Mathematics of Thermoacoustic and Photoacoustic Tomography

Regents Of The University Of Idaho, Moscow ID

Investigators

Abstract

Thermoacoustic tomography is a hybrid method of biomedical imaging. It combines heating the tissues by microwave energy with detecting the induced ultrasound signals to achieve simultaneously high contrast and high resolution. Photoacoustic tomography is a sibling method, which uses laser light instead of microwaves to heat up the tissues. The two modalities have the same mathematical model, the observability problem of wave equation. The project is aimed to study several important mathematical issues relevant to these modalities. Firstly, it deals with the case of constant acoustic speed, addressing the range description, inversion formulas, and injectivity of the restricted spherical mean transform. Secondly, it studies the case of variable ultrasound speed. Topics include limited data, generalized spherical transform, and layered acoustic medium. Lastly, it considers the problem of finding the unknown ultrasound speed. The results from this project will contribute to the developments of new promising techniques in biomedical imaging. These developments will greatly impact the life science research, as they will help to provide better diagnostic information of non-transparent biological objects, e.g. patients' bodies. It is planned to distribute the results through publications in high quality journals as well as conference and colloquium/seminar presentations. It is also planned to attract students to work in the exciting area of mathematics of biomedical imaging.