# Publications

2021
Alejandro Bertolet, Eric Wehrenberg-Klee, Mislav Bobić, Clemens Grassberger, Joseph Perl, Harald Paganetti, and Jan Schuemann. 12/16/2021. “Pre- and post-treatment image-based dosimetry in 90Y-microsphere radioembolization using the TOPAS Monte Carlo toolkit.” Physics in Medicine and Biology, In press. Publisher's VersionAbstract
Objective: To evaluate the pre-treatment and post-treatment imaging-based dosimetry of patients treated with 90Y-microspheres, including accurate estimations of dose to tumor, healthy liver and lung. To do so, the Monte Carlo (MC) TOPAS platform is in this work extended towards its utilization in radionuclide therapy. Approach: Five patients treated at the Massachusetts General Hospital were selected for this study. All patients had data for both pre-treatment SPECT-CT imaging using 99mTc-MAA as a surrogate of the 90Y-microspheres treatment and SPECT-CT imaging immediately after the 90Y activity administration. Pre- and post-treatment doses were computed with TOPAS using the SPECT images to localize the source positions and the CT images to account for tissue inhomoegeneities. We compared our results with analytical calculations following the voxel-based MIRD scheme. Main results: TOPAS results largely agreed with the MIRD-based calculations in soft tissue regions: the average difference in mean dose to the liver was 0.14 Gy/GBq (2.6%). However, dose distributions in the lung differed considerably: absolute differences in mean doses to the lung ranged from 1.2 Gy/GBq to 6.3 Gy/GBq and relative differences from 153% to 231%. We also found large differences in the intra-hepatic dose distributions between pre- and post-treatment imaging, but only limited differences in the pulmonary dose. Significance: Doses to lung were found to be higher using TOPAS with respect to analytical calculations which may significantly underestimate dose to the lung, suggesting the use of MC methods for 90Y dosimetry. According to our results, pre-treatment imaging may still be representative of dose to lung in these treatments.
Anna Baratto-Roldán, Alejandro Bertolet, Giorgio Baiocco, Alejandro Carabe, and Miguel Antonio Cortés-Giraldo. 10/27/2021. “Microdosimetry and Dose-Averaged LET Calculations of Protons in Liquid Water: A Novel Geant4-DNA Application.” Frontiers in Physics, 9, October, Pp. 726787. Publisher's VersionAbstract

The spatial distribution of energy deposition events is an essential aspect in the determination of the radiobiological effects of ionizing radiation at the cellular level. Microdosimetry provides a theoretical framework for the description of these events, and has been used in several studies to address problems such as the characterization of Linear Energy Transfer (LET) and Relative Biological Effectiveness (RBE) of ion beams for proton therapy applications. Microdosimetry quantities and their distributions can be obtained by means of Monte Carlo simulations. In this work, we present a track structure Monte Carlo (MC) application, based on Geant4-DNA, for the computation of microdosimetric distributions of protons in liquid water. This application provides two sampling methods uniform and weighted , for the scoring of the quantities of interest in spherical sites, with diameters ranging from 1 to 10 μm. As an element of novelty, the work shows the approach followed to calculate, without resorting to dedicated simulations, the distribution of energy imparted to the site per electronic collision of the proton, which can be used to obtain the macroscopic dose-averaged LET as proposed by Kellerer. Furthermore, in this work the concept of effective mean chord length is proposed to take into account δ-ray influx and escape in the calculation of macroscopic dose-averaged LET for proton track segments and retrieve the agreement predicted by Kellerer’s formula. Finally, the results obtained demonstrate that our MC application is reliable and computational-efficient to perform calculations of microdosimetric distributions and dose-averaged LET of proton track segments in liquid water.

Alejandro Bertolet, Ramin Abolfath, David J. Carlson, Robert A. Lustig, Christine Hill-Kayser, Michelle Alonso-Basanta, and Alejandro Carabe. 2021. “Correlation of LET with MRI changes in brain and potential implications for normal tissue complication probability for meningioma patients treated with pencil beam scanning proton therapy.” International Journal of Radiation Oncology Biology Physics, In press. Publisher's VersionAbstract

### Purpose

To investigate the correlation between imaging changes in brain normal tissue and the spatial distribution of linear energy transfer (LET) for a cohort of meningioma patients treated with scanned proton beams. Then, assuming imaging changes are induced by cell lethality, to study the correlation between normal tissue complication probability and LET.

