Fractal analysis of mammographic lesions: a feasibility study quantifying the difference between benign and malignant...

The increased use of screening mammography has led to increased pressure to differentiate between benign and malignant lesions. Even those lesions considered "suspicious" by qualitative radiologists' interpretations may prove malignant in less than 30% of cases. Fractal analysis is a mathematical technique that quantifies complex shapes. The hypothesis tested is that fractal analysis can quantify the difference between the shapes of benign and malignant lesions as imaged by mammography. Ten mammograms from patients with biopsy-proven invasive ductal carcinoma and 10 mammograms from patients with biopsy-proven benign disease were compared using the box-counting technique of fractal analysis. The fractal dimension of the mediolateral and craniocaudal views were added together to derive the composite fractal dimension. Statistical analysis was done using the Mann-Whitney U test. The median composite fractal dimension for benign lesions was 1.831 (range 1.359-2.009) and for malignant lesions 2.477 (range 2.084-3.158) (P < 0.0001). In addition, all benign lesions had fractal dimensions < or = 2.009, and all malignant lesions had fractal dimensions > or = 2.084. In this sample of 10 mammograms of malignant lesions versus 10 mammograms of benign masses, the composite fractal dimension was perfectly discriminatory. Fractal analysis may be useful to evaluate mammographically discovered breast masses. A blinded, prospective trial will be needed to determine its ultimate usefulness.