Nanodosimetry: Bridging the gap to radiation biophysics

Integrating microdosimetricin vitroRBE models for particle therapy into TOPAS MC using the MicrOdosimetry-based modeliNg for RBE ASsessment (MONAS) tool

Objective.In this paper, we present MONAS (MicrOdosimetry-based modelliNg for relative biological effectiveness (RBE) ASsessment) toolkit. MONAS is a TOPAS Monte Carlo extension, that combines simulations of microdosimetric distributions with radiobiological microdosimetry-based models for predicting cell survival curves and dose-dependent RBE.Approach.MONAS expands TOPAS microdosimetric extension, by including novel specific energy scorers to calculate the single- and multi-event specific energy microdosimetric distributions at different micrometer scales. These spectra are used as physical input to three different formulations of themicrodosimetric kinetic model, and to thegeneralized stochastic microdosimetric model(GSM2), to predict dose-dependent cell survival fraction and RBE. MONAS predictions are then validated against experimental microdosimetric spectra andin vitrosurvival fraction data. To show the MONAS features, we present two different applications of the code: (i) the depth-RBE curve calculation from a passively scattered proton SOBP and monoenergetic12C-ion beam by using experimentally validated spectra as physical input, and (ii) the calculation of the 3D RBE distribution on a real head and neck patient geometry treated with protons.Main results.MONAS can estimate dose-dependent RBE and cell survival curves from experimentally validated microdosimetric spectra with four clinically relevant radiobiological models. From the radiobiological characterization of a proton SOBP and12C fields, we observe the well-known trend of increasing RBE values at the distal edge of the radiation field. The 3D RBE map calculated confirmed the trend observed in the analysis of the SOBP, with the highest RBE values found in the distal edge of the target.Significance.MONAS extension offers a comprehensive microdosimetry-based framework for assessing the biological effects of particle radiation in both research and clinical environments, pushing closer the experimental physics-based description to the biological damage assessment, contributing to bridging the gap between a microdosimetric description of the radiation field and its application in proton therapy treatment with variable RBE.

Electron Impact Ionization of Adenine: Partial Cross Sections

Electron ionization of a genetically important nucleobase, adenine, was investigated from threshold to 500 eV using crossed electron beam–effusive molecular beam geometry and time-of-flight mass spectrometry. We measured the complete set of absolute partial cross sections for adenine using the relative flow technique (RFT) up to an electron energy of 500 eV. Normalization to absolute values was performed using electron ionization cross sections for argon and the vapor pressure data of adenine. The total cross sections obtained by summing the partial cross sections were compared with the existing theoretical and experimental data. The appearance energies of various fragment ions were also measured and compared with the reported data. The prominence of ions with mass (HCN)n+ (n = 1 to 5) indicated a possible pathway to form adenine in the interstellar medium through aggregation of HCN units. Analysis of the partial cross sections for various groups of fragment ions as a function of electron energy was found to give insights into their composition.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Dose-mean lineal energy values for electrons by different Monte Carlo codes: Consequences for estimates of radiation quality in photon beams

BACKGROUND

The microdosimetric quantity lineal energy and its mean values have proven useful for quantifying radiation quality in many situations. The ratio of dose-mean lineal energies is perhaps the simplest quantity for quantifying differences between two radiation qualities. However, published dose-mean lineal energy values from different codes may differ significantly with potential influence on radiation quality estimates.

PURPOSE

The purpose was to compare dose-mean lineal energy values from different track-structure data sets for condensed water vapor and liquid water, and to evaluate the influence on radiation quality estimations for some photon sources.

METHODS

Published dose-mean lineal energy values for 0.1 keV to 1 MeV electrons in spheres with diameters 2 nm to 1 μm, calculated with water vapor and liquid water track structure codes and proximity functions, were collected, analyzed, and compared. Data for cylinders were converted to spheres using a theoretical transformation published by Kellerer. A new set of dose-mean lineal energy values was calculated to cover the whole range of volumes of interest here using the GEANT4-DNA code. The influence from the differences between codes on radiation quality calculations was estimated using dose-mean lineal energy ratios for the photon sources ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co.

RESULTS

The theoretical relation for converting the dose-mean lineal energy between different geometrical volumes, results in differences up to 10% between cylinders and spheres depending on electron energy and target size, in agreement with published simulated results. For spheres with diameter above 100 nm, dose-mean lineal energy values for condensed water vapor and liquid water are with few exceptions within ±10%. Below 100 nm, the difference increases with decreasing diameter reaching a factor of two at 2 nm. The values from water vapor codes are in general larger than from liquid water codes. If the dose-mean lineal energy ratio is based on condensed water vapor instead of liquid water, the ratio differs less than 9% for the nuclides ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co independent of the volume simulated. However, a specific value of the dose-mean lineal energy ratio, is found at a larger target diameter in liquid water than in condensed water vapor.

