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We summarize recent results and ongoing activities in mathematical algorithmsand computer science methods related to proton computed tomography (pCT) andintensity-modulated particle therapy (IMPT) treatment planning. Proton therapynecessitates a high level of delivery accuracy to exploit the selectivetargeting imparted by the Bragg peak. For this purpose, pCT utilizes the protonbeam itself to create images. The technique works by sending a low-intensitybeam of protons through the patient and measuring the position, direction, andenergy loss of each exiting proton. The pCT technique allows reconstruction ofthe volumetric distribution of the relative stopping power (RSP) of the patienttissues for use in treatment planning and pre-treatment range verification. Wehave investigated new ways to make the reconstruction both efficient andaccurate. Better accuracy of RSP also enables more robust inverse approaches toIMPT. For IMPT, we developed a framework for performing intensity-modulation ofthe proton pencil beams. We expect that these developments will lead toadditional project work in the years to come, which requires a regular exchangebetween experts in the fields of mathematics, computer science, and medicalphysics. We have initiated such an exchange by organizing annual workshops onpCT and IMPT algorithm and technology developments. This report is, admittedly,tilted toward our interdisciplinary work and methods. We offer a comprehensiveoverview of results, problems, and challenges in pCT and IMPT with the aim ofmaking other scientists wanting to tackle such issues and to strengthen theirinterdisciplinary collaboration by bringing together cutting-edge know-how frommedicine, computer science, physics, and mathematics to bear on medical physicsproblems at hand.

Developments in Mathematical Algorithms and Computational Tools for Proton CT and Particle Therapy Treatment Planning