A TOPAS model for lens-based proton radiography

Objective. Proton Radiography can be used in conjunction with proton therapy for patient positioning, real-time estimates of stopping power, and adaptive therapy in regions with motion. The modeling capability shown here can be used to evaluate lens-based radiography as an instantaneous proton-based radiographic technique. The utilization of user-friendly Monte Carlo program TOPAS enables collaborators and other users to easily conduct medical- and therapy- based simulations of the Los Alamos Neutron Science Center (LANSCE). The resulting transport model is an open-source Monte Carlo package for simulations of proton and heavy ion therapy treatments and concurrent particle imaging. Approach. The four-quadrupole, magnetic lens system of the 800-MeV proton beamline at LANSCE is modeled in TOPAS. Several imaging and contrast objects were modelled to assess transmission at energies from 230–930 MeV and different levels of particle collimation. At different proton energies, the strength of the magnetic field was scaled according to βγ, the inverse product of particle relativistic velocity and particle momentum. Main results. Materials with high atomic number, Z, (gold, gallium, bone-equivalent) generated more contrast than materials with low-Z (water, lung-equivalent, adipose-equivalent). A 5-mrad collimator was beneficial for tissue-to-contrast agent contrast, while a 10-mrad collimator was best to distinguish between different high-Z materials. Assessment with a step-wedge phantom showed water-equivalent path length did not scale directly according to predicted values but could be mapped more accurately with calibration. Poor image quality was observed at low energies (230 MeV), but improved as proton energy increased, with sub-mm resolution at 630 MeV. Significance. Proton radiography becomes viable for shallow bone structures at 330 MeV, and for deeper structures at 630 MeV. Visibility improves with use of high-Z contrast agents. This modality may be particularly viable at carbon therapy centers with accelerators capable of delivering high energy protons and could be performed with carbon therapy.


