Single proton LET characterization with the Timepix detector and artificial intelligence for advanced proton therapy treatment planning.

Objective.Protons have advantageous dose distributions and are increasingly used in cancer therapy. At the depth of the Bragg peak range, protons produce a mixed radiation field consisting of low- and high-linear energy transfer (LET) components, the latter of which is characterized by an increased ionization density on the microscopic scale associated with increased biological effectiveness. Prediction of the yield and LET of primary and secondary charged particles at a certain depth in the patient is performed by Monte Carlo simulations but is difficult to verify experimentally.Approach.Here, the results of measurements performed with Timepix detector in the mixed radiation field produced by a therapeutic proton beam in water are presented and compared to Monte Carlo simulations. The unique capability of the detector to perform high-resolution single particle tracking and identification enhanced by artificial intelligence allowed to resolve the particle type and measure the deposited energy of each particle comprising the mixed radiation field. Based on the collected data, biologically important physics parameters, the LET of single protons and dose-averaged LET, were computed.Main results.An accuracy over 95% was achieved for proton recognition with a developed neural network model. For recognized protons, the measured LET spectra generally agree with the results of Monte Carlo simulations. The mean difference between dose-averaged LET values obtained from measurements and simulations is 17%. We observed a broad spectrum of LET values ranging from a fraction of keVµm-1to about 10 keVµm-1for most of the measurements performed in the mixed radiation fields.Significance.It has been demonstrated that the introduced measurement method provides experimental data for validation of LETDor LET spectra in any treatment planning system. The simplicity and accessibility of the presented methodology make it easy to be translated into a clinical routine in any proton therapy facility.

Comparative accuracy and resolution assessment of two prototype proton computed tomography scanners.

BACKGROUND: Improving the accuracy of relative stopping power (RSP) in proton therapy may allow reducing range margins. Proton computed tomography (pCT) has been shown to provide state-of-the-art RSP accuracy estimation, and various scanner prototypes have recently been built. The different approaches used in scanner design are expected to impact spatial resolution and RSP accuracy. PURPOSE: The goal of this study was to perform the first direct comparison, in terms of spatial resolution and RSP accuracy, of two pCT prototype scanners installed at the same facility and by using the same image reconstruction algorithm. METHODS: A phantom containing cylindrical inserts of known RSP was scanned at the phase-II pCT prototype of the U.S. pCT collaboration and at the commercially oriented ProtonVDA scanner. Following distance-driven binning filtered backprojection reconstruction, the radial edge spread function of high-density inserts was used to estimate the spatial resolution. RSP accuracy was evaluated by the mean absolute percent error (MAPE) over the inserts. No direct imaging dose estimation was possible, which prevented a comparison of the two scanners in terms of RSP noise. RESULTS: In terms of RSP accuracy, both scanners achieved the same MAPE of 0.72% when excluding the porous sinus insert from the evaluation. The ProtonVDA scanner reached a better overall MAPE when all inserts and the body of the phantom were accounted for (0.81%), compared to the phase-II scanner (1.14%). The spatial resolution with the phase-II scanner was found to be 0.61 lp/mm, while for the ProtonVDA scanner somewhat lower at 0.46 lp/mm. CONCLUSIONS: The comparison between two prototype pCT scanners operated in the same clinical facility showed that they both fulfill the requirement of an RSP accuracy of about 1%. Their spatial resolution performance reflects the different design choices of either a scanner with full tracking capabilities (phase-II) or of a more compact tracker system, which only provides the positions of protons but not their directions (ProtonVDA).

The role of Monte Carlo simulation in understanding the performance of proton computed tomography.

Proton computed tomography (pCT) is a promising tomographic imaging modality allowing direct reconstruction of proton relative stopping power (RSP) required for proton therapy dose calculation. In this review article, we aim at highlighting the role of Monte Carlo (MC) simulation in pCT studies. After describing the requirements for performing proton computed tomography and the various pCT scanners actively used in recent research projects, we present an overview of available MC simulation platforms. The use of MC simulations in the scope of investigations of image reconstruction, and for the evaluation of optimal RSP accuracy, precision and spatial resolution omitting detector effects is then described. In the final sections of the review article, we present specific applications of realistic MC simulations of an existing pCT scanner prototype, which we describe in detail.

