Charles-Antoine Collins-Fekete

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

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 estimates precision is compared to the Monte Carlo simulated path. Every ion from hydrogen to carbon is simulated in two scenarios, (1) where the range is fixed and (2) 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). However, this scenario is identified as the configuration that maximizes the dose while minimizing the path resolution. In the scenario where the initial velocity is fixed, the maximal root-mean-square error between the estimated path and the Monte Carlo path drops significantly between the proton path estimate (0.29 mm) and the helium path estimate (0.09 mm) but increases for heavier ions up to carbon (0.12 mm). As a result, helium is found to be the particle with the most accurate path estimate for the lowest dose, potentially leading to tomographic images of higher spatial resolution.

A maximum likelihood method for high resolution proton radiography/proton CT.

Multiple Coulomb scattering (MCS) is the largest contributor to blurring in proton imaging. In this work, we developed a maximum likelihood least squares estimator that improves proton radiographys spatial resolution. The water equivalent thickness (WET) through projections defined from the source to the detector pixels were estimated such that they maximizes the likelihood of the energy loss of every proton crossing the volume. The length spent in each projection was calculated through the optimized cubic spline path estimate. The proton radiographies were produced using Geant4 simulations. Three phantoms were studied here: a slanted cube in a tank of water to measure 2D spatial resolution, a voxelized head phantom for clinical performance evaluation as well as a parametric Catphan phantom (CTP528) for 3D spatial resolution. Two proton beam configurations were used: a parallel and a conical beam. Proton beams of 200 and 330 MeV were simulated to acquire the radiography. Spatial resolution is increased from 2.44 lp cm-1 to 4.53 lp cm-1 in the 200 MeV beam and from 3.49 lp cm-1 to 5.76 lp cm-1 in the 330 MeV beam. Beam configurations do not affect the reconstructed spatial resolution as investigated between a radiography acquired with the parallel (3.49 lp cm-1 to 5.76 lp cm-1) or conical beam (from 3.49 lp cm-1 to 5.56 lp cm-1). The improved images were then used as input in a photon tomography algorithm. The proton CT reconstruction of the Catphan phantom shows high spatial resolution (from 2.79 to 5.55 lp cm-1 for the parallel beam and from 3.03 to 5.15 lp cm-1 for the conical beam) and the reconstruction of the head phantom, although qualitative, shows high contrast in the gradient region. The proposed formulation of the optimization demonstrates serious potential to increase the spatial resolution (up by 65[Formula: see text]) in proton radiography and greatly accelerate proton computed tomography reconstruction.

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

Abstract A precise relative stopping power map of the patient is crucial for accurate particle therapy. Charged particle imaging determines the stopping power either tomographically – particle computed tomography (pCT) – or by combining prior knowledge from particle radiography (pRad) and x-ray CT. Generally, multiple Coulomb scattering limits the spatial resolution. Compared to protons, heavier particles scatter less due to their lower charge/mass ratio. A theoretical framework to predict the most likely trajectory of particles in matter was developed for light ions up to carbon and was found to be the most accurate for helium comparing for fixed initial velocity. To further investigate the potential of helium in particle imaging, helium computed tomography (HeCT) and radiography (HeRad) were studied at the Heidel-berg Ion-Beam Therapy Centre (HIT) using a prototype pCT detector system registering individual particles, originally developed by the U.S. pCT collaboration. Several phantoms were investigated: modules of the Catphan QA phantom for analysis of spatial resolution and achievable stopping power accuracy, a paediatric head phantom (CIRS) and a custom-made phantom comprised of animal meat enclosed in a 2 % agarose mixture representing human tissue. The pCT images were reconstructed applying the CARP iterative reconstruction algorithm. The MTF10% was investigated using a sharp edge gradient technique. HeRad provides a spatial resolution above that of protons (MTF1010%=6.07 lp/cm for HeRad versus MTF10%=3.35 lp/cm for proton radiography). For HeCT, the spatial resolution was limited by the number of projections acquired (90 projections for a full scan). The RSP accuracy for all inserts of the Catphan CTP404 module was found to be 2.5% or better and is subject to further optimisation. In conclusion, helium imaging appears to offer higher spatial resolution compared to proton imaging. In future studies, the advantage of helium imaging compared to other imaging modalities in clinical applications will be further explored.

Inter-comparison of relative stopping power estimation models for proton therapy.

Theoretical stopping power values were inter-compared for the Bichsel, Janni, ICRU and Schneider relative stopping power (RSP) estimation models, for a variety of tissues and tissue substitute materials taken from the literature. The RSPs of eleven plastic tissue substitutes were measured using Bragg peak shift measurements in water in order to establish a gold standard of RSP values specific to our centres proton beam characteristics. The theoretical tissue substitute RSP values were computed based on literature compositions to assess the four different computation approaches. The Bichsel/Janni/ICRU approaches led to mean errors in the RSP of  -0.1/+0.7/-0.8%, respectively. Errors when using the Schneider approach, with I-values from the Bichsel, Janni and ICRU sources, followed the same pattern but were generally larger. Following this, the mean elemental ionisation energies were optimized until the differences between theoretical RSP values matched measurements. Failing to use optimized I-values when applying the Schneider technique to 72 human tissues could introduce errors in the RSP of up to  -1.7/+1.1/-0.4% when using Bichsel/Janni/ICRU I-values, respectively. As such, it may be necessary to introduce an additional step in the current stoichiometric calibration procedure in which tissue insert RSPs are measured in a proton beam. Elemental I-values can then optimized to match these measurements, reducing the uncertainty when calculating human tissue RSPs.

