Exploration of differentiability in a proton computed tomography simulation framework.

Objective.Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications.Approach.This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques.Main results.The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a 'fuzzy voxels' approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem.Significance.Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary.

Uncertainty-aware spot rejection rate as quality metric for proton therapy using a digital tracking calorimeter.

Objective.Proton therapy is highly sensitive to range uncertainties due to the nature of the dose deposition of charged particles. To ensure treatment quality, range verification methods can be used to verify that the individual spots in a pencil beam scanning treatment fraction match the treatment plan. This study introduces a novel metric for proton therapy quality control based on uncertainties in range verification of individual spots.Approach.We employ uncertainty-aware deep neural networks to predict the Bragg peak depth in an anthropomorphic phantom based on secondary charged particle detection in a silicon pixel telescope designed for proton computed tomography. The subsequently predicted Bragg peak positions, along with their uncertainties, are compared to the treatment plan, rejecting spots which are predicted to be outside the 95% confidence interval. The such-produced spot rejection rate presents a metric for the quality of the treatment fraction.Main results.The introduced spot rejection rate metric is shown to be well-defined for range predictors with well-calibrated uncertainties. Using this method, treatment errors in the form of lateral shifts can be detected down to 1 mm after around 1400 treated spots with spot intensities of 1 × 107protons. The range verification model used in this metric predicts the Bragg peak depth to a mean absolute error of 1.107 ± 0.015 mm.Significance.Uncertainty-aware machine learning has potential applications in proton therapy quality control. This work presents the foundation for future developments in this area.

Investigating particle track topology for range telescopes in particle radiography using convolutional neural networks.

BACKGROUND: Proton computed tomography (pCT) and radiography (pRad) are proposed modalities for improved treatment plan accuracy and in situ treatment validation in proton therapy. The pCT system of the Bergen pCT collaboration is able to handle very high particle intensities by means of track reconstruction. However, incorrectly reconstructed and secondary tracks degrade the image quality. We have investigated whether a convolutional neural network (CNN)-based filter is able to improve the image quality. MATERIAL AND METHODS: The CNN was trained by simulation and reconstruction of tens of millions of proton and helium tracks. The CNN filter was then compared to simple energy loss threshold methods using the Area Under the Receiver Operating Characteristics curve (AUROC), and by comparing the image quality and Water Equivalent Path Length (WEPL) error of proton and helium radiographs filtered with the same methods. RESULTS: The CNN method led to a considerable improvement of the AUROC, from 74.3% to 97.5% with protons and from 94.2% to 99.5% with helium. The CNN filtering reduced the WEPL error in the helium radiograph from 1.03 mm to 0.93 mm while no improvement was seen in the CNN filtered pRads. CONCLUSION: The CNN improved the filtering of proton and helium tracks. Only in the helium radiograph did this lead to improved image quality.

Helium radiography with a digital tracking calorimeter-a Monte Carlo study for secondary track rejection.

Radiation therapy using protons and heavier ions is a fast-growing therapeutic option for cancer patients. A clinical system for particle imaging in particle therapy would enable online patient position verification, estimation of the dose deposition through range monitoring and a reduction of uncertainties in the calculation of the relative stopping power of the patient. Several prototype imaging modalities offer radiography and computed tomography using protons and heavy ions. A Digital Tracking Calorimeter (DTC), currently under development, has been proposed as one such detector. In the DTC 43 longitudinal layers of laterally stacked ALPIDE CMOS monolithic active pixel sensor chips are able to reconstruct a large number of simultaneously recorded proton tracks. In this study, we explored the capability of the DTC for helium imaging which offers favorable spatial resolution over proton imaging. Helium ions exhibit a larger cross section for inelastic nuclear interactions, increasing the number of produced secondaries in the imaged object and in the detector itself. To that end, a filtering process able to remove a large fraction of the secondaries was identified, and the track reconstruction process was adapted for helium ions. By filtering on the energy loss along the tracks, on the incoming angle and on the particle ranges, 97.5% of the secondaries were removed. After passing through 16 cm water, 50.0% of the primary helium ions survived; after the proposed filtering 42.4% of the primaries remained; finally after subsequent image reconstruction 31% of the primaries remained. Helium track reconstruction leads to more track matching errors compared to protons due to the increased available focus strength of the helium beam. In a head phantom radiograph, the Water Equivalent Path Length error envelope was 1.0 mm for helium and 1.1 mm for protons. This accuracy is expected to be sufficient for helium imaging for pre-treatment verification purposes.

