Abstract

Purpose:

Relative biological effectiveness (RBE) accounts for the differences in biological effect from different radiation types. The RBE for proton therapy remains uncertain, as it has been shown to vary from the clinically used value of 1.1. In this work we investigated the RBE of protons and correlated the biological differences with the underlying physical quantities.

Materials and Methods:

Three cell lines were irradiated (CHO, Chinese hamster ovary; A549, human lung adenocarcinoma; and T98, human glioma) and assessed for cell survival by using clonogenic assay. Cells were irradiated with 71- and 160-MeV protons at depths along the Bragg curve and 6-MV photons to various doses. The dose-averaged lineal energy (D) was measured under similar conditions as the cells by using a microdosimeter. Dose-averaged linear energy transfer (LETd) was also calculated by using Monte Carlo (MC) simulations. Survival data were fit by using the linear quadratic model. The RBE values were calculated by comparing the physical dose (D6MV/Dp) that results in 50% (RBE0.5) and 10% (RBE0.1) cell survival, and survival after 2 Gy (RBE2Gy).

Results:

Proton RBE values ranged from 0.89 to 2.40. The RBE for all 3 cell lines increased with decreasing proton energy and was higher at 50% survival than at 10% survival. Additionally, both A549 and T98 cells generally had higher RBE values relative to the CHO cells, indicating a greater biological response to protons. An increase in RBE corresponded with an increase in D and LETd.

Conclusion:

Proton RBE was found to depend on mean proton energy, survival end point, and cell type. Changes in both D and LETd were also found to impact proton RBE values, but consideration of the energy spectrum may provide additional information. The RBE values in this study vary greatly, indicating the clinical value of 1.1 may not be suitable in all cases.

Introduction

Proton therapy (PT) is becoming a more prevalent modality in the treatment of cancer. Proton therapy can be advantageous for certain cancers, as protons deposit highly concentrated radiation dose to a specific (tumor) location while sparing surrounding healthy tissue much more than x-ray therapy [1]. A potential related advantage PT has with respect to x-ray therapy is the biological damage caused by protons or the resulting biological effect. The difference in biological effect between these 2 modalities can be quantified by the relative biological effectiveness (RBE). The RBE is a ratio of physical doses that cause the same biological effect and can be calculated by:

 
formula

In this equation Dcontrol is the physical dose of a reference radiation modality (ie, x-rays) and Dtest is the physical dose of the radiation modality being investigated (eg, protons) [2]. An averaged value of 1.1 has been adopted for PT, but it is widely accepted that this static value does not represent the true range of RBE for PT [37].

Over the past few decades, numerous studies [717] and review articles [35, 18, 19] have sought to quantify the RBE of PT and provide insight into the complexity of this problem. The review by Paganetti [4] in 2014 showed the averaged proton RBE values across a spread-out Bragg peak range from 0.9 to 1.7. A substantial body of evidence for the variation in PT RBE in vitro has been published and subsequently collected in the online, open-access Particle Irradiation Data Ensemble (PIDE) database [20]. Previous data have shown proton RBE to be a dynamic value dependent on many factors including cell type, position of measurement along the Bragg curve (BC), and linear energy transfer (LET), or how protons deposit energy. Current information suggests that the RBE is most enhanced in the distal edge of the Bragg peak (BP) where LET rapidly increases [21]. This enhanced region may be placed outside the tumor, potentially within a critical normal tissue, owing to physical uncertainties, and thus has the potential to have significant clinical consequences, either actual [22, 23] or predicted [20, 2427]. Although most PT patients do not experience side effects related to the uncertainty of proton RBE, this potential to inadvertently biologically overdose normal tissues is why proton RBE needs to be better understood and managed. Therefore, quantifying energy deposition at the cellular level and characterizing the relationship between the energy transferred and the subsequent biological effects is important for accurate PT treatment planning. The 2 physical parameters that describe how energy is transferred to a material are lineal energy (y) and LET. Although these parameters have similarities, there exist distinct differences between y and LET that have been previously described [28].

The purpose of this study was to confirm the previously reported variation of proton RBE with respect to 6-MV x-rays (6 MV) and correlate the underlying physical principles governing the changes in proton RBE by measuring y and calculating LET. Additionally, this work focused on reducing experimental uncertainties by ensuring precise positioning of the setup along the Bragg curve and accurate dosimetry to verify each measurement.

