Theoretical and algorithmic foundations of novel medical imaging modalities

Since the invention of computer-aided tomography, numerous imaging modalities have been introduced and have demonstrated increasing value as diagnostic instruments in biology and medicine. These include Thermoacoustic and Photoacoustic Tomography (TAT and PAT), Magnetoacoustoelectric Tomography (MAET), and UltraSound Current Density Imaging (USCDI), which combine the high resolution of ultrasound with the sensitivity of electromagnetic waves to optical absorption and conductivity of the tissues, or to biological currents in the heart or in the brain.

Sharp abnormalities in the latter physical parameters are good markers of breast cancer, thrombosis, ischemia, epilepsy and other medical conditions. These new techniques overcome limitations of classical tomography, and deliver otherwise unavailable, potentially life-saving diagnostic information — at a lesser cost and with less harm to a patient.

The images in these modalities are obtained by complex mathematical procedures, rather than through direct acquisition. The underlying mathematics and the image reconstruction algorithms required by these methods are at very early stages of development. The investigator, in collaboration with domain scientists and medical engineers will work to resolve some of the central theoretical challenges and develop efficient numerical techniques for PAT, TAT, MAET and UCSDI.

A graduate student will play a significant role in the project, gaining exposure to practical and theoretical skills lying at the junction of exact sciences, medicine, and biology. The results of this project will be disseminated through publications in high quality research journals, presentations at national and international conferences, and a series of lectures at various major venues. The algorithms and the experimental data will be made publicly available.

The mathematics underlying and enabling such modalities as PAT, TAT, MAET and UCSDI scattering, contains a number of challenging open questions, important from both the theoretical and applied points of view. The investigator, with his graduate student and colleagues at several universities, aims to gain theoretical understanding and to develop efficient image reconstruction algorithms for these modalities.

In particular, they plan to (1) derive range conditions for the wave operator arising in TAT and PAT, defined on a spherical domain with a reduced measurement interval, (2) develop fast algorithms enabling deep learning techniques in data-intensive inverse problems of TAT and PAT (3) and on deriving, justify and explore an accurate model of ultrasound current detection in acoustically perturbed medium.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.