Investigating the impact of alpha/beta and LETd on relative biological effectiveness in scanned proton beams: An in vitro study based on human cell lines

Purpose A relative biological effectiveness (RBE) of 1.1 is commonly used in clinical proton therapy, irrespective of tissue type and depth. This in vitro study was conducted to quantify the RBE of scanned protons as a function of the dose‐averaged linear energy transfer (LETd) and the sensitivity factor (α/ß)X. Additionally, three phenomenological models (McNamara, Rørvik, and Jones) and one mechanistic model (repair‐misrepair‐fixation, RMF) were applied to the experimentally derived data. Methods Four human cell lines (FaDu, HaCat, Du145, SKMel) with differential (α/ß)X ratios were irradiated in a custom‐designed irradiation setup with doses between 0 and 6 Gy at proximal, central, and distal positions of a 80 mm spread‐out Bragg peak (SOBP) centered at 80 mm (setup A: proton energies 66.5–135.6 MeV) and 155 mm (setup B: proton energies 127.2–185.9 MeV) depth, respectively. LETd values at the respective cell positions were derived from Monte Carlo simulations performed with the treatment planning system (TPS, RayStation). Dosimetric measurements were conducted to verify dose homogeneity and dose delivery accuracy. RBE values were derived for doses that resulted in 90 % (RBE90) and 10 % (RBE10) of cell survival, and survival after a 0.5 Gy dose (RBE0.5Gy), 2 Gy dose (RBE2Gy), and 6 Gy dose (RBE6Gy). Results LETd values at sample positions were 1.9, 2.1, 2.5, 2.8, 4.1, and 4.5 keV/µm. For the cell lines with high (α/ß)X ratios (FaDu, HaCat), the LETd did not impact on the RBE. For low (α/ß)X cell lines (Du145, SKMel), LQ‐derived survival curves indicated a clear correlation of LETd and RBE. RBE90 values up to 2.9 and RBE10 values between 1.4 and 1.8 were obtained. Model‐derived RBE predictions slightly overestimated the RBE for the high (α/ß)X cell lines, although all models except the Jones model provided RBE values within the experimental uncertainty. For low (α/ß)X cell lines, no agreement was found between experiments and model predictions, that is, all models underestimated the measured RBE. Conclusions The sensitivity parameter (α/ß)X was observed to be a major influencing factor for the RBE of protons and its sensitivity toward LETd changes. RBE prediction models are applicable for high (α/ß)X cell lines but do not estimate RBE values with sufficient accuracy in low (α/ß)X cell lines.


