Experimental comparison of relative stopping power evaluation between proton CT and x-ray CT for pre-clinical proton irradiation studies of small animals

Objective. Proton therapy experiments in small animals are useful not only for pre-clinical and translational studies, but also for the development of advanced technologies for high-precision proton therapy. While treatment planning for proton therapy is currently based on the stopping power of protons relative to water (i.e. the relative stopping power (RSP)), estimated by converting the CT number into RSP (Hounsfield unit (HU)-RSP conversion) in reconstructed x-ray computed tomography (XCT) images, the HU-RSP conversion causes uncertainties in RSP, which affect the accuracy of dose simulation in patients. Proton computed tomography (pCT) has attracted a great deal of attention due to its potential to reduce RSP uncertainties in clinical treatment planning. However, as the proton energies for irradiating small animals are much lower than those used clinically, the energy dependence of RSP may negatively affect pCT-based RSP evaluation. Here, we explored whether the low-energy pCT approach provided more accurate RSPs when planning proton therapy treatment for small animals. Approach. We evaluated the RSPs of 10 water- and tissue-equivalent materials with known constituent elements based on pCT measurements conducted at 73.6 MeV, then compared them with XCT-based and calculated RSPs to investigate energy dependence and achieve more accurate RSPs for treatment planning in small animals. Main results. Despite the low proton energy, the pCT approach for RSP evaluation yields a smaller root mean square deviation (1.9%) of RSP from the theoretical prediction, compared to conventional HU-RSP conversion with XCT (6.1%). Significance. Low-energy pCT is expected to improve the accuracy of proton therapy treatment planning in pre-clinical studies of small animals if the RSP variation that can be attributed to energy dependence is identical to the variation in the clinical proton energy region.


Introduction
Proton therapy is therapeutically beneficial in terms of the dose distribution in the patient because the proton beam deposits the maximum energy at almost the end of the beam path (the so-called Bragg peak), and the dose can be concentrated in the tumor volume by controlling the beam direction and range. The accuracy of dose delivery during treatment planning is crucial to realize the benefits of proton therapy. In proton therapy plans, the dose distribution in the patient has generally been calculated based on reconstructed x-ray computed tomography (XCT) images, through conversion of CT numbers (Hounsfield unit (HU)) to proton relative stopping power (RSP), which is the stopping power in matter divided by that in water, based on stoichiometric calibration (Schneider et al 1996). However, XCT-based treatment planning is susceptible to uncertainties due to the HU-RSP conversion. For example, uncertainties of around 3% have been reported for XCT-based RSPs (Yang et al 2012). Any RSP uncertainty affects the range calculation, such that safety margins are required during treatment planning.
Proton computed tomography (pCT) could provide more accurate RSPs than XCT, and is expected to reduce the uncertainties originating from the HU-RSP conversion in conventional treatment planning. Over the past two decades, a wide range of experimental and theoretical studies on pCT have been performed (Williams 2004, Schulte et al 2008, Hurley et al 2012, Arbor et al 2015, Bashkirov et al 2016, Dedes et al 2019, Meyer et al 2020 to obtain reconstructed images of RSP with higher accuracy and better spatial resolution, and they have yielded promising results in terms of clinical applications (i.e. proton therapy).
Pre-clinical experimental proton therapy studies using small animals are useful for assessing the efficacy of novel therapeutic strategies, as they provide a better understanding of the biological responses of tumors to proton and heavy ion exposure. They can also be used to develop advanced beam handling and dose monitoring technologies for high-precision proton therapy (Parodi et al 2019, Meyer et al 2020. As with clinical use, accurate Bragg peak location and dose delivery are needed in experiments with small animals. At present, clinical proton therapy treatment planning assumes that the energy dependence of RSP is negligible throughout the beam path in the presence of high-energy protons (ICRU 1993, Arbor et al 2015, and calculates dose distributions in the patient based on the RSP at a given fixed energy until the proton stops at the tumor site (Kanematsu et al 2003, Yang et al 2012. Although treatment planning for clinical proton therapy is unlikely to be influenced by the energy-dependence of RSP at high incident beam energies of around 200 MeV, dose simulation in small animals at much lower energies (<50 MeV for mice) does not necessarily correspond to the clinical situation with higher proton energies, because the RSP varies significantly at < 100 MeV (as the proton slows down in the material), and the variation of RSP in the low-energy region differs among materials (Arbor et al 2015).