Applications of nanodosimetry in particle therapy planning and beyond.

This topical review summarizes underlying concepts of nanodosimetry. It describes the development and current status of nanodosimetric detector technology. It also gives an overview of Monte Carlo track structure simulations that can provide nanodosimetric parameters for treatment planning of proton and ion therapy. Classical and modern radiobiological assays that can be used to demonstrate the relationship between the frequency and complexity of DNA lesion clusters and nanodosimetric parameters are reviewed. At the end of the review, existing approaches of treatment planning based on relative biological effectiveness (RBE) models or dose-averaged linear energy transfer are contrasted with an RBE-independent approach based on nandosimetric parameters. Beyond treatment planning, nanodosimetry is also expected to have applications and give new insights into radiation protection dosimetry.

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.

Experimental comparison of proton CT and dual energy x-ray CT for relative stopping power estimation in proton therapy.

Proton computed tomography (pCT) has been proposed as an alternative to x-ray computed tomography (CT) for acquiring relative to water stopping power (RSP) maps used for proton treatment planning dose calculations. In parallel, it has been shown that dual energy x-ray CT (DECT) improves RSP accuracy when compared to conventional single energy x-ray CT. This study aimed at directly comparing the RSP accuracy of both modalities using phantoms scanned at an advanced prototype pCT scanner and a state-of-the-art DECT scanner. Two phantoms containing 13 tissue-mimicking inserts of known RSP were scanned at the pCT phase II prototype and a latest generation dual-source DECT scanner (Siemens SOMATOM Definition FORCE). RSP accuracy was compared by mean absolute percent error (MAPE) over all inserts. A highly realistic Monte Carlo (MC) simulation was used to gain insight on pCT image artifacts which degraded MAPE. MAPE was 0.55% for pCT and 0.67% for DECT. The realistic MC simulation agreed well with pCT measurements ([Formula: see text]). Both simulation and experimental results showed ring artifacts in pCT images which degraded the MAPE compared to an ideal pCT simulation ([Formula: see text]). Using the realistic simulation, we could identify sources of artifacts, which are attributed to the interfaces in the five-stage plastic scintillator energy detector and calibration curve interpolation regions. Secondary artifacts stemming from the proton tracker geometry were also identified. The pCT prototype scanner outperformed a state-of-the-art DECT scanner in terms of RSP accuracy (MAPE) for plastic tissue mimicking inserts. Since artifacts tended to concentrate in the inserts, their mitigation may lead to further improvements in the reported pCT accuracy.

Fast calculation of nanodosimetric quantities in treatment planning of proton and ion therapy.

Details of the pattern of ionization formed by particle tracks extends knowledge of dose effects on the nanometer scale. Ionization detail (ID), frequently characterized by ionization cluster size distributions (ICSD), is obtained through time-consuming Monte Carlo (MC) track-structure simulations. In this work, TOPAS-nBio was used to generate a highly precise database of biologically significant ID quantities, sampled with randomly oriented 2.3 nm diameter cylinders, 3.4 nm (10 base pairs) long, inside a chromatin-size cylinder, irradiated by 1-1000 MeV/u ions of Z = 1-8. A macroscopic method developed to utilize the database using condensed-history MC was used to calculate distributions of the ICSD first moment [Formula: see text] and cumulative probability [Formula: see text] in a 20 × 20 × 40 cm3 water phantom irradiated with proton and carbon spread-out Bragg peak (SOBP) of 10.5 cm range, 2 cm width. Results were verified against detailed MC track-structure simulations using phase space scored at several depths. ID distributions were then obtained for intensity modulated proton and carbon radiotherapy plans in a digitized anthropomorphic phantom of a base of skull tumor to demonstrate clinical application of this approach. The database statistical uncertainties were 0.5% (3 standard deviations). Fluence-averaged ID as implemented proved unsuitable for macroscopic calculation. E dep-averaged ID agreed with track-structure results within 0.8% for protons. For carbon, maximum absolute differences of 2.9% ± 1.6% and 5.6% ± 1.9% for [Formula: see text], 1.7% ± 0.8% and 1.9% ± 0.4% (1 standard deviation) for [Formula: see text], were found in the plateau and SOBP, respectively, up to 11.5% ± 5.6% in the tail region. Macroscopic ID calculation was demonstrated for a realistic treatment plan. Computation times with or without ID calculation were comparable in all cases. Pre-calculated nanodosimetric data may be used for condensed-history MC for nanodosimetric ID-based treatment planning in ion radiotherapy in the future. The macroscopic approach developed has the calculation speed of condensed-history MC while approaching the accuracy of full track structure simulations.

