P Pater

Monte Carlo role in radiobiological modelling of radiotherapy outcomes

Radiobiological models are essential components of modern radiotherapy. They are increasingly applied to optimize and evaluate the quality of different treatment planning modalities. They are frequently used in designing new radiotherapy clinical trials by estimating the expected therapeutic ratio of new protocols. In radiobiology, the therapeutic ratio is estimated from the expected gain in tumour control probability (TCP) to the risk of normal tissue complication probability (NTCP). However, estimates of TCP/NTCP are currently based on the deterministic and simplistic linear-quadratic formalism with limited prediction power when applied prospectively. Given the complex and stochastic nature of the physical, chemical and biological interactions associated with spatial and temporal radiation induced effects in living tissues, it is conjectured that methods based on Monte Carlo (MC) analysis may provide better estimates of TCP/NTCP for radiotherapy treatment planning and trial design. Indeed, over the past few decades, methods based on MC have demonstrated superior performance for accurate simulation of radiation transport, tumour growth and particle track structures; however, successful application of modelling radiobiological response and outcomes in radiotherapy is still hampered with several challenges. In this review, we provide an overview of some of the main techniques used in radiobiological modelling for radiotherapy, with focus on the MC role as a promising computational vehicle. We highlight the current challenges, issues and future potentials of the MC approach towards a comprehensive systems-based framework in radiobiological modelling for radiotherapy.

Proton and light ion RBE for the induction of direct DNA double strand breaks

PURPOSE To present and characterize a Monte Carlo (MC) tool for the simulation of the relative biological effectiveness for the induction of direct DNA double strand breaks (RBEDSB (direct)) for protons and light ions. METHODS The MC tool uses a pregenerated event-by-event tracks library of protons and light ions that are overlaid on a cell nucleus model. The cell nucleus model is a cylindrical arrangement of nucleosome structures consisting of 198 DNA base pairs. An algorithm relying on k-dimensional trees and cylindrical symmetries is used to search coincidences of energy deposition sites with volumes corresponding to the sugar-phosphate backbone of the DNA molecule. Strand breaks (SBs) are scored when energy higher than a threshold is reached in these volumes. Based on the number of affected strands, they are categorized into either single strand break (SSB) or double strand break (DSB) lesions. The number of SBs composing each lesion (i.e., its size) is also recorded. RBEDSB (direct) is obtained by taking the ratio of DSB yields of a given radiation field to a (60)Co field. The MC tool was used to obtain SSB yields, DSB yields, and RBEDSB (direct) as a function of linear energy transfer (LET) for protons ((1)H(+)), (4)He(2+), (7)Li(3+), and (12)C(6+) ions. RESULTS For protons, the SSB yields decreased and the DSB yields increased with LET. At ≈24.5 keV μm(-1), protons generated 15% more DSBs than (12)C(6+) ions. The RBEDSB (direct) varied between 1.24 and 1.77 for proton fields between 8.5 and 30.2 keV μm(-1), and it was higher for iso-LET ions with lowest atomic number. The SSB and DSB lesion sizes showed significant differences for all radiation fields. Generally, the yields of SSB lesions of sizes ≥2 and the yields of DSB lesions of sizes ≥3 increased with LET and increased for iso-LET ions of lower atomic number. On the other hand, the ratios of SSB to DSB lesions of sizes 2-4 did not show variability with LET nor projectile atomic number, suggesting that these metrics are independent of the radiation quality. Finally, a variance of up to 8% in the DSB yields was observed as a function of the particle incidence angle on the cell nucleus. This simulation effect is due to the preferential alignment of ion tracks with the DNA nucleosomes at specific angles. CONCLUSIONS The MC tool can predict SSB and DSB yields for light ions of various LET and estimate RBEDSB (direct). In addition, it can calculate the frequencies of different DNA lesion sizes, which is of interest in the context of biologically relevant absolute dosimetry of particle beams.

Microdosimetry calculations for monoenergetic electrons using Geant4-DNA combined with a weighted track sampling algorithm

The aim of this study was to calculate microdosimetric distributions for low energy electrons simulated using the Monte Carlo track structure code Geant4-DNA. Tracks for monoenergetic electrons with kinetic energies ranging from 100 eV to 1 MeV were simulated in an infinite spherical water phantom using the Geant4-DNA extension included in Geant4 toolkit version 10.2 (patch 02). The microdosimetric distributions were obtained through random sampling of transfer points and overlaying scoring volumes within the associated volume of the tracks. Relative frequency distributions of energy deposition f(>E)/f(>0) and dose mean lineal energy ([Formula: see text]) values were calculated in nanometer-sized spherical and cylindrical targets. The effects of scoring volume and scoring techniques were examined. The results were compared with published data generated using MOCA8B and KURBUC. Geant4-DNA produces a lower frequency of higher energy deposits than MOCA8B. The [Formula: see text] values calculated with Geant4-DNA are smaller than those calculated using MOCA8B and KURBUC. The differences are mainly due to the lower ionization and excitation cross sections of Geant4-DNA for low energy electrons. To a lesser extent, discrepancies can also be attributed to the implementation in this study of a new and fast scoring technique that differs from that used in previous studies. For the same mean chord length ([Formula: see text]), the [Formula: see text] calculated in cylindrical volumes are larger than those calculated in spherical volumes. The discrepancies due to cross sections and scoring geometries increase with decreasing scoring site dimensions. A new set of [Formula: see text] values has been presented for monoenergetic electrons using a fast track sampling algorithm and the most recent physics models implemented in Geant4-DNA. This dataset can be combined with primary electron spectra to predict the radiation quality of photon and electron beams.