In this study, we derived RSPs of 10 water-and tissue-equivalent materials with known constituent elements based on pCT using a 73.6 MeV proton beam. We explored the feasibility of the low-energy pCT approach for achieving more accurate RSPs for proton therapy treatment planning in small animals by experimentally comparing the RSPs evaluated in pCT with conventional XCT-based and calculated RSPs.

Materials used for XCT and pCT measurements
We performed XCT and pCT measurements using tissue substitute materials: water, ethanol, and 40% K 2 HPO 4 solution (by weight) for calibration of HU-RSP conversion; five aqueous solutions (50% ethanol, 30% MgCl 2 , 20% KCl, 30% CaCl 2 , and 20% FeCl 3 (by weight)); and resins of polymethylmethacrylate (PMMA) and polyethylene. In terms of aqueous solutions, we chose inorganic salt solutions of MgCl 2 , KCl, CaCl 2 , and FeCl 3 because these elements are found in large quantities in the human body, and they have high effective atomic numbers (table 1). The liquids were kept in polyethylene vials with an inner diameter of 30 mm and height of 45 mm. The PMMA and polyethylene phantoms were cylindrical in shape, 30 mm in diameter, and 45 mm in height.
Although the materials used in this study are not exclusive to murine tissue, we presume that they most closely reflect the differences between XCT-based and pCT-based RSPs because the solutions exert larger photoelectric effects on XCT-based RSP evaluation, compared with other materials of lower effective atomic numbers. However, materials of high effective atomic numbers that mimic bone may in fact minimally affect the proton beam range in patients. We presume that the RSP errors of such materials are more significant during proton irradiation of small animals than in clinical situations. For example, when tumor cells are transplanted to the hind leg of a mouse, the leg bone becomes surrounded by tumor tissue. Thus, the proton dose is delivered to both the tumor and the leg bone. Therefore, we used materials of high effective atomic number in this measurement.

Stoichiometric calibration and x-ray CT measurements
For the HU-RSP conversion, we employed a calibration method based on the polybinary tissue model proposed by Kanematsu et al (2003), which has been widely used for planning proton and carbon therapy in Japan. This method is based on radiological properties, such as the linear attenuation coefficient m, the electron density r , e and the RSP. These radiological properties are calculated based on the stoichiometric calibration (Schneider et al 1996) of a series of body tissue compositions reported by the International Commission on Radiation Units and Measurements (ICRU 1992) and the formalism for m described by Rutherford et al (1976)  where K , ph K , coh and s KN are the coefficients for the photoelectric effect, coherent scattering, and Compton scattering, respectively.Z andẐ are the effective atomic numbers of the material for the photoelectric effect and coherent scattering, respectively. These quantities are given by i and w i are the atomic number, atomic weight, and proportion by weight of the i th element, respectively. Kanematsu et al (2003) confirmed that the correlation between the attenuation coefficient of a material relative to that of water m rel and electron density of the material relative to water r e,rel is well described by a single polyline with line segments for lung tissue (m rel 0.6), soft tissue (0.85 m rel 1.1), bone (1.3 m rel ), and their gaps (0.6 < m rel < 0.85 and 1.1 < m rel < 1.3). In addition, the correlation between m rel and RSP has also been shown to be well described by another polyline with similar line segments (Kanematsu et al 2003).