Two-dimensional noise reconstruction in proton computed tomography using distance-driven filtered back-projection of simulated projections.

We present a formalism for two-dimensional (2D) noise reconstruction in proton computed tomography (pCT). This is necessary for the application of fluence modulated pCT (FMpCT) since it permits image noise prescription and the corresponding proton fuence optimization. We aimed at extending previously published formalisms to account for the impact of multiple Coulomb scattering (MCS) on projection noise, and the use of filtered back projection (FBP) reconstruction along curved paths with distance driven binning (DDB). 2D noise reconstruction for a beam of protons with parallel initial momentum vectors, and for projections binned both at the rear tracker and with DDB, was established. Monte Carlo (MC) simulations of pCT scans of a water cylinder were employed to generate pCT projections and to calculate their noise for use in 2D noise reconstruction. These were compared to results from an analytical model accounting for MCS for rear tracker binning as well as against the previously published central pixel model which ignores MCS. Image noise reconstructed with the formalism for rear tracker binning and DDB were compared to MC results using annular regions of interest (ROIs). Agreement better than 8% was obtained between the noise of projections calculated with MC simulation and our model. Noise from annular ROIs agreed with our noise reconstructions for rear tracker binning and DDB. The central pixel model ignoring MCS underestimated projection and thus image noise by up to 40% towards the object's edge. The use of DDB decreased the image noise towards the object's edge when compared to rear tracker binning and yielded more uniform noise throughout the image. MCS should not be neglected when predicting image noise for pixels away from the center of an object in a pCT scan due to the increasing influence of the gradient of the object's hull closer to the edges.

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.

Experimental fluence-modulated proton computed tomography by pencil beam scanning.

PURPOSE: This experimental study is aimed at demonstrating, using a simple cylindrical water phantom, the feasibility of fluence-modulated proton computed tomography (FMpCT) by pencil beam scanning (PBS) proton computed tomography (pCT). METHODS: The phase II pCT prototype of the Loma Linda U. and U. C. Santa Cruz was operated using the PBS beam line of the Northwestern Medicine Chicago Proton Center. A 20 × 10 grid of 1.37 cm full width half maximum pencil beams (PB) equally spaced by 1 cm was used to acquire 45 projections in step and shoot mode. The PB pattern's fluence was modified to allow FMpCT scans with fluence modulation factors (FMF) of 50% and 20%. A central FMpCT region of interest (FMpCT-ROI) was used to define a high image quality region. Reconstructed images were evaluated in terms of relative stopping power (RSP) accuracy and noise using annular ROIs. The FMpCT dose savings were estimated by Monte Carlo (MC) simulation of the pCT acquisitions using beam phase space distributions. PBS pCT results with homogeneous fluence were additionally compared to broad beam results in terms of RSP accuracy and noise. RESULTS: PBS pCT scans with acceptable pileup were possible, and images were comparable to previously acquired broad beam pCT images in terms of both noise and accuracy. In the FMpCT-ROI, the noise and accuracy from full fluence (FF) scans were preserved. Dose savings of up to 60% were achieved at the object's edge when using FMF of 20%. CONCLUSION: In this study, we have demonstrated that PBS pCT scans can achieve equivalent accuracy as those obtained from broad beams. The feasibility of FMpCT scans was demonstrated; image accuracy and noise were successfully preserved in the central FMpCT-ROI chosen for this study, and dose reduction of up to 60% at the object's edge was realized.

