Photoacoustic Tomography

Photoacoustic tomography (PAT) is a recently developed medical imaging paradigm that combines the high spatial resolution of ultrasound imaging with the high contrast of optical imaging [Bea11, Kru99, XuWan06]. When a semitransparent sample is illuminated with a short pulse of electromagnetic energy near the visible range, then parts of the optical energy will be absorbed inside the sample, which causes a rapid, non-uniform increase of temperature. The increase of temperature yields a spatially varying thermoelastic expansion, which in turn induces an acoustic pressure wave. The acoustic pressure wave is measured outside of the object of interest, and mathematical algorithms are used to recover an image of the interior. PAT provides a good imaging contrast in soft tissues making it a very promising technique for detecting various types of early cancer, such as breast cancer or skin melanoma.

In our group, we develop and analyze various mathematical models and methods relevant for PAT. For example, in [Hal14, HP14, HP15] we derive theoretically exact reconstruction formulas for the cases that the imaging function imaging is supported inside spheres, ellipsoids, and other quadric hyper-surfaces. Mathematical models for PAT taking acoustic attenuation into account are developed and analyzed in [Kow14, KS12]. In another direction of research, we develop models and algorithms for PAT using integrating detectors (see, for example, [PNHB09, ZHS09]).

References:

[Bea11] P. Beard. Biomedical photoacoustic imaging. Interface focus, 1(4): 602–631, 2011

[Hal14] M. Haltmeier. Universal inversion formulas for recovering a function from spherical means. SIAM J. Math. Anal., 46(1):214–232, 2014.

[HP14] M. Haltmeier and S. Pereverzyev Jr. The universal back-projection formula for spherical means and the wave equation on certain quadric hypersurfaces, 2014, submitted. [pdf ]

[HP15] M. Haltmeier and S. Pereverzyev Jr. Recovering a function from circular means or wave data on the boundary of parabolic domains. SIAM J. Imaging Sci., 2015, to appear. [pdf ]

[Kow14] R. Kowar. On time reversal in photoacoustic tomography for tissue similar to water. SIAM J. Imaging Sci. 7(1):509–527, 2014. [arxiv.org]

[Kru99] R. A. Kruger, K. K. Kopecky, A. M. Aisen, Reinecke D. R., G. A. Kruger, and W. L. Kiser. Thermoacoustic CT with radio waves: A medical imaging paradigm. Radiology 200(1): 275–278, 1999.

[KS12] R. Kowar and O. Scherzer. Attenuation models in photoacoustics. In Mathematical modeling in biomedical imaging II, pp. 85-130, 2012.

[PNHB09] G. Paltauf, R. Nuster, M. Haltmeier, P. Burgholzer. Photoacoustic tomography with integrating area and line detectors  Chapter 20 in L.-H. Wang (Editor): Photoacoustic imaging and spectroscopy, CRC Press, 2009

[XuWan06] M. Xu and L. V. Wang. Photoacoustic imaging in biomedicine. Rev. Sci. Instrum., 77(4): 041101 (22pp), 2006.

[ZHS09] G. Zangerl, M. Haltmeier, O. Scherzer. Exact series reconstruction in photoacoustic tomography with circular integrating detectors. Commun. Math. Sci. 7(3): 665-678, 2009 [arxiv.org]