Fractal characterization of chromatin appearance for diagnosis in breast cytology

• Published in: The Journal of pathology Vol. 185; no. 4; pp. 366 - 381
• Main Authors: Einstein, Andrew J., Wu, Hai-Shan, Sanchez, Miguel, Gil, Joan
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.08.1998; Wiley
• Subjects: artificial neural networks; Biological and medical sciences; Biopsy, Needle; Breast - ultrastructure; breast cytology; Breast Neoplasms - diagnosis; Breast Neoplasms - ultrastructure; Carcinoma, Ductal, Breast - diagnosis; Carcinoma, Ductal, Breast - ultrastructure; Chromatin - ultrastructure; Epithelial Cells - ultrastructure; Female; fractal dimension; Fractals; Genital system. Mammary gland; Humans; image analysis; Image Processing, Computer-Assisted - methods; Investigative techniques, diagnostic techniques (general aspects); lacunarity; Logistic Models; logistic regression; Medical sciences; morphometry; Neural Networks (Computer); Pathology. Cytology. Biochemistry. Spectrometry. Miscellaneous investigative techniques; Human; Chromatin; Carcinoma; Fractal system; Malignant tumor; Neural network; Aspiration punction; Differential diagnostic; Fine needle aspiration biopsy; Mammary gland diseases; Pathology; Image analysis; Fine needle; Biopsy; Cytopathology; Mammary gland; Technique; Benign neoplasm; Morphometry
• ISSN: 0022-3417; 1096-9896
• DOI: 10.1002/(SICI)1096-9896(199808)185:4<366::AID-PATH122>3.0.CO;2-C

This study explores the use of fractal analysis in the numerical description of chromatin appearance in breast cytology. Images of nuclei from fine‐needle aspiration biopsies of the breast are characterized in terms of their Minkowski and spectral fractal dimensions, for 19 patients with benign epithelial cell lesions and 22 with invasive ductal carcinomas. Chromatin appearance in breast epithelial cell nuclear images is demonstrated to be fractal, suggesting that the three‐dimensional chromatin structure in these cells also has fractal properties. A statistically significant difference between the mean spectral dimensions of the benign and malignant cases is demonstrated. The two fractal dimensions are very weakly correlated. A statistically significant difference between the benign and malignant cases in lacunarity, a fractal property characterizing the size of holes or gaps in a texture, is found over a wide range of scales. These differences are particularly pronounced at the smallest and largest scales, corresponding respectively to fine‐scale texture, indicating whether chromatin is clumped or fine, and to large‐scale structures like nucleoli. Logistic regression and artificial neural network classification models are developed to classify unknown cases on the basis of fractal measures of chromatin texture. Using leave‐one‐out cross‐validation, the best logistic regression classifier correctly diagnoses 95·1 per cent of the cases. The best neural network model can correctly classify all of the cases, but it is unclear whether this is due to overtraining. Fractal dimensions and lacunarity are useful tools for the quantitative characterization of chromatin appearance, and can potentially be incorporated into image analysis devices to assure the quality and reproducibility of diagnosis by breast fine‐needle aspiration biopsy. © 1998 John Wiley & Sons, Ltd.