Microwaves Touted for Breast Screening

Microwave tomography can provide a cheaper and safer method of screening for breast cancer than X-ray mammography. Theoretically.

That’s the conclusion of a paper published this week in the SIAM Journal on Applied Mathematics. (SIAM is the Society for Industrial and Applied Mathematics.) In the paper, the authors describe a mathematical model for imaging breast tumors using microwave tomography (MT).

MT bombards the breast with low-power microwaves from different positions. The resulting scattered signals are collected and analyzed. Cancerous cells have a higher water content than normal tissue and thus create more scattering. MT also can produce an estimate of breast density. Dense breast tissue not only is a risk factor for breast cancer but also can make X-ray mammograms hard to read.

So MT should be cheaper, safer (because microwaves are nonionizing), and more accurate than conventional mammograms. Except that, as an SIAM news release puts it, “There is room for improvement in the mathematical method that currently exists for image reconstruction in microwave tomography.”

Specifically, there is an inverse scattering problem. It’s difficult to solve because it’s highly nonlinear. “In addition,” the news release says, “it is an ill-posed problem, which means that it does not have a solution in the strict sense, [and] the solutions are not usually unique, and may not depend continuously on the data.”

Yup; sounds like a problem.

The paper analyzes several approaches to solving it. We’re sure that, ill-posed or not, the issue will be resolved, thus presenting radiologists with a few problems of their own: Should they adopt this new technology? If so, how quickly? And how much will they have to spend?

Stay tuned.

Related seminar: Breast & Women’s Imaging Seminar