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

Abstract

In this work, a generic rigorous Bayesian formalism is introduced to predict the most likely path of any ion crossing a medium between two detection points. The path is predicted based on a combination of the particle scattering in the material and measurements of its initial and final position, direction and energy. The path estimate's precision is compared to the Monte Carlo simulated path. Every ion from hydrogen to carbon is simulated in two scenarios to estimate the accuracy achievable: one where the range is fixed and one where the initial velocity is fixed. In the scenario where the range is kept constant, the maximal root-mean-square error between the estimated path and the Monte Carlo path drops significantly between the proton path estimate (0.50 mm) and the helium path estimate (0.18 mm), but less so up to the carbon path estimate (0.09 mm). In the scenario where the initial velocity is kept constant, helium have systematically the minimal root-mean-square error throughout the path. As a result, helium is found to be the optimal particle for ion imaging.

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

“…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. Additionally, the complex, time-consuming MLP algorithm was linked to the recent, more efficient phenomenological approach [8].…”

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

“…It can be seen by the fact that the 2 mm wide steps could be clearly resolved for the images with tracking, while they could not be separately perceived in the images without tracking. The tracking of the ions is of importance, as the MCS of the helium ions — although less pronounced than for protons — plays a not negligible role for helium‐beam radiography . This is in contrast to carbon ion imaging, where many detection systems were developed without tracking capabilities based on the assumption that the image blurring due MCS of carbon ions is sufficiently small …”

“…The tracking of the ions is of importance, as the MCS of the helium ionsalthough less pronounced than for protonsplays a not negligible role for helium-beam radiography. 18,30 This is in contrast to carbon ion imaging, where many detection systems were developed without tracking capabilities based on the assumption that the image blurring due MCS of carbon ions is sufficiently small. 19,20,58 The presented detection system that allows helium ion tracking behind the object leads to good spatial resolutions (MTF 10% > 1.15 lp mm À1 ) in the case, where the feature of interest is located at the rear of the object.…”

“…28,29 However, there is still no combination of detection system and hadron that has been shown to be optimal for the clinical application of hadron imaging. Topics of ongoing discussion include the choice of suitable hadrons, 30 which influences the spatial resolution and the applied dose, the reduction of the thickness/material budget of the particle trackers that affect the spatial resolution due to MCS, 31 and the use of different detection systems for the energy/range measurement that influence the density resolution. 32, ‡ .…”

Helium CT: Monte Carlo simulation results for an ideal source and detector with comparison to proton CT

“…Ions heavier than protons are affected much less by MCS than protons due to the smaller charge‐to‐mass ratio. Comparing protons, helium, lithium, beryllium, boron, and carbon ions of the same initial energy (350 MeV/u), the minimum RMS error of most likely path (MLP) estimates was found to be smallest for helium ions, and only a minor improvement for heavier ions than helium was seen when the comparison was made at the same range . Therefore, helium ions were hypothesized to be optimal for imaging and in particular, an increase in image resolution is expected for helium CT (HeCT) compared to pCT.…”