TU-FG-BRB-04: A New Optimization Method for Pre-Treatment Patient-Specific Stopping-Power by Combining Proton Radiography and X-Ray CT

PURPOSE The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work is to develop a robust and systematic method that yields accurate patient specific RSPs by combining pre-treatment X-ray CT and daily proton radiography. METHODS The method is formulated as a penalized least squares optimization (PLSO) problem min(|Ax-B|). The matrix A represents the cumulative path-length crossed in each material computed by calculating proton trajectories through the X-ray CT. The material RSPs are denoted by x and B is the pRad, expressed as water equivalent thickness. The equation is solved using a convex-conic optimizer. Geant4 simulations were made to assess the feasibility of the method. RSP extracted from the Geant4 materials were used as a reference and the clinical HU-RSP curve as a comparison. The PLSO was first tested on a Gammex RMI-467 phantom. Then, anthropomorphic phantoms of the head, pelvis and lung were studied and resulting RSPs were evaluated. A pencil beam was generated in each phantom to evaluate the proton range accuracy achievable by using the optimized RSPs. Finally, experimental data of a pediatric head phantom (CIRS) were acquired using a recently completed experimental pCT scanner. RESULTS Numerical simulations showed precise RSP (<0.75%) for Gammex materials except low-density lung (LN-300) (1.2%). Accurate RSP have been obtained for the head (µ=-0.10%, 1.5σ=1.12%), lung (µ=-0.33, 1.5σ=1.02%) and pelvis anthropomorphic phantoms (µ=0.12, 1.5σ=0,99%). The range precision has been improved with an average R80 difference to the reference (µ±1.5σ) of -0.20±0.35%, -0.47±0.92% and -0.06±0.17% in the head, lung and pelvis phantoms respectively, compared to the 3.5% clinical margin. Experimental HU-RSP curve have been produced on the CIRS pediatric head. CONCLUSION The proposed PLSO with prior knowledge X-ray CT shows promising potential (R80 σ<1.0% over all sites) to decrease the range uncertainty.

SU-C-204-04: Patient Specific Proton Stopping Powers Estimation by Combining Proton Radiography and Prior-Knowledge X-Ray CT Information

Purpose: The material relative stopping power (RSP) uncertainty is the highest contributor to the range uncertainty in proton therapy. The purpose of this work is to develop a robust and systematic method that yields accurate, patient specific, RSP by combining 1) pre-treatment x-ray CT and 2) daily proton radiograph of the patient. Methods: The method is formulated as a linear least-square optimization problem (min||Ax-B||2). The parameter A represents the pathlength crossed by the proton in each material. The RSPs for the materials (water equivalent thickness (WET)/physical thickness) are denoted by x. B is the proton radiograph expressed as WET crossed. The problem is minimized using a convex-conic optimization algorithm with xi

The impact of secondary fragments on the image quality of helium ion imaging

Single-event ion imaging enables the direct reconstruction of the relative stopping power (RSP) information required for ion-beam therapy. Helium ions were recently hypothesized to be the optimal species for such technique. The purpose of this work is to investigate the effect of secondary fragments on the image quality of helium CT (HeCT) and to assess the performance of a prototype proton CT (pCT) scanner when operated with helium beams in Monte Carlo simulations and experiment. Experiments were conducted installing the U.S. pCT consortium prototype scanner at the Heidelberg Ion-Beam Therapy Center (HIT). Simulations were performed with the scanner using the TOPAS toolkit. HeCT images were reconstructed for a cylindrical water phantom, the CTP404 (sensitometry), and the CTP528 (line-pair) [Formula: see text] ® modules. To identify and remove individual events caused by fragmentation, the multistage energy detector of the scanner was adapted to function as a [Formula: see text] telescope. The use of the developed filter eliminated the otherwise arising ring artifacts in the HeCT reconstructed images. For the HeCT reconstructed images of a water phantom, the maximum RSP error was improved by almost a factor 8 with respect to unfiltered images in the simulation and a factor 10 in the experiment. Similarly, for the CTP404 module, the mean RSP accuracy improved by a factor 6 in both the simulation and the experiment when the filter was applied (mean relative error 0.40% in simulation, 0.45% in experiment). In the evaluation of the spatial resolution through the CTP528 module, the main effect of the filter was noise reduction. For both simulated and experimental images the spatial resolution was  ∼4 lp cm-1. In conclusion, the novel filter developed for secondary fragments proved to be effective in improving the visual quality and RSP accuracy of the reconstructed images. With the filter, the pCT scanner is capable of accurate HeCT imaging.