### Methods

MRI T2/FLAIR acquired at different intervals after proton radiation were co-registered with the planning CT images from 26 patients diagnosed with meningioma with abnormalities after proton radiotherapy. For this purpose, the T2/FLAIR areas not on the original MRIs were contoured and LET values for each voxel in the patient geometry were calculated to investigate the correlation between the position of imaging changes and LET at those positions. To separate the effect of dose as inductor of these changes, we compared LET in these areas with a sample of voxels matching the dose distributions across the image change areas. Patients with higher LET in image change areas were grouped to verify whether they shared common characteristics.

### Results

11 of the patients showed higher LETd in imaging change regions than in group of voxels with the same dose. This group of patients had significantly shallower targets for their treatment than the other 15 and used fewer beams and angles.

### Conclusion

This study points towards the possibility of areas with imaging change are more likely to occur in regions with high dose or in those areas with lower dose but increased LETd. The effect of LETd on imaging changes seems to be more relevant when treating superficial lesions with few non opposed beams. However, most of the patients did not show spatial correlation between their image changes and the LETd values, limiting the cases for the possible role of high LET as a toxicity inductor.

Alejandro Bertolet, Miguel A. Cortés-Giraldo, and Alejandro Carabe-Fernandez. 2021. “Implementation of the microdosimetric kinetic model using analytical microdosimetry in a treatment planning system for proton therapy.” Physica Medica, 81, Pp. 69–76. Publisher's VersionAbstract

### Purpose

To implement RBE calculations in treatment planning systems based on the Microdosimetric Kinetic Model (MKM) upon analytical calculations of dose-mean lineal energy (yD). MKM relies on the patterns of energy deposition in sub-nuclear structures called domains, whose radii are cell-specific and need to be determined.

### Methods and material

The radius of a domain (rd) can be determined from the linear-quadratic (LQ) curves from clonogenic experiments for different cell lines exposed to X-ray and proton beams with known yD. In this work, LQ parameters for two different human lung cell lines (H1299 and H460) are used, and yD among cells is calculated through an analytical algorithm. Once rd is determined, MKM-based calculations of RBE are implemented in a treatment planning system (TPS). Results are compared to those produced by phenomenological models of RBE, such as Carabe and McNamara.

### Results

Differences between model-based predictions and experimentally determined RBE are analyzed for yD=5 keV/μm. For the H1299 line, mean differences in RBE are 0.13, −0.29 and −0.27 for our MKM-based calculation, Carabe and McNamara models, respectively. For the H460 line, differences become −0.044, −0.091 and −0.048, respectively. RBE is computed for these models in a simple plan, showing MKM the best agreement with the experimentally obtained RBE, keeping deviations below 0.08.

### Conclusions

Microdosimetry calculations at the TPS-level provide tools to improve predictions of RBE using the MKM with actual values of yD instead of LET. The radius of the characteristic domain needs to be determined to tailor the RBE prediction for each cell or tissue.

Héctor Miras, Antonio Ortiz Lora, Alejandro Bertolet, and José Antonio Terrón León. 2021. “A Monte Carlo dose calculation system for ophthalmic brachytherapy based on a realistic eye model.” Medical Physics, 48, 8, Pp. 4542-4559. Publisher's VersionAbstract

### Purpose

There is a growing trend towards the adoption of model-based calculation algorithms (MBDCAs) for brachytherapy dose calculations which can properly handle media and source/applicator heterogeneities. However, most of dose calculations in ocular plaque therapy are based on homogeneous water media and standard in-silico ocular phantoms, ignoring non-water equivalency of the anatomic tissues and heterogeneities in applicators and patient anatomy. In this work, we introduce EyeMC, a Monte Carlo (MC) model-based calculation algorithm for ophthalmic plaque brachytherapy using realistic and adaptable patient-specific eye geometries and materials.

