Geometrical nuclear diagnosis and total paths of cervical cell evolution from normality to cancer

Background: The diagnosis of cervix cytology has problems of inter-observer reproducibility. Methodologies based on fractal geometry objectively differentiated normal, low-grade squamous intraepithelial lesion (L-SIL) and high-grade squamous intraepithelial lesion (H-SIL) states. Aims: The aim was to develop a mathematical-physical diagnosis and a theoretical generalization of the evolution paths of cervical cells from normal to carcinoma based on their occupation in the box-counting space. Subjects and Methods: Overlaying a grid of 8x8 pixels, the a number of squares occupying the nucleus surface and cytoplasm of 5 normal cells, 5 ASCUS, 5 L-SIL and 5 H-SIL were evaluated, as well as the ratio C/N, establishing differences between states. Sensitivity, specificity, negative likelihood ratio, and Kappa coefficient over the gold standard were calculated. Also was developed a generalization of all possible paths from normality to carcinoma. Results: The occupancy spaces of the nuclear surface allow differentiating normal L-SIL and H-SIL thus avoiding the indeterminacy of ASCUS cells. Compared to the Gold Standard, this method has sensitivity and specificity of 100%, negative likelihood ratio of 0, and Kappa coefficient of 1. 62,900 possible routes of evolution were determined between normal and H-SIL, states, based on the structural basis of the cells. Conclusions: it was obtained an objective and reproducible diagnostic methodology of the development of preneoplastic and neoplastic cervical cells for clinical application. Additionally were developed all possible paths of preneoplastic cellular alteration to carcinoma which facilitates the tracking of patients over time to clinical level, warning of alterations that lead to malignancy, based on the spatial occupation measurements of the nucleus in fractal space regardless of causes or risk factors.