SU‐E‐T‐581: On the Value of LET as a Radiation Quality Descriptor for RBE

Purpose: To investigate the relationship between linear energy transfer (LET) and relative biological effectiveness (RBE) for protons and light ions, and the corresponding role of LET as a descriptor of radiation quality of hadron therapy. Methods: Monte Carlo (MC) proton and light ion (He, Li, C) tracks with LET < 30 eV nm-1 were generated in an event-by-event mode. They were overlaid on a cell nucleus model containing 6×109 nucleotide base pairs using an isotropic irradiation procedure that provides electronic equilibrium. Strand breaks (sbs) were scored in the DNA sugar-phosphate groups and further sub-classified into single or double sbs (ssbs or dsbs). Distributions of ssbs and dsbs for 2 Gy fractions were calculated to estimate RBE for the induction of initial dsbs with reference to 60Co. Additionally, sbs were classified based on their complexity (i.e. the number of sbs in each cluster). Results: An increase in LET for light ions of the same atomic number or a decrease in atomic number for ions of the same LET resulted in a lower kinetic energy of emitted secondary electrons. The clustering of DNA damage was more pronounced as reflected by the increase in proton RBE from ∼ 1.75 to 4 for LET values of 7 to 28 eV nm-1. A significant RBE decrease between protons, He, Li and C ions of the same LET was also noticed as function of the atomic number. Significant differences in ssbs and dsbs complexities were also seen for particles with the same LET, potentially supporting a clustering-based radiation quality descriptor. Conclusion: The LET-RBE relationships were simulated for proton and light ions and exhibited expected trends, including different RBEs for particles with the same LET but different atomic numbers. A complexity based radiation quality descriptor may allow better differentiation of RBE between radiation fields of similar LET. We would like to acknowledge support from the Fonds de recherche du Quebec Sante (FRQS), from the CREATE Medical Physics Research Training Network grant (number 432290) of NSERC, support from NSERC under grants RGPIN 397711-11 and RGPIN-2014-06475 and support from CIHR under grants MOP-114910, MOP-136774 and MOP-102550.

SU-E-T-494: Influence of Proton Track-Cell Nucleus Incidence Angle On Relative Biological Effectiveness

Influence of Proton Track-Cell Nucleus Incidence Angle On Relative Biological Effectiveness

WE‐E‐BRE‐11: New Method to Simulate DNA Damage Using Ionization Cross‐Sections and a Geometrical Nucleosome Model

PURPOSE To obtain probability distributions of various DNA damage types as a function of the incident electron kinetic energy. METHODS Using Geant4-DNA electron ionization cross-sections, we calculated path length distributions for electrons of energies between 10 eV and 1 MeV, defined as the length between two subsequent interactions. These path lengths were then convolved with probability distributions for the creation of same-strand damage, opposite-strand damage, clustered damage, isolated damage, and same DNA strand target damage. These probability distributions of DNA damage were obtained by a Monte Carlo routine calculating probabilities of interaction in DNA targets inside a nucleosome geometrical model. Results represent the probability of a secondary electron, initially created inside a DNA strand target, of undergoing its next interaction: (1) in the opposite strand (DSB), (2) in the same strand (SSB+), (3) in either the opposite or same-strand (clustered), (4) in the same DNA target (multiple-hit) or (5) more than 10 base pairs away (isolated). RESULTS Electrons with kinetic energy between 50 and 250 eV have a maximal probability of creating DSB, SSB+, clustered damage and multiple-hits in the same target The probabilities for these damage patterns have values of 2.5%, 4.3%, 6.7% and 5.4%, respectively. Isolated damage is most probable between 700 eV to 900 eV with a probability of 0.2%. CONCLUSION We obtained DNA damage probability distributions as a function of electron incident energy. We showed that electrons with kinetic energies between 50 and 250 eV have the highest probability of producing complex forms of DNA damage (DSB, SSB+). We also showed that a double ionization within the same DNA target is the most frequent outcome occurring 5% of the time. It is expected that electron slowing down spectra can be convolved with our formalism to calculate source specific DNA damage patterns. Research grants from governments of Canada and Quebec. PP acknowledges partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (Grant number: 432290).

