The mathematical basis for the increased sensitivity in cancer detection in air-dried cytopreparations

It is known that the volume of a sphere is 4/3 pi r3, the area of a circle is pi r2, and the nuclear volume remains constant even when a cell is flattened. The effect of air-drying that flattens a spherical nucleus with a radius of r to a discoid nucleus with an expanded radius of R and a thickness of T can be stated as follows: pi R2 = (4/3 pi r3)/T. Based on this formula, a graph was plotted to illustrate the effect of air-drying on the observed nuclear areas (ONA) of cells of various size. The ONA of ethanol-fixed Pap/H&E-stained cells or cells in tissue sections is pi r2; the ONA of air-dried Diff-Quik-stained cells is pi R (2), i.e., (4/3 pi r3)/T. The former follows a first-order straight line, and the latter follows a second-order curve. As a consequence, the subtle "nuclear size enlargement" and "broader nuclear size distribution" of low-grade cancer cells, detectable only by statistical analysis of the data obtained by an image analyzer in ethanol-fixed cytopreparations or in formaldehyde-fixed tissue sections, become augmented to such a degree on the air-dried Diff-Quik-stained preparations that they are easily detected by direct microscopic observation. In conclusion, the increased sensitivity in cancer detection in air-dried cytopreparations is due to the fact that the ONA of air-dried cells reflects nuclear volume.