Abstract

An accurate system matrix is required for quantitative proton CT (pCT) image reconstruction with
iterative projection algorithms. The system matrix is composed of chord lengths of individual
proton path intersections with reconstruction pixels. In previous work, reconstructions were performed
assuming constant intersection chord lengths, which led to systematic errors of the reconstructed
proton stopping powers. The purpose of the present work was to introduce a computationally
efficient variable intersection chord length in order to improve the accuracy of the system
matrix. An analytical expression that takes into account the discrete stepping nature of the pCT
most likely path (MLP) reconstruction procedure was created to describe an angledependent effective
mean chord length function. A pCT dataset was simulated with GEANT4 using a parallel
beam of 200 MeV protons intersecting a computerized head phantom consisting of tissueequivalent
materials with known relative stopping power. The phantom stopping powers were
reconstructed with the constant chord length, exact chord length, and effective mean chord length
approaches, in combination with the algebraic reconstruction technique. Relative stopping power
errors were calculated for each anatomical phantom region and compared for the various methods.
It was found that the error of approximately 10% in the mean reconstructed stopping power value
for a given anatomical region, resulting from a system matrix with a constant chord length, could be
reduced to less than 0.5% with either the effective mean chord length or exact chord length
approaches. Reconstructions with the effective mean chord length were found to be approximately
20% faster than reconstructions with an exact chord length. The effective mean chord length
method provides the possibility for more accurate, computationally efficient quantitative pCT
reconstructions.