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

Yair Censor, Keith E. Schubert, Reinhard W. Schulte

Research output: Contribution to journalArticlepeer-review


We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensity-modulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself to create images. The technique works by sending a low-intensity beam of protons through the patient and measuring the position, direction, and energy loss of each exiting proton. The pCT technique allows reconstruction of the volumetric distribution of the relative stopping power (RSP) of the patient tissues for use in treatment planning and pretreatment range verification. We have investigated new ways to make the reconstruction both efficient and accurate. Better accuracy of RSP also enables more robust inverse approaches to IMPT. For IMPT, we developed a framework for performing intensity modulation of the proton pencil beams. We expect that these developments will lead to additional project work in the years to come, which requires a regular exchange between experts in the fields of mathematics, computer science, and medical physics. We have initiated such an exchange by organizing annual workshops on the pCT and IMPT algorithm and technology developments. This report is, admittedly, tilted toward our interdisciplinary work and methods. We offer a comprehensive overview of results, problems, and challenges in pCT and IMPT with the aim of making other scientists wanting to tackle such issues and to strengthen their interdisciplinary collaboration by bringing together cutting-edge know-how from medicine, computer science, physics, and mathematics to bear on medical physics problems at hand.

Original languageEnglish
Pages (from-to)313-324
Number of pages12
JournalIEEE Transactions on Radiation and Plasma Medical Sciences
Issue number3
StatePublished - 1 Mar 2022

Bibliographical note

Publisher Copyright:
© 2017 IEEE.


  • Blob basis functions
  • Monte Carlo (MC) simulation
  • data partitioning
  • digital phantoms
  • intensity-modulated therapy
  • motion-adapted reconstruction
  • proton computed tomography (pCT)
  • proton therapy
  • superiorization

ASJC Scopus subject areas

  • Instrumentation
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


Dive into the research topics of 'Developments in Mathematical Algorithms and Computational Tools for Proton CT and Particle Therapy Treatment Planning'. Together they form a unique fingerprint.

Cite this