Mathematical models for breast cancer detection with microwave tomography are cheaper and less risky

Jul 07, 2010

The most popular method of breast cancer detection today is X-ray mammography, which takes images of a compressed breast by low-dose ionizing radiation. However, there are several disadvantages to using X-rays for breast cancer screening, chief among them being the invasivity of radiation and the high costs, which limit their wide use and can deter women from getting them. In addition, depending on the age of the patient and tissue density, X-ray mammograms often result in false positives and negatives.

Microwave tomography can provide a cheaper and less risky alternative to X-ray mammography. In a paper published today in the SIAM Journal on Applied Mathematics, the authors describe a mathematical model for imaging tumors in the breast using microwave tomography. Microwave tomography detects cancers by measuring inhomogeneities in the of breast tissue. An array of low-power microwaves are transmitted into the breast from different positions and the resulting scattered signals are collected by antennas surrounding it. The malignant-to-normal tissue contrast arises because have higher water content, and are hence stronger scatterers than normal tissue.

The electrical properties measured by microwaves are sensitive to physiological parameters such as water content, temperature and vascularization. In addition, they can give an estimate of mammographic , which is a crucial factor in evaluating a patient's risk of . The distribution of these electrical parameters in space is used to reconstruct the image of the breast with the help of carefully designed algorithms.

There is room for improvement in the that currently exists for image reconstruction in microwave tomography. The problem to be solved is an inverse scattering problem. At microwave frequencies, the inverse problem is difficult to solve accurately because it is highly nonlinear. In addition, it is an ill-posed problem, which means that it does not have a solution in the strict sense, the solutions are not usually unique, and may not depend continuously on the data.

Different approaches have been used to circumvent these. One involves linearizing the problem, but this can result in significant loss of accuracy. A second approach uses nonlinear optimization and relies on initial apriori information on object shape and electric properties. While this yields more accurate results, its reliability depends on the accuracy of the initial information and is computationally expensive.

A more recent approach uses a qualitative method utilizing "sets" of linear integral equations of the first kind. While these are faster and don't require apriori information, they can only provide estimates for sets of points. In this paper, the authors use a linear sampling method in combination with a gap functional to take into account near fields instead of far fields. This results in higher accuracy.

Explore further: Heat distributions help researchers to understand curved space

More information: Access to the paper is available at: www.siam.org/journals/newpost.php

add to favorites email to friend print save as pdf

Related Stories

New breast cancer test under study

Jul 22, 2008

Whether a painless, portable device that uses electrical current rather than X-ray to look for breast cancer could be an alternative to traditional mammograms is under study at the Medical College of Georgia.

New breast imaging technology targets hard-to-detect cancers

Dec 03, 2008

Breast-specific gamma imaging (BSGI) is effective in the detection of cancers not found on mammograms or by clinical exam, according to a study presented today at the annual meeting of the Radiological Society of North America ...

Recommended for you

Computer games give a boost to English

10 hours ago

If you want to make a mark in the world of computer games you had better have a good English vocabulary. It has now also been scientifically proven that someone who is good at computer games has a larger ...

Saddam Hussein—a sincere dictator?

15 hours ago

Are political speeches manipulative and strategic? They could be – when politicians say one thing in public, and privately believe something else, political scientists say. Saddam Hussein's legacy of recording private discussions ...

Oldest representative of a weird arthropod group

15 hours ago

Biologists at Ludwig-Maximilians-Universitaet (LMU) in Munich have assigned a number of 435-million-year-old fossils to a new genus of predatory arthropods. These animals lived in shallow marine habitats ...

User comments : 0