Introduction
Proton therapy has the potential to drastically improve patient treatment outcomes by sparing healthy tissues (Hoppe et al 2010, Van De Water et al 2011, Barten et al 2015) and better conforming to treatment volumes (Liu and Chang 2011).Despite this potential, proton therapy presently lacks a method to accurately estimate proton stopping powers to within a percent (Taasti et al 2018), which could help to make possible the full realization of the available dose deposition accuracy through treatment using the proton's Bragg peak (Bonnett 1993).Furthermore, proton therapy lacks a method to position a patient using a beam'seye-view imaging modality, typically utilizing instead orthogonal x-ray imaging (Shimizu et al 2014).Both increased accuracy in measurements of stopping power and beam's-eye-view imaging techniques could maximize the dose deposition accuracy provided by proton therapy.
One method that could provide these capabilities is proton radiography (Schneider and Pedroni 1995, Durante and Stöcker 2012, Varentsov et al 2013, Prall et al 2016, Varentsov et al 2016).Proton radiography could improve the estimations of proton stoppingpower in a patient by providing a proton-CT dataset during the treatment planning process (Doolan et al 2015, Poludniowski et al 2015).Additionally, the provision of a proton-based imaging technique could enable real-time image guidance: day-to-day changes in proton stopping power within the patient, such as those commonly seen during treatments through the lung region (Veiga et al 2016), could be compensated with a real-time estimate of proton stopping power, facilitating adaptive therapy.Development of a proton radiography modality would benefit not only clinical proton therapy centers, but also carbon and heavy ion therapy centers, many of which have concurrent capabilities of proton acceleration.Additionally, these facilities usually have accompanying infrastructure, such as larger facility space and quadrupole magnets, that would facilitate proton radiography.
Proton radiography based on a magnetic lens system (Mottershead andZumbro 1997, King et al 1999) can provide instantaneous estimations of proton stopping power that could be used to make real-time adjustments to a patient's treatment plan (Yan et al 1997, Freeman et al 2018).Such a system exploits the charge of the proton to focus an image with magnetic fields to a focal point downstream of the patient, while collimation at a Fourier plane within the lens provides a high level of sensitivity to changes in patient thickness (Merrill 2015).The resolution of such a system is sensitive to two properties.First, it scales with ΔE/E, the spread in energies of transmitted protons vs. the focal energy of the lens (Mariam et al 2012): equation (1) shows how particle position, leading to blurring, changes with chromatic aberration: where x f is the final particle position, x is the original particle position, C x is the chromatic length of the lens system, j is the deviation angle, and Δ is the fractional momentum deviation (Mottershead and Zumbro 1997).Resolution also scales with the amount of multiple-Coulomb scattering (MCS) acquired in traversing a patient, the angular relation of which is given in equation (2) (Zyla et al 2020): where β is the particle relativistic velocity, p is the particle momentum, L is the integrated areal density through the object, and X 0 is the radiation length of the material.This term scales as 1/βp.Due to these contributing factors, instantaneous proton radiography is better suited to operate at higher energies where there is less spread in energy contributing to the chromatic blur and less MCS from the object.
In this work, a system is modelled after the 800-MeV proton radiography system at the Los Alamos Neutron Science Center (LANSCE) (Lisowski and Schoenberg 2006), using the Tool for PArticle Simulation (TOPAS) (Perl et al 2012).The Geant4 (Agostinelli et al 2003) based TOPAS program incorporates the physics of Geant4 in a package that is user friendly.While LANSCE has previously been modeled for nonmedical applications (Sjue et al 2016, Freeman et al 2017), the utility of TOPAS enables files to be more easily shared amongst collaborators or others interested in conducting their own simulations with the beamline files.Additionally, user-friendly definitions of basic geometries allows some components (such as the magnetic quadrupoles) to be more easily modified and the resulting effects to be explored more easily.Thus, models developed in TOPAS are relatively easy to deploy as open-source tools to be utilized by the medical community, making this model more appropriate for medical applications, such as proton-based FLASH therapy (Hughes and Parsons 2020).Though previous work has looked at the utility of using protons below 400 MeV u −1 for medical imaging (Schneider et al 2004, Gianoli et al 2019), this work explores the feasibility of using the much higher energy 800 MeV proton beamline for such medical imaging.To this end, several medical imaging phantoms are simulated to quantitatively assess the system and determine the size of structures that would be visible with this modality and the efficacy in calculating parameters such as water-equivalent path length.Finally, the proton radiography system was scaled from 230 MeV to 930 MeV to determine at what energy the proton radiography system described here becomes viable.

Materials and methods
The lens-based proton radiography system was designed using the differential algebraic-based beamline design code, COSY INFINITY (Makino and Berz 2006).The lens magnetic field values were then used to model the proton radiography system in TOPAS (version 3.3.p1).The physics list 'QGSP BERT HP' was used; all other parameters were TOPAS defaults.The beam consisted of 800 MeV protons (unless specified) with a Gaussian spread of σ = 0.085 cm.To generate enough statistics for a reasonable trade-off between image quality and computation time, 10 8 particles were used per simulation except for the CT phantom, which used 10 9 particles.

Description of the 800 MeV LANSCE proton radiography system
The simulated imaging system is shown in figure 1.A summary of system parameters is provided in tables 1 (beam-forming components) and 2 (imaging components).The system begins with a thin tantalum diffuser foil (shown in dark blue, marked as object 'A') that the proton beam strikes.The beam shape is then formed in three quadrupoles (shown in purple and marked as 'B-D') to create the matching conditions, described in detail in table 1, to produce a Fourier plane within the downstream lens system.All quadrupoles are modeled as vacuum cylinders with x-and y-electromagnetic field gradients to minimize interactions with the beam and speed up the simulations.The gradient of the quadrupole magnetic field in the x-and y-directions were B x = 0.3075 rad m −1 and B y = −0.3075rad m −1 (Freeman et al 2017).
After the beam has formed in the aforementioned 'beam forming' quadrupoles, it strikes the phantom or subject at the 'patient location' (shown as object 'E' in figure 1).This system can measure a 20 cm diameter circular field of view due to the size of the quadrupole magnets and the limitations of field uniformity.The transmitted protons then pass through two quadrupoles (marked as 'F' and 'G' in figure 1) before reaching the Fourier plane (marked as 'H'), where unscattered protons pass through the center and widely scattered protons pass through the periphery.For some simulations, a steel collimator (also marked as 'H') is placed at the location of the Fourier plane to remove protons scattered beyond 5 mRad or 10 mRad.The remaining protons then travel through the remaining two quadrupoles (marked as 'J' and 'K'), returning the protons to the angular position they held at the 'patient location.'Finally, the protons strike a detector (marked as 'L') placed at the imaging plane, modeled as a 15 cm × 15 cm × 0.2 cm Lutetiumyttrium oxyorthosilicate (LYSO) plate; this LYSO plate is similar to what is commonly used for fast detection in the LANSCE system (Malone et al 2018).Further description and images can be found in Sidebottom et al 2021.