INTRODUCTION
Proton therapy (PT) is an emerging treatment modality within radiation oncology with 77 facilities currently in operation (www.ptcog.ch). Compared to most advanced treatment techniques with high-energy photon beams, the advantageous physical ballistics of protons enable highly conformal treatments with reduced organs-at-risk doses, especially in the low and medium dose range, and a substantially reduced integral dose. 1 Due to the effective sparing of normal tissues without compromised target coverage, PT is primarily applied in pediatric oncology and for malignancies close to critical anatomical structures, that is, for head-and-neck and skull base region as well as re-irradiations. [2][3][4] In addition to the favorable inverted depth dose profile, protons are biologically more effective than high-energy photon beams. Hence, the relative biological effectiveness (RBE) was introduced as a conversion factor, defined as the ratio of physical dose required to yield the same biological effect. 5,6 Today's clinical practice in PT is still based on a constant RBE of 1.1, a value which was chosen conservatively in the 1960s and 1970s. 7,8 However, the knowledge gained from several studies suggests a variable, rather than a constant RBE. Fractional doses, physical beam characteristics, biological parameters, and the investigated endpoints were identified as influencing factors. Especially the increased linear energy transfer (LET) at the distal end of the spread-out Bragg peak (SOBP) is associated with increased biological efficacy. 9,10 However, none of these parameters have so far been implemented in clinical routine, largely due to uncertainties within these complex interactions and the broad range of reported RBE values from 0.8 to 2. 11,12 These variations in RBE can be partly attributed to the use of different reference irradiation qualities, beam delivery techniques and energies, endpoint assessment at different positions within the beam line, and chosen radiobiological model systems. 11,[13][14][15] To account for a potential variable RBE, several mathematical models have been developed to predict the RBE. All phenomenological models are empirical data-based, generally taking into account the dose, dose-averaged linear energy transfer (LET d ), and tissue-specific parameters generated from a collection of in vitro data with clonogenic death as biological endpoint. In contrast, mechanistic models are derived from predicting the interaction probability of particles within the biological system, including, to a varying extent, DNA double-strand break (DSB) repair dynamics. Again, clinical implementation so far was hindered due to uncertainties in the fitting data. 16 Concerning the beam delivery, pencil beam scanning with active or passive depth modulation has eclipsed the traditional passive scattering techniques. The latter was the basic mode of beam delivery in which almost all experimentally available RBE data were acquired. As very recently pointed out, the physical characterization of particle beams and the standardization of dosimetric reporting are essential steps to reduce uncertainties in RBE determination. 13,17 In summary, during the last decades the scientific knowledge, methodological approaches, and the mode of proton beam delivery have changed and progressed considerably.
The aim of the present study was to investigate the correlation of RBE, LET d , and the tissue-specific fractionation sensitivity factor of photons (a/b) X for scanned proton beams with an active energy variation in experimental conditions that mimic typical clinical scenarios (e.g., dose, energy range). More specifically, the LET d dependency of the proton RBE was assessed for four human cell lines with high (≥10) and low (≤5) (a/b) X values using typical clinical proton energy ranges, provided by the synchrotron at the MedAustron facility.
Our experimentally derived RBE values were compared to three phenomenological models (McNamara, 18 Rørvik,19 and Jones 20 ) as well as one mechanistic model (repair-misrepairfixation (RMF) model 21 ). These models were specially chosen according to their data sets. The McNamara (MCN) model is based on experimental data reviewed and summarized by Paganetti et al. 22 In more detail, 285 data points were extracted from experiments with several different cell lines and LET d values ranging of up to 20 keV/µm. Thus this model covers a large range of (a/b) X -as well as LET d values, although the database is dominated by Chinese hamster cell lines with a low (a/b) X ratio and LET d values lower than 5 keV/µm. Furthermore, MCN assumes that the RBEs at extreme high and low dose levels, RBE min and RBE max , depends on (a/b) X and LET d . The Rørvik (RØR) model database contains 85 data points extracted from experiments with low and high (a/b) X cell lines, but is, similar to the MCN model, dominated by low (a/b) X cell lines. RØR has the most uniform range of LET d , including the highest values, from all phenomenological models tested. The RØR model assumes an (a/b) X -and LET d dependency of the RBE max but utilizes a constant RBE min of 1. The Jones (JON) model compromises a simpler LET efficiency approach and is based on data from protons and ions, for example, helium, carbon, and neon. Different to the MCN and the RØR model, the JON model exclusively contains data points with LET d larger than 5 keV/µm. In contrast to the other two phenomenological models, JON's tissue dependency is based on the absolute values of a x and b x independent of each other and the input data are solely from tissues with low (a/b) X values. 23 The mechanistic RMF model, which itself is based on the double-strand break (DSB) model, 24 was chosen due to the availability of the DSB model in the treatment planning system (TPS, RayStation 5.99) being used in this study. The RMF model RBE estimates correspond to the exact position of the cell layers within the planned target volume (PTV).

2.A. Cell cultures and procedures
Four human cell lines were chosen, which represent two in vitro models with a high (a/b) X ratio, head-and-neck squamous cell carcinoma (FaDu), and normal skin keratinocytes (HaCat), as well as two models with a low (a/b) X , melanoma (SKMel) and prostate carcinoma (Du145).
All cells were cultured at 37°C in a humidified atmosphere with 95% air and 5% CO 2 . Cells were seeded in chamber slide flasks (Nunc TM Lab-Tek TM II Chamber Slide TM System) with plastic slides at 2.5 to 5 9 10 5 cells per flask 24-48 hr before irradiation to achieve 70-80% confluency at the time of irradiation. Immediately prior to the irradiation, the chamber slide flasks were filled air-bubble free with the respective unsupplemented medium.

