Study of cervical cancer through fractals and a method of clustering based on quantum mechanics

Abstract

Tumor growth in the cervix is a complex process. Understanding this phenomena is quite relevant in order to establish proper diagnosis and therapy strategies and a possible startpoint is to evaluate its complexity through the scaling analysis, which define the tumor growth geometry. In this work, tumor interface from primary tumors of squamous cells and adenocarcinomas for cervical cancer were extracted. Fractal dimension and local roughness exponent (Barabási and Stanley (1996)), α_loc, were calculated to characterize the in vivo 3-D tumor growth. Image acquisition was carried out according to the standard protocol used for cervical cancer radiotherapy, i.e., axial, magnetic resonance T1 - weighted contrast enhanced images comprising the cervix volume for image registration. Image processing was carried out by a classification scheme based on quantum clustering algorithm (Mussa et al. (2015)) combined with the application of the K-means procedure upon contrasted images (Demirkaya et al. (2008)). The results show significant variations of the parameters depending on the tumor stage and its histological origin.

Keywords: Algorithm; Cervix; Fractal; K-means; Local roughness.