Proton computed tomography (pCT) is an imaging modality that has been suggested as a means for reducing the range uncertainty during proton radiation treatments. By measuring the spatial location of individual protons pre- and post-patient, as well as the energy lost along the proton path, three dimensional maps of patient water equivalent electron densities can be directly generated. These images can then be used by the treatment planning software to more accurately predict treatment dose distributions than the currently used X-ray CT conversion methods. In pCT, the spatial measurements are employed in a maximum likelihood proton path formalism that models multiple Coulomb scattering within the patient, maximizing the spatial resolution of the reconstructed image. The energy measurements are converted to the integral relative electron density along this predicted path with the Bethe-Bloch equation. Algebraic reconstruction techniques (ART) are an attractive reconstruction method for accommodating the nonlinear proton paths through the image space. However, pCT reconstructions with the standard ART algorithm have been found to require too much time for clinical practicality. This paper explores the possibility of using parallel compatible block-iterative and string-averaging algebraic reconstruction techniques, which can speed up the reconstruction by allowing simultaneous execution over multiple processing units. With the use of a Monte Carlo simulated pCT data set, we compared the performance, in terms of image quality, of a number of block-iterative and string-averaging algorithms. It was concluded that reconstructions with the block-iterative and string-averaging algorithms did not degrade the image quality relative to the standard ART algorithm. Thus, we are confident that with the appropriate computing hardware, 3D pCT images are capable of being generated in clinically relevant time frames, without sacrificing image quality.
in: Y. Censor, M. Jiang and G. Wang (Editors), Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Medical Physics Publishing, Madison, WI, USA, 2009 to appear, accepted for publication.