Body tissues in the polybinary tissue model are approximated by mixtures of two components (binary systems), i.e. mixtures of muscle-air, muscle-fat, and muscle-bone mineral for lung tissue, soft tissue, and bone, respectively. The calibration procedure for the HU-RSP conversion utilizes water, ethanol, and 40% K 2 HPO 4 aqueous solution as tissue substitutes for muscle, adipose tissue, and bone, respectively. TheẐ term in equation (1) is generally less important (Schaffner and Pedroni 1998). Kanematsu et al (2003) confirmed good linear correlations betweenZ and r e,rel (Z -r e,rel correlation), and betweenZ and RSP (Z -RSP correlation), based on the calculation for ICRU body tissues, and obtained linear fits for these correlation data. Therefore, for calibration in the polybinary tissue model (polybinary calibration), they defined ICRU body tissues corresponding to adipose tissue, muscle, and bone with the sameZ values as the tissue substitutes of ethanol, water, and 40% K 2 HPO 4 solution, respectively, in accordance with theZ -r e,rel andZ -RSP linear correlations, by ignoring small differences inẐ and I. The values of RSP (RSP t ) for these ICRU body tissues (adipose tissue, muscle, and bone) are estimated from the results of the linear fit. In addition, relative linear attenuation coefficients m rel t can be obtained by the following equation , 5 ,rel and m rel s are the relative electron density for the corresponding body tissue, relative electron density for the tissue substitute (ethanol, water, or 40% K 2 HPO 4 ), and relative attenuation coefficients for the tissue substitutes. The value of r e t ,rel is estimated in the same manner as RSP t , and r e s ,rel can be calculated for materials with known elemental compositions. The values of m rel s are obtained from the CT numbers of the tissue substitutes and air using a CT scanner based on the relationship between m rel and the CT number of the material of interest where H, H , a and H w are the CT numbers for the material, air, and water, respectively. As a result, we can determine a single polyline with line segments for the m rel -RSP correlation in the entire tissue region based on a set of calibration points (m , rel t RSP t ) for the body tissues, and finally obtain the relationship for HU-RSP conversion for treatment planning.
The polybinary calibration was performed with ethanol, water, 40% K 2 HPO 4 aqueous solution, and air phantoms using a CT scanner (Activion 16; Toshiba) in helical scanning mode, with an x-ray tube voltage and current of 120 kV and 150 mA, respectively. We reconstructed XCT images of the phantoms via iterative image reconstruction. The imaging dose per phantom was 13.0 mGy. We obtained CT numbers for all of the materials used in this study under the same conditions, then evaluated their XCT-based RSPs through the HU-RSP conversion resulting from the polybinary calibration.

Proton CT measurements
The pCT measurements for evaluating RSPs of the sample materials were performed using a proton beam of the AVF cyclotron (Model 930; Sumitomo Heavy Industries) operating at a nominal 80 MeV at the Cyclotron and Radioisotope Center (CYRIC), Tohoku University, Japan. Usually, the energy of the beam from the cyclotron slightly deviates from the nominal energy. The actual energy E of the beam used for pCT measurements was 78.13 MeV, measured using a dipole magnet with an internal nuclear magnetic resonance probe that measured beam momentum p. The momentum resolution Δp/p of the system was 1/2400, corresponding to a proton beam energy resolution ΔE/E of 1/1200. The beam energy stability was 10 −4 based on the stability of current to the main magnet of the cyclotron. The pCT scans of the materials were performed using a beam irradiation system dedicated to proton therapy research with small animals at CYRIC (Terakawa et al 2008(Terakawa et al , 2011. We used a translate-rotate geometry (Hanson et al 1981) to acquire pCT images. The experimental setup for pCT is illustrated in figure 1. The proton beam from the cyclotron with a beam size of about 10 mm (full width at half maximum; FWHM) was collimated using a 15 mm thick brass collimator with an aperture 1 mm in diameter, to provide a spot beam (approximately 1 mm FHWM) at the target. We acquired pCT data with a beam intensity monitor (BI-monitor) and energy detector (E-detector) located before and after the target, respectively, by measuring the residual energies of protons traveling through the target using the E-detector in current mode operation, and with correction of the effect of beam intensity fluctuation on the energy measurement using the BI-monitor (because the intensity of the beam from the cyclotron usually varies by approximately 20% during measurement). The BI-monitor was a 1 mm thick CsI(Tl) scintillator measuring 10 × 10 mm 2 equipped with a Si-PIN photodiode (Hamamatsu Photonics S2744-08), which was placed in a lightproof box with 12 μm thick aluminum windows for beam entrance and exit. The output current of the Si-PIN photodiode was measured using a current ammeter (Keithley 6517B). The E-detector was designed and built with a 20 mm thick CsI(Tl) scintillator measuring 10 × 10 mm 2 , in the same manner as for the BI-monitor. The beam size at the CsI scintillator of the E-detector was approximately 1.5 mm based on Monte Carlo simulation using the PHITS code (version 3.21) (Sato et al 2018). All protons passing through the phantom were presumed to attain the active area of the scintillator. We added a 20 mm thick brass collimator with an aperture 15 mm in diameter before the pCT system, and a 15 mm thick brass collimator with an aperture 2.5 mm in diameter before the BI-monitor to eliminate background protons (which were mainly due to beam halo and scattered protons from the beam exit window at the end of the beamline), and to protect the pCT system. We did not use any device dedicated to improving the spatial resolution of the reconstructed images affected by multiple Coulomb scattering, because Figure 1. Schematic overview of the proton CT (pCT) system used in this study. The pCT data were acquired using a translate-rotate geometry. The proton beam size was controlled by a brass collimator with 1 mm aperture placed immediately before the phantom. The proton residual energies were measured using the CsI(Tl) energy detector in current mode operation, in combination with the CsI (Tl) beam intensity monitor, to correct for beam intensity fluctuation.