### Methods

We used the MC code PENELOPE in EyeMC to model Bebig IsoSeed I25.S16 seeds in COMS plaques and 106Ru/106Rh applicators that are coupled onto a customizable eye model with realistic geometry and composition. To significantly reduce calculation times, we integrated EyeMC with CloudMC, a cloud computing platform for radiation therapy calculations. EyeMC is equipped with an evaluation module that allows the generation of isodose distributions, dose–volume histograms, and comparisons with Plaque Simulator three-dimensional dose distribution. We selected a sample of patients treated with 125I and 106Ru isotopes in our institution, covering a variety of different type of plaques, tumor sizes, and locations. Results from EyeMC were compared to the original plan calculated by the TPS Plaque Simulation, studying the influence of heterogeneous media composition as well.

### Results

EyeMC calculations for Ru plaques agreed well with manufacturer’s reference data and data of MC simulations from Hermida et al. (2013). Significant deviations, up to 20%, were only found in lateral profiles for notched plaques. As expected, media composition significantly affected estimated doses to different eye structures, especially in the 125I cases evaluated. Dose to sclera and lens were found to be about 12% lower when considering real media, while average dose to tumor was 9% higher. 106Ru cases presented a 1%–3% dose reduction in all structures using real media for calculation, except for the lens, which showed an average dose 7.6% lower than water-based calculations. Comparisons with Plaque Simulator calculations showed large differences in dose to critical structures for 106Ru notched plaques. 125I cases presented significant and systematic dose deviations when using the default calculation parameters from Plaque Simulator version 5.3.8., which were corrected when using calculation parameters from a custom physics model for carrier-attenuation and air-interface correction functions.

### Conclusions

EyeMC is a MC calculation system for ophthalmic brachytherapy based on a realistic and customizable eye-tumor model which includes the main eye structures with their real composition. Integrating this tool into a cloud computing environment allows to perform high-precision MC calculations of ocular plaque treatments in short times. The observed variability in eye anatomy among the selected cases justifies the use of patient-specific models.

Alejandro Bertolet, José Ramos-Méndez, Harald Paganetti, and Jan Schuemann. 2021. “The relation between microdosimetry and induction of direct damage to DNA by alpha particles.” Physics in Medicine and Biology, 66, 15, Pp. 155016. Publisher's VersionAbstract

In radiopharmaceutical treatments α-particles are employed to treat tumor cells. However, the mechanism that drives the biological effect induced is not well known. Being ionizing radiation, α- particles can affect biological organisms by producing damage to the DNA, either directly or indirectly. Following the principle that microdosimetry theoryaccounts for the stochastic wayin which radiation deposits energy in sub-cellular sized volumes via physical collisions, we postulate that microdosimetry represents a reasonable framework to characterize the statistical nature of direct damage induction by α-particles to DNA. We used the TOPAS-nBio Monte Carlo package to simulate direct damage produced bymonoenergetic alpha particles to different DNAstructures. In separate simulations, we obtained the frequency-mean lineal energy (yF) and dose-mean lineal energy (yD) of microdosimetric distributions sampled with spherical sites ofdifferent sizes. The total number of DNA strand breaks, double strand breaks (DSBs) and complex strand breaks per track were quantified and presented as a function of either yF or yD. The probability ofinteraction between a track and the DNA depends on how the base pairs are compacted. To characterize this variability on compactness, spherical sites of different size were used to match these probabilities ofinteraction, correlating the size-dependent specific energy (z) with the damage induced. The total number of DNA strand breaks per track was found to linearly correlate with yF and zF when using what we defined an effective volume as microdosimetric site, while the yield of DSB per unit dose linearly correlated with yD or zD, being larger for compacted than for unfolded DNA structures. The yield ofcomplex breaks per unit dose exhibited a quadratic behavior with respect to yD and a greater difference among DNA compactness levels. Microdosimetric quantities correlate with the direct damage imparted on DNA.