SU‐E‐T‐306: Electronic Equilibrium in RBE of DSB Induction in Monte Carlo Simulations of Low Energy Photon and Electron Track Structures

PURPOSE The study of DNA double-strand breaks (DSB) induction by ionizing radiation can provide understanding of linear quadratic formalism failures for complex cases such as stereotactic body radiation therapy. Using Monte Carlo simulations in cell nuclear volumes and adequate DNA modelling, estimation of DSBs is possible for various radiation fields. This study aims to evaluate the impact of electronic equilibrium (EE) and lack-thereof on dosimetric quantities such as dose, number of ionizations and excitations and subsequently on simulated DSBs and on the relative biological effectiveness (RBE). METHODS Using Geant4 with the newly added Geant4-DNA low energy processes, we simulated track structures of mono-energetic photons and electrons (0.280 to 20 keV), including Auger electrons and fluorescence photons deexcitation products, and scored energy deposition interactions inside liquid water micro-volumes of various shapes and sizes. Electronic equilibrium conditions were varied by changing the relative size of the particle source and volume of interest. RESULTS The total number of energy depositions interactions inside the volume varied around 0.62+/-0.04 interactions/eV and was almost constant for all analyzed EE conditions. However, the spatial distribution is affected by EE conditions and lack of interactions around the edges of the volume of 30% were scored. When coupled to a fixed position geometrical DNA model, simulated strand breaks are underestimated by up to 10% influencing the RBE of DSBs induction as a function of particle energy. CONCLUSION In order to speed up miro-dosimetric calculations, source sizes violating electronic equilibrium are often used. Simulated DSBs in a fixed geometrical model for different incident particle energies in electronic deequilibrium conditions, can thus be skewed by up to 10%. To circumvent this effect, sources satisfying electronic equilibrium in the volume for all energies or probabilistic delocalized DNA models need to be used. Fond de Recherche en Sante du Quebec Canadian Institutes of Health Research.

SU‐E‐T‐05: Comparing DNA Strand Break Yields for Photons under Different Irradiation Conditions with Geant4‐DNA

PURPOSE To validate and scrutinize published DNA strand break data with Geant4-DNA and a probabilistic model. To study the impact of source size, electronic equilibrium and secondary electron tracking cutoff on direct relative biological effectiveness (DRBE). METHODS Geant4 (v4.9.5) was used to simulate a cylindrical region of interest (ROI) with r = 15 nm and length = 1.05 mm, in a slab of liquid water of 1.06 g/cm3 density. The ROI was irradiated with mono-energetic photons, with a uniformly distributed volumetric isotropic source (0.28, 1.5 keV) or a plane beam (0.662, 1.25 MeV), of variable size. Electrons were tracked down to 50 or 10 eV, with G4-DNA processes and energy transfer greater than 10.79 eV was scored. Based on volume ratios, each scored event had a 0.0388 probability of happening on either DNA helix (break). Clusters of at least one break on each DNA helix within 3.4 nm were found using a DBSCAN algorithm and categorized as double strand breaks (DSB). All other events were categorized as single strand breaks (SSB). RESULTS Geant4-DNA is able to reproduce strand break yields previously published. Homogeneous irradiation conditions should be present throughout the ROI for DRBE comparisons. SSB yields seem slightly dependent on the primary photon energy. DRBEs show a significant increasing trend for lower energy incident photons. A lower electron cutoff produces higher SSB yields, but decreases the SSB/DSB yields ratio. The probabilistic and geometrical DNA models can predict equivalent results. CONCLUSIONS Using Geant4, we were able to reproduce previously published results on the direct strand break yields of photon and study the importance of irradiation conditions. We also show an ascending trend for DRBE with lower incident photon energies. A probabilistic model coupled with track structure analysis can be used to simulate strand break yields. NSERC, CIHR.

SU‐E‐T‐112: 18 MV X‐Ray Beam Commissioning with the IC Profiler: A Fast 3D Relative Dosimetry Technique Using An Ion Chamber Array in a Solid Tissue‐Equivalent Phantom

Purpose: To devise a technique of 3D relative dosimetry using an ion chamber array with solid phantom to significantly reduce overall measurement time needed for photon beam modeling. Methods: Measurement setup of the array was determined by comparison of acquired profiles in the array and in a water tank. Software was developed to queue measurements in step‐and‐shoot sequences and process the resulting IC array data. Beam profiles and PDDs necessary for beam modeling were acquired with the IC array for 18 MV. A model was created with the IC array data using the Pinnacle TPS and compared to a model created from water tank measurements. Both models were first compared by measuring differences between profiles and PDDs. Secondly, 3D dose distributions predicted by both models were compared using a gamma metric for a pair of treatment plans. Results: The IC array model was found to match the water tank model for most profiles. Due to fixed chamber depth in the IC array, PDDs near the surface differed in the IC array model from the water tank model. For a prostate case treatment plan, comparison of 3D dose distributions from both models showed that 90.4 % of voxels agreed within a gamma of (1%, 1 mm). This tolerance was violated near air‐tissue interfaces due to differences in the measured PDDs between both models. The devised technique allowed most measurements necessary for beam modeling, except for output factors, to be made for a single energy in under 8 hours. Conclusions: The IC array with solid phantom setup allows substantially faster beam acquisition than a water tank. Further investigation is required for measuring exact PDDs in the IC array setup. Future work will study lower photon energies and electron beam modeling with IC array acquisitions. Funding for the presenting author was provided for this study by Sun Nuclear Corporation during the summer of 2010.