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Center for Nonlinear Studies |
The national “Moonshot†initiative in cancer research was recently formed by President Obama in order to eliminate cancer as we know it. This new research impetus will leverage the National Strategic Computing Initiative’s Exascale Computing Project to analyze growing collections of imaging data from cancer patients with the goal of improving early diagnosis and screening. In 2015, approximately 230,000 new cases of breast cancer were diagnosed in women in the U.S. and about 1 in 8 U.S. women are expected to develop invasive breast cancer in their lifetime. To reduce the scale of screening data better imaging methods for early detection of breast cancer are being developed. Current common screening methods like x-ray tomography, MRI, and ultrasound have many shortcomings such as poor contrast for cancerous tissue, the use of ionizing radiation, or reliance on contrast agents with their own side effects. For these reasons, thermoacoustic tomography (TAT) has been developed as a low cost, non-ionizing, non-invasive, method for imaging the electromagnetic properties of breast tissue to aid in cancer detection. The electromagnetic absorption in malignant tissue is around 4 times that of healthy breast tissue and the contrast between the dielectric-properties of malignant tissue and healthy tissue can be as much as 10:1. This makes thermoacoustic tomography an attractive diagnostic tool. However, there are still mathematical challenges to the implementation of TAT imaging. A major hurdle for TAT has been the effect of unknown acoustic heterogeneities on the image reconstruction process. The extent to which TAT data uniquely determines both acoustic and electromagnetic properties is unknown. This talk will begin with an overview of thermoacoustic imaging. We then prove that acoustic and electromagnetic properties are uniquely determined within the class of radially symmetric acoustic profiles. Our results pave the way for variational inversion approaches to simultaneous reconstruction of electro-acoustic properties using TAT measurements. In particular we show that variational reconstruction methods are feasible when the acoustic profile is close to radially symmetric.