Materials and Methods

Cell Lines and Clonogenic Assay

Details regarding cell lines, culture conditions, and clonogenic assay plating have been previously described [29]. Briefly, 3 types of cells were used in this study: CHO cells, Chinese hamster ovary; A549 cells, human lung adenocarcinoma; and T98 cells, human glioma. Clonogenic assays were conducted to measure cell survival after radiation exposure. Three independent runs were conducted with triplicate wells for each treatment. Colonies were fixed, stained, and manually counted. A group of cells was considered a colony if >50 cells were present in the group.

6-MV Irradiation

The x-ray irradiation protocol has been previously described [29], therefore an abbreviated version is presented here. A Truebeam linear accelerator was used (Varian Medical Systems, Palo Alto, California) at a dose rate of 600 cGy/min and energy of 6 MV. Before each cell irradiation, the machine output was measured by using a calibrated Farmer ionization chamber. Dosimetry for the irradiated cells was done by using EBT3 Gafchromic film placed in the 3 wells adjacent to the wells holding cells. Cells plated in a 6-well plate were then immobilized in an acrylic jig for reproducible setup (Figure 1a). An anterior beam was used to irradiate cells located at 10-cm depth of water equivalent material with a field size of 20 × 20 cm2.

Figure 1

Experimental set up for (a) 6-MV x-rays and (b) protons. The plate of cells is in an acrylic jig for reproducible positioning. The Markus chamber is included in the proton setup. (c) The proton experimental setup.

Figure 1

Experimental set up for (a) 6-MV x-rays and (b) protons. The plate of cells is in an acrylic jig for reproducible positioning. The Markus chamber is included in the proton setup. (c) The proton experimental setup.

Proton Irradiation

For proton irradiation, the experimental setup was closely matched to the 6-MV protocol. Film was not used in the proton irradiations owing to its LET-dependent response [30]. Instead, the Markus chamber was chosen, where the sensitive volume is 0.02 cm3 and measurements are accurate to within 1% of the primary ionization chamber used for clinical dosimetry [31]. The acrylic jig used in the 6-MV experiments was modified to accommodate the Markus chamber in the radiation field next to the 6-well plates (Figure 1b). The water equivalent thicknesses below both the cells and sensitive volume of the Markus chamber were equal, ensuring that the cells and Markus chamber were at the same depth (±0.1 mm) for each experimental run. Cells were irradiated with a posterior beam as shown in Figure 1c.

Two proton energies were delivered from the scanning nozzle of a Probeat5 PT system (Hitachi America Ltd, Tarrytown, New York): 71 MeV, the lowest energy available with the highest associated LET values; and 160 MeV, a midrange energy used often in patient treatments. The spot spacing and field size used were chosen to ensure a uniform dose was delivered to the cells and Markus chamber (approximately 20 × 20 cm2 field size). Four points of measurement (POMs) were chosen for each of these energies to compare the change in proton RBE relative to depth (or mean proton energy) and LET (Figure 2). Depth was modulated by placing various thicknesses of water equivalent material underneath the cell setup for protons.

Figure 2

Monoenergetic Bragg curves for (a) 71 and (b) 160 MeV labeled with points of measurement.

Figure 2

Monoenergetic Bragg curves for (a) 71 and (b) 160 MeV labeled with points of measurement.

Data Analysis

Surviving fraction and dose were related by fitting the data to the linear quadratic model. This fit was obtained with MINUIT (CERN, Geneva, Switzerland), a numerical minimization program, using X2 nonlinear regression to solve for α and β. Proton RBE was then calculated for the physical doses that resulted in 50% and 10% cell survival. Additionally, an RBE value was calculated directly from the data by taking the ratio of surviving fractions after a dose of 2 Gy. The uncertainty in RBE was calculated by taking the standard deviation for both α and β, including the correlation, and propagating through the linear quadratic model.

Measuring D and Calculating LETd

A solid-state microdetector, the MicroPlus probe, was used for the measurement of dose-mean lineal energy (D), and has been previously described [32, 33]. The MicroPlus probe was tested and verified for use at our clinical proton facility. The experimental setup is depicted in Supplementary Figure 1. The probe was placed in a water-equivalent (polymethyl methacrylate) phantom with the proton gantry at 0° pointed vertically downward with the incident beam perpendicular to the plane of the detector. The same acrylic slabs used for each cell POM were stacked on top of the detector, similar to the setup for cell irradiation, to change the POM along the BC. This setup ensured accurate positioning to ±0.1 mm. Measurements were taken at each POM for the 71- and 160-MeV beams with a radiation field size of 20 × 20 cm2.