CONCLUSIONS

When ratios of the dose-mean lineal energy are used as a measure of the radiation quality it is important to compare values for geometrically equal target shapes. A practical method of converting values for cylinders of equal diameter and height to spheres was demonstrated. Although dose-mean lineal energy values calculated with water vapor and liquid water codes may differ significantly, the radiation quality, in terms of ratios of dose-mean lineal energy, for the three photon sources ¹⁹² Ir, ¹⁶⁹ Yb, and ¹²⁵ I relative to ⁶⁰ Co, agree within 9%. The same ratio appears at a larger diameter when a liquid water code is used. It is therefore important to use the same code in radiation quality investigations. The present findings may be of special interest in studies related to the relative biological effectiveness (RBE).

Monte Carlo track-structure for the radionuclide Copper-64: characterization of S-values, nanodosimetry and quantification of direct damage to DNA

TOPAS-nBio was used to simulate, collision-to-collision, the complete trajectories of electrons in water generated during the explicit simulation of ⁶⁴Cu decay. S-values and direct damage to the DNA were calculated representing the cell (C) and the cell nucleus (N) with concentric spheres of 5 μm and 4 μm in radius, respectively. The considered 'target'←'source' configurations, including the cell surface (Cs) and cytoplasm (Cy), were: C←C, C←Cs, N←N, N←Cy and N←Cs. Ionization cluster size distributions were also calculated in a cylinder immersed in water corresponding to a DNA segment of 10 base-pairs in length (diameter 2.3 nm, length 3.4 nm), modeling a radioactive point source moving from the central axis to the edge of the cylinder. For that, the first moment (M₁) and cumulative probability of having a cluster size of 2 or more ionizations in the cylindrical volume (F₂) were obtained. Finally, the direct damage to the DNA was estimated by quantifying double-strand breaks (DSBs) using the clustering algorithm DBSCAN. The S-values obtained with TOPAS-nBio for ⁶⁴Cu were 7.879 × 10^-4 ± 5 × 10^-7, 4.351 × 10^-4 ± 6 × 10^-7, 1.442 × 10^-3 ± 1 × 10^-6, 2.596 × 10^-4 ± 8 × 10^-7, 1.127 × 10^-4 ± 4 × 10^-7 Gy Bq-s^-1 for the configurations C←C, C←Cs, N←N, N←Cy and N←Cs, respectively. The difference of these values, compared with previously reported S-values for ⁶⁴Cu with the code MNCP and software MIRDCell, ranged from -4% to -25% for the configurations N←N and N←Cs, respectively. On the other hand, F₂ was maximum with the source at the center of the cylinder 0.373 ± 0.001, and monotonically decreased until reaching a value of 0.058 ± 0.001 at 2.3 nm. The same behavior was observed for M₁ with values ranging from 2.188 ± 0.004 to 0.242 ± 0.002. Finally, the DBSCAN algorithm showed that the mean number of DNA DSBs per decay were 0.187 ± 0.001, 0.0317 ± 0.0005, and 0.0125 ± 0.0002 DSB-(Bq-s)^-1 for the configurations N←N, N←Cs, and N←Cy, respectively. In conclusion, the results of the S-values show that the absorbed dose strongly depends on the distribution of the radionuclide in the cell, the dose being higher when ⁶⁴Cu is internalized in the cell nucleus, which is reinforced by the nanodosimetric study by the presence of DNA DSBs attributable to the Auger electrons emitted during the decay of ⁶⁴Cu.

Internal microdosimetry of alpha-emitting radionuclides

At the tissue level, energy deposition in cells is determined by the microdistribution of alpha-emitting radionuclides in relation to sensitive target cells. Furthermore, the highly localized energy deposition of alpha particle tracks and the limited range of alpha particles in tissue produce a highly inhomogeneous energy deposition in traversed cell nuclei. Thus, energy deposition in cell nuclei in a given tissue is characterized by the probability of alpha particle hits and, in the case of a hit, by the energy deposited there. In classical microdosimetry, the randomness of energy deposition in cellular sites is described by a stochastic quantity, the specific energy, which approximates the macroscopic dose for a sufficiently large number of energy deposition events. Typical examples of the alpha-emitting radionuclides in internal microdosimetry are radon progeny and plutonium in the lungs, plutonium and americium in bones, and radium in targeted radionuclide therapy. Several microdosimetric approaches have been proposed to relate specific energy distributions to radiobiological effects, such as hit-related concepts, LET and track length-based models, effect-specific interpretations of specific energy distributions, such as the dual radiation action theory or the hit-size effectiveness function, and finally track structure models. Since microdosimetry characterizes only the initial step of energy deposition, microdosimetric concepts are most successful in exposure situations where biological effects are dominated by energy deposition, but not by subsequently operating biological mechanisms. Indeed, the simulation of the combined action of physical and biological factors may eventually require the application of track structure models at the nanometer scale.

