title: Fractal dimension in aspiration cytology smears of breast and cervical lesions.
abstract: OBJECTIVE
  To standardize the automated measurement of fractal dimension on cytologic smears and compare the fractal dimension of benign and malignant breast cells and cervical lesions on cytologic material to evaluate its role in the discrimination of benign from malignant cells.
  
  
  METHODS
  We randomly selected fine needle aspiration cytology smears of 42 cases of infiltrating duct carcinoma and 38 cases of fibroadenoma of the breast. Similarly, 16 cervical carcinoma and 20 normal cervical smears were selected for study. Ten cells were selected randomly from each case. Box counting of fractal dimension of malignant and benign cells was achieved with an image cytometer (Leica, Cambridge, England) using Quantimet 600 software (Leica). Then a well-spaced grid with multiple small boxes of a particular pixel length was superimposed on the cell. The dimension of the box was selected as 4, 8 and 16 pixels. With the help of a logical "AND" operation, we counted the number of boxes touching the peripheral margin of the cell nuclei. For each cell, the log-log graph of 1 per box size was plotted against the number of boxes touching the peripheral rim of the cell. The slope of each graph was identified using the least-squares method of regression analysis.
  
  
  RESULTS
  The mean fractal dimension of malignant cells was 0.8536 +/- 0.1120 as compared to 0.8403 +/- 0.1115 in benign cell groups. The Mann-Whitney U test showed a significant difference in fractal dimension in these 2 groups (P = .05). The mean fractal dimension of malignant cells from the cervix was 0.8656 +/- 0.1499 as compared to 0.8315 +/- 0.1312 in benign cells. The Mann-Whitney U test showed a significant difference in fractal dimension in these 2 groups (P < .02).
  
  
  CONCLUSIONS
  Fractal dimension may be a helpful adjunctive technique to discriminate between benign and malignant cells.
authors.affiliation: Department of Pathology, Post Graduate Institute of Medical Education and Research, Chandigarh, India.
authors.forename: Shivani
authors.initials: S
authors.lastname: Ohri
authors.forename: Pranab
authors.initials: P
authors.lastname: Dey
authors.forename: Raje
authors.initials: R
authors.lastname: Nijhawan
mesh_terms: D000465:Algorithms; D001707:Biopsy, Needle; D001943:Breast Neoplasms / Q000175:diagnosis / Q000473:pathology*; D002277:Carcinoma / Q000175:diagnosis / Q000473:pathology*; D018270:Carcinoma, Ductal, Breast / Q000175:diagnosis / Q000473:pathology*; D002467:Cell Nucleus / Q000473:pathology; D005260:Female; D018226:Fibroadenoma / Q000175:diagnosis / Q000473:pathology*; D017709:Fractals; D006801:Humans; D019044:Image Cytometry; D007091:Image Processing, Computer-Assisted; D002583:Uterine Cervical Neoplasms / Q000175:diagnosis / Q000473:pathology*