title: Regular form factor. A new concept and calculating method for quantitative form description.
abstract: OBJECTIVE
  To quantitatively describe the shape of two-dimensional particles based on combined consideration of area (A), circumference (C), and major and minor diameter (d1 and d2, respectively).
  
  
  METHODS
  A regular form factor (RFF), a new concept and calculating method for form description, was defined as the extent to which a structure differs from an ellipse or circle of which the major and minor diameters, respectively, are equal to the described structure. Based on the definition of RFF, formulae were deduced in accordance with mathematical principles.
  
  
  RESULTS
  The deduced formulae were as follows: RFF = A [1.5(a + b) - square root of (a b)]/(a b C) and RFF = A [3 (d1 + d2) - 2 square root of (d1 d2)]/(d1 d2 C). In the formulae, a = d1/2, and b = d2/2. RFF = 1 for ellipses and circles, and < 1 for irregular particles. The more similar to an ellipse or circle, the closer to 1 is RFF. The more irregular the structures are, the smaller the values of RFF. An error analysis was also made, and a rectified formula for RFF was deduced. An example is given to show how to calculate RFF. A practical test of RFF was made in colorectal adenoma and adenocarcinoma in human material, and the results show that RFF of glands of colorectal adenoma and adenocarcinoma have significant differences between normal, adenoma and adenocarcinoma.
  
  
  CONCLUSIONS
  RFF was compared with the parameter Form AR, and the results showed that RFF is more sensitive in describing the irregularity of a structure than Form AR. RFF is of practical significance for describing structures in human material.
authors.affiliation: Department of Pathology, First Military Medical University, Guangzhou, People's Republic of China.
authors.forename: H
authors.initials: H
authors.lastname: Shen
mesh_terms: D000230:Adenocarcinoma / Q000473:pathology; D000236:Adenoma / Q000473:pathology; D002277:Carcinoma / Q000473:pathology; D003106:Colon / Q000166:cytology; D015179:Colorectal Neoplasms / Q000473:pathology; D006801:Humans; D019044:Image Cytometry / Q000379:methods* / Q000706:statistics & numerical data; D007091:Image Processing, Computer-Assisted / Q000379:methods* / Q000706:statistics & numerical data; D008432:Mathematical Computing; D008499:Medical Records / Q000706:statistics & numerical data