3-D fractal tumor growth of epithelial ovarian cancer

Purpose: A fractal is a shape made of parts similar to the whole. Our objective was to determine whether surface growth patterns in malignant epithelial ovarian tumors are 3-D fractal, and if the mean fractal dimension differs according to histologic types.

Methods: After the images of photographs of 139 resected malignant epithelial ovarian tumors were digitized, the fractal dimensions of surface of solid portions were measured using 3-D fractal analysis software.

Results: The mean fractal dimensions of the surface of a solid area of tumor in serous, mucinous, endometrioid, and clear cell adenocarcinoma were 2.320, 2.224, 2.229, and 2.298, respectively. Those of serous and mucinous cystadenoma of low malignant potential (LMP) were 2.398 and 2.282, respectively. These values were significantly greater than the topological dimension of a surface (= 2). The mean fractal dimensions of a solid area of tumor inside the cyst for serous, mucinous, endometrioid, and clear cell carcinoma were 2.347, 2.223, 2.228, and 2.310, respectively. The values for serous and mucinous cystadenoma of LMP were 2.398 and 2.282, respectively.

Conclusion: This study shows that the surface of a solid area of malignant epithelial ovarian tumors has a 3-D fractal structure, and the mean fractal dimension may differ according to histologic types.

Epithelial ovarian cancer; Fractals; Fractal analysis; Fractal dimension; Fractal geometry

[1] Mandelbrot B.B.: "The fractal geometry of nature". New York, Freeman, 1982.

[2] Feder J.: "Fractals". New York, Plenum, 1988, 11.

[3] Mandelbrot B.B.: "How long is the coast of Britain? Statistical self-similarity and fractional dimension". Science, 1967, 156, 636.

[4] Kikuchi A., Kozuma S., Sakamaki K., Saito M., Marumo G., Yasugi T., Taketani Y.: "Fractal tumor growth of ovarian cancer: Sonographic evaluation". Gynecol. Oneal., 2002, 87, 295.

[5] Sasaki H., Shibata S., Hatanaka T.: "An evaluation method of Japanese lawn grass (Zoysia japonica STEUD.) for three different ecological functions (in Japanese with English summary)". Bull Natl. Grassl. Res. Inst., 1994, 49, 17.

[6] Pentland A.P.: "Fractal-based description of natural scenes". IEEE Trans. Pattern Anal Machine Intel!., 1984, PAMI-6, 661.

[7] Keller J.M., Chen S., Crownover R.M.: "Texture description and segmentation through fractal geometry". Computer Vision, Graphics, and Image Processing, 1989, 45, 150.

[8] Theiler J.: "Estimating fractal dimension". J. Opt. Soc. Amer. A., 1990, 7, 1055.

[9] Huang Q., Lorch J.R., Dubes R.C.: "Can the fractal dimension of images measured?". Pattern Recognition, 1994, 27, 339.

[10] J Kikuchi A., Kozuma S., Yasugi T., Taketani Y.: "Fractal analysis of surface growth patterns in endometrioid endometrial adenocarcinoma". Gynecol. Obstet. Invest., 2004, 58, 61.

[11] FIGO Cancer Committee: "Staging announcement". Gynecol Oncol., 1986, 25, 383.

[12] Sedivy R., Mader R.M.: "Fractals, chaos, and cancer: Do they coincide?". Cancer Invest., 1997, 15, 601.

[13] Smolle J.: "Fractal tumor stromal border in a noneguilibnum growth model". Analyt. Quant. Cytol. Histol., 1998, 20, 7.

[14] Hart W.R.:''Pathology of malignant and borderline epithelial tumors of ovary". In: Coppleson M. (ed.). Gynecologic Oncology, 2nd edition, Edinburgh, Churchill Livingstone, 1992, 863.

[15] Ozols R.F., Rubin S.C., Thomas G.M., Robboy S.J.: "Epithelial ovarian cancer". In: Hoskins W.J., Perez C.A., Young R.C. (eds.): Principles and Practice of Gynecologic Oncology, 3rd edition, Philadelphia, Lippincott Williams & Wilkins, 2000, 981.

[16] W heeler J.E.: "Pathology of malignant ovarian epithelial tumors and miscellaneous and rare ovarian and paraovarian neoplasms". In: Rubin S.C., Sutton G.P. (eds.): Ovarian Cancer (2rd edition), Philadelphia, Lippincott Williams & Wilkins, 2001, 99.

[17] Landini G.. Rippin J.W.: "Fractal dimensions of the epithelial-connective tissue interfaces in premalignant and malignant epithelial lesions of the floor of the mouth". Anal. Quant. Cytol. Histol., 1993, 15, 144.

[18] Cross S.S., Bury J.P., Silcocks P.B., Stephenson T.J., Cotton D.W.K.: "Fractal geometric analysis of colorectal polyps". J. Pathol., 1994, 172, 317.

[19] Velanovich V.: "Fractal analysis of mammographic lesions: A prospective blinded trial". Breast. Cancer Res. Treat., 1998, 49, 245.