Fractals--objects whose parts resemble the whole--have been used to describe everything from the twists and turns of coastlines to the distribution of distant galaxies. Now there may be a very human application--as a tool for diagnosing malignant breast cancer. The technique, which appears in the 12 January issue of Physical Review Letters, gauges the extent of tangles in a cell's DNA.
Breast cancer diagnosis often begins with mammography, followed by a biopsy. During a common type of biopsy, a thin needle is used to suck out a few cells from suspicious tissue. Although extraordinarily difficult, a trained physician can eyeball cancerous cells in the lab, in part because chromatin--the twisted mass of proteins and DNA that form chromosomes--appears more clumped in malignant cells than in benign ones. To the naked eye, says biopsy expert Shahla Masood, a pathologist at the University of Florida, Gainesville, diagnosing breast cancer from a few cells "is like looking through a keyhole and trying to see the whole room."
Indeed, it's often an agonizing call with only a few cells, says Andrew Einstein, a team member at Mount Sinai School of Medicine in New York. "A top-notch cytologist should make the diagnosis correctly most of the time," he says. But with less skilled physicians behind the microscope, cancerous cells are sometimes falsely deemed healthy.
Hoping to develop an easier and more reliable approach, Einstein and two colleagues assessed a variety of mathematical techniques to measure the lacunarity--or size of gaps between chromatin regions--of cells, and to extract a "fractal dimension" of the nucleus. Just like a branch usually resembles a whole tree, close-ups of chromatin resemble larger scale images. The scale of that "self-similarity" is called the fractal dimension.
The team tested the technique on high-resolution images of cell nuclei from 41 patients, 22 of whom were known to have breast cancer. After digitizing the images, a computer measured the fractal dimension and lacunarity and made the right diagnosis in 39 out of 41 cases--a success rate that rivals that of the best physicians. Malignant cells tended to have lower fractal dimensions, or less self-similarity, which Einstein says supports the view that cancer is associated with a "loss of complexity" in a cell's structure.
"I don't really understand the math," concedes Alberto Marchevsky, a pathologist at Cedars-Sinai Medical Center, Los Angeles, "but it could be a very useful technique." Masood agrees, but says more tests are necessary before computer diagnosis can be used clinically. Einstein says those tests are under way, and that an improved technique using neural nets is on the horizon.