A maximum likelihood proton path formalism for application in proton computed tomography
The limited spatial resolution in proton computed tomography (pCT) in comparison to x-ray CT is related to multiple Coulomb scattering (MCS) within the imaged object. The current generation pCT design utilizes silicon detectors that measure the position and direction of individual protons prior to and post-traversing the patient to maximize the knowledge of the path of the proton within the imaged object. For efficient reconstruction with the proposed pCT system, one needs to develop compact and flexible mathematical formalisms that model the effects of MCS as the proton traverses the imaged object. In this article, a compact, matrix-based most likely path (MLP) formalism is presented employing Bayesian statistics and a Gaussian approximation of MCS. Using GEANT4 simulations in a homogeneous 20 cm water cube, the MLP expression was found to be able to predict the Monte Carlo tracks of 200 MeV protons to within 0.6 mm on average when employing 3σ cuts on the relative exit angle and exit energy. These cuts were found to eliminate the majority of events not conforming to the Gaussian model of MCS used in the MLP derivation.