Fractal and Euclidean geometric diagnostic methodology of uterine cervix cells

Abstract

Background: Pathological interpretation of cellular form in cervical cytology is very important for prevention of cervical cancer. The methods most frequently used for assessment of this test have reproducibility and inter-observer variability problems.

Objective: To make fractal and Euclidean measurements to mathematically diagnose normal and premalignant cells of cervical squamous epithelium.

Methodology: 21 cells with normal, ASCUS or LSIL diagnosis according to the Bethesda system were assessed. Fractal and Euclidean geometric measures of three mathematical objects were calculated: cytoplasm, nucleus and whole cell. Mathematical proportions between these measurements were calculated in order to compare them with conventional classification methods.

Results: It was found that the nuclear border measures calculated with the 2-pixel grill and the surface measures could mathematically and objectively differentiate normal cells from the pre-malignant ones (ASCUS and LSIL).

Conclusions: An objective and reproducible diagnostic method was developed; it allows to identify the evolution towards malignant cellular states based on simultaneous fractal and Euclidean measures, establishing the severity level of ASCUS and LSIL cells.