our main aim was to evaluate RSPs with single-material targets 30 mm in diameter via pCT using low-energy protons at~80 MeV.
The overall energy loss of the proton beam due to the pCT system, including the window foil at the end of the beamline and air, was calculated; the energy of protons delivered to the target was estimated to be 73.6 MeV. Before the pCT measurements, we performed tests for beam intensity correction. Although the beam intensity fluctuated by up to 17% (relative standard deviation; RSD) during the measurements, the effect on energy measurement with the E-detector in current mode operation was kept to within 3% by correction with the BImonitor. However, it was difficult to fully correct for the effects of short-term intensity fluctuations (<1 s) using the BI-monitor. Such effects compromise the overall energy resolution of pCT. The current output of the E-detector was calibrated according to various residual energies of protons passing through a PMMA energy degrader with a thickness of 5-50 mm (intervals of 5 mm) and the known water-equivalent lengths for corresponding thicknesses. The output current of the E-detector was converted to the water-equivalent length based on the calibration data for the output current against the water-equivalent length. We obtained the pCT data by moving the target 64 mm at intervals of 0.5 mm in the direction lateral to the beam, in combination with rotation of the target through 180°at intervals of 3.6°. Thus, the proton beam was delivered to 6400 positions. The acquisition time per phantom was 1 h, associated with the delivery of~6.2 × 10 7 protons per position. We reconstructed pCT images via filtered backprojection. The imaging dose to the phantom was estimated to be 1.2 kGy. Although this dose is much higher than the dose used for treatment planning, the pCT system was not designed for real-world irradiation of small animals; it was designed for RSP evaluation of phantom materials using pCT at proton energies appropriate for small animal irradiation. Schneider et al (1996) calculated the RSP values of various tissues using the following approximation of the Bethe-Bloch equation where I and I w are the mean excitation energies of the material of interest and water, respectively; m , e c, and b are the electron mass, the speed of light in vacuum, and the speed of the proton relative to c, respectively. Several corrections used in the calculation of stopping power (i.e. the shell, density, and Barkas and Block correction terms) are neglected in equation (4) because their contributions were assumed to be small for biological materials. In contrast, the RSP calculation is affected by the I-values. For example, Doolan et al (2016) showed that the root-mean-square error of RSP based on equation (4) with different sets of I-values was 1%-2%.

RSP calculation
In this study, we obtained a theoretical RSP through calculation of the stopping power of a material, divided by the stopping power of water, using SRIM software (Ziegler 2013). We used a default set of I-values for comparisons with the values obtained via XCT and pCT. The SRIM code includes these corrections when calculating the stopping power. The overall accuracy of the SRIM stopping calculations is 4.0% for the SRIM-2010 version (Ziegler 2013). Stopping power calculations for high-energy ions (to 2 GeV/atomic mass unit) are reportedly accurate to 2% (Ziegler 1980). Therefore, we used 2% as the RSP error.

Results of XCT measurement
For each phantom material used in this study, we obtained the CT number from the mean pixel value, and the CT-number error from the RSD of the pixel values in a circular region of interest (ROI) 20 mm in diameter located in the center of the reconstructed image. The correlation between CT numbers and calculated RSPs for the materials is shown together with the HU-RSP relationship based on the polybinary calibration (Kanematsu et al 2003) in figure 2. The XCT-based RSPs obtained from the HU-RSP relationship are listed and compared with the calculated RSPs in table 1. The errors of XCT-based RSPs were estimated from the CT-number errors ( i.e. fluctuations (RSD ≈ 0.2%) of pixel values in the ROI of the XCT). The HU-RSP conversion caused deviations from the calculated results ranging from −6.9% to 12.6% (ΔRSP). The ΔRSP uncertainties were calculated by reference to the error propagations of the XCT-based and calculated RSPs. We obtained the large positive deviations of the XCT-based RSPs from the calculated values for 20% KCl, 30% CaCl 2 , and 20% FeCl 3 solutions. Because these materials have larger effective atomic numbers compared to other materials, their HU-RSP conversions are presumably affected to a greater extent by the photoelectric effect.