Image quality of list-mode proton imaging without front trackers.

List mode proton imaging relies on accurate reconstruction of the proton most likely path (MLP) through the patient. This typically requires two sets of position sensitive detector systems, one upstream (front) and one downstream (rear) of the patient. However, for a clinical implementation it can be preferable to omit the front trackers (single-sided proton imaging). For such a system, the MLP can be computed from information available through the beam delivery system and the remaining rear tracker set. In this work, we use Monte Carlo simulations to compare a conventional double-sided (using both front and rear detector systems) with a single-sided system (only rear detector system) by evaluating the spatial resolution of proton radiographs (pRad) and proton CT images (pCT) acquired with these set-ups. Both the pencil beam spot size, as well as the spacing between spots was also adjusted to identify the impact of these beam parameters on the image quality. Relying only on the pencil beam central position for computing the MLP resulted in severe image artifacts both in pRad and pCT. Using the recently extended-MLP formalism that incorporate pencil beam uncertainty removed these image artifacts. However, using a more focused pencil beam with this algorithm induced image artifacts when the spot spacing was the same as the beam spot size. The spatial resolution tested with a sharp edge gradient technique was reduced by 40% for single-sided (MTF 10% = 3.0 lp/cm) compared to double-sided (MTF 10% = 4.9 lp/cm) pRad with ideal tracking detectors. Using realistic trackers the difference decreased to 30%, with MTF 10% of 4.0 lp/cm for the realistic double-sided and 2.7 lp/cm for the realistic single-sided setup. When studying an anthropomorphic paediatric head phantom both single- and double-sided set-ups performed similarly where the difference in water equivalent thickness (WET) between the two set-ups were less than 0.01 mm in homogeneous areas of the head. Larger discrepancies between the two set-ups were visible in high density gradients like the facial structures. A complete CT reconstruction of a Catphan[Formula: see text] module was performed. Assuming ideal detectors, the obtained spatial resolution was 5.1 lp/cm for double-sided and 3.8 lp/cm for the single-sided setup. Double- and single-sided pRad with realistic tracker properties returned a spatial resolution of 3.8 lp/cm and 3.2 lp/cm, respectively. Future studies should investigate the development of dedicated reconstruction algorithms targeted for single-sided particle imaging.

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

Data filtering is crucial for accurate relative stopping power (RSP) reconstruction in proton CT (pCT). In this work, we assess different filters and their performance for the US pCT collaboration prototype pCT system in Monte Carlo (MC) simulations. The potential of using the recently proposed [Formula: see text]-E filter for removing nuclear interactions that occurred in the energy/range detector of the pCT system is investigated. Full pCT scans were acquired with the TOPAS MC simulated version of the prototype scanner that comprises two tracking detectors and a five stage energy/range detector. An ideal water cylinder and a water cylinder with five tissue inserts were investigated. Before image reconstruction, a [Formula: see text] WEPL filter was applied as the only filter, or in addition to filters acting on the energy deposit in each of the energy detector stages, as done currently with the prototype. The potential of the [Formula: see text]-E filter that was recently proposed for helium imaging was assessed. The results were compared to simulations for which nuclear interactions were disabled representing ground truth. The [Formula: see text] WEPL filter alone was not sufficient to filter out all nuclear interaction events and systematic fluctuations in the form of ring artifacts were present in the pCT reconstructed images. Applying energy filters currently used with the device prior to the [Formula: see text] WEPL filter only slightly improved the image quality. A [Formula: see text] WEPL filter improved the mean RSP accuracy, but could not fully remove the systematic fluctuations. The [Formula: see text]-E filter in addition to the current reconstruction procedure efficiently removed the systematic fluctuations and the achieved RSP accuracy closely matched the simulation without nuclear interactions. This study demonstrates the dependence of the accuracy of the usual [Formula: see text] WEPL filter on uncertainties arising within the energy detector. By enabling to remove such uncertainties, the [Formula: see text]-E method proved to yield some potential for improving the accuracy of pCT.

