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 r(3), the area of a circle is pi r(2), 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 radi us of R and a thickness of T can be stated as follows: pi R(2) = (4/3 pi r(3))/T. Based on this formula, a graph was plotted to illustrate t he effect of air-drying on the observed nuclear areas (ONA) of cells o f various size. The ONA of ethanol-fixed Pap/H&E-stained cells or cell s in tissue sections is pi r(2); the ONA of air-dried Diff-Quik-staine d cells is pi R (2), i.e., (4/3 pi r(3))/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 n uclear size distribution'' of low-grade cancer cells, detectable only by statistical analysis of the data obtained by an image analyzer in e thanol-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 obse rvation. In conclusion, the increased sensitivity in cancer detection in air-dried cytopreparations is due to the fact that the ONA of air-d ried cells reflects nuclear volume.