2020
Alejandro Bertolet and Alejandro Carabe-Fernandez. 2020. “Clinical implications of variable relative biological effectiveness in proton therapy for prostate cancer.” Acta Oncologica, 59, 10, Pp. 1171–1177. Publisher's VersionAbstract
Purpose: To study the potential consequences of differences in the evaluation of variable versus uniform relative biological effectiveness calculations in proton radiotherapy for prostate cancer. Methods and material: Experimental data with proton beams suggest that relative biological effectiveness increases with linear energy transfer. This relation also depends on the (Formula presented.) ratio, characteristic of a tissue and a considered endpoint. Three phenomenological models (Carabe et al., Wedenberg et al. and McNamara et al.) are compared to a mechanistic model based on microdosimetry (microdosimetric kinetic model) and to the current assumption of uniform relative biological effectiveness equal to 1.1 in a prostate case. Results and conclusions: Phenomenological models clearly predict higher relative biological effectiveness values compared to microdosimetric kinetic model, that seems to approach to the constant value of 1.1 adopted in the clinics, at least for low linear energy transfer values achieved in typical prostate proton plans. All models predict a higher increase of the relative biological effectiveness-weighted dose for the prostate tumor than for the rest of structures involved due to its lower (Formula presented.) ratio, even when linear energy transfer is, in general, lower in the tumor than on the surroundings tissues. Prostate cancer is, therefore, a good candidate to take advantage of variable relative biological effectiveness, especially if linear energy transfer is enhanced within the tumor. However, the discrepancies among models hinder the clinical implementation of variable relative biological effectiveness.
Alejandro Bertolet, Miguel A. Cortés-Giraldo, and Alejandro Carabe-Fernandez. 2020. “On the concepts of dose-mean lineal energy, unrestricted and restricted dose-averaged LET in proton therapy.” Physics in Medicine and Biology, 65, 7, Pp. ab730a. Publisher's VersionAbstract
To calculate 3D distributions of microdosimetric-based restricted dose-averaged LET (LETd) and dose-mean lineal energy (yD) in order to explore their similarities and differences between each other and with the traditional unrestricted LETd. Additionally, a new expression for optimum restricted LETd calculation is derived, allowing for disregarding straggling-associated functions in the classical microdosimetric theory. Restricted LETd and yD for polyenergetic beams can be obtained by integrating previously developed energy-dependent microdosimetric functions over the energetic spectrum of these beams. This calculation is extended to the entire calculation volume using an algorithm to determine spectral fluence. Equivalently, unrestricted LETd can be obtained integrating the stopping power curve on the spectrum. A new expression to calculate restricted LETd is also derived. Results for traditional and new formulas are compared for a clinical 100 MeV proton beam. Distributions of unrestricted LETd, restricted LETd and yD are analyzed for a prostate case, for microscopic spherical sites of 1 µm and 10 µm in diameter. Traditional and new expressions for restricted LETd remarkably agree, being the mean differences 0.05 ± 0.04 keV µm-1 for the 1 µm site and 0.05 ± 0.02 keV µm-1 for the 10 µm site. In the prostate case, the ratio between the maximum and the central value for central axis (CAX) profiles is around 2 for all the quantities, being the highest for restricted LETd for 1 µm (2.17) and the lowest for yD for 1 µm (1.78). Unrestricted LETd, restricted LETd and yD can be analytically computed and compared for clinical plans. Two important consequences of the calculation of yD are: (1) its distribution can be verified by directly measuring it in clinical beams; and (2), optimization of proton treatments based on these quantities is enabled as well as future developments of RBE models based on them.
Alejandro Bertolet. 2020. “Microdosimetry applied to proton radiotherapy”.
Alejandro Bertolet, Amadeo Wals, Héctor Miras, and José Macías. 2020. “Organic generation of real-world real-time data for clinical evidence in radiation oncology.” International Journal of Medical Informatics, 144, April, Pp. 104301. Publisher's VersionAbstract