2.B. Photon and proton irradiation and dosimetry
For both, reference x-ray as well as proton irradiation, dedicated polymethyl methacrylate (PMMA) irradiation setup were developed to accommodate for the horizontal beam geometry and to ensure standardized sample positioning (see Figures S1 and S2). Detailed dosimetric verification of the PMMA irradiation setup preceded the experiments. 25 Cells were irradiated with 0.5, 1, 2, 4, and 6 Gy physical dose. For each experiment an equally processed, nonirradiated negative control was carried out. The negative control was filled with unsupplemented medium and left inside of the irradiation rooms (x-rays as well as proton irradiation room) for the duration of a 6 Gy irradiation. The flask holder itself was designed so that the transition zones between PMMA and cell medium were limited (see Figure S1). This is of essential importance as dose levels can change significantly in such transition zones. The dosimetric impact caused by different cell media and water was investigated in a preceding experiment, where no significant differences were found. For each dose level and beam quality, at least three independent irradiation sessions were conducted.

2.B.1. Reference x-ray irradiation
Reference irradiation was performed in a 200 kV beam, generated by a YXLON unit (Type TU 32-D03, YXLON GmbH, Hamburg, Germany). For details of the dosimetric commissioning of this reference x-ray irradiator please see Kuess et al. 26 For the experiments described in this study, the following filtration was used: 3 mm Be + 3 mm Al + 0.5 mm Cu. The cell layer was positioned at 40 cm distance from the beam exit window (see Figure S1). Absolute dosimetry was conducted for this irradiation geometry with a Farmer type ionization chamber (T31013, PTW Freiburg, Germany) within a cell flask to account for attenuation of the plastic walls. Furthermore, dosimetric measurements were conducted using EBT3-type Gafchromic films to verify dose homogeneity and with PinPoint Ionization chambers (T31015, PTW Freiburg, Germany) for absolute dosimetry, applying dose determination methodologies similar to patient-specific quality assurance procedures. [26][27][28] The size of the films was chosen to completely cover the slide of the chamber flask where the cells were growing. Using films in combination with the ionization chamber was beneficial to account for realistic x-ray backscatter produced by the cell medium and the flasks itself. The dose homogeneity of the irradiated area of the chamber slide flask was within AE3%.

2.B.2 Proton irradiation
The PMMA setup for proton irradiation was built to a depth of 40 cm to allow chamber slide flasks or detectors to be positioned along the entire range of clinically relevant energies up to 250 MeV. Multiple chamber slide flasks can be inserted and irradiated simultaneously. The remaining space of either unused slots or around inserted chamber slide flasks was filled with water to prevent range uncertainties caused by air gaps in the setup. A computed tomography (CT) scan of the setup in experimental condition (filled with flasks and water) was used for treatment planning. Using the TPS RayStation (V5.99, RaySearch Laboratories, Sweden), two different irradiation scenarios were planned, each with a SOBP of 80-mm longitudinal dimension. The employed Monte Carlo code in the TPS RayStation 5.99 considers primary protons and secondary ions (protons, deuterons, and alpha particles). Primary and secondary protons are accounted for by class II transport method while the energy loss of heavier secondaries is approximated via a continuous slowing down approximation. In setup A, the more proximal target, the center of the SOBP was located at 80 mm, with beam energies ranging from 66.5 to 135.6 MeV to cover the entire SOBP. In the more distal located setup B, the center of the SOBP was positioned at a depth of about 155 mm with beam energies ranging from 127.2 to 185.9 MeV. The TPS has been specifically commissioned for the proton beam line in the research room at MedAustron following the procedures in the clinical beam lines. 29 In contrast to the experimental validation of the dose calculation, LET d calculations of the TPS have been validated against independent Monte Carlo particle transport simulations using GATE/Geant4, which itself also applies a dedicated proton beam model tracking all particles through the entire nozzle. The LET d of the TPS agreed very well with the independent Monte Carlo simulations for all tested voxel sizes, where only a minor deviation Medical Physics, 47 (8), August 2020 (max. 5% at the distal edge) could be observed toward the end of the beam range due to the steep LET d gradient and the moderate beam range differences of the TPS and the Monte Carlo simulations. 30 Chamber slide flasks were positioned at a proximal, a central, and a distal SOBP position for each setup. More specifically, cell layers were located at 55, 80, and 105 mm in setup A, and at 130, 155, and 180 mm in setup B, respectively. Corresponding LET d values were derived from Monte Carlo calculations performed with the TPS, based on the energy and beam spot information of the underlying treatment plan. 31