LETd was calculated for the 2 proton beams by using an in-house graphics processing unit-based MC [34]. The calculation of LETd from this MC simulation has been validated against values produced by TOPAS [35] and is in good agreement [34]. The grid size used for these MC calculations was 1 mm. This grid size was chosen as it is typical of normal dose calculations in a clinical setting. The same setup geometry as described for the D measurements was simulated.

Results

6-MV and Proton Dosimetry

The 6-MV dose was found to be within ±3.5% for all dose points and experiments as previously reported [29]. Positional uncertainties were within 0.1 mm and dosimetric uncertainty was less than 10% for protons with only 2 POMs exceeding 5%. The greatest dose uncertainty occurred at the distal edge of the BC, as dose gradient is steepest at this point. For example, a shift in depth of 0.1 mm can result in a 10% dose difference on the distal edge of the 71-MeV BC.

Cell Survival Curves

The 6-MV and proton cell survival curves, for CHO, A549, and T98 cells are shown in Figure 3. The fit parameters for the linear quadratic model are listed in Supplementary Table 1 along with the RBE values at 50% and 10% survival and the RBE value after 2 Gy delivered. For 10% and 50% survival, the RBE for CHO, A549, and T98 cell lines overall increased with proton depth as expected and was higher at 50% survival than at 10% survival. Both A549 and T98 survival curves from the 160-MeV experiments had slight fluctuations in RBE that did not strictly follow the trend for D1, D2, and D3 depth points, but maintained the trend of increasing RBE with depth within the reported error. Additionally, the RBE at 2 Gy followed the same trend of increasing RBE values with increasing depth in CHO cells but deviated for A549 and T98 cells at certain POMs. Even with these deviations, both A549 and T98 cells had increasing RBE values as depth increased to within the reported error.

Figure 3

Survival curves for CHO cells: (a) 71 and (b) 160 MeV; A549 cells: (c) 71 and (d) 160 MeV; and T98 cells: (e) 71 and (f) 160 MeV.

Figure 3

Survival curves for CHO cells: (a) 71 and (b) 160 MeV; A549 cells: (c) 71 and (d) 160 MeV; and T98 cells: (e) 71 and (f) 160 MeV.

The experimental values for D and LETd were similar at all POMs for 160-MeV protons. This is not the case for 71-MeV protons, where at the distal edge POM (D4) the D value was greater than LETd. The measured D values range from 2.82 to 9.96 and 2.39 to 7.62 keV/μm for 71- and 160-MeV protons, respectively, across the 4 POMs. The LETd values for the 71-MeV protons range from 1.78 to 7.34 keV/μm and for the 160-MeV protons, from 0.99 to 7.29 keV/μm.

The resulting D and LETd values for the 4 POMs at both proton energies are listed in Supplementary Table 2 with the corresponding RBE values (RBE0.5, RBE0.1, and RBE2Gy) from all 3 cell lines. The relationship between RBE and D or RBE and LETd are shown graphically in Figures 4 and 5. For RBE0.5 and RBE0.1, the relationships between both D and LETd are somewhat linear. The general trend follows that an increase in D or LETd results in increased RBE values. Additionally, this trend appears cell line independent, as the data points for each cell line at the 4 measurement points are the same within the reported error. This is not the case for the RBE2Gy data (Figure 4e and 4f and Figure 5e and 5f), which shows a large spread between the 3 cell lines and their relationship between RBE2Gy and D or LETd.

Figure 4

Plots from 71-MeV experiments comparing the following quantities: (a) RBE_0.5 and yd; (b) RBE_0.5 and LETD; (c) RBE_0.1 and yd; (d) RBE_0.1 and LETD; (e) RBE_2Gy and yd; and (f) RBE_2Gy and LETD. Colors indicate individual cell lines: CHO, blue; A549, red; and T98, green. Error bars represent the error reported in Supplementary Table 1 for RBE. The black line indicates RBE = 1.1.