THE COMPLEXITY OF QUANTITIES IN RADIATION DOSIMETRY: THE ISSUE OF RADIATION QUALITY

When Harald Rossi developed a new radiation measurement instrument more than 60 years ago-the tissue equivalent low-pressure proportional counter, also called Rossi Counter-his initial intention was to provide a technique to measure LET. He realized soon that the measurements provided insight into the stochastic nature of the interactions of ionizing radiation with matter and that the measured results represented an alternative to characterize radiation quality in terms of stochastic or microdosimetric quantities. Progress in cellular and molecular radiation biology and in simulating charged particle tracks in biological entities are now essential features and have extended the original delineation of the field of microdosimetry. This general field of microdosimetry, as part of an interdisciplinary approach for the study of molecular mechanisms and cellular radiation effects, continues to be an important area of radiation research, documented by 13 previous Microdosimetry Symposia and, again, at this Symposium. However, the quantification of radiation quality remains a subject of practical importance. In fact, the issue has gained in importance due to the application of ions for therapy and due to the need for protection from exposures to complex and high-energy radiation fields, for example, to cosmic radiation in civil aviation and space missions. In practice pragmatic, empirical approaches are being used which has led to a complex set of dosimetric quantities and terms.

Simultaneous optimization of RBE-weighted dose and nanometric ionization distributions in treatment planning with carbon ions

Inverse treatment planning in intensity modulated particle therapy (IMPT) with scanned carbon-ion beams is currently based on the optimization of RBE-weighted dose to satisfy requirements of target coverage and limited toxicity to organs-at-risk (OARs) and healthy tissues. There are many feasible IMPT plans that meet these requirements, which allows the introduction of further criteria to narrow the selection of a biologically optimal treatment plan. We propose a novel treatment planning strategy based on the simultaneous optimization of RBE-weighted dose and nanometric ionization details (ID) as a new physical characteristic of the delivered plan beyond LET. In particular, we focus on the distribution of large ionization clusters (more than 3 ionizations) to enhance the biological effect across the target volume while minimizing biological effect in normal tissues. Carbon-ion treatment plans for different patient geometries and beam configurations generated with the simultaneous optimization strategy were compared against reference plans obtained with RBE-weighted dose optimization alone. Quality indicators, inhomogeneity index and planning volume histograms of RBE-weighted dose and large ionization clusters were used to evaluate the treatment plans. We show that with simultaneous optimization, ID distributions can be optimized in carbon-ion radiotherapy without compromising the RBE-weighted dose distributions. This strategy can potentially be used to account for optimization of endpoints closely related to radiation quality to achieve better tumor control and reduce risks of complications.

Clinically relevant nanodosimetric simulation of DNA damage complexity from photons and protons

Relative Biological Effectiveness (RBE), the ratio of doses between radiation modalities to produce the same biological endpoint, is a controversial and important topic in proton therapy. A number of phenomenological models incorporate variable RBE as a function of Linear Energy Transfer (LET), though a lack of mechanistic description limits their applicability. In this work we take a different approach, using a track structure model employing fundamental physics and chemistry to make predictions of proton and photon induced DNA damage, the first step in the mechanism of radiation-induced cell death. We apply this model to a proton therapy clinical case showing, for the first time, predictions of DNA damage on a patient treatment plan. Our model predictions are for an idealised cell and are applied to an ependymoma case, at this stage without any cell specific parameters. By comparing to similar predictions for photons, we present a voxel-wise RBE of DNA damage complexity. This RBE of damage complexity shows similar trends to the expected RBE for cell kill, implying that damage complexity is an important factor in DNA repair and therefore biological effect.

Relative Biological Effectiveness (RBE) is a controversial and important topic in proton therapy. This work uses Monte Carlo simulations of DNA damage for protons and photons to probe this phenomenon, providing a plausible mechanistic understanding.