Pre-treatment patient-specific stopping power by combining list-mode proton radiography and x-ray CT

The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining (1) pre-treatment x-ray CT and (2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin([Formula: see text])). The parameter A represents the cumulative path-length crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness/physical thickness) are denoted by x. The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linear-solver with [Formula: see text]. A was computed by superposing proton trajectories calculated with a cubic or linear spline approach to the CT. The materials RSP assigned in Geant4 were used for reference while the clinical HU-RSP calibration curve was used for comparison. The Gammex RMI-467 phantom was first investigated. The standard deviation between the estimated material RSP and the calculated RSP is 0.45%. The robustness of the techniques was then assessed as a function of the number of projections and initial proton energy. Optimization with two initial projections yields precise RSP (⩽1.0%) for 330 MeV protons. 250 MeV protons have shown higher uncertainty (⩽2.0%) due to the loss of precision in the path estimate. Anthropomorphic phantoms of the head, pelvis, and lung were subsequently evaluated. Accurate RSP has been obtained for the head ([Formula: see text]), the lung ([Formula: see text]) and the pelvis ([Formula: see text]). The range precision has been optimized using the calibration curves obtained with the algorithm, yielding a mean [Formula: see text] difference to the reference of 0.11  ±0.09%, 0.28  ±  0.34% and [Formula: see text] in the same order. The solutions accuracy is limited by the assumed HU/RSP bijection, neglecting inherent degeneracy. The proposed formulation of the problem with prior knowledge x-ray CT demonstrates potential to increase the accuracy of present RSP estimates.

Extension of the Fermi–Eyges most-likely path in heterogeneous medium with prior knowledge information

Particle imaging suffers from poor spatial resolution due to the multiple Coulomb scattering deflections undergone by the particles throughout their path. To account for these deflections, a most-likely path (MLP) formalism was developed based on a Bayesian adaption of the Fermi-Eyges theory. Previous work calculated the MLP formalism in a homogeneous water medium as an initial estimate. However, this potentially reduces the accuracy of the MLP estimate as well as the achievable resolution of the subsequent tomographic reconstruction. This work investigates the potential gain of introducing prior-knowledge on the medium composition and density to improve the MLP accuracy. To do so, a Monte Carlo (MC) Geant4 algorithm was used to simulate protons ([Formula: see text]) crossing three different anthropomorphic phantoms representing the lung, abdomen, and head. The prior-knowledge information is gathered from (1) the MC simulation for ground-truth (MLP-GT), or from (2) a recent DECT material decomposition technique (MLP-DECT). The reconstructed path accuracy using prior-knowledge methods is compared with (3) the path reconstructed in homogeneous water (MLP-Water) and (4) a path reconstruction method where the proton path is projected onto a Hull at the boundary of the phantom with a subsequent MLP-Water calculation (MLP-Hull). For each path reconstruction method, the maximal root-mean-square error (RMSmax) is compared between the reconstructed and the MC path. In every phantom, the RMSmax is decreased between the MLP-Water and the three other path algorithms that take into account heterogeneities ([Formula: see text] for the lung, [Formula: see text] for the abdomen and [Formula: see text] for the head), with no significant differences between each (MLP-DECT, MLP-GT and MLP-Hull). In conclusion, the introduction of prior-knowledge in the MLP formalism decreases the RMS uncertainty to the MC path, but no further than the use of a simpler Hull contour algorithm. The use of this Hull algorithm is suggested for future particle imaging applications.

Sci-Fri PM: Radiation Therapy, Planning, Imaging, and Special Techniques - 01: On the use of proton radiography to reduce beam range uncertainties and improve patient positioning accuracy in proton therapy

To present two related developments of proton radiography (pRad) to minimize range uncertainty in proton therapy. The first combines a pRad with an X-ray CT to produce a patient-specific relative stopping power (RSP) map. The second aims to improve the pRad spatial resolution for accurate registration prior to the first. The enhanced-pRad can also be used in a novel proton-CT reconstruction algorithm. Monte Carlo pRad were computed from three phantoms; the Gammex, the Catphan and an anthropomorphic head. An optimized cubic-spline estimator derives the most likely path. The length crossed by the protons voxel-by-voxel was calculated by combining their estimated paths with the CT. The difference between the theoretical (length×RSP) and measured energy loss was minimized through a least squares optimization (LSO) algorithm yielding the RSP map. To increase pRad spatial resolution for registration with the CT, the phantom was discretized into voxels columns. The average column RSP was optimized to maximize the proton energy loss likelihood (MLE). Simulations showed precise RSP (<0.75%) for Gammex materials except low-density lung (<1.2%). For the head, accurate RSP were obtained (µ=−0.10%1.5σ=1.12%) and the range precision was improved (ΔR80 of −0.20±0.35%). Spatial resolution was increased in pRad (2.75 to 6.71 lp/cm) and pCT from MLE-enhanced pRad (2.83 to 5.86 lp/cm). The LSO decreases the range uncertainty (R80σ<1.0%) while the MLE-enhanced pRad spatial resolution (+244%) and is a great candidate for pCT reconstruction.