title: The Ebbeson-Tang formula. Theoretical background of an alternative to the disector in stereologic cell count studies.
abstract: OBJECTIVE
  To evaluate the formula of Ebbeson and Tang (FET) with respect to the disector (DS) principle.
  
  
  METHODS
  The DS principle has been proposed for avoiding cell count bias. 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 slice. The resulting number divided by the thickness of the DS gives an accurate figure for cell number by volume. FET applies two sections of different thickness, usually cut adjacent. Cells seen in the sections are counted by area, the figures are subtracted from each other, and the difference is divided by the difference between the thicknesses of the sections. The result is cell number by volume: NV = (NA1 - NA2)/(t1 - t2).
  
  
  RESULTS
  FET and the DS principle superficially appear different. However, from a geometric point of view they are based on the same principle. When the thickness of the thinner section of FET approaches zero, the situation is in all respects equal to the DS principle. The formula for DS can thus be written: NV = (NA1 - NA2)/t1.
  
  
  CONCLUSIONS
  The result proves that in principle DS and FET are equivalent methods of counting cell numbers by volume in tissues. FET may be more easily applied in histopathology practice because visual comparison of the sections is not necessary. Section thickness, however, has to be measured from vertically embedded sections or with scanning laser confocal microscopy. FET shares the stereologically unbiased character of the DS principle and is independent of the size and shape of structures counted.
authors.affiliation: Department of Pathology, University of Turku, Finland.
authors.forename: Y
authors.initials: Y
authors.lastname: Collan
mesh_terms: D002452:Cell Count / Q000379:methods*; D006801:Humans; D019044:Image Cytometry / Q000379:methods*; D008853:Microscopy / Q000379:methods; D008954:Models, Biological