Figure 4

Plots from 71-MeV experiments comparing the following quantities: (a) RBE_0.5 and yd; (b) RBE_0.5 and LETD; (c) RBE_0.1 and yd; (d) RBE_0.1 and LETD; (e) RBE_2Gy and yd; and (f) RBE_2Gy and LETD. Colors indicate individual cell lines: CHO, blue; A549, red; and T98, green. Error bars represent the error reported in Supplementary Table 1 for RBE. The black line indicates RBE = 1.1.

Figure 5

Plots from 160-MeV experiments comparing the following quantities: (a) RBE_0.5 and yd; (b) RBE_0.5 and LETD; (c) RBE_0.1 and yd; (d) RBE_0.1 and LETD; (e) RBE_2Gy and yd; and (f) RBE_2Gy and LETD. Colors indicate individual cell lines: CHO, blue; A549, red; and T98, green. Error bars represent the error reported in Supplementary Table 1 for RBE. The black line indicates RBE = 1.1.

Figure 5

Plots from 160-MeV experiments comparing the following quantities: (a) RBE_0.5 and yd; (b) RBE_0.5 and LETD; (c) RBE_0.1 and yd; (d) RBE_0.1 and LETD; (e) RBE_2Gy and yd; and (f) RBE_2Gy and LETD. Colors indicate individual cell lines: CHO, blue; A549, red; and T98, green. Error bars represent the error reported in Supplementary Table 1 for RBE. The black line indicates RBE = 1.1.

Discussion

As PT has become widely used in the treatment of certain cancers, such as pediatric cancer, clinical data have provided insight into the advantages and limitations of this modality [1]. One limitation of PT remains the uncertainty related to RBE and the question of using a static RBE value for all cases and conditions. Recent reports have hypothesized that toxicities observed following PT may be due to the use of a static RBE value [22]. For example, Indelicato et al [23] showed an incidence of serious brainstem toxicity of 2.1% with higher rates of incidence (10.7%) for patients with posterior fossa tumors. Another study done by the same group reported that approximately one-third of patients with thoracic Ewing sarcoma would develop acute esophagitis when treated with chemotherapy and PT [36]. Therefore, these negative secondary effects suggest that an in-depth look at understanding the biological dose is warranted [22].

RBE values ranging from 0.9 to 2.1 have been measured experimentally; however, a clinical value of 1.1 remains in use. Additionally, the proton LETd is known to increase toward the end of the proton range; this variation in LETd has implications for biological effects in patients undergoing proton beam therapy [4]. Therefore, previous studies have looked into the relationship between RBE and LETd to gather further evidence on the underlying physical processes associated with changes in proton RBE [7, 1113, 37]. The purpose of this investigation was to study the dependencies of the RBE for protons at various points along the BC with respect to 6 MV for different cell types and to correlate the underlying physics via LET (and D). Having a better understanding of the scale at which the RBE for protons changes, as well as the mechanism behind the change, is important in how treatments are designed.

Proton RBE Dependence on Cell Type, End Point, and Mean Proton Energy

Clonogenic assays were conducted with protons at 71 and 160 MeV and 6-MV photons for 3 cell lines to evaluate the biological dose response. The CHO cell line was chosen as a historical line to compare to studies done previously [17, 38]. The A549 and T98 human tumor cell lines serve as in vitro models of human tumors that may benefit from being treated with protons and have not been studied previously for determination of RBE [3941]. The RBE values were calculated at 50% and 10% cell survival and after a single dose of 2 Gy. We chose to include RBE2Gy, as it is a direct calculation of RBE from the data and does not depend on the parameters of a model fit. Additionally, 2 Gy is a clinically relevant dose point as many treatment schemes use approximately 2 Gy fractions.

Results showed proton RBE is dependent on mean proton energy, end point, and cell type. All 3 cell lines resulted in RBE values that increased from the entrance point to the distal edge of the BC or as mean proton energy decreased. Proton RBE values ranged from 0.99 to 2.40 for the entire data set, implying changes in radiation response due to protons could be much larger than the traditional 10% enhancement as compared to 6 MV. Proton RBE was dependent on the biological end point, specifically, RBE values were less pronounced at 10% survival than 50% survival. This may be due to the lower doses (2–3 Gy) at the level of 50% survival, resulting in larger ratio of doses for 6 MV compared to protons. Finally, evaluation of the cell-dependent biologic response to protons was done by using 3 distinctive cell lines. The RBE values were found to be least dependent on cell type as compared to LET and end point.