Purpose: We introduce a system devoted to automatically produce structured data in radiotherapy to: (i) relate clinical outcomes with any variable; and (ii) optimize resources and procedures. Methods and material: We have designed a detailed workflow for a patient to follow during radiotherapy treatments. Four elements of Oncology Information Systems (OISs) can be mainly interrelated in our system: (a) task lists to be accomplished by the staff; (b) forms to fill in at each step of the workflow; (c) generation of reports; and (d) a system to trigger new tasks, forms or reports when an needed, either automatically or manually. We handle the data dumped into reports with Visual Basic for Word code to store structured data for patients in electronic medical records (EMRs). These EMRs can be further analyzed, generating clinical real-world data in real time, i.e., at any step of the process. Results: Our system was implemented about the beginning of 2019, producing a database filled with a pool of 1,184 patients in a year. Although one year is not long enough to produce statistically clinical outcomes, we show our results for cancer by anatomical location so far to meet the first goal stated above. With respect to the second goal, we here (1) show the distribution of times taken for the whole radiotherapy process divided by anatomical locations for, (2) study the fractionations schemes used throughout 2019, and (3) evaluate the number of missed sessions of treatment in our institution. Our system also leads to better communication among staff members, dramatically reducing misunderstandings because of the centralization of the information. Conclusions: We present an integrated customization of an OIS, yet adaptable to others, that makes possible an optimized performance of the department by driving an automatized paperless workflow; and allows for an automatized and effortless collection of structured data throughout the radiotherapy process.
Alejandro Bertolet, Miguel A. Cortés-Giraldo, and Alejandro Carabe-Fernandez. 2020. “An Analytical Microdosimetric Model for Radioimmunotherapeutic Alpha Emitters.” Radiation Research, 194, 4, Pp. 403–410. Publisher's VersionAbstract
In this work, we present a methodology to analytically determine microdosimetric quantities in radioimmunotherapy and targeted radiotherapy with alpha particles. Monte Carlo simulations using the Geant4-DNA toolkit, which provides interaction models at the microscopic level, are performed for monoenergetic alpha particles traversing spherical sites with diameters of 1, 5 and 10 µm. An analytical function is fitted against the data in each case to model the energy imparted by monoenergetic particles to the site, as well as the variance of the distribution of energy imparted. Those models allow us to obtain the mean and dose-mean values of specific energy (z) and lineal energy (y) for polyenergetic arrangements of alpha particles. The energetic spectrum is estimated by considering the distance that each particle needs to travel to reach the sensitive target. We apply this methodology to a simple case in radioimmunotherapy: a spherical cell that has its membrane uniformly covered by 211At, an alpha emitter, with a spherical target representing the nucleus, placed at the center of the cell. We compare the results of our analytical method with calculations using Geant4-DNA of this specific setup for three nucleus sizes corresponding to our three functions. For nuclei with diameter of 1 µm and 5 µm, all mean and dose-mean quantities for y and z were in an agreement within 4% to Geant4-DNA calculations. This agreement improves to approximately 1% for dose-mean lineal energy and dose-mean specific energy. For the 10-µm-diameter case, discrepancies scale to approximately 9% for mean values and 3% for dose-mean values. Dose-mean values are within Geant4-DNA uncertainties in all cases. Our method provides accurate analytical calculations of dose-mean quantities that may be further employed to characterize radiobiological effectiveness of targeted radiotherapy. The spatial distributions of sources and targets are required to calculate microdosimetric-relevant quantities.
Alejandro Bertolet, Veljko Grilj, Consuelo Guardiola, Andrew D. Harken, Miguel A. Cortés-Giraldo, Anna Baratto-Roldán, Celeste Fleta, Manuel Lozano, and Alejandro Carabe. 2020. “Experimental validation of an analytical microdosimetric model based on Geant4-DNA simulations by using a silicon-based microdosimeter.” Radiation Physics and Chemistry, 176, Pp. 109060. Publisher's VersionAbstract