Results of pCT measurements
A typical reconstructed image (RSP map) of pCT obtained for the water phantom is shown in figure 3. The mean pixel values and RSDs of the pixel values were used to evaluate the RSPs and their errors, respectively, in the same manner as for the XCT measurements. The RSD denoting RSP errors was approximately 3%. The RSPs according to the pCT measurements are listed along with the calculated values in table 2. The differences between the experimental and calculated RSPs were within~3% (ΔRSP). The ΔRSP uncertainties were calculated by reference to the error propagations of the pCT-based and calculated RSPs.
The energy resolution of the detector affects the measurement of the residual proton energies, which promotes accurate RSP evaluation by pCT. Missaghian et al (2010) tested a CsI calorimeter developed for their pCT scanner using 35, 100, and 200 MeV protons in combination with energy degraders; they achieved an energy resolution <3% for proton energies of 26-100 MeV, compared to 0.6% for those higher than 100 MeV in pulse mode operation. We checked the energy resolution for the CsI(Tl) E-detector by monitoring the stability of its output current, with correction for the beam intensity fluctuation effect, using the BI-monitor at the same proton energy as the pCT measurement without a phantom. To determine the energy resolution of the detector that was not affected by short-term beam intensity fluctuations (<1 s), we evaluated the output current stability over 1 min in the absence of beam intensity fluctuations. The current output fluctuation for the E-detector resulted in an RSD of approximately 2% compared with 3% for the RSP. Therefore, the errors in RSP evaluation in this study were mainly attributable to the energy resolution of the pCT system.
The results of RSP evaluation using the XCT and pCT approaches are compared with the calculated RSPs in figure 4. The pCT-based RSPs showed better agreement with the calculated RSPs than those based on XCT. The root mean square (RMS) deviations of the XCT and pCT results with respect to the calculation were 6.1% and  1.9%, respectively, demonstrating that, despite the low proton energy (<100 MeV), the pCT approach for RSP evaluation still provided smaller deviations from the calculation compared to the conventional procedure with the HU-RSP conversion. Note that the X-based RSPs were derived using the polybinary calibration specific for clinical proton energies. Kanematsu et al (2003) confirmed that the RSP variation between β = 0.4 and 0.7 was approximately 0.5% for cortical bone. This is the worst case based on equation (4) using the ICRU I-value (ICRU 1993). As the clinical proton beam energies are within this β range, the effective proton velocity in the body was approximated using a constant β = 0.6 (230 MeV) during polybinary calibration. Thus, if calibration is adjusted to employ β < 0.4 (80 MeV) during irradiation of small animals, the accuracy of XCT-based RSP would improve.

Discussion
The phantom materials used cover a wide range of effective atomic numbers (Z = 5.54-14.02). Thus, they highlight the photoelectric effect on RSP evaluation during HU-RSP calibration, associated with RSP differences between XCT and pCT because RSP evaluation via pCT is based on interactions of protons with matter (e.g. Coulomb and nuclear interactions). Aqueous inorganic salt solutions such as 20% KCl, 30% CaCl 2 , and 20% FeCl 3 (all w/v) have higher effective atomic numbers (Z = 12-14), compared with other materials (Z = 5.5-7.5). RSP evaluation based on XCT of high-Z materials is more influenced by photoelectric effects, Figure 4. Comparison between RSPs obtained using the XCT and pCT approaches and the calculated values for the materials. When the XCT-or pCT-based RSP was identical to the calculated RSP, the data were plotted on the dashed line. Table 2. Comparison of pCT-based and calculated relative stopping powers (RSPs). The RSPs were adjusted such that the RSP of water was 1.00, and the errors reflect the fluctuations (RSDs) of pixel values in the ROI of the pCT images.