Results from this study agreed well with previously published data. In the 2002 review article from Paganetti et al [3] collecting all proton RBE data, in vitro results indicated an RBE range from 0.9 to 2.1 across various cell lines and proton energies [3]. More recently, a study from Guan et al [7] measured the RBE of protons in a 79.7-MeV pristine beam, evaluating clonogenic survival as their end point in 2 human cell lines. Guan and colleagues [7] found an increase in RBE with depth along the BP where values ranged from 0.89 to 3.28 depending on the cell line for 10% survival relative to 137Cs. These values were higher than those found in our study but may be due to the POMs taken on the distal edge of the BP. In either case, the trend toward significantly higher RBE toward the end of range is clear [7].

Proton RBE, LETd, and D

Previous research investigating the underlying physics associated with changes in proton RBE has either measured lineal energy or calculated LETd. Owing to the varied data on these 2 quantities and their relationship to RBE, this study aimed to provide additional data for potential clarification. Microdosimetric measurements were taken at the same points along the BC where the cells were irradiated in order to correlate the experimentally measured proton RBE values with D at that point. The experimental setup was then recreated by using MC simulation to calculate LETd. The decision to investigate both D and LETd stemmed from the need to look into both, as these 2 quantities can differ in certain circumstances [28].

The volume of interest in the measurement of y is always focused on the center of the charged particle track and therefore is defined for a single energy deposition event. On the other hand, LET is defined in a volume chosen arbitrarily in the irradiated material and therefore could potentially be crossed only by resulting delta rays produced by the charged particle tracks. On the macroscopic scale, these 2 quantities are similar. However, as the volume of interest gets smaller, LET will fail to characterize the true energy imparted at all arbitrary volumes within the irradiated material [28]. Therefore, while in some cases y and LET are similar, it is important to compare these 2 quantities by measuring y with a microdetector in order to verify the corresponding calculated LET.

Our results showed the measured D and calculated LETd values follow the trend of RBE where the values increase along the BC as mean proton energy decreases. The magnitude of increase in D or LETd differs for the 2 proton beams with energies of 71 and 160 MeV. These differences are especially apparent at the POM on the distal edge of the 71-MeV beam where D is 9.96 keV/μm and LETd is 7.34 keV/μm. This difference may be due to the calculation volume of LETd where the arbitrary volume of interest (step size of 1 mm) is large enough such that the averaging of the energy transferred by the protons does not represent the energy transferred on the microscopic scale. Recall, as incident protons interact with a material, the rate of energy transfer increases as the proton energy decreases. For the 71-MeV proton beam, most protons come to their end of range in close proximity to one another, creating an energy spectrum that is relatively narrow as compared to that of a 160-MeV proton beam. This narrow energy spectrum for 71-MeV protons can be detected by the microdetector and in turn, D is able to accurately represent the energy transferred along the particle track. The ability for LETd calculations to accurately represent the energy transferred by protons depends on the step size used in MC simulation. In this study, the step size used was 1 mm and an averaging effect of this larger volume of interest may point to the smaller value of LETd for the same POM. This difference is not seen at the distal edge POM for the 160-MeV beam, as the energy spectrum is more spread out and therefore the changes in energy transfer are not as sharp. The difference between D and LETd at the distal edge of the 71-MeV proton beam highlights the potential limitations associated with using LETd as a surrogate for investigating changes in energy transfer.

Another interesting difference between D and LETd is shown at the entrance region of the BC or D1 for both energies. At these points for both incident proton energies, D was found to be larger than LETd. This mismatch may also be attributed to the voxel size. Previous studies have shown similar values for D and LETd are achieved when the voxel size is reduced by an order of magnitude (from 1–2 mm down to 0.1–0.2 mm) [42, 43].

Finally, discrepancies between points with similar D values and varying RBE values were noted. For example, the D values for POM D1 at 71 MeV and D2 at 160 MeV were 2.82 and 2.81 keV/μm, respectively. However, RBE0.5 values for the A549 cell line were 1.32 and 1.09 for the D1 and D2 POM, respectively. Though these 2 data points are similar to within the reported error, the results indicate D values alone may not be the most accurate method determining proton RBE values. As D is a mean value taken from the lineal energy spectrum and the shapes of these spectra can be quite different but still yield the same D value, the spectral shape may be more closely related to proton RBE. As an example, the differences in spectral shape with similar D values for the 2 points mentioned are shown in Figure 6.