### Purpose

To study the agreement between proton microdosimetric distributions measured with a silicon-based cylindrical microdosimeter and a previously published analytical microdosimetric model based on Geant4-DNA in-water Monte Carlo simulations for low energy proton beams.

### Methods and material

Distributions for lineal energy (y) are measured for four proton monoenergetic beams with nominal energies from 2.0 MeV to 4.5 MeV, with a tissue equivalent proportional counter (TEPC) and a silicon-based microdosimeter. The actual energy for protons traversing the silicon-based microdosimeter is simulated with SRIM. Monoenergetic beams with these energies are simulated with Geant4-DNA code by simulating a water cylinder site of dimensions equal to those of the microdosimeter. The microdosimeter response is calibrated by using the distribution peaks obtained from the TEPC. Analytical calculations for y‾F and y‾D using our methodology based on spherical sites are also performed choosing the equivalent sphere to be checked against experimental results.

### Results

Distributions for y at silicon are converted into tissue equivalent and compared to the Geant4-DNA simulated, yielding maximum deviations of 1.03% for y‾F and 1.17% for y‾D. Our analytical method generates maximum deviations of 1.29% and 3.33%, respectively, with respect to experimental results.

### Conclusion

Simulations in Geant4-DNA with ideal cylindrical sites in liquid water produce similar results to the measurements in an actual silicon-based cylindrical microdosimeter properly calibrated. The found agreement suggests the possibility to experimentally verify the calculated clinical y‾D with our analytical method.

Alejandro Bertolet, Miguel A. Cortés-Giraldo, Kevin Souris, and Alejandro Carabe. 2020. “A kernel-based algorithm for the spectral fluence of clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest.” Medical Physics, 47, 6, Pp. 2495–2505. Publisher's VersionAbstract
Purpose: To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy. Material and methods: A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results. Results: Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average (Formula presented.) equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average (Formula presented.) of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average (Formula presented.) of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of −0.007 ± 0.008 keV/$μ$m with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/$μ$m including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/$μ$m. Conclusion: This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.
Alejandro Bertolet and Alejandro Carabe. 2020. “Modelling dose effects from space irradiations: combination of high-LET and low-LET radiations with a modified Microdosimetric Kinetic Model.” Life, 10, 9, Pp. 161. Publisher's VersionAbstract
The Microdosimetric Kinetic Model (MKM) to predict the effects of ionizing radiation on cell colonies is studied and reformulated for the case of high-linear energy transfer (LET) radiations with a low dose. When the number of radiation events happening in a subnuclear domain follows a Poisson distribution, the MKM predicts a linear-quadratic (LQ) survival curve. We show that when few events occur, as for high-LET radiations at doses lower than the mean specific energy imparted to the nucleus, zF,n, a Poisson distribution can no longer be assumed and an initial pure linear relationship between dose and survival fraction should be observed. Predictions of survival curves for combinations of high-LET and low-LET radiations are produced under two assumptions for their comparison: independent and combined action. Survival curves from previously published articles of V79 cell colonies exposed to X-rays, α particles, Ar-ions, Fe-ions, Ne-ions and mixtures of X-rays and each one of the ions are predicted according to the modified MKM. We conclude that mixtures of high-LET and low-LET radiations may enhance the effect of individual actions due to the increase of events in domains provided by the low-LET radiation. This hypothesis is only partially validated by the analyzed experiments.
Alejandro Bertolet and Alejandro Carabe. 2020. “Proton monoenergetic arc therapy (PMAT) to enhance LETd within the target.” Physics in Medicine and Biology, 65, 16, Pp. 165006. Publisher's VersionAbstract
