The Ebbeson-Tang formula - Theoretical background of an alternative to thedisector in stereologic cell count studies

OBJECTIVE: To evaluate the formula of Ebbeson and Tang (FET) with respect t o the disector (DS) principle. STUDY DESIGN: The DS principle has been proposed for avoiding cell count bi as. DS is a slice of tissue, and from it those cells by area are counted in microscopy; the cells are not in contact with one of the surfaces of the s lice. The resulting number divided by the thickness of the DS gives an accu rate figure for cell number by volume. FET applies two sections of differen t thickness, usually cut adjacent. Cells seen in the sections are counted b y area, the figures are subtracted from each other, and the difference is d ivided by the difference between the thicknesses of the sections. The resul t is cell number by volume: N-V = (N-A1-N-A2)/(t(1)-t(2)). RESULTS: FET and the DS principle superficially appear different. However, from a geometric point of view they are based on the same principle. When t he thickness of the thinner section of FET approaches zero, the situation i s in all respects equal to the DS principle. The formula for DS can thus be written: N-V = (N-A1-N-A2)/t(1). CONCLUSION: The result proves that in principle DS and FET are equivalent m ethods of counting cell numbers by volume in tissues. FET may be more easil y applied in histopathology practice because visual comparison of the secti ons is not necessary. Section thickness, however, has to be measured from v ertically embedded sections or with scanning laser confocal microscopy. FET shares the stereologically unbiased character of the DS principle and is i ndependent of the size and shape of structures counted.