2.C. Clonogenic survival assay
Standard clonogenic survival assays were performed after reference x-ray or proton irradiation. Cells were harvested immediately after irradiation, diluted with supplemented medium appropriate for the cell line and seeded in 6-well plate in concentrations according to the dose level: 250 cells (0, 0.5 Gy), 500 cells (1, 2 Gy), 1000 cells (4 Gy), and 2000 cells (6 Gy) per well, respectively. Following a cell linespecific incubation period (7-14 days), cells were fixed with 96 % methanol, stained with 0.5% crystal violet solution, and colonies of more than 50 cells were considered as surviving clones.

2.D. RBE modeling and statistical analyses
Data points in all following tables and figures represent the mean values including the standard deviation of at least three independent experiments. Correlation of the parameters was tested using a F-test on data fitted with linear regression. GraphPad Prism (GraphPad Software, Inc.) and Python 3.6 programming language (Python Software Foundation, https:// www.python.org) were used for statistical procedures and the graphical illustration. 32,33

2.D.1. Linear-quadratic model
Based on the linear-quadratic (LQ) formalism, surviving fractions in relation to the plating efficiency of nonirradiated control samples were calculated for each value of the delivered physical dose in Gy. The mean values and standard deviation results from a minimum of 18 individual values, corresponding to a minimum of three independent 6-well plate per dose group. The margin of errors results from error propagation. A 1/r-weighted minimum chi-square estimation was applied to the LQ model for survival curve fitting. 34 Both parameters, a and b, were calculated for both radiation types using the same fitting method. For cells irradiated with protons, RBE values were calculated for the physical doses that reduced the cell survival to 90%, and 10%, respectively. To compare the experimental data to the model-based predictions, RBEs were determined as a function of the LQ model parameters and the physical proton dose 35 : Calculation of the RBE. 22,35 The Eq. (1) can be rewritten as a function of RBE max and the RBE min RBE as a function of the RBE max and the RBE min . All applied phenomenological models have Eq. (2) in common but differ in their definition of the RBE max and RBE min functions. More details on the RBE models are summarized in the supplementary information (S3-S5). RBE values derived from the experiments and models were determined at dose levels of 0.5, 2, and 6 Gy.
The DSB model, with the endpoint of DSB induction (RBE DSB ), predicts the repair kinetics of damaged cells considering the particle type, kinetic energy, and oxygen concentration. The computation was performed directly in the TPS (5.99) with Monte Carlo Damage Simulation software including the relation between particle LET and cell oxygen effects. The applied mechanistic RMF model, based on the auxiliary DSB model, can be well approximated by the LQ cell survival model for doses comparable or smaller than (a/ß) x values. Parameters a and ß for proton radiation are then related to the reference radiation LQ parameters (a x , ß x ) as well as to the outcome of DSB model RBE DSB by Ref. [21]: LQ parameters for protons used in the RMF model. The term z F describes the frequency mean-specific energy that depends on the diameter of the cell nucleus and the nucleus mass density. Parameters given in Stewart et al., 21 were used for z F calculations. The survival-based RBE was subsequently computed using the Eq. (1).

3.A. Reference dosimetry and LET d
The dose homogeneity in both the 200 kV reference irradiation setup and the two proton setup was within 3% for the area covering a chamber slide flask. For the reference irradiation, the dose rate at the object surface was 1.28 AE 0.02 Gy/ min. This value was measured with EBT3 radiochromic films, which were calibrated against a Farmer type ionization    Table II.

