Collaborative Research: Mathematical Methods for Emerging Techniques of Biomedical Imaging

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A number of inexpensive, safe, and high contrast medical imaging procedures like Electrical Impedance Tomography (EIT) and Optical Tomography (OT) have been introduced in the recent decades. However, EIT and OT are plagued by instability and low resolution. To overcome these difficulties, novel hybrid methods are being currently developed that combine different types of radiation (e.g., ultrasound and electromagnetic waves). The idea is to combine the advantages of these waves, while alleviating their individual deficiencies. Among these methods, the project will concentrate mostly on the Thermoacoustic Tomography, Ultrasound-Modulated Optical Tomography, and Acousto-Electric Tomography, as well as possibly some newer emerging imaging modalities. It is devoted to developing mathematical analytic and numerical tools needed in these techniques, which are currently in their early (sometimes infant) stages of development. Computerized tomography is a major method of biomedical imaging, as well as of industrial non-destructive testing, geology, and other areas. Various modalities have been developed, including for instance the usual X-ray clinical ``CAT scan'', MRI, Optical, Ultrasound, and Electrical Impedance Tomography. All of them have their advantages and deficiencies in terms of resolution, cost, and safety. Thus a quest continues for new safer, cheaper, and reliable methods. In recent years, novel hybrid methods have been emerging, which promise to become cheap, safe and effective medical diagnostics tools. The project addresses the mathematical issues that are central in their development, since images have to be obtained by complex mathematical procedures rather than direct acquisition. Besides the significant impact on the development and implementation of several new inexpensive and safe methods of biomedical imaging, one can also envision a possibility of applications to non-destructive industrial testing and other areas where imaging of non-transparent objects is required.