title: Fractal analysis of surface growth patterns in endometrioid endometrial adenocarcinoma.
abstract: OBJECTIVE
  A fractal is a shape made of parts similar to the whole in some way. The objective of this study was to determine whether surface growth patterns in endometrioid endometrial adenocarcinoma are fractal, and the mean fractal dimension differs according to histologic grades and depth of myometrial invasion.
  
  
  METHODS
  After the images of photographs of 120 resected uteri with endometrial cancers were digitized, the fractal dimensions of surface of tumors were measured using a fractal analysis software.
  
  
  RESULTS
  The mean fractal dimensions of surface growth patterns in G1, G2, and G3 adenocarcinoma were 2.318, 2.303, and 2.383, respectively. These values were significantly greater than the topological dimension of a surface (= 2). The value was significantly higher in G3 than in G2 (p = 0.03). And although not statistically significant, the value of G3 was greater than G1 (p = 0.10) and than (G1 and G2) group (p = 0.06). No significant difference nor tendency was found in the fractal dimension of the surface of the tumor according to depth of invasion.
  
  
  CONCLUSIONS
  This study shows that the surface of endometrioid endometrial adenocarcinoma has a fractal structure, and the mean fractal dimension may differ according to histologic grades. Our report proposes a new way of looking at endometrial cancer pathology. We believe that fractal geometry gives insights into tumor morphology and becomes a useful tool for analyzing complex and irregular tumor growth patterns mathematically.
authors.affiliation: Department of Obstetrics, Center for Perinatal Medicine, Nagano Children's Hospital, Nagano, Japan. dr-kiku@yj8.so-net.ne.jp
authors.forename: Akihiko
authors.initials: A
authors.lastname: Kikuchi
authors.forename: Shiro
authors.initials: S
authors.lastname: Kozuma
authors.forename: Toshiharu
authors.initials: T
authors.lastname: Yasugi
authors.forename: Yuji
authors.initials: Y
authors.lastname: Taketani
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D001707:Biopsy, Needle; D018450:Disease Progression; D016889:Endometrial Neoplasms / Q000473:pathology* / Q000601:surgery; D005260:Female; D017709:Fractals; D006801:Humans; D007044:Hysterectomy / Q000379:methods; D007150:Immunohistochemistry; D008875:Middle Aged; D009361:Neoplasm Invasiveness / Q000473:pathology*; D009367:Neoplasm Staging; D011379:Prognosis; D012189:Retrospective Studies; D012494:Sampling Studies; D012680:Sensitivity and Specificity; D046509:Tissue Culture Techniques