Fractal tumor growth of ovarian cancer: sonographic evaluation.

Objective: The objective of this study was to determine whether sonographically depicted ovarian tumor growth is fractal, and the mean fractal dimension differs according to stages of the disease and histologic types.
Methods: The fractal dimensions of outlines of sonographically depicted solid components in 160 ovarian tumors were measured using a box-counting method.
Results: The mean fractal dimensions of the surface of intracystic solid components in serous, mucinous, endometrioid, and clear cell adenocarcinoma were 1.259, 1.243, 1.238, and 1.182, respectively. These values were significantly greater than the topological dimension of a line (=1). The value was significantly higher in stage I or II (1.381) than stage III or IV (1.205) in serous carcinoma (P = 0.02), but not significantly different in clear cell carcinoma (1.187 and 1.172, respectively). In stage I or II, the value of serous carcinoma (1.381) was significantly higher than that of clear cell carcinoma (1.187) (P = 0.03). The value of mucinous cystadenoma of low malignant potential was 1.337, which was also significantly greater than 1. The mean fractal dimensions of outlines of solid tumors in cases with dysgerminoma and thecoma-fibroma were 1.036 and 1.023, respectively. These values were not significantly different from 1.
Conclusion: This study shows that the surface of solid components in cystic epithelial ovarian cancers has a fractal structure, and the mean fractal dimension may differ according to stages of the disease and histologic types. Fractal geometry, a vocabulary of irregular shapes, can be useful for describing the pathological architecture of ovarian tumors and for yielding insights into the mechanisms of tumor growth.