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.

Flagged uniform particle splitting for variance reduction in proton and carbon ion track-structure simulations.

Flagged uniform particle splitting was implemented with two methods to improve the computational efficiency of Monte Carlo track structure simulations with TOPAS-nBio by enhancing the production of secondary electrons in ionization events. In method 1 the Geant4 kernel was modified. In method 2 Geant4 was not modified. In both methods a unique flag number assigned to each new split electron was inherited by its progeny, permitting reclassification of the split events as if produced by independent histories. Computational efficiency and accuracy were evaluated for simulations of 0.5-20 MeV protons and 1-20 MeV u-1 carbon ions for three endpoints: (1) mean of the ionization cluster size distribution, (2) mean number of DNA single-strand breaks (SSBs) and double-strand breaks (DSBs) classified with DBSCAN, and (3) mean number of SSBs and DSBs classified with a geometry-based algorithm. For endpoint (1), simulation efficiency was 3 times lower when splitting electrons generated by direct ionization events of primary particles than when splitting electrons generated by the first ionization events of secondary electrons. The latter technique was selected for further investigation. The following results are for method 2, with relative efficiencies about 4.5 times lower for method 1. For endpoint (1), relative efficiency at 128 split electrons approached maximum, increasing with energy from 47.2 ± 0.2 to 66.9 ± 0.2 for protons, decreasing with energy from 51.3 ± 0.4 to 41.7 ± 0.2 for carbon. For endpoint (2), relative efficiency increased with energy, from 20.7 ± 0.1 to 50.2 ± 0.3 for protons, 15.6 ± 0.1 to 20.2 ± 0.1 for carbon. For endpoint (3) relative efficiency increased with energy, from 31.0 ± 0.2 to 58.2 ± 0.4 for protons, 23.9 ± 0.1 to 26.2 ± 0.2 for carbon. Simulation results with and without splitting agreed within 1% (2 standard deviations) for endpoints (1) and (2), within 2% (1 standard deviation) for endpoint (3). In conclusion, standard particle splitting variance reduction techniques can be successfully implemented in Monte Carlo track structure codes.

Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy.

A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy treatment planning with dose-volume constraints included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) methods. We propose an iterative algorithmic framework for solving such a problem by applying the feasibility-seeking CQ-algorithm of Byrne combined with the automatic relaxation method that uses cyclic projections. Detailed implementation instructions are furnished. Functionality of the algorithm was demonstrated through the creation of an intensity-modulated proton therapy plan for a simple 2D C-shaped geometry and also for a realistic base-of-skull chordoma treatment site. Monte Carlo simulations of proton pencil beams of varying energy were conducted to obtain dose distributions for the 2D test case. A research release of the Pinnacle 3 proton treatment planning system was used to extract pencil beam doses for a clinical base-of-skull chordoma case. In both cases the beamlet doses were calculated to satisfy dose-volume constraints according to our new algorithm. Examination of the dose-volume histograms following inverse planning with our algorithm demonstrated that it performed as intended. The application of our proposed algorithm to dose-volume constraint inverse planning was successfully demonstrated. Comparison with optimized dose distributions from the research release of the Pinnacle 3 treatment planning system showed the algorithm could achieve equivalent or superior results.

Nanodosimetry-Based Plan Optimization for Particle Therapy.

