values of curves of a sine function and to show the definition and applications of such features.

A simple example of a sine feature can be modeled to yield the value zero if all cells are diploid or polyploid, with values of 2c, 4c or 8c, and to yield the value 100 if all cells are aneuploid, with DNA values of 3c, 6c or 12c-e.g., cells that are probably from a malignant lesion or indicate proliferation. All other values are multiplied by the corresponding sine value. We folded the logarithmic DNA histogram with a sine curve with positive values only.

Correlation with ploidy balance was -0.94, demonstrating the similarity of both features. The sine features, however, avoid cutpoints between diploid and aneuploid values and are therefore less influenced by minor mistakes in standardization of DNA histograms. We introduced deviation factors as variants; that led to higher sine values for higher c values. For breast carcinoma (N = 306) the sine values were spread from very low to very high values, whereas esophageal carcinomas (N = 125) were centered at a sine value of 50. In breast carcinoma the sine features also correlated with prognostic factors, including hormone receptor status.

Description of DNA histogram features by graphic demonstration of their weight functions improves understanding of features. Since functions respect the cyclic events in proliferation and are not influenced by polyploidization.