DNA damage interactions on both nanometer and micrometer scale determine overall cellular damage

DNA double strand breaks (DSB) play a pivotal role for cellular damage, which is a hazard encountered in toxicology and radiation protection, but also exploited e.g. in eradicating tumors in radiation therapy. It is still debated whether and in how far clustering of such DNA lesions leads to an enhanced severity of induced damage. Here we investigate - using focused spots of ionizing radiation as damaging agent - the spatial extension of DNA lesion patterns causing cell inactivation. We find that clustering of DNA damage on both the nm and µm scale leads to enhanced inactivation compared to more homogeneous lesion distributions. A biophysical model interprets these observations in terms of enhanced DSB production and DSB interaction, respectively. We decompose the overall effects quantitatively into contributions from these lesion formation processes, concluding that both processes coexist and need to be considered for determining the resulting damage on the cellular level.

In Silico Non-Homologous End Joining Following Ion Induced DNA Double Strand Breaks Predicts That Repair Fidelity Depends on Break Density

This work uses Monte Carlo simulations to investigate the dependence of residual and misrepaired double strand breaks (DSBs) at 24 hours on the initial damage pattern created during ion therapy. We present results from a nanometric DNA damage simulation coupled to a mechanistic model of Non-Homologous End Joining, capable of predicting the position, complexity, and repair of DSBs. The initial damage pattern is scored by calculating the average number of DSBs within 70 nm from every DSB. We show that this local DSB density, referred to as the cluster density, can linearly predict misrepair regardless of ion species. The models predict that the fraction of residual DSBs is constant, with 7.3% of DSBs left unrepaired following 24 hours of repair. Through simulation over a range of doses and linear energy transfer (LET) we derive simple correlations capable of predicting residual and misrepaired DSBs. These equations are applicable to ion therapy treatment planning where both dose and LET are scored. This is demonstrated by applying the correlations to an example of a clinical proton spread out Bragg peak. Here we see a considerable biological effect past the distal edge, dominated by residual DSBs.

Nanodosimetric Simulation of Direct Ion-Induced DNA Damage Using Different Chromatin Geometry Models

Monte Carlo based simulation has proven useful in investigating the effect of proton-induced DNA damage and the processes through which this damage occurs. Clustering of ionizations within a small volume can be related to DNA damage through the principles of nanodosimetry. For simulation, it is standard to construct a small volume of water and determine spatial clusters. More recently, realistic DNA geometries have been used, tracking energy depositions within DNA backbone volumes. Traditionally a chromatin fiber is built within the simulation and identically replicated throughout a cell nucleus, representing the cell in interphase. However, the in vivo geometry of the chromatin fiber is still unknown within the literature, with many proposed models. In this work, the Geant4-DNA toolkit was used to build three chromatin models: the solenoid, zig-zag and cross-linked geometries. All fibers were built to the same chromatin density of 4.2 nucleosomes/11 nm. The fibers were then irradiated with protons (LET 5-80 keV/μm) or alpha particles (LET 63-226 keV/μm). Nanodosimetric parameters were scored for each fiber after each LET and used as a comparator among the models. Statistically significant differences were observed in the double-strand break backbone size distributions among the models, although nonsignificant differences were noted among the nanodosimetric parameters. From the data presented in this article, we conclude that selection of the solenoid, zig-zag or cross-linked chromatin model does not significantly affect the calculated nanodosimetric parameters. This allows for a simulation-based cell model to make use of any of these chromatin models for the scoring of direct ion-induced DNA damage.

Evaluation of Acridine Orange Derivatives as DNA-Targeted Radiopharmaceuticals for Auger Therapy: Influence of the Radionuclide and Distance to DNA

A new family of ^99mTc(I)- tricarbonyl complexes and ¹²⁵I-heteroaromatic compounds bearing an acridine orange (AO) DNA targeting unit was evaluated for Auger therapy. Characterization of the DNA interaction, performed with the non-radioactive Re and ¹²⁷I congeners, confirmed that all compounds act as DNA intercalators. Both classes of compounds induce double strand breaks (DSB) in plasmid DNA but the extent of DNA damage is strongly dependent on the linker between the Auger emitter (^99mTc or ¹²⁵I) and the AO moiety. The in vitro evaluation was complemented with molecular docking studies and Monte Carlo simulations of the energy deposited at the nanometric scale, which corroborated the experimental data. Two of the tested compounds, ¹²⁵I-C₅ and ^99mTc-C₃, place the corresponding radionuclide at similar distances to DNA and produce comparable DSB yields in plasmid and cellular DNA. These results provide the first evidence that ^99mTc can induce DNA damage with similar efficiency to that of ¹²⁵I, when both are positioned at comparable distances to the double helix. Furthermore, the high nuclear retention of ^99mTc-C₃ in tumoral cells suggests that ^99mTc-labelled AO derivatives are more promising for the design of Auger-emitting radiopharmaceuticals than the ¹²⁵I-labelled congeners.