We show the performance and feasibility of a proton arc technique so-called proton monoenergetic arc therapy (PMAT). Monoenergetic partial arcs are selected to place spots at the middle of a target and its potential to enhance the dose-averaged linear energy transfer (LETd) distribution within the target. Single-energy partial arcs in a single 360 degree gantry rotation are selected to deposit Bragg's peaks at the central part of the target to increase LETd values. An in-house inverse planning optimizer seeks for homogeneous doses at the target while keeping the dose to organs at risk (OARs) within constraints. The optimization consists of balancing the weights of spots coming out of selected partial arcs. A simple case of a cylindrical target in a phantom is shown to illustrate the method. Three different brain cancer cases are then considered to produce actual clinical plans, compared to those clinically used with pencil beam scanning (PBS). The relative biological effectiveness (RBE) is calculated according to the microdosimetric kinetic model (MKM). For the ideal case of a cylindrical target placed in a cylindrical phantom, the mean LETd in the target increases from 2.8 keV $μ$m-1 to 4.0 keV $μ$m-1 when comparing a three-field PBS plan with PMAT. This is replicated for clinical plans, increasing the mean RBE-weighted doses to the CTV by 3.1%, 1.7% and 2.5%, respectively, assuming an ratio equal to 10 Gy in the CTV. In parallel, LETd to OARs near the distal edge of the tumor decrease for all cases and metrics (mean LETd, LD,2% and LD,98%). The PMAT technique increases the LETd within the target, being feasible for the production of clinical plans meeting physical dosimetric requirements for both target and OARs. Thus, PMAT increases the RBE within the target, which may lead to a widening of the therapeutic index in proton radiotherapy that would be highlighted for low ratios and hyperfractionated schedules.
Alejandro Carabe, Ilias V. Karagounis, Kiet Huynh, Alejandro Bertolet, Noelle François, Michele M. Kim, Amit Maity, Eric Abel, and Roger G. Dale. 2020. “Radiobiological effectiveness difference in proton arc beams versus conventional proton and photon beams.” Physics in Medicine and Biology, 65, 16, Pp. 165002. Publisher's VersionAbstract
This paper aims to demonstrate the difference in biological effectiveness of proton monoenergetic arc therapy (PMAT) compared to intensity modulated proton therapy (IMPT) and conventional 6 MV photon therapy, and to quantify this difference when exposing cells of different radiosensitivity to the same experimental conditions for each modality. V79, H1299 and H460 cells were cultured in petri dishes placed in the central axis of a cylindrical and homogeneous solid water phantom of 20 cm in diameter. For the PMAT plan, cells were exposed to 13 mono-energetic proton beams separated every 15° over a 180° arc, designed to deliver a uniform dose of higher LET to the petri dishes. For the IMPT plans, 3 fields were used, where each field was modulated to cover the full target. Cells were also exposed to 6 MV photon beams in petri dishes to characterize their radiosensitivity. The relative biological effectiveness of the PMAT plans compared with those of IMPT was measured using clonogenic assays. Similarly, in order to study the quantity and quality of the DNA damage induced by the PMAT plans compared to that of IMPT and photons, $\gamma$-H2AX assays were conducted to study the relative amount of DNA damage induced by each modality, and their repair rate over time. The clonogenic assay revealed similar survival levels to the same dose delivered with IMPT or x-rays. However, a systematic average of up to a 43% increase in effectiveness in PMAT plans was observed when compared with IMPT. In addition, the repair kinetic assays proved that PMAT induces larger and more complex DNA damage (evidenced by a slower repair rate and a larger proportion of unrepaired DNA damage) than IMPT. The repair kinetics of IMPT and 6 MV photon therapy were similar. Mono-energetic arc beams offer the possibility of taking advantage of the enhanced LET of proton beams to increase TCP. This study presents initial results based on exposing cells with different radiosensitivity to other modalities under the same experimental conditions, but more extensive clonogenic and in-vivo studies will be required to confirm the validity of these results.
Alejandro Carabe-Fernandez, Alejandro Bertolet, Ilias V. Karagounis, Kiet Huynh, and Roger G. Dale. 2020. “Is there a role for arcing techniques in proton therapy?” The British Journal of Radiology, 93, Pp. 20190469. Publisher's VersionAbstract

