A maximum likelihood proton path formalism for application in proton computed tomography

Abstract

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 3sigma 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. M riszwana Banu

Stopping power accuracy and achievable spatial resolution of helium ion imaging using a prototype particle CT detector system

“…Particle rate was set to roughly 1 MHz to avoid events pile up in the energy calorimeter. For radiography ~10 7 histories were recorded, for tomography, 90 projections consisting of 2.5-4x10 6 histories each were acquired.…”

“…The most widely used path reconstruction algorithm, the MLP, is a probabilistic method to estimate the particles lateral displacement and angular deflection at certain depth [4] [11]. Schulte et al [6] proposed a matrix based Bayesian MLP formalism, that derives the proton path solving the maximum likelihood problem based on Fermi-Eyges theory. Recently, Collins-Fekete et al [9] revisited and extended the Bayesian approach to work for the estimation of heavier ions trajectories.…”

“…To overcome the problem of MCS, various path estimation algorithms have been proposed for protons, of which the most likely path (MLP) algorithm is the most widely used [4][5][6][7][8]. Compared to protons, heavier ions suffer less from MCS, due to on average smaller deflection angles per scattering.…”

Development of a Proton Computed Tomography system for pre-clinical tests

“…The MLP concept has been introduced by Williams [3] and generalized by Schulte et al [19]. Given eight constraints at the boundaries of the phantom (2D-point and direction, both at entrance and exit of the phantom) is it possible to obtain an analytical expression of the most probable trajectory in a uniform medium.…”

Fast and Accurate Proton Computed Tomography Image Reconstruction for Applications in Proton Therapy

“…In one of the current generation pCT designs [5], individual protons are tracked pre-and post-patient with 2D sensitive silicon strip detectors (SSDs), providing information about proton position and direction at the boundaries of the image space. This allows the effects of multiple Coulomb scattering within the object to be accounted for in a most likely path (MLP) estimation [6], [7].…”