Microdosimetry of DNA conformations: relation between direct effect of (60)Co gamma rays and topology of DNA geometrical models in the calculation of A-, B- and Z-DNA radiation-induced damage yields

In order to obtain the energy deposition pattern of ionizing radiation in the nanometric scale of genetic material and to investigate the different sensitivities of the DNA conformations, direct effects of (60)Co gamma rays on the three A, B and Z conformations of DNA have been studied. For this purpose, single-strand breaks (SSB), double-strand breaks (DSB), base damage (BD), hit probabilities and three microdosimetry quantities (imparted energy, mean chord length and lineal energy) in the mentioned DNA conformations have been calculated and compared by using GEometry ANd Tracking 4 (Geant4) toolkit. The results show that A-, B- and Z-DNA conformations have the highest yields of DSB (1.2 Gy(-1) Gbp(-1)), SSB (25.2 Gy(-1) Gbp(-1)) and BD (4.81 Gy(-1) Gbp(-1)), respectively. Based on the investigation of direct effects of radiation, it can be concluded that the DSB yield is largely correlated to the topological characteristics of DNA models, although the SSB yield is not. Moreover, according to the comparative results of the present study, a reliable candidate parameter for describing the relationship between DNA damage yields and geometry of DNA models in the theoretical radiation biology research studies would be the mean chord length (4 V/S) of the models.

Communication: Electron ionization of DNA bases

No reliable experimental data exist for the partial and total electron ionization cross sections for DNA bases, which are very crucial for modeling radiation damage in genetic material of living cell. We have measured a complete set of absolute partial electron ionization cross sections up to 500 eV for DNA bases for the first time by using the relative flow technique. These partial cross sections are summed to obtain total ion cross sections for all the four bases and are compared with the existing theoretical calculations and the only set of measured absolute cross sections. Our measurements clearly resolve the existing discrepancy between the theoretical and experimental results, thereby providing for the first time reliable numbers for partial and total ion cross sections for these molecules. The results on fragmentation analysis of adenine supports the theory of its formation in space.

Developments and trends in bioequivalent dosimetry

Significant progress in radiobiology has refined the understanding of radiation-induced biological response at the cellular level and challenged the conventional application of a macroscopic description of radiation action to dosimetry in favour of a microscopic approach. Pioneering experiments, which investigated the stochastics of energy deposition from ionising radiations in volumes of cellular dimensions, contributed to the recognition of microdosimetry as a new scientific discipline. The first quantitative applications of Monte Carlo track structure simulations in radiobiology, however, supported evidence for target sizes of particular biological importance being in the nanometre regime. Bioequivalent dosimetry attempts to link particular features of the response of physical detectors with biological endpoints, exploiting clusters of multiple ionisations within nanometre scales in solid-state, gas- and water-filled devices. This approach supports the continued development of new concepts and quantities in radiation protection to permit evaluation of the biological effectiveness of radiations of different quality independently of dose and dose rate.

Comparison of nanodosimetric parameters of track structure calculated by the Monte Carlo codes Geant4-DNA and PTra

The concept of nanodosimetry is based on the assumption that initial damage to cells is related to the number of ionizations (the ionization cluster size) directly produced by single particles within, or in the close vicinity of, short segments of DNA. The ionization cluster-size distribution and other nanodosimetric quantities, however, are not directly measurable in biological targets and our current knowledge is mostly based on numerical simulations of particle tracks in water, calculating track structure parameters for nanometric target volumes. The assessment of nanodosimetric quantities derived from particle-track calculations using different Monte Carlo codes plays, therefore, an important role for a more accurate evaluation of the initial damage to cells and, as a consequence, of the biological effectiveness of ionizing radiation. The aim of this work is to assess the differences in the calculated nanodosimetric quantities obtained with Geant4-DNA as compared to those of the ad hoc particle-track Monte Carlo code 'PTra' developed at Physikalisch-Technische Bundesanstalt (PTB), Germany. The comparison of the two codes was made for incident electrons of energy in the range between 50 eV and 10 keV, for protons of energy between 300 keV and 10 MeV, and for alpha particles of energy between 1 and 10 MeV as these were the energy ranges available in both codes at the time this investigation was carried out. Good agreement was found for nanodosimetric characteristics of track structure calculated in the high-energy range of each particle type. For lower energies, significant differences were observed, most notably in the estimates of the biological effectiveness. The largest relative differences obtained were over 50%; however, generally the order of magnitude was between 10% and 20%.