Proton arc therapy (PAT) has been proposed as a possible evolution for proton therapy. This commentary uses dosimetric and cancer risk evaluations from earlier studies to compare PAT with intensity modulated proton therapy. It is concluded that, although PAT may not produce better physical dose distributions than intensity modulated proton therapy, the radiobiological considerations associated with particular PAT techniques could offer the possibility of an increased therapeutic index.

2019
Alejandro Bertolet, Miguel A. Cortés-Giraldo, Kevin Souris, Marie Cohilis, and Alejandro Carabe-Fernandez. 2019. “Calculation of clinical dose distributions in proton therapy from microdosimetry.” Medical Physics, 46, 12, Pp. 5816–5823. Publisher's VersionAbstract
Purpose: To introduce a new algorithm—MicroCalc—for dose calculation by modeling microdosimetric energy depositions and the spectral fluence at each point of a particle beam. Proton beams are considered as a particular case of the general methodology. By comparing the results obtained against Monte Carlo computations, we aim to validate the microdosimetric formalism presented here and in previous works. Material and methods: In previous works, we developed a function on the energy for the average energy imparted to a microdosimetric site per event and a model to compute the energetic spectrum at each point of the patient image. The number of events in a voxel is estimated assuming a model in which the voxel is completely filled by microdosimetric sites. Then, dose at every voxel is computed by integrating the average energy imparted per event multiplied by the number of events per energy beam of the spectral distribution within the voxel. Our method is compared with the proton convolution superposition (PCS) algorithm implemented in Eclipse™ and the fast Monte Carlo code MCsquare, which is here considered the benchmark, for in-water calculations, using in both cases clinically validated beam data. Two clinical cases are considered: a brain and a prostate case. Results: For a SOBP beam in water, the mean difference at the central axis found for MicroCalc is of 0.86% against 1.03% for PCS. Three-dimensional gamma analyses in the PTVs compared with MCsquare for criterion (3%, 3 mm) provide gamma index of 95.07% with MicroCalc vs 94.50% with PCS for the brain case and 99.90% vs 100.00%, respectively, for the prostate case. For selected organs at risk in each case (brainstem and rectum), mean and maximum difference with respect to MCsquare dose are analyzed. In the brainstem, mean differences are 0.25 Gy (MicroCalc) vs 0.56 Gy (PCS), whereas for the rectum, these values are 0.05 Gy (MicroCalc) vs 0.07 Gy (PCS). Conclusions: The accuracy of MicroCalc seems to be, at least, not inferior to PCS, showing similar or better agreement with MCsquare in the considered cases. Additionally, the algorithm enables simultaneous computation of other quantities of interest. These results seem to validate the microdosimetric methodology in which the algorithm is based on.
Alejandro Bertolet, Anna Baratto-Roldán, Sofia Barbieri, Giorgio Baiocco, Alejandro Carabe, and Miguel A. Cortés-Giraldo. 2019. “Dose-averaged LET calculation for proton track segments using microdosimetric Monte Carlo simulations.” Medical Physics, 46, 9, Pp. 4184–4192. Publisher's VersionAbstract
Purpose: There is an increasing interest in calculating linear energy transfer (LET) distributions for proton therapy treatments in order to assess the influence of this quantity in biological terms. Microdosimetric Monte Carlo (MC) simulations are useful tools to calculate dose-averaged LET, as this has been broadly proposed as the most adequate quantity to characterize these biological effects. However, a straightforward uniform sampling of the scoring site turns out to be computationally unaffordable. In contrast, some issues have been pointed out with the more efficient weighted sampling approach, frequently used in literature. Here, we address the issues associated with the latter method and propose adequate corrections to achieve reliable calculations of dose-averaged LET values from microdosimetry. Methods and materials: Proton track structures have been simulated with Geant4-DNA considering two different approaches. One version employs a uniform sampling for placing the spherical site and is used as the reference. The other one uses a weighted sampling by considering the spatial distribution of transfer points. Some corrections are proposed for calculating a dose-averaged LET comparable to the reference case. An additional MC approach is proposed to obtain the weighted mean of the energy imparted per electronic collision of the proton within the site, the $δ$2 function, related to the straggling distribution, as an intermediate step in the LET calculation. Results: Energy imparted per event distributions are different when employing either sampling methods, due to the different geometrical randomness. We have found an agreement below (0.15 ± 0.05) keV/$μ$m in the worst case for uniform and weighted methods in dose-averaged LET values when the weighted sampling results are corrected according to our proposal. Our analysis is restricted to spherical sites of 1 and 10 $μ$m diameter and monoenergetic beams in the range from 2 to 90 MeV. Conclusions: This work shows a reliable and computational-efficient method to perform calculations of track segment dose-averaged LET using MC simulations for proton therapy beams, including the necessary considerations for obtaining the straggling distribution characteristics. The validity of this approach remains as long as the stopping power of the proton can be considered as constant along its track within the site.
José Macías, Alejandro Bertolet, Héctor Miras, and J.C. Reyes Moreno. 2019. “Modelado bidimensional de la falta de uniformidad de la respuesta del sistema escáner-película radiocrómica.” Revista de Física Médica, 20, 1, Pp. 69–79. Publisher's VersionAbstract
Radiochromic films are increasingly used as a verification method for radiotherapy treatments. This work aims at characte- rizing and correcting the non-uniformity artifacts introduced by the scanner-radiochromic film system. We have found signs of an appreciable pattern not only at the lateral dimension but also along the other dimension. To study this, the dose distribution per monitor unit (MU) on a plane at a reference depth is measured by an ionization chamber array PTW 729. Corresponding distributions for different doses are measured with radiochromic films (EBT3) from distinct batches, whose reading is performed by using two scanners EPSON EXPRESSION 10000XL. By fitting 2D polynomial functions to the resulting images, we model the bidimensional behavior of scanner-radiochromic film system. Therefore, a family of surfaces for each color channel and for a range of considered doses, equivalently optical density (OD), is employed to correct the artifacts. A consistent two-dimensional pattern has been found for both scanners and all the studied ODs. On the film corner areas, both effects may join thus the com- bined correction becomes necessary. Consequently, a new two-dimensional correction method is proposed and built together with an in-house software for a quick setup in any institution. Key