The work is aimed on the study of the peculiarities for the distribution of optical density of DNA in the in-terphase nuclei of buccal epithelium upon the pathology of mammary glands, from the point of view of statistical and geometrical theory of pattern recognition. Two new indices characterizing this distribution-ratio of modal class volumes and relief index-are proposed. The smears of buccal epithelium were obtained from patients with breast diseases cured in the Department of Breast Cancer

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... of the Institute of Oncology (Kyiv, Ukraine). Age of the patients was in the range of 25 to 50 years. The scanograms of the interphase nuclei of buccal epithelium in patients suffering from fibroade-noma (FA, n = 12), fibroadenomatosis (FAM, n = 14), and cancer of the mammary gland (n = 41): infiltrative ductal cancer (IDC, n = 11), infiltrative lobular cancer (ILC, n = 18), infiltrative ductal-lobular cancer (IDLC, n = 10) and scirrhus (n = 2) are investigated. For the purposes of this study smears from various depth of the spinous layer were obtained (conventio-nally they were denoted as median and deep), after gargling and removing the superficial cell layer of the buccal mucous. The smears were dried out under room temperature and fixed for 30 min in Nikiforov's mixture. Then, a Feulgen reaction was made with cold hydroly-sis in 5 N HCl for 15 min at 21-22 °C. Optical density of the nuclei was registered by scanning cytospectropho-tometry at wave length of 575 nm and probe 0.05 µm. Aim: To study from the point of view of statistical and geometrical theory of pattern recognition, the peculiarities of the distribution of optical density of DNA in the interphase nuclei of mammary buccal epithelium upon pathology. Methods: Cytogenetic investigation of buccal smears and computer-based image analysis were used. Results: It is shown that in malignant neoplasms of the mammary glands compared with its values in benign, the optical density of DNA in the nuclei of buccal epithelium increase in a range from 0.15 to 0.30 conventional units. The sensitivity of that criterium varied from 80.5% to 96.8%, and specificity was 92.3%. Conclusion: The method proposed may be recommended as an additional one for improvement of the diagnosis of mammary pathologies. Abbreviations used: FA-fibroadenoma; FAM-fibroadenoma-tosis; IDC-infiltrative ductal cancer; ILC-infiltrative lobular cancer; IDLC-infiltrative ductal-lobular cancer. In each preparation, 10 to 20 nuclei were investigated. The DNA-fuchsine content in the nuclei of the epithe-liocytes was defined as a product of the density and area (in terms of conventional units). The scanograms obtained as a results of the investigations of the nuclei of the cells were analyzed using statistical and geometrical methods of pattern recognition [1-4]. The scanogram of the DNA distribution is a rectangular matrix R r ij i m j n = = = 1 1 , , , where r ij are values of pointwise optical density of chro-matin in interphase nuclei of the cell, expressed in terms of conventional unit of measure, and n, m are the numbers of points of the scanogram along vertical and horizontal lines, respectively. Usually the scanogram contains 8 or 9 rows and columns, hence it consists of 64 or 81 numbers. The first index, termed the ratio of modal class volumes (RMCV), is obtained by considering the set of all scanograms as an unarranged set of random values from some general population, and by distributing this set into 3 modal classes consisting of the random values from the predefined ranges M 1 = {s ij : 0 ≤ s ij < 0.15}, M 2 = {s ij : 0.15 ≤ s ij ≤ 0.30}, M 3 = {s ij : s ij > 0.30}, and, finally, by calculating the ratio of volumes of the modal classes M 1 and M 2 in kth scan-ogram: V card M card M k k k = 1 2 () () , where card M j (k) , j = 1, 2 is the number of the elements from the modal class M j (k) (for example, card M 2 (k) is the number of the points in k th scanograms where the DNA