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

PURPOSE: A pixel-based range telescope for tracking particles during proton imaging is described. The detector applies a 3D matrix of stacked Monolithic Active Pixel Sensors with fast readout speeds. This study evaluates different design alternatives of the range telescope on basis of the protons' range accuracy and the track reconstruction efficiency. METHOD: Detector designs with different thicknesses of the energy-absorbing plates between each sensor layer are simulated using the GATE/Geant4 Monte Carlo software. Proton tracks traversing the detector layers are individually reconstructed, and a Bragg curve fitting procedure is applied for the calculation of each proton's range. RESULTS: Simulations show that the setups with 4 mm and thinner absorber layers of aluminum have a low range uncertainty compared to the physical range straggling, systematic errors below 0.3 mm water equivalent thickness and a track reconstruction capability exceeding ten million protons per second. CONCLUSIONS: In order to restrict the total number of layers and to yield the required tracking and range resolution properties, a design recommendation is reached where the proposed range telescope applies 3.5 mm thick aluminum absorber slabs between each sensor layer.

Accuracy of low-dose proton CT image registration for pretreatment alignment verification in reference to planning proton CT.

PURPOSE: Proton CT (pCT) has the ability to reduce inherent uncertainties in proton treatment by directly measuring the relative proton stopping power with respect to water, thereby avoiding the uncertain conversion of X-ray CT Hounsfield unit to relative stopping power and the deleterious effect of X- ray CT artifacts. The purpose of this work was to further evaluate the potential of pCT for pretreatment positioning using experimental pCT data of a head phantom. METHODS: The performance of a 3D image registration algorithm was tested with pCT reconstructions of a pediatric head phantom. A planning pCT simulation scan of the phantom was obtained with 200 MeV protons and reconstructed with a 3D filtered back projection (FBP) algorithm followed by iterative reconstruction and a representative pretreatment pCT scan was reconstructed with FBP only to save reconstruction time. The pretreatment pCT scan was rigidly transformed by prescribing random errors with six degrees of freedom or deformed by the deformation field derived from a head and neck cancer patient to the pretreatment pCT reconstruction, respectively. After applying the rigid or deformable image registration algorithm to retrieve the original pCT image before transformation, the accuracy of the registration was assessed. To simulate very low-dose imaging for patient setup, the proton CT images were reconstructed with 100%, 50%, 25%, and 12.5% of the total number of histories of the original planning pCT simulation scan, respectively. RESULTS: The residual errors in image registration were lower than 1 mm and 1° of magnitude regardless of the anatomic directions and imaging dose. The mean residual errors ranges found for rigid image registration were from -0.29 ± 0.09 to 0.51 ± 0.50 mm for translations and from -0.05 ± 0.13 to 0.08 ± 0.08 degrees for rotations. The percentages of sub-millimetric errors found, for deformable image registration, were between 63.5% and 100%. CONCLUSION: This experimental head phantom study demonstrated the potential of low-dose pCT imaging for 3D image registration. Further work is needed to confirm the value pCT for pretreatment image-guided proton therapy.

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.

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

PURPOSE: To evaluate the accuracy of relative stopping power and spatial resolution of images reconstructed with simulated helium CT (HeCT) in comparison to proton CT (pCT). METHODS: A Monte Carlo (MC) study with the TOPAS tool was performed to compare the accuracy of relative stopping power (RSP) reconstruction and spatial resolution of low-fluence HeCT to pCT, both using 200 MeV/u particles. An ideal setup consisting of a flat beam source and a totally absorbing energy-range detector was implemented to estimate the theoretically best achievable RSP accuracy for the calibration and reconstruction methods currently used for pCT. The phantoms imaged included a cylindrical water phantom with inserts of different materials, sizes, and positions, a Catphan phantom with a module containing high-contrast line pairs (CTP528) and a module with cylindrical inserts of different RSP (CTP404), as well as a voxelized 10-year-old female phantom. Dose to the cylindrical water phantom was also calculated. The RSP accuracy was studied for all phantoms except the CTP528 module. The latter was used for the estimation of the spatial resolution, evaluated as the modulation transfer function (MTF) at 10%. RESULTS: An overall error under 0.5% was achieved for HeCT for the water phantoms with the different inserts, in all cases better than that for pCT, in some cases by a factor 3. The inserts in the CTP404 module were reconstructed with an average RSP accuracy of 0.3% for HeCT and 0.2% for pCT. Anatomic structures (brain, bones, air cavities, etc.) in the digitized head phantom were well recognizable and no artifacts were visible with both HeCT and pCT. The three main tissue materials (soft tissue, brain, and cranium) were well identifiable in the reconstructed RSP-volume distribution with both imaging modalities. Using 360 projection angles, the spatial resolution was 4 lp/cm for HeCT and 3 lp/cm for pCT. Generally, spatial resolution increased with the number of projection angles and was always higher for HeCT than for pCT for the same number of projections. When HeCT and pCT scan were performed to deliver the same dose in the phantom, the resolution for HeCT was higher than pCT. CONCLUSION: MC simulations were used to compare HeCT and pCT image reconstruction. HeCT images had similar or better RSP accuracy and higher spatial resolution compared to pCT. Further investigation of the potential of helium ion imaging is warranted.

