Grant Gullberg

Research Interests

Study of inverse problems with application to medicine and biology

Research Summary

My research interests involve the study of inverse problems with application to medicine and biology that involve the use of computed tomography, magnetic resonance imaging (MRI), acoustic imaging, and magnetocardiography (MCG). Specifically, these interests include the study of the attenuated Radon transform, the development of reconstruction algorithms for single photon emission computed tomography (SPECT) with cone beam geometry, the development of methods for attenuation correction in SPECT using transmission computed tomography, the development of mechanical models for the heart to better model cardiac deformation using gated SPECT, the development of V-projection algorithms for reconstruction of Compton camera data, and the development of dynamic SPECT using kinetic modeling techniques to estimate perfusion and kinetic parameters of in vivo physiological processes. In addition, my interests include the development of angiographic techniques using MRI, the study of flow in vessels comparing MRI experimental results with mathematical models using finite difference techniques to solve systems of partial differential equations, the development of methods to measure tissue perfusion using magnetic resonance imaging, and the application of tensor tomography in MRI to measure in vivo diffusion tensor and in acoustic imaging to measure in vivo elasticity tensor. Also, more recently my interests have involved the study of MCG. In summary, my research interests are the application of mathematical physics to the solution of inverse problems in medical imaging, the development of physiological kinetic models for dynamic SPECT applications, the study of the physics of hemodynamic flow in vessels, the measurement of in vivo perfusion and diffusion processes using MRI, the study of the relationship between cardiac function and cardiac deformation, and the study of mechanical and electromagnetic inverse problems associated with cardiac function.

Selected Publications

Gullberg GT, Morgan HT, Zeng GL, Christian PE, Di Bella EVR, Tung C-H, Maniawski PJ, Hsieh Y-L, Datz FL. The design and performance of a simultaneous transmission and emission tomography system. IEEE Trans on Nucl Sci 45:1676-1698, 1998.

Gullberg GT, Wehrli FW, Shimakawa A, Simons MA. MR vascular imaging with a fast gradient refocusing pulse sequence and reformatted images from transaxial sections. Radiology 165:241-246, 1987.

Gullberg GT, Huesman RH, Ross SG, Di Bella EVR, Zeng GL, Reutter BW, Christian PE, Foresti SA. Dynamic cardiac single-photon emission computed tomography. In Nuclear Cardiology: State of the Art and Future Directions, BL Zaret and GA Beller, Eds. (St. Louis, Missouri: Mosby, Inc.), pp. 137-187, 1999.

Gullberg GT, Defrise M, Panin VY, Zeng GL. Efficient cardiac diffusion tensor MRI by three-dimensional reconstruction of solenoidal tensor fields. Magn Reson Imag 19:233-256, 2001.

Gullberg GT, Zeng GL, Datz FL, Christian PE, Tung C-H, Morgan HT. Review of convergent beam tomography in single photon emission computed tomography. Phys Med Biol 37:507-534, 1992.