3.C. Proton sensitivity
After proton irradiation, survival curves and (a/b) parameters were calculated for all four cell lines, the respective survival parameters are summarized in Table II. Cell survival curves as a function of dose are depicted in Fig. 2, sorted from lowest LET d to highest LET d (also see Figure S6).
For HaCat and FaDu, the RBE values ranged from 0.72 AE 0.09 to 1.13 AE 0.18 for all levels of cell survival and for every LET d value. In contrast, the low (a/b) X cell lines, Du145 and SKMel exhibited RBE values substantially higher than the currently clinically used 1.1 for all levels of cell survival. For Du145 and SKMel cells, RBE values between 1.95 AE 0.17 and 2.92 AE 0.25 were obtained for the low dose range at 90% of cell survival and between 1.28 AE 0.03 and 1.76 AE 0.05 for 10% of cell survival (Table II).
To test a potential correlation of LET d and RBE, the experimental RBE values were fitted with linear regression (Fig. 3) Off note, the model estimates were found to agree well within themselves for all RBE values within the investigated LET d range. In contrast, all models underestimated the RBE 2Gy for the low (a/b) x cell lines selected for our study, even though the model databases contain low (a/b) x and low LET d (< 5 keV/µm) data points.

DISCUSSION
With the increasing number of patients treated with PT, the concept of using a constant RBE of 1.1 is increasingly discussed but will probably remain an accepted approximation until the uncertainties concerning physical and biological parameters can be substantially reduced. 36,37 Recent publications raised concerns that a constant RBE is not beneficial to certain tissues and can cause adverse effects after PT. 12,38,39 Most of the published studies on RBE dependencies focused only on one factor of influence and often assessed only one position within a SOBP. In addition, they were conducted using passive scattering, which historically was the most widely used beam delivering technique. 9,40,41 This study aimed to overcome some of the limitations of previous investigations. The abovementioned considerable uncertainties in reported RBE from in vitro and in vivo studies can partly be attributed to nonstandardized experimental techniques and limited reporting on the experiment´s physical aspects, such as beam characteristics and dosimetry.
In order to reduce experimental uncertainties in radiobiological experiments for subsequent correlation between biological response and physical parameters, standardized irradiation setup for both, x-ray reference and proton irradiation, were subjected to extensive dosimetric assessment prior to this study. 25 The focus was set on clinically relevant proton energies and corresponding LET d values. Finally, four human cell lines were selected to address differences in RBE dependencies for high and low (a/b) X .
An inverse relationship between RBE and dose per fraction was proposed 5,11,42 and confirmed by our study, however, only for low (a/b) x cell lines. We observed the highest RBE values in the low dose range for melanoma (SKMel) and prostate carcinoma (Du145) cells, both having an (a/b) x < 5. The high (a/b) x cell lines (HaCat and FaDu) did not show a similar response.
As far as LET d dependencies of the RBE are concerned, multiple studies demonstrated a positive correlation and thus an increased RBE toward the distal end of a SOBP, even in proton beams. [43][44][45] Our study confirms the LET d -RBE relationship, however, only for low (a/b) X cell lines. In this context, our results complement previous studies, which suggest higher RBE values for tissues with low (a/b) X . 46   Less literature data are available for human low (a/b) X lines and thus for benchmarking our melanoma or prostate carcinoma data. Petrovic et al. determined an RBE 2Gy in a range of 1.69 to 2.14 for their melanoma cell line, which agrees well with our date. 51 The higher LET d associated with scanned protons and range uncertainties might result in excess dose and LET d outside of the PTV. In our study we tried to mimic clinical scenarios concerning the irradiation conditions, for example, the SOBP size and the target depth. Despite the low LET d values resulting from clinically relevant proton energy ranges for an irradiation volume of 8 9 10 9 10 cm 3 located at a depth of 80 and 155 mm, still substantial RBE variations could be observed. For tissues with high (a/b) X , the higher LET d of scanned protons appears to be negligible. RBE values around unity, as found in this study and previously reported for tumors displaying high (a/b) x values (e.g., medulloblastoma and head-and-neck malignancies), indicate a slight RBE overestimation in current practice. 46,52 Assuming that the cell/tissue sensitivity toward increased LET d is determined by its (a/ b) X value, RBE values that differ considerably from the constant 1.1 can be expected toward the distal end of the SOBP, predominantly for low doses per fraction and low (a/b) X ratio systems. Typical low (a/b) X normal tissues adjacent to the PTV, such as the central nervous system, may need special attention in treatment planning given the current practice of treatment planning.