Description of the 230-930 MeV proton radiography systems
The 230-MeV imaging system was as described in 2.1 but with all quadrupole magnetic field strengths adjusted.The proton's magnetic rigidity (dR), or resistance to being bent by a magnetic field, scales with equation (3), where β is the relativistic speed of the proton and γ is the relativistic correction factor (Wiedemann 1993, Edwards andSyphers 2008).
The magnetic strength is then adjusted incrementally to optimize image clarity.Because of this, at 230 MeV, the strength of the magnets is dialed down to 49.0% of the field strength required to focus protons at 800 MeV, from 0.054574 T cm −1 to Figure 1.pRad proton radiography imaging system.From the left, the components are:. A. Tantalum diffuser foil, which disperses the beam to fully illuminate the object plane; B. Matching Quadrupole 1; C. Matching Quadrupole 2; D. Matching Quadrupole 3, where the strength of 'matching' quadrupoles 1-3 are chosen to provide the matching conditions to produce a Fourier plane downstream; E. patient location, where the imaging phantoms are placed in this work; F: Focusing Quadrupole 1; G. De-focusing Quadrupole 2; H: Collimator and location of the Fourier plane, which removes scattered protons from the beam; J. Focusing Quadrupole 3; K: Defocusing Quadrupole 4, which together with (de)-focusing quadrupoles 1-4 form the conditions to provide an image at L. the imaging plane.
Table 1.Description of the 3-quadrupole matching, or beam-forming, system upstream of the patient location.The first column shows a label corresponding to the component shown in figure 1.  known nuclear attenuation coefficients for water to estimate the equivalent path length of water to induce the same angular spread in induced proton scatter, θ 0 (Zyla et al 2020).Transmission through the system is given by T e e 1 4 x 2 In converting the inferred angular scatter (itself measured by transmission) to relate the equivalent energy loss from one material to another, it is important to also consider changes in stopping power, dE/dx, in MeV/g/cm 2 .Water has a dE/dx of 1.99 MeV g −1 cm −2 compared against Aluminum's 1.91 MeV/g/cm 2 .Tissues in the body, composed mostly of water, will have very similar dE/dx; however, differences can be measured and accounted for to calibrate the conversion to water equivalent dE/dx (and thus, WEPL).In this way, the measured transmission of any material is converted to measured angular scatter, which then relates to water equivalent energy loss by applying this conversion factor for changes in LET.

Results
In lens-based proton radiography, areal density of material directly maps to a specific transmission.Herein, 'transmission' is the fraction of the beam passing through the phantom.In order to have the best estimates of areal densities in a specific region, the change in transmission at this point, as a function of areal density, should be optimized for the thickness  of material under study.In order to discern the difference between two materials, the change in transmission should be the highest.This can be dialed in and optimized through choice of collimator.In general, the statistical uncertainty associated with the simulations is approximately 1%: a simulation of 10 8 particles corresponds to approximately 10 4 protons per pixel.

