A comprehensive theoretical comparison of proton imaging set-ups in terms of spatial resolution

Abstract

We present a comprehensive analytical comparison of four types of proton imaging set-ups and, to this end, develop a mathematical framework to calculate the width of the uncertainty envelope around the most likely proton path depending on set-up geometry, detector properties, and proton beam parameters. As a figure of merit for the spatial resolution achievable with each set-up, we use the frequency [Formula: see text] at which the modular transfer function of a density step decreases below 10%. We verify the analytical results with Monte Carlo simulations. We find that set-ups which track the angle and position of individual protons in front of and behind the phantom would yield an average spatial resolution of 0.3-0.35 lp mm assuming realistic geometric parameters (i.e. 30-40 cm distance between detector and phantom, 15-20 cm phantom thickness). For set-ups combining pencil beam scanning with either a position sensitive detector, e.g. an x-ray flat panel, or with a position insensitive detector, e.g. a range telescope, we find an average spatial resolution of about 0.1 lp mm for an 8 mm FWHM beam spot size. The pixel information improves the spatial resolution by less than 10%. In both set-up types, performance can be significantly improved by reducing the pencil beam size down to 2 mm FWHM. In this case, the achievable spatial resolution reaches about 0.25 lp mm. Our results show that imaging set-ups combining double scattering with a pixel detector can provide sufficient spatial resolution only under very stringent conditions and are not ideally suited for computed tomography applications. We further propose a region-of-interest method for set-ups with a pixel detector to filter out protons which have undergone nuclear reactions and discuss the impact of tracker detector uncertainties on the most likely path.

Design optimization of a pixel-based range telescope for proton computed tomography

“…(MCS) of the protons inside the patient, a separate set of positional detectors are usually placed upstream and downstream relative to the patient, so that each proton's curved path can be estimated using Bayesian methods [8].…”

Improving single-event proton CT by removing nuclear interaction events within the energy/range detector

“…While pCT exhibits other benefits (Schulte et al 2005, Depauw & Seco 2011, Oancea et al 2018, the achievable spatial resolution is limited due to multiple Coulomb scattering (MCS). To reduce the uncertainty introduced by MCS, in single-event pCT, the trajectory of each proton through the object is estimated during image reconstruction (Williams 2004, Li et al 2006, Schulte et al 2008, Erdelyi 2009, Collins-Fekete et al 2015, Collins-Fekete et al 2017, Krah et al 2018. The use of path reconstruction techniques requires sophisticated detector systems capable of acquiring the proton track information before and after the object to be imaged, as well as the residual energy/range on a single-event basis (Schulte et al 2004, Schulte et al 2008, Sadrozinski et al 2013.…”

Regularised patient-specific stopping power calibration for proton therapy planning based on proton radiographic images

“…In this work, we consider a proton imaging set-up which combines pencil beam scanning with a range telescope (Rinaldi et al 2013, 2014, Farace et al 2016. It can be employed in clinical practice potentially using available quality assurance (QA) equipment and without further hardware modifications in the treatment room (Krah et al 2018). It is therefore of interest to develop the mathematical tools necessary to perform a patient-specific CT-RSP calibration in combination with such a set-up.…”

“…For each scanned beam spot, the range telescope recorded a (discretised) Bragg curve from which the water equivalent thickness (WET) was determined using a data processing procedure detailed in (Krah et al 2018). From the list of beam spot coordinates and WET values, the proton radiography was constructed as 2D image so that each spot corresponded to one pixel in the proton radiography.…”