Distribution of gland-like structures in human gallbladder adenocarcinomas possesses fractal dimension
✍ Scribed by Waliszewski, Przemyslaw
- Book ID
- 101219701
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 77 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0022-4790
No coin nor oath required. For personal study only.
✦ Synopsis
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) ס 0.038, n ס 100 sections), and 1.340 (moderately differentiated adenocarcinomas, SD ס 0.044, n ס 100 sections). While both nuclear area and nucleo-cytoplasmic ratio in those tissues remain within a similar range (Analysis of Variance (ANOVA), F 0 ס 0.791 < F ␣ ס 3.84, P ס 3 × 10 -3 and F 0 ס 0.077 < F ␣ ס 3.84, P ס 10 -6 , respectively, for k ס 20,000 cells, in which F 0 is a value of the test function, F ␣ is a critical, limit value of the F-test at the constant confidence value ␣ ס 0.05), a difference of fractal dimension is significant (F 0 ס 3.94 > F ␣ ס 0.693, n ס 100 sections, P ס 2 × 10 -3 ). Also, variablity of fractal dimension between tumor sections is significant (moderately differentiated adenocarcinomas, F 0 ס 1.9856 > F ␣ ס 1.4262, n ס 100 sections, P ס 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.