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Background  Fractal geometry has been the basis for the development of a diagnosis of preneoplastic and neoplastic cells that clears up the undetermination of the atypical squamous cells of undetermined significance (ASCUS).    Methods  Pictures of 40 cervix cytology samples diagnosed with conventional parameters were taken. A blind study was developed in which the clinic diagnosis of 10 normal cells, 10 ASCUS, 10 L-SIL and 10 H-SIL was masked. Cellular nucleus and cytoplasm were evaluated in the generalized Box-Counting space, calculating the fractal dimension and number of spaces occupied by the frontier of each object. Further, number of pixels occupied by surface of each object was calculated. Later, the mathematical features of the measures were studied to establish differences or equalities useful for diagnostic application. Finally, the sensibility, specificity, negative likelihood ratio and diagnostic concordance with Kappa coefficient were calculated.    Results  Simultaneous measures of the nuclear surface and the subtraction between the boundaries of cytoplasm and nucleus, lead to differentiate normality, L-SIL and H-SIL. Normality shows values less than or equal to 735 in nucleus surface and values greater or equal to 161 in cytoplasm-nucleus subtraction. L-SIL cells exhibit a nucleus surface with values greater than or equal to 972 and a subtraction between nucleus-cytoplasm higher to 130. L-SIL cells show cytoplasm-nucleus values less than 120. The rank between 120–130 in cytoplasm-nucleus subtraction corresponds to evolution between L-SIL and H-SIL. Sensibility and specificity values were 100%, the negative likelihood ratio was zero and Kappa coefficient was equal to 1.    Conclusions  A new diagnostic methodology of clinic applicability was developed based on fractal and euclidean geometry, which is useful for evaluation of cervix cytology.

Diagnosis of cervical cells based on fractal and Euclidian geometrical measurements: Intrinsic Geometric Cellular Organization