Figure 6

Microdosimetric spectra and the corresponding D values for 2 selected POMs: (a) D1 for 71-MeV protons and (b) D2 for 160-MeV protons.

Figure 6

Microdosimetric spectra and the corresponding D values for 2 selected POMs: (a) D1 for 71-MeV protons and (b) D2 for 160-MeV protons.

Few studies have experimentally measured both RBE and D as well as calculated LETd. The most similar study to this work was originally done by Bettega et al [44] and more recently by Chaudhary et al [12] in a 62-MeV pristine proton beam with 2 cell lines (AG01522 and U87). In general, the same relationship between RBE and LETd, where RBE increases with LETd, was shown in both studies. However, differences in methodology between studies resulted in varied absolute values of measured RBE and calculated LETd. Chaudhary and colleagues [12] used Geant4 to calculate LETd for 6 POMs across the 62-MeV pristine peak. The LETd values ranged from 1.11 to 22.6 keV/μm. Three of the 6 POMs used in the study by Chaudhary et al [12] were similar enough to the LETd values calculated in this work for comparison. Further, the U87 cell line is a human glioma cell line, similar to that of our T98 cell line, allowing a comparison of the RBE values for the U87 and T98 cell lines. The LETd values of 1.11, 4.02, and 7.0 keV/μm from Chaudhary et al [12] are similar to D1, D2, and D4 POM from our 71 MeV of 1.78, 4.35, and 7.34 keV/μm. The RBE0.1 values ranged from 1.15 to 1.35 for U87 and from 1.07 to 1.71 for T98 at these points of similarly calculated LETd [12]. These values seem to differ significantly, which may have a number of causes. First, the reference radiations differed between these 2 studies with ours using 6-MV x-rays and theirs using 225-kVp x-rays. Because the reference radiation was different in the experiment of Chaudhary and colleagues [12], compared to this study, any relative RBE between 6-MV and 225-kVp x-rays would need to be taken into account to do a direct comparison of proton RBE in these 2 studies [45]. Second, the MC used for calculations of LETd was different (Geant4 and our in-house MC) and therefore the scorer embedded in the MC could differ between the two [43]. Finally, the voxel size for calculating LETd may have differed, which directly impacts calculation.

The motivation for investigating both D and LETd was to find a good surrogate for describing the underlying physics in hopes of more accurately predicting proton RBE values. Most previous proton RBE studies have used LETd as a surrogate for predicting proton RBE; however, in establishing the PIDE database, Friedrich and colleagues [20] point out the shortcomings of using LETd, as it is highly dependent on track structure. The results comparing D and LETd in this study have shown instances where the 2 values differ, pointing toward a potential advantage to using D, as it is not affected by particle track structure like LETd. Therefore, it may be appropriate to recommend measuring D in various clinical ion beams during the commissioning process and include D data into the treatment planning system; however, further evidence is needed.

Conclusions

The goal of this study was to investigate the dynamic changes of proton RBE along the BC for various cell types. To determine the relationship between physical dose and biological effect, the end point of cell survival was quantified by using the clonogenic assay and 3 different cell lines (CHO, A549, and T98). Further, to investigate the physical principles causing RBE changes, this study quantified the energy deposition of protons by measuring D and calculating LETd. Proton RBE values ranging from 0.99 to 2.40 show the dependence of RBE on cell type, end point, and POM. Overall, these results give further evidence that proton RBE can differ greatly from the clinically used value of 1.1 and quantities such as D or LETd may provide additional insight to the scale at which RBE changes.

This work approached the complex problem of characterizing proton RBE and demonstrated RBE dependence on end point, cell type, mean proton energy, and LET. While additional studies are needed before clinical translation, we have presented evidence supporting the variability of proton RBE in human cell lines not previously studied and the potential instances where the clinical value of 1.1 could be improved upon.

ADDITIONAL INFORMATION AND DECLARATIONS

Conflicts of Interest: The authors have no conflicts of interest to disclose.

Acknowledgments: This work was supported by the National Institutes of Health (NIH) through a National Heart, Lung and Blood Institute grant T32 HL105355 and the Mayo Graduate School. The authors would like to acknowledge support from the Department of Radiation Oncology. This work was presented at the 2017 Particle Therapy Co-Operative Group, Yokohama, Japan, on May 13, 2017.

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