Material
pCT Calculation ΔRSP(%) Ethanol 0.82 ± 0.02 0.82 ± 0.02 0.0 ± 3.5 Water 1.00 ± 0.03 1.00 ± 0.02 0.0 ± 3.6 40% K 2 HPO 4 aqueous solution 1.27 ± 0.04 1.30 ± 0.03 −2.3 ± 3.8 Polyethylene 1.00 ± 0.03 1.00 ± 0.02 0.0 ± 3.6 PMMA 1.15 ± 0.03 1.16 ± 0.02 −0.9 ± 3.1 50% ethanol aqueous solution 0.89 ± 0.03 0.92 ± 0.02 −3.3 ± 3.9 30% MgCl 2 aqueous solution 1.20 ± 0.04 1.18 ± 0.02 1.7 ± 3.8 20% KCl aqueous solution 1.09 ± 0.03 1.08 ± 0.02 0.9 ± 3.3 30% CaCl 2 aqueous solution 1.16 ± 0.03 1.19 ± 0.02 −2.5 ± 3.0 20% FeCl 3 aqueous solution 1.08 ± 0.03 1.11 ± 0.02 −2.7 ± 3.2 compared with RSP evaluation based on XCT of low-Z materials. The calculated RSPs are significantly lower than the calibration line of figure 2. Accordingly, XCT-based RSPs for aqueous inorganic salt solutions are significantly larger than the calculated RSPs; XCT-based RSPs for polyethylene, PMMA, and 50% (w/v) ethanol (Z = 5.5-7.1) are less affected by photoelectric effects, such that they are only slightly smaller than or close to the calculated results. In contrast, the pCT approach was generally associated with lower deviations from the calculations. Notably, we obtained the RSPs of the materials from the pCT measurements at a proton energy of 73.6 MeV, which is a significantly lower than that of clinical proton beams (~200 MeV); we assumed that the energy dependence of RSP remains negligible throughout the phantom material, although the RSP varies gradually as the proton energy decreases in the low-energy region. To verify this assumption, we calculated RSPs for the materials used for this measurement to confirm their energy dependence in the proton energy range of 10-200 MeV. The calculated RSPs at specific proton energies divided by the RSPs at 200 MeV (RSP200) (as functions of energy) are shown in figure 5(a). RSP200 significantly varies in the low energy region, especially at <50 MeV, compared with the higher energy region (>100 MeV). Furthermore, the variation in the low energy region substantially differs among the materials. The values of RSP200 for low-Z materials increase as the proton energy decreases, whereas the high-Z materials exhibit the reverse tendency.
When pCT was performed in the energy range of 80-200 MeV, the variations in the RSP200 were <0.5%, although they attained 1.8% (40% K 2 HPO 4 solution) in the entire energy range (10-200 MeV). In our pCT scenario, the lowest residual energies of protons passing through the phantoms were around 30 MeV. Thus, the RSPs relative to those at 80 MeV (RSP80) are also shown in figure 5(b). We confirmed that the RSP80 variations were <0.6% in the energy range of 30-80 MeV. On the other hand, the variations increased to >1.5% (40% K 2 HPO 4 solution), reducing RSP accuracy when the lowest residual energy was reduced from 30 to 10 MeV using a thicker phantom. We should be able to avoid significant effects of RSP energy dependence on RSP accuracy in this pCT measurement when the residual energies are 30 MeV. Therefore, we presume that one reason for the pCT at 73.6 MeV to be associated with smaller deviations from the calculations is that the RSP variations under such conditions are almost identical to the RSP variations over the energy range of 80-200 MeV.
Although we compared the RSPs derived via both pCT and XCT with the RSPs calculated using SRIM software (Ziegler 2013), the RSPs should in fact be compared to the measured RSPs. Doolan et al (2016) determined the RSPs for tissue substitutes; the uncertainties were 0.1%-0.7% based on measurements of shifts in the Bragg peak positions using a 159 MeV proton beam with and without the materials in the beam path. As RSP measurement is susceptible to set-up and range errors, Doolan et al used thick (70 mm) inserts and obtained precise Bragg peak shifts of 20-114 mm with uncertainties of 0.1-0.4 mm depending on the material. In contrast, our proton beam energy was much lower (73.6 MeV) than the clinical proton energies at which previous RSP measurements were performed (Hurley et al 2012, Doolan et al 2016. The extent of Bragg peak shift is limited to a few cm in our experimental setup because the beam range is less than 50 mm in water, creating larger RSP uncertainties than those of Doolan et al 2016. For example, if we obtain a Bragg peak shift of 22.0 mm with uncertainties of 0.1-0.5 mm using an inserted material of thickness 20.0 ± 0.1 mm (RSP = 1.10), the RSP uncertainties are 0.007-0.026 (0.6%-2.4%). If we increase the Bragg peak shifts using thicker materials to reduce the RSP uncertainties, the energy-dependence of RSP negatively affects RSP measurements because the energy of protons passing through the materials becomes even lower, although RSP measurements using thick materials at clinical proton energies evidence almost no RSP energy-dependence. Therefore, we decided to use the RSPs calculated employing the SRIM software (with uncertainties of 2%; Ziegler 1980), to compare the XCT-and pCT-based RSPs.
