Distribution of gland-like structures in human gallbladder adenocarcinomas possesses fractal dimension.

BACKGROUND AND OBJECTIVES: Epithelial cells form tissue patterns of higher order such as gland-like structures. A question arises whether distribution of those patterns in adenocarcinomas is subject to certain regularity.
METHODS: Due to the pilot nature of this study, gallbladder adenocarcinomas were preselected by histopathological, immunohistochemical, and morphometric analysis to ensure relative homogeneity of the patterns analyzed. A box-counting method was applied to investigate a relationship between a number of gland-like structures and a radius of the expanding family of the concentric circles.
RESULTS: The coefficient of linear regression characterizing that relationship possesses noninteger value. It is 1. 585 (well-differentiated adenocarcinomas, standard deviation (SD) = 0.038, n = 100 sections), and 1.340 (moderately differentiated adenocarcinomas, SD = 0.044, n = 100 sections). While both nuclear area and nucleo-cytoplasmic ratio in those tissues remain within a similar range (Analysis of Variance (ANOVA), F(0) = 0.791 < F(alpha) = 3.84, P = 3 x 10(-3) and F(0) = 0.077 < F(alpha) = 3.84, P = 10(-6), respectively, for k = 20,000 cells, in which F(0) is a value of the test function, F(alpha) is a critical, limit value of the F-test at the constant confidence value alpha = 0.05), a difference of fractal dimension is significant (F(0) = 3.94 > F(alpha) = 0.693, n = 100 sections, P = 2 x 10(-3)). Also, variablity of fractal dimension between tumor sections is significant (moderately differentiated adenocarcinomas, F(0) = 1.9856 > F(alpha) = 1.4262, n = 100 sections, P = 0.189).
CONCLUSIONS: There is fractal regularity in distribution of gland-like structures in human gallbladder adenocarcinomas. Fractal dimension is a holistic parameter which can be applied to evaluate tumor grading in a quantitative manner. Copyright 1999 Wiley-Liss, Inc.