Effect of collimator
The transmission per collimator and material in a Jaszczak phantom is shown in figure 4. While a small ROI was taken at the center of each sphere, the depth varied over the ROI, likely resulting in a lower transmission value and higher error.The 5 mrad collimator tended to result in the lowest transmission and 'no' collimator gave the highest transmission.For the 3.18 cm sphere, for which the depth can be assumed to vary least over the ROI due to its size, a 5 mrad collimator reduced transmission by 93% for the 68 Ga sphere; by 95% for the gold sphere; and by 29% for the water sphere.Adding a 10 mrad collimator decreased transmission by 76% for the 68 Ga sphere; by 85% for the gold sphere; and by 4% for the water sphere.An increase in transmission was seen for the 0.5 cm, Au-filled sphere with no collimator, resulting in the transmission value being greater than 1.This increase is due to limning.Limning effects are worse when there is no collimator, as limning is caused by blurred protons, and collimators remove some of the blur from the final image by rejecting the most highly scattered protons.

Evaluating material transmission 3.2.1. Materials in vacuum
The effect of different materials is shown in figure 3, where each sub-figure shows the same collimation.For the system with no collimator (figure 3(A)), the impact of material decreases with decreasing diameter: compared to water, 68 Ga resulted in a 21% lower transmission for the 3.18 cm sphere but only 8% decrease in transmission for the 0.63 cm sphere (the smallest resolvable diameter for all three materials).Similarly, the gold spheres produced an 82% decrease in transmission compared to water for the largest diameter, compared to 22% increase compared to the smallest diameter (a difference likely attributed to scatter and uncertainty in ROI selection, which was very large for the water ROI).The difference with diameter was much less profound when the 5 mrad collimator was introduced: compared to water, 68 Ga spheres produced 93% decrease in transmission for 3.18 cm, which steadily decreased to 70% decreased transmission for the 0.63 cm sphere.Similarly, the gold sphere produced 99% decrease in transmission for the largest diameter and 93% decrease in transmission for the smallest.For the 10 mrad collimator, the difference is larger as diameter decreases, with 68 Ga producing 80% decreased transmission over water for the largest diameter and 26% for the smallest; the gold spheres produced 97% decreased transmission over the water spheres for the largest diameter and 82% for the smallest.

Materials in water
Jaszczak sphere phantoms in figures 4(B) and (C) were material-filled objects in vacuum cylinders.However, if these materials were used to locate tumors in humans, they would be immersed in tissue.Therefore, transmission in a water-filled Jaszczak sphere phantom was also assessed, deemed appropriate because tissue has a similar effective atomic number to water.The transmission through these phantoms is shown in figure 4(A); a comparison between transmission for water-filled and vacuum-filled cylinders is shown in figure 4(B).Adding water resulted in a 93%-96% decrease in transmission across all diameters for 68 Ga-filled spheres, with greater differences seen for smaller diameters.For gold-filled spheres, a 91%-94% decrease in transmission was seen, with no correlation between sphere diameter and decrease percent transmission.
In addition to the decreased transmission, the image quality was predictably degraded with the introduction of water in the cylinder: for the filled cylinders, the smallest volumes were not visible, and all volumes are visibly blurrier.This is due to the increased amounts of MCS introduced by the water, which cannot be overcome by the lens system.

Tissue-equivalent materials
Various tissues in the body have different atomic properties that would affect their visibility in proton radiography.Therefore, the CT phantom was imaged  to assess the visibility of various tissue-equivalent materials.Figure 5 shows that while most tissues have similar transmission (adipose, brain, and lung), bone has much lower transmission, indicating it would be most easily visible via proton radiography.Adipose and brain have similar transmission to the background material (water), making them difficult to distinguish.The similarity in transmission of the other tissues means that they would be harder to distinguish via this modality without some sort of contrast agent.However, changes in WEPL do translate into distinguishable changes in transmission that can be quantified.

