The investigator and his colleague develop mathematical techniques, both analytic and numerical, for obtaining images of biological tissues. They concentrate on mathematical issues that arise in recently introduced imaging methods for which there is little mathematical theory: Thermoacoustic Tomography (TAT), Ultrasound-Modulated Optical Tomography (UOT), and Acousto-Electric Tomography (AET).
Computerized tomography has become a major method of medical diagnostic imaging and industrial non-destructive testing. Over time, many modalities have been developed, such as X-ray tomography (usual CAT scan), MRI, Emission Tomography, Optical Tomography (OT) and Electrical Impedance Tomography (EIT), to name only a few. All of them have their advantages and disadvantages in terms of contrast between different biological tissues, resolution, cost of devices and procedures, and safety of the patient. For instance, cheap and safe procedures like EIT and OT are plagued by low resolution. Recent years have brought novel methods of imaging that intend to overcome these problems and have a high potential for becoming cheap, safe and effective diagnostic tools. These are Thermoacoustic Tomography (TAT), Ultrasound-Modulated Optical Tomography (UOT), and Acousto-Electric Tomography (AET). They all combine different types of radiation to overcome the known difficulties of methods involving only one of these modalities (e.g., optical tomography, ultrasound imaging, or electrical impedance tomography), such as, for example, low contrast of ultrasound imaging and high instability and low resolution of optical and electrical impedance imaging. Mathematical issues are among the most crucial in development of these methods, because images have to be obtained by sophisticated mathematical procedures rather than by direct acquisition as in the standard (non-tomographic) X-ray imaging. However, in all these modalities necessary analytic and numerical tools are essentially absent or at very early stages of development. Thus, the investigators develop mathematical analytic and numerical techniques for obtaining images of biological tissues, with the primary targets being TAT, UOT, and AET. The project aids development and implementation of several new, cheap, and safe methods of medical diagnostic imaging to be used in clinics. Some applications for non-destructive industrial testing are also possible. Graduate students play a significant role in the project, and some of the project's techniques and results are incorporated into graduate-level classes. This prepares students for work in exciting contemporary areas at the junction of exact sciences and medicine and biology.
