Document Type : Original Article


1 Department of Chemistry, Khajeh Nasir Toosi University of Technology, Tehran, Iran

2 Research Center Karaj Moallem, Karaj, Iran


Hepatocellular carcinoma (HCC) is one of the deadliest types of cancer. The HCC is the most common (80%) of all primary liver cancers with mortality rate of 4.5 per 100 000 person/year. Early diagnosis of HCC can be an important factor in reducing mortality and timely treatment. One of diagnosis methods is the microscopic study of suspected cancer tissue and histopathology. In histopathology, tissue changes are investigated over time and the results are reported based on patterns. Since this comparison is often done visually and with the doctor's own diagnosis, it is not without errors. Therefore, HCC must be diagnosed early, and this is not possible except by carefully studying the liver tissue. In this way, HCC cancer should be detected from its early days and from liver tissue changes. This work requires identifying changes in liver tissue from a cellular perspective and studying the fractal patterns resulting from these changes. In this research, a fractal pattern similar to hepatocellular carcinoma (FPS-HCC) has been found in the Mandelbrot collection, which is an achievement in the recognition of fractal patterns of HCC. The study and source of the FPS-HCC paves the way for early recognition of HCC cancer.

Graphical Abstract

Fractal Pattern Similar to Hepatocellular Carcinoma (FPS-HCC) in the Mandelbrot set


Main Subjects


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[1]. Baish J.W., Jain R.K. Cancer Res., 2000, 60:3683 [Google Scholar], [Publisher]
[2]. Lee Y.T., Wang J.J., Luu M., Noureddin M., Kosari K., Agopian V.G., Rich N.E., Lu S.C., Tseng H.-R., Nissen N.N. JNCI: J. Natl. Cancer Inst., 2021, 113:1531 [Crossref], [Google Scholar], [Publisher]
[3]. D’Anselmi F., Valerio M., Cucina A., Galli L., Proietti S., Dinicola S., Pasqualato A., Manetti C., Ricci G., Giuliani A. Int. J. Biochem. Cell Biol., 2011, 43:1052 [Crossref], [Google Scholar], [Publisher]
[4]. Nanou A., Crespo M., Flohr P., De Bono J.S., Terstappen L.W. Cancers, 2018, 10:416 [Crossref], [Google Scholar], [Publisher]
[5]. Grizzi F., Spadaccini M., Chiriva-Internati M., Hegazi M.A., Bresalier R.S., Hassan C., Repici A., Carrara S. WJG, 2023, 29:4036 [Crossref], [Google Scholar], [Publisher]
[6]. Liebovitch L.S., Shehadeh L.A. Tutrorials in contemporary nonlinear methods, 2003, 24:178 [Google Scholar]
[7]. Delides A., Panayiotides I., Alegakis A., Kyroudi A., Banis C., Pavlaki A., Helidonis E., Kittas C. Anticancer Res., 2005, 25:2141 [Google Scholar], [Publisher]
[8]. Jiang K., Al-Diffalha S., Centeno B.A. Cancer Control, 2018, 25 [Crossref], [Google Scholar], [Publisher]
[9]. Vaysse P.-M., Grabsch H.I., van den Hout M.F., Bemelmans M.H., Heeren R.M., Damink S.W.O., Siegel T.P. Lab. Invest., 2021, 101:381 [Crossref], [Google Scholar], [Publisher]
[10]. Shiah A., Ong K.K., Musielak Z.E. Fractals, 1994, 2:111 [Crossref], [Google Scholar], [Publisher]
[11]. Peitgen H.-O., Jürgens H., Saupe D.  Fractals for the classroom: part two: complex systems and mandelbrot set. Springer Science & Business Media, 2012. [Google Scholar],
[12]. Devarasetty M., Dominijanni A., Herberg S., Shelkey E., Skardal A., Soker S. Sci. Rep., 2020, 10:9832 [Crossref], [Google Scholar], [Publisher]
[13]. Calderaro J., Ziol M., Paradis V., Zucman-Rossi J. J. Hepatol., 2019, 71:616 [Crossref], [Google Scholar], [Publisher]
[14]. Wang Q., Chen N., Yu C., Wei Z., Li Z., Jin Z. JBUON, 2019, 24:1408 [Google Scholar]
[15]. Michallek F., Sartoris R., Beaufrère A., Dioguardi Burgio M., Cauchy F., Cannella R., Paradis V., Ronot M., Dewey M., Vilgrain V. Insights Imaging, 2022, 13:1 [Crossref], [Google Scholar], [Publisher]