Evaluating the proton radiography system at different energies to determine radiographic viability
Radiographic images of the bone contrast phantom are shown in figure 6(A).Resolution across the bone  edge was assessed at all energies and depths for the head phantom and is reported in figure 6(B).Resolution is defined as the sigma of the error function fit to the bone edge.Bone is visible with all energies at 4 cm of tissue thickness; at 8 cm, a sub-mm resolution image is obtained starting at 330 MeV, with resolution decreasing at higher energies due to edge effects; for 12 cm, at least 530 MeV is required for sub-mm spatial resolution; and 630 MeV required for 16 cm of tissue.Transmission was assessed through each bone and tissue depth and is reported in figure 6(C); recall that 'transmission' is the fraction of the beam passing through the phantom.Objects qualitatively determined to be visible by visual inspection around 40% transmission; the line in figure 6(C) denotes this threshold and delineates which objects are visible.While the bone was visible for the smallest tissue depth starting at 330 MeV, it only became visible at the greatest depth starting at 630 MeV.

Evaluating step-wedges for predictable transmission
The step wedge phantom was used to show the effect of material thickness or depth on transmission.Figure 7 shows this trend: as the thickness of the step increases, the transmission decreases.However, the transmission did not scale directly according to the transmission equations due to the emittance of the beam.In a perfect system, where every proton strikes the diffuser uniformly, the transmission would scale as expected.However, the inherent emittance propagates through the system resulting in uncertainties in the collimation efficiency.A solution to this problem is to use the direct measurement of a ground truth object to calibrate the conversion from transmission to areal density, given the accelerator tune on a given day, to be able to obtain accurate measurements of water equivalence.

Evaluating WEPL in a water phantom
The transmission image of the step wedge phantom (figure 7) was used to calculate the WEPL.The WEPL image of the wedge is shown in figure 8(A).A profile across the wedge is shown in figure 8(B): an ROI was taken across the wedge and averaged over several pixels.Standard deviation is not shown for clarity due to the number of points.For each step, an ROI was selected; the value therein was averaged over the number of pixels to get the calculated depth for that step.The difference between that value and the true step depth was taken and is expressed in figure 8(C).While the difference was large for the smallest step, it was small for steps above 3 cm.This demonstrates the importance of characterizing a system with regular quality assurance checks against a known standard, to be able to accurately map a transmission measurement to an estimate of WEPL, based on the tune of the accelerator available that day.Overall, WEPL images are expected to be accurate to 1% per pixel, corresponding to N 1/2 N −1 .In practice, the true accuracy depends on calibrations against similar measurements in real water.

