Developing a phenomenological model of the proton trajectory within a heterogeneous medium required for proton imaging

Abstract

To develop an accurate phenomenological model of the cubic spline path estimate of the proton path, accounting for the initial proton energy and water equivalent thickness (WET) traversed. Monte Carlo (MC) simulations were used to calculate the path of protons crossing various WET (10-30 cm) of different material (LN300, water and CB2-50% CaCO3) for a range of initial energies (180-330 MeV). For each MC trajectory, cubic spline trajectories (CST) were constructed based on the entrance and exit information of the protons and compared with the MC using the root mean square (RMS) metric. The CST path is dependent on the direction vector magnitudes (|P0,1|). First, |P0,1| is set to the proton path length (with factor Λ(Norm)(0,1) = 1.0). Then, two optimal factor Λ(0,1) are introduced in |P0,1|. The factors are varied to minimize the RMS difference with MC paths for every configuration. A set of Λ(opt)(0,1) factors, function of WET/water equivalent path length (WEPL), that minimizes the RMS are presented. MTF analysis is then performed on proton radiographs of a line-pair phantom reconstructed using the CST trajectories. Λ(opt)(0,1) was fitted to the WET/WEPL ratio using a quadratic function (Y = A + BX(2) where A = 1.01,0.99, B = 0.43,- 0.46 respectively for Λ(opt)(0), Λ(opt)(1)). The RMS deviation calculated along the path, between the CST and the MC, increases with the WET. The increase is larger when using Λ(Norm)(0,1) than Λ(opt)(0,1) (difference of 5.0% with WET/WEPL = 0.66). For 230/330 MeV protons, the MTF10% was found to increase by 40/16% respectively for a thin phantom (15 cm) when using the Λ(opt)(0,1) model compared to the Λ(Norm)(0,1) model. Calculation times for Λ(opt)(0,1) are scaled down compared to MLP and RMS deviation are similar within standard deviation.B ased on the results of this study, using CST with the Λ(opt)(0,1) factors reduces the RMS deviation and increases the spatial resolution when reconstructing proton trajectories.

Proof of principle of helium‐beam radiography using silicon pixel detectors for energy deposition measurement, identification, and tracking of single ions

“…22,27,32 The trajectory information of the particle could then be used in most likely path (MLP) algorithms for the optimization of the spatial resolution. [23][24][25][26] The helium-beam radiograph at a clinical dose level showed high CNR values ( > 3.5) for relative thickness differences of 1.2% in a WET range of the phantom of approximately 6 mm 9 WEPL PMMA %7mm. The upper limit of this range is given by the WET, at which the emerging ions are close to the end of their range in the last thin detection layer.…”

“…In the course of an eventual clinical translation of the reported helium‐beam radiography, an additional measurement of the position and direction of the helium ions in front of the object could be implemented as already pointed out in several works about proton tomography . The trajectory information of the particle could then be used in most likely path (MLP) algorithms for the optimization of the spatial resolution …”

“…9 The pCT Collaboration (Loma Linda University, University of California Santa Cruz, Northern Illinois University, California State University San Bernadino) used silicon strip detectors in order to measure the entrance/ exit position and direction 6,22 for the application in pCT. The additional directional information was used in so-called most likely path algorithms [23][24][25][26] to improve the spatial resolution. There are several further groups, for example, AQUA, PRIMA, and PRaVDA, working on tracking systems with a variety of different detection technologies for pCT 27 and pRad.…”

A theoretical framework to predict the most likely ion path in particle imaging

“…This equation bears a striking resemblance to the natural cubic spline formalism for the most likely path presented in Fekete et al (2015) ( Equation 12).…”

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

“…The faithful reconstruction of proton RSP maps, in terms of accuracy and reproducibility, is an important part of the successful clinical implementation of pCT. The approach that has been selected as the most promising in recent years, although technologically demanding, is to track individual protons through the patient and to predict their most likely path (MLP) [10], [11] in addition to measuring the energy loss of each proton and converting it to water-equivalent pathlength (WEPL). This has led to pCT reconstruction algorithms that are based on solving large and sparse linear equation systems, where each equation has the linear combination of intersection lengths of tracked protons through individual object voxels and the unknown RSP of those voxels on the left-hand side of the equation and the measured WEPL on the right-hand side of the equation.…”