Fractals - objects whose parts resemble the whole - were used to describe all the meandering coastline in the distribution of distant galaxies. Now there may be a very human application - as a tool for the diagnosis of malignant breast cancer. The technique, which appears in January 12 number of Physical Review Letters , gauges the extent of entanglement in the DNA of a cell.
Breast cancer diagnosis often begins with mammography, followed by a biopsy. In a common type of biopsy, a thin needle is used to aspirate some suspicious tissue cells. Although extremely difficult, a trained doctor can eyeball cancer cells in the laboratory, in part because the chromatin - the twisted mass of proteins and DNA that make up chromosomes - appears agglomerated in malignant cells than in benign. To the naked eye, according to a biopsy expert Shahla Masood, a pathologist at the University of Florida, Gainesville, breast cancer diagnosis from a few cells "is like looking through a keyhole and try to see the whole room. "
Indeed, it is often an anguished appeal with only a few cells, said Andrew Einstein, a team member at Mount Sinai School of Medicine in New York. "An upscale cytologist should be diagnosed correctly most of the time," he said.. But with less qualified doctors behind the microscope, cancer cells are sometimes falsely considered healthy
In hope to develop an easier and more reliable approach, Einstein and two colleagues evaluated a variety of mathematical techniques to measure lacunarity - or the size of the spaces between the regions of chromatin - cells, and to extract a "fractal dimension" the core. as a branch usually looks like a whole tree, chromatin close-ups look like larger pictures a large scale. the scale of this "self-similarity" is called fractal dimension.
The team tested the technique on high resolution cell nuclei images from 41 patients, 22 were known to have breast cancer. After scanning images, a computer measured the fractal dimension and lacunarity and made the correct diagnosis in 39 of 41 cases - a success rate that rivals that of the best doctors. Malignant cells tend to have lower fractal dimensions, or less self-similarity, which Einstein said supports the idea that cancer is associated with a "loss of complexity" in a cell structure.
"I really do not understand the math," concedes Alberto Marchevsky, a pathologist at Cedars-Sinai Medical Center, Los Angeles, "but it could be a very useful technique. "Masood agreed, but said more tests are needed before the diagnosis of the computer can be used clinically. Einstein said that these trials are underway and that an improved technique using neural networks is to the horizon.
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