Discussion
Lens-based proton radiography can be used to probe objects for their WEPLs.However, transmission does not scale perfectly according to the transmission equations shown here, necessitating a calibration against a known standard, such as a step-wedge in water, or water-equivalent plastic.In practice this could be done against solid water, or an acrylic enclosure housing distilled water.Other factors, not modeled here, will also come into play when calculating WEPL from transmission from accelerator-based measurements, including factors that can change from day-to-day, such as the tune and emittance of the proton beam, the level of vacuum within the system, or even the centering of the beam.Thus, for any accurate measure of WEPL, a stepwedge-based waterequivalence should be performed each day against which to calibrate transmission measurements.
In general, the collimator size impacted the transmission of the imaging system.This is due to the collimator removing scattered protons, resulting in fewer protons making it to the scintillator; as the collimator removes protons, there are fewer that have the potential to be transmitted.Transmission was also impacted by the ROI chosen because of the nature of the images acquired, which were a 2D project of the 3D imaging object.
While introducing high-Z materials produced substantial transmission decreases in all systems, the smallest difference between 68 Ga and gold transmission was seen for the 5 mrad collimator system, indicating that this system would be most beneficial if using 68 Ga or a similar high-Z material to obtain good levels of tissue-to-contrast agent contrast.However, the differences in transmission between materials was greatest for the 10 mrad collimator, indicating that it would be best to distinguish different high-Z materials, such as between contrast agents or if the patient has any metal implants.
While these simulations indicate the feasibility of high-energy lens-based proton radiography, many facilities have lower energy proton beams, necessitating an analysis of the threshold at which proton radiography becomes viable.An analysis of proton radiography images of the bone contrast phantom at various energies shows that proton radiography becomes viable for imaging shallow bones at 330 MeV.However, to resolve bony structure within the full depth of the human body, a higher proton energy of order 630 MeV is needed.These results would undoubtedly be degraded by the addition of overlapping bone structures, such as would be seen in a patient's head or torso.Therefore, while lens-refocused proton radiography at clinical energies may be viable for shallow or small structures, such as a hand, higher energy would be needed for larger structures of interest, such as the head.It is not surprising that the lens design utilized at LANSCE, which was optimized for 800 MeV protons, does not work so well at lower energies.However, with some changes to the design, the principles of lens-based proton radiography may yield much better results at lower energies.One potential design change would be the implementation of shorter, stronger magnetic lenses, which would have reduced chromatic effects that could enable high quality radiographs at more attainable (lower) proton energies.This would help greatly in tightly-constrained clinical environments where space is at a premium to be able to fit a magnetic lens in the space of a few meters.
While feasible for imaging shallow structures at the 330 MeV level studied, this imaging modality may most readily benefit facilities with higher-mass isotopes, such as Carbon ion therapy, whose accelerators intrinsically have the ability to deliver higher energy protons than typically clinically available (Kamada et al 2015, Malouff et al 2020).These higher energy protons could then be utilized to perform high-energy lens-based proton radiography in conjunction with carbon therapy (Schanz 2019).Such facilities often operate around 400-430 MeV u −1 (Particle Therapy Co-Operative Group 2022); as shown in section 3.3, this energy is more than adequate to view shallow bone structures and the beginning of deep-seated structures.

Conclusions
In this work, we demonstrate the ability to model a lens-based proton radiography system as implemented at LANSCE.Simulated imaging of contrast phantoms demonstrates the tunability of the system, in that transmission can be dialyzed in through selection of a collimator that is optimized for a target of interest.The LANSCE-based lens system requires higher proton energies than typically available clinically in order to image at human scale but could be optimized toward imaging at lower energies with shorter, more powerful lens systems.With a regular calibration procedure to account for changes in accelerator tune that affect transmission, this method could provide an instantaneous measure of water equivalent path length.
20180238ER and 20210419ER.This project was also supported in part by the Graduate Fellowship in STEM Diversity as part of the GFSD fellowship.

Figure 2 .
Figure 2. Contrast imaging Phantoms, modeled on clinically used imaging phantoms.From left to right, top row:.A. Jaszczak sphere phantom, consisting of spheres of various diameters in a larger cylinder; B. CT phantom, consisting of cylinders of different tissueequivalent materials in a larger cylinder; Bottom row: C. Wedge phantom, consisting of blocks of water-equivalent material in a larger box; and D. Bone Contrast Phantom, consisting of stacked cylinders of tissue-equivalent material positioned over a bone-equivalent plus-sign.

Figure 3 .
Figure3.Effect of Material on Transmission.The 'transmission' is the fraction of the beam passing through the phantom.For each collimator, transmission decreased with increasing atomic number (Z).The largest difference between each material transmission was seen for the 10 mrad collimator.The transmission value greater than 1 with no collimator is due to limning.

Figure 4 .
Figure 4. Comparison of transmission for water-filled and vacuum-filled cylinders.The 'transmission' is the fraction of the beam passing through the phantom.Transmission decreased substantially when the cylinders were filled with water, with visibility for smaller structures decreasing as well.

Figure 5 .
Figure 5. A: Fraction transmission through tissue-equivalent materials; the 'transmission' is the fraction of the beam passing through the phantom.10 9 protons were used.While transmission through most tissues (adipose, brain, lung) was similar, it was lower for bone, indicating that bone would be most visible on a proton radiograph.An intensity image of the CT phantom is shown on right (B).