Based on the concerns regarding a constant RBE value of 1.1, several RBE models have been developed to predict RBE values taking into account the physical and biological factors. The phenomenological models are based on the widely accepted and used LQ formalism and incorporate tissuespecific survival parameters, dose and LET d . Differences in input parameters and model assumptions, however, were recently shown to result in variations of the RBE predictions. 19 In this study three phenomenological models were selected to predict the RBE values. The experimental in vitro data were systematically compared to model predictions. The applied phenomenological models assume an inverse relationship of RBE and photon-derived (a/b) X . For the high (a/  Furthermore, all chosen models include low (a/b) x cell lines in their databases, but most of them are non-human low (a/ b) x cell lines, such as the V-79 Chinese hamster fibroblasts. Of all phenomenological models investigated, only the MCN model database contains one of our investigated cell lines, that is, the Du145 cell line. This fact may contribute to the differences between model predictions and experimentally derived RBE 2Gy values.
In addition to the three phenomenological models, one mechanistic model was applied. In order to evaluate a survival-based endpoint with all models, the mechanistic model was fitted with the LQ model, based on DSB induction predictions (RBE DSB ). RMF model RBE estimates aligned well with the phenomenological model predictions. Similar to all tested phenomenological models, the RMF model predicted the RBE well within uncertainties for the high (a/b) X cell lines. No agreement of RMF estimates and experimentally derived RBE 2Gy could be observed for the cell lines with low (a/b) X , SKMel, and Du145.
This study focused on the irradiation response of 2D monocultures. This is in line with the fact that several biological optimization algorithms used in TPS for particle therapy, especially for heavier ions, are based on 2D in vitro data. Most of the studies concerning RBE determination are in essence done with 2D cultures because of their simple and fast handling and well-established endpoint methods. 9,[44][45][46] What differentiates this study from others is the application of clinically relevant doses and energy ranges and the use of a scanning pencil beam delivery system. However, multicellular 3D models of malignancies gain increasing importance in cancer research. Stromal disease components and 3D-associated factors such as signaling gradients and diffusion as well as perfusion limitations contribute significantly to the therapy response in vivo. 53-57 These factors have not been considered in our study, as the main intention was to benchmark our data with already existing in vitro data and to specifically assess the RBE as a function of (a/b) X , derived from the basic LQ formula that is only applicable to 2D in vitro date. 58 A major challenge remains if and how to account for the growing body of evidence that the RBE of protons is not constant. Accounting for the increase of LET d with depth, similar to the clinical practice of carbon ion therapy, and the adaptation of an (a/b) X -weighting factor could improve PT treatment planning and consequently safety and effectiveness. Given the reliance of treatment planning and modeling in both proton and carbon ion therapy on in vitro data, research to complement the increasing clinical utilization of particle therapy needs to build on high dosimetric accuracy and detailed reporting on relevant physical data. Only then model refinement can improve patient outcomes, but will directly depend on well-characterized experiments to generate data with minimized physical and biological uncertainties.

CONCLUSIONS
The tissue-specific fractionation sensitivity factor of photons, that is, the (a/ß) X ratio, is a clear determinant of the RBE of protons and a predictor for its sensitivity toward LET d changes. Higher RBE values than 1.1 can be expected for low (a/ß) X tissues at proton beam end-of-range positions within the clinical practice of applied fractional doses. Current practice might slightly overestimate the RBE of protons for tissues with high (a/ß) X ratios.

ACKNOWLEDGMENTS
The authors wish to thank Mr. Anton Kerschbaum, BSc, MedAustron Control Systems Group, for providing the python script used for data analyses in this study. The introduction into python programming and the valuable continuous support in python programming is greatly acknowledged.

SUPPORTING INFORMATION
Additional supporting information may be found online in the Supporting Information section at the end of the article. Two culture flasks were irradiated simultaneously. Fig. S2. Experimental set-up designed for proton irradiation. Clinically relevant target energies were chosen, covering slots 3-5 (set-up A) and slots 6-8 (set-up B) in the PMMA block (a). CT images (b) were used for the treatment planning of the two SOPB positions. Accurate and standardized positioning was ensured with an in-room laser system and a high precision robotic couch (c).