Turning to the imaging dose and time of our pCT system, these are inappropriate for pre-clinical studies with small animals. The cyclotron was designed to deliver various beams (from protons to heavy ions) at variable energies; the cyclotron is a multipurpose device. The normal beam intensity, at which we derived pCT measurements, was much higher than the clinical beam intensity (the dose rate). Also, beam control during proton therapy, or the need to maintain the dose-rate stable during irradiation, is more difficult for multipurpose than medical accelerators. Although multipurpose accelerators may not be appropriate for preclinical studies on small animals, it is possible to ease the restrictions on imaging dose and time when using phantoms and tissue substitutes. Thus, we suggest that the method we used for pCT measurements yields useful pre-clinical data on the RSPs of phantom materials based on the normal operation of multipurpose accelerators.
In this study, we focused on deriving RSP with low-energy pCT, and investigated its applicability as a better RSP derivation method for proton therapy research with small animals. Although this measurement did not prioritize the spatial resolution of the RSP maps obtained with our pCT system, we evaluated the spatial resolution based on an additional pCT measurement using a cylindrical PMMA phantom (30 mm in diameter and 45 mm in height) with four cylindrical insert holes (1, 2, 5, and 10 mm in diameter), as illustrated in figure 6(a). The pCT scan was performed under the same conditions as for the other phantoms, except for rotation of the target through 360°. The reconstructed pCT image is shown in figure 6(b). The 1 mm hole in the reconstructed image was indistinct, while the other holes were readily recognized. To evaluate the spatial resolution of the reconstructed image, we assumed that a line profile passing through the center of the phantom was approximated by an error function (i.e. the integral of the Gaussian) for the phantom surface. We obtained a spatial resolution of 1.3 mm (FWHM) by fitting the error function to the line profile. The spatial resolution of pCT is affected by physical and experimental conditions, such as multiple Coulomb scattering effects, range struggling, and beam properties. The resulting resolution was considered to arise primarily from the beam spot size (approximately 1 mm), which was formed when the collimator was 5 mm before the phantom. Although it was not necessary to improve the spatial resolution specifically for the purpose of this study, it is important to achieve not only RSP accuracy but also high spatial resolution of the reconstructed images, to take full advantage of pCT for treatment planning of proton therapy, including pre-clinical studies using small animals.
Recently, to reduce the multiple Coulomb scattering effects and improve the spatial resolution of reconstructed images, various detailed investigations have been performed based on proton path estimation models, such as the most likely path (Williams 2004, Schulte et al 2008, Erdelyi 2009 or cubic spline path (Fekete et al 2015), using sophisticated single-particle tracking detectors placed before and after the object in the pCT scanner systems; these studies have yielded promising results. However, note that such detectors do not necessarily improve the spatial resolution of pre-clinical pCT studies using small animals because the proton penetration depth is much less than the depth achieved under clinical conditions; this difference counteracts the effect of increased, multiple Coulomb scattering at lower energies. Meyer et al (2020) performed a very detailed investigation of a pCT system for pre-clinical small animal imaging (based on Monte Carlo simulation); they found that the utilities of proton path estimation models (e.g. most-likely or cubic-spline paths) were limited, compared with a straight-line path through the object. Additionally, they noted that some objects can cause large uncertainties in proton direction estimation models; the performance of the straight-line path was superior.

Conclusion
We evaluated RSPs based on pCT performed at 73.6 MeV for experimental comparison with those obtained by conventional XCT. The RMS deviations of RSP from the theoretical values were 1.9% and 6.1% for pCT and XCT, respectively. This study demonstrated that pCT maintains superiority over XCT for RSP evaluation even when applied at low energies relevant to small animal irradiation, and is expected to improve the accuracy of proton therapy treatment planning for pre-clinical studies using small animals.