Figure 6 .
Figure 6.(Top, figure 6(A)): Transmission images of bone contrast phantom per energy.(Bottom left, figure 6(B)): Spatial resolution across bone edge for each tissue depth and energy.(Bottom right, figure 6(C)): Transmission through bone and various tissue depths.The black line denotes the point at which the delineation was no longer visible.

Figure 7 .
Figure 7. Transmission through the step wedge phantom.The 'transmission' is the fraction of the beam passing through the phantom.As the thickness traversed increases, the transmission decreases.The trend is relatively linear.The original, flattened wedge image is shown on the right.

Figure 8 .
Figure 8. WEPL Through Phantoms.Figure 8(A) (Upper left) shows the WEPL-converted wedge.Figure 8(B) (upper right) shows the profile of WEPL across the wedge as a function of position.Figure 8(C) (bottom left) shows the calculated depth per step, with the difference shown in grey.
, respectively.Collimation cut angles remain the same: a 10-mrad collimator at 800 MeV is still a 10-mrad cut angle at 230 MeV as the geometric properties remain the same.A particular collimator deflection will map to the same position at the Fourier plane no matter the initial starting energy.However, For each beam energy and collimation setting, a beam image was acquired with no phantom present.This beam image was blurred with a two-sigma Gaussian filter.The phantom image was then divided by the blurred beam image pixel-wise in ImageJ to produce a 'flattened' image, or a phantom image normalized to the beam conditions provided in the simulation (Schindelin et al 2012).
more scatter is introduced at 230 MeV; therefore, a 10mrad collimator will cut more of the 230 MeV beam and reduce the number of protons transmitted to the detector.Simulations were done in COSY INFINITY(Makino and Berz 2006)to verify the collimator size.All other energy imaging systems (330 MeV-930 MeV) were scaled similarly, with the quadrupole magnetic field strengths adjusted to focus energy in the same manner.2.2.Descriptions of imaging phantomsSeveral phantoms were used to assess the resolution of the system and amount of contrast agent needed to produce an image.A description of each phantom is provided in table 3; images of the phantoms are given in figure2.The 'Jaszczak sphere phantom' was modeled after the Jaszczak nuclear medicine phantom with corresponding cylinder dimension and sphere diameters (Biodex) and demonstrates the contrast of different sized objects.Similarly, the CT phantom was modeled as a CT Tissue Mimicking Phantom (D'Souza et al 2001) and demonstrates the contrast of The energy deposited in the scintillator is scored by TOPAS to create an image.This scored quantity was used to determine the transmission of the protons through the imaging object.The detector was divided into 1500 × 1500 bins in a 2-dimensional histogram, and the amount of energy deposited in each bin scored.A resulting intensity image of energy per bin was generated in Python.2.3.2.Extracting quantitative metrics2.3.2.1.TransmissionTransmission and water-equivalent path length (WEPL) were calculated using ImageJ (Schindelin et al 2012) and MATLAB (Mathworks 2020).WEPL is the equivalent amount of water to provide that same amount of scatter as the object being measured.For a known amount of material and transmission, the scattering angle through the medium can be calculated and related to the equivalent amount of water that would provide the same amount of scatter and transmission.Starting with a flattened phantom image (described in section 2.3.1), a region of interest (ROI) of consistent size was selected from the center of the image; the ROI was applied to images of the same phantom type.The mean value within the ROI was defined as the transmission; the standard deviation of values within the ROI was also determined.The transmission is the fraction of beam that is transmitted through the object.c is the collimation cut angle.Since this equation is not invertible, a look-up table is created using intervals of 0.01 g cm −2 areal density.An example look-up table is provided as table 4. The transmission of any material can be converted to a water equivalent transmission by comparing the measured transmission against the transmission predicted by equation (4) using the

Table 2 .
Description of the 4-quadrupole imaging-forming system downstream of the patient location.The first column shows a label corresponding to the component shown in figure 1.

Table 3 .
Summary of the imaging phantoms used, including a description of the phantom; dimensions of the phantom and any sub-components; list of materials used; and density of each material.

Table 4 .
An example look-up table for 800 MeV protons.