Software platform for simulation of a prototype proton CT scanner.

PURPOSE: Proton computed tomography (pCT) is a promising imaging technique to substitute or at least complement x-ray CT for more accurate proton therapy treatment planning as it allows calculating directly proton relative stopping power from proton energy loss measurements. A proton CT scanner with a silicon-based particle tracking system and a five-stage scintillating energy detector has been completed. In parallel a modular software platform was developed to characterize the performance of the proposed pCT. METHOD: The modular pCT software platform consists of (1) a Geant4-based simulation modeling the Loma Linda proton therapy beam line and the prototype proton CT scanner, (2) water equivalent path length (WEPL) calibration of the scintillating energy detector, and (3) image reconstruction algorithm for the reconstruction of the relative stopping power (RSP) of the scanned object. In this work, each component of the modular pCT software platform is described and validated with respect to experimental data and benchmarked against theoretical predictions. In particular, the RSP reconstruction was validated with both experimental scans, water column measurements, and theoretical calculations. RESULTS: The results show that the pCT software platform accurately reproduces the performance of the existing prototype pCT scanner with a RSP agreement between experimental and simulated values to better than 1.5%. CONCLUSIONS: The validated platform is a versatile tool for clinical proton CT performance and application studies in a virtual setting. The platform is flexible and can be modified to simulate not yet existing versions of pCT scanners and higher proton energies than those currently clinically available.

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

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 Heidelberg 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 custommade 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.

A Fast Experimental Scanner for Proton CT: Technical Performance and First Experience with Phantom Scans.

We report on the design, fabrication, and first tests of a tomographic scanner developed for proton computed tomography (pCT) of head-sized objects. After extensive preclinical testing, pCT is intended to be employed in support of proton therapy treatment planning and pre-treatment verification in patients undergoing particle-beam therapy. The scanner consists of two silicon-strip telescopes that track individual protons before and after the phantom, and a novel multistage scintillation detector that measures a combination of the residual energy and range of the proton, from which we derive the water equivalent path length (WEPL) of the protons in the scanned object. The set of WEPL values and the associated paths of protons passing through the object over a 360° angular scan are processed by an iterative, parallelizable reconstruction algorithm that runs on modern GP-GPU hardware. In order to assess the performance of the scanner, we have performed tests with 200 MeV protons from the synchrotron of the Loma Linda University Medical Center and the IBA cyclotron of the Northwestern Medicine Chicago Proton Center. Our first objective was calibration of the instrument, including tracker channel maps and alignment as well as the WEPL calibration. Then we performed the first CT scans on a series of phantoms. The very high sustained rate of data acquisition, exceeding one million protons per second, allowed a full 360° scan to be completed in less than 10 minutes, and reconstruction of a CATPHAN 404 phantom verified accurate reconstruction of the proton relative stopping power in a variety of materials.

Optimization of a general-purpose, actively scanned proton beamline for ocular treatments: Geant4 simulations.

The Italian National Center for Hadrontherapy (CNAO, Centro Nazionale di Adroterapia Oncologica), a synchrotron-based hospital facility, started the treatment of patients within selected clinical trials in late 2011 and 2012 with actively scanned proton and carbon ion beams, respectively. The activation of a new clinical protocol for the irradiation of uveal melanoma using the existing general-purpose proton beamline is foreseen for late 2014. Beam characteristics and patient treatment setup need to be tuned to meet the specific requirements for such a type of treatment technique. The aim of this study is to optimize the CNAO transport beamline by adding passive components and minimizing air gap to achieve the optimal conditions for ocular tumor irradiation. The CNAO setup with the active and passive components along the transport beamline, as well as a human eye-modeled detector also including a realistic target volume, were simulated using the Monte Carlo Geant4 toolkit. The strong reduction of the air gap between the nozzle and patient skin, as well as the insertion of a range shifter plus a patient-specific brass collimator at a short distance from the eye, were found to be effective tools to be implemented. In perspective, this simulation toolkit could also be used as a benchmark for future developments and testing purposes on commercial treatment planning systems.