The Fractal Doctor
Fractals-objects whose individual parts repeat their whole-can be used to describe everything from the meanders and curves of a coastline to the distribution of distant galaxies. Now there may be another use for fractals: as a diagnostic tool for malignant breast cancer. Diagnosis of breast cancer often begins with mammography, followed by a biopsy. In a common type of biopsy, the doctor sucks a few cells out of suspicious tissue with a thin needle. A trained doctor is able to distinguish cancer cells from he althy cells in the laboratory - although this is very difficult. The distinguishing feature is that the chromatin appears more clumped in malignant cells than in benign ones. According to Shahla Masood of the University of Florida, Gainesville, diagnosing breast cancer from a few cells "is like looking through a keyhole to see the whole room."
According to Andrew Einstein of the Mount Sinai School of Medicine in New York, diagnosis from just a few cells is really often an agonizing task. He says: "A first-class cytologist usually diagnoses correctly." However, less experienced doctors sometimes mistake cancer cells for he althy cells under the microscope.
In hopes of finding an easier and more reliable method, Einstein and two of his colleagues evaluated various mathematical techniques to measure the size of the gaps between individual chromatin regions of cells and to extract a fractal dimension of the nucleus (Physical Review Letters, January 12, 1998 issue). Just as a branch usually resembles the entire tree, close-up chromatin images resemble corresponding images of larger sections. A measure of how densely all branches together fill the available space is called fractal dimension.
The team tested the technique on high-resolution nuclear images of 41 patients, 22 of whom were known to have breast cancer. After digitizing the images, the fractal dimension and the size of the gaps in the chromatin were measured by a computer. The result of the automatic diagnosis was correct in 39 out of 41 cases. This corresponds to the success rate of the best doctors. Malignant cells tend to have a lower fractal dimension. This, according to Einstein, supports the view that cancer is associated with a loss of complexity in cell structure.