Treatment planning for particle therapy is currently an active field of research due uncertainty in how to modify physical dose in order to create a uniform biological dose response in the target. A novel treatment plan optimization strategy based on measurable nanodosimetric quantities rather than biophysical models is proposed in this work. Simplified proton and carbon treatment plans were simulated in a water phantom to investigate the optimization feasibility. Track structures of the mixed radiation field produced at different depths in the target volume were simulated with Geant4-DNA and nanodosimetric descriptors were calculated. The fluences of the treatment field pencil beams were optimized in order to create a mixed field with equal nanodosimetric descriptors at each of the multiple positions in spread-out particle Bragg peaks. For both proton and carbon ion plans, a uniform spatial distribution of nanodosimetric descriptors could be obtained by optimizing opposing-field but not single-field plans. The results obtained indicate that uniform nanodosimetrically weighted plans, which may also be radiobiologically uniform, can be obtained with this approach. Future investigations need to demonstrate that this approach is also feasible for more complicated beam arrangements and that it leads to biologically uniform response in tumor cells and tissues.

Tissue equivalency of phantom materials for neutron dosimetry in proton therapy.

PURPOSE: Previous Monte Carlo and experimental studies involving secondary neutrons in proton therapy have employed a number of phantom materials that are designed to represent human tissue. In this study, the authors determined the suitability of common phantom materials for dosimetry of secondary neutrons, specifically for pediatric and intracranial proton therapy treatments. METHODS: This was achieved through comparison of the absorbed dose and dose equivalent from neutrons generated within the phantom materials and various ICRP tissues. The phantom materials chosen for comparison were Lucite, liquid water, solid water, and A150 tissue equivalent plastic, These phantom materials were compared to brain, muscle, and adipose tissues. RESULTS: The magnitude of the doses observed were smaller than those reported in previous experimental and Monte Carlo studies, which incorporated neutrons generated in the treatment head. The results show that for both neutron absorbed dose and dose equivalent, no single phantom material gives agreement with tissue within 5% at all the points considered. Solid water gave the smallest mean variation with the tissues out of field where neutrons are the primary contributor to the total dose. CONCLUSIONS: Of the phantom materials considered, solid water shows best agreement with tissues out of field.

Reconstruction for proton computed tomography by tracing proton trajectories: a Monte Carlo study.

Proton computed tomography (pCT) has been explored in the past decades because of its unique imaging characteristics, low radiation dose, and its possible use for treatment planning and on-line target localization in proton therapy. However, reconstruction of pCT images is challenging because the proton path within the object to be imaged is statistically affected by multiple Coulomb scattering. In this paper, we employ GEANT4-based Monte Carlo simulations of the two-dimensional pCT reconstruction of an elliptical phantom to investigate the possible use of the algebraic reconstruction technique (ART) with three different path-estimation methods for pCT reconstruction. The first method assumes a straight-line path (SLP) connecting the proton entry and exit positions, the second method adapts the most-likely path (MLP) theoretically determined for a uniform medium, and the third method employs a cubic spline path (CSP). The ART reconstructions showed progressive improvement of spatial resolution when going from the SLP [2 line pairs (lp) cm(-1)] to the curved CSP and MLP path estimates (5 lp cm(-1)). The MLP-based ART algorithm had the fastest convergence and smallest residual error of all three estimates. This work demonstrates the advantage of tracking curved proton paths in conjunction with the ART algorithm and curved path estimates.

Density resolution of proton computed tomography.

Conformal proton radiation therapy requires accurate prediction of the Bragg peak position. Protons may be more suitable than conventional x-rays for this task since the relative electron density distribution can be measured directly with proton computed tomography (CT). However, proton CT has its own limitations, which need to be carefully studied before this technique can be introduced into routine clinical practice. In this work, we have used analytical relationships as well as the Monte Carlo simulation tool GEANT4 to study the principal resolution limits of proton CT. The noise level observed in proton CT images of a cylindrical water phantom with embedded tissue-equivalent density inhomogeneities, which were generated based on GEANT4 simulations, compared well with predictions based on Tschalar's theory of energy loss straggling. The relationship between phantom thickness, initial energy, and the relative electron density resolution was systematically investigated to estimate the proton dose needed to obtain a given density resolution. We show that a reasonable density resolution can be achieved with a relatively small dose, which is comparable to or even lower than that of x-ray CT.