Fast calculation of nanodosimetric quantities in treatment planning of proton and ion therapy

Biophysical modeling of low-energy ion irradiations with NanOx

BACKGROUND

Targeted radiotherapies with low-energy ions show interesting possibilities for the selective irradiation of tumor cells, a strategy particularly appropriate for the treatment of disseminated cancer. Two promising examples are boron neutron capture therapy (BNCT) and targeted radionuclide therapy with α $\alpha$ -particle emitters (TAT). The successful clinical translation of these radiotherapies requires the implementation of accurate radiation dosimetry approaches able to take into account the impact on treatments of the biological effectiveness of ions and the heterogeneity in the therapeutic agent distribution inside the tumor cells. To this end, biophysical models can be applied to translate the interactions of radiations with matter into biological endpoints, such as cell survival.

PURPOSE

The NanOx model was initially developed for predicting the cell survival fractions resulting from irradiations with the high-energy ion beams encountered in hadrontherapy. We present in this work a new implementation of the model that extends its application to irradiations with low-energy ions, as the ones found in TAT and BNCT.

METHODS

The NanOx model was adapted to consider the energy loss of primary ions within the sensitive volume (i.e., the cell nucleus). Additional assumptions were introduced to simplify the practical implementation of the model and reduce computation time. In particular, for low-energy ions the narrow-track approximation allowed to neglect the energy deposited by secondary electrons outside the sensitive volume, increasing significantly the performance of simulations. Calculations were performed to compare the original hadrontherapy implementation of the NanOx model with the present one in terms of the inactivation cross sections of human salivary gland cells as a function of the kinetic energy of incident α $\alpha$ -particles.

RESULTS

The predictions of the previous and current versions of NanOx agreed for incident energies higher than 1 MeV/n. For lower energies, the new NanOx implementation predicted a decrease in the inactivation cross sections that depended on the length of the sensitive volume.

CONCLUSIONS

We reported in this work an extension of the NanOx biophysical model to consider irradiations with low-energy ions, such as the ones found in TAT and BNCT. The excellent agreement observed at intermediate and high energies between the original hadrontherapy implementation and the present one showed that NanOx offers a consistent, self-integrated framework for describing the biological effects induced by ion irradiations. Future work will focus on the application of the latest version of NanOx to cases closer to the clinical setting.

Nanodosimetric investigation of the track structure of therapeutic carbon ion radiation part2: detailed simulation

Objectivea previous study reported nanodosimetric measurements of therapeutic-energy carbon ions penetrating simulated tissue. The results are incompatible with the predicted mean energy of the carbon ions in the nanodosimeter and previous experiments with lower energy monoenergetic beams. The purpose of this study is to explore the origin of these discrepancies.Approachdetailed simulations using the Geant4 toolkit were performed to investigate the radiation field in the nanodosimeter and provide input data for track structure simulations, which were performed with a developed version of the PTra code.Main resultsthe Geant4 simulations show that with the narrow-beam geometry employed in the experiment, only a small fraction of the carbon ions traverse the nanodosimeter and their mean energy is between 12% and 30% lower than the values estimated using the SRIM software. Only about one-third or less of these carbon ions hit the trigger detector. The track structure simulations indicate that the observed enhanced ionization cluster sizes are mainly due to coincidences with events in which carbon ions miss the trigger detector. In addition, the discrepancies observed for high absorber thicknesses of carbon ions traversing the target volume could be explained by assuming an increase in thickness or interaction cross-sections in the order of 1%.Significancethe results show that even with strong collimation of the radiation field, future nanodosimetric measurements of clinical carbon ion beams will require large trigger detectors to register all events with carbon ions traversing the nanodosimeter. Energy loss calculations of the primary beam in the absorbers are insufficient and should be replaced by detailed simulations when planning such experiments. Uncertainties of the interaction cross-sections in simulation codes may shift the Bragg peak position.

Nanodosimetric investigation of the track structure of therapeutic carbon ion radiation part 1: measurement of ionization cluster size distributions

At the Heidelberg Ion-Beam Therapy Center, the track structure of carbon ions of therapeutic energy after penetrating layers of simulated tissue was investigated for the first time. Measurements were conducted with carbon ion beams of different energies and polymethyl methacrylate (PMMA) absorbers of different thicknesses to realize different depths in the phantom along the pristine Bragg peak. Ionization cluster size (ICS) distributions resulting from the mixed radiation field behind the PMMA absorbers were measured using an ion-counting nanodosimeter. Two different measurements were carried out: (i) variation of the PMMA absorber thickness with constant carbon ion beam energy and (ii) combined variation of PMMA absorber thickness and carbon ion beam energy such that the kinetic energy of the carbon ions in the target volume is constant. The data analysis revealed unexpectedly high mean ICS values compared to stopping power calculations and the data measured at lower energies in earlier work. This suggests that in the measurements the carbon ion kinetic energies behind the PMMA absorber may have deviated considerably from the expected values obtained by the calculations. In addition, the results indicate the presence of a marked contribution of nuclear fragments to the measured ICS distributions, especially if the carbon ion does not cross the target volume.

Radial dependence of ionization clustering around a gold nanoparticle irradiated by X-rays under charged particle equilibrium

Objective.This work explores the enhancement of ionization clustering and its radial dependence around a gold nanoparticle (NP), indicative of the induction of DNA lesions, a potential trigger for cell-death.Approach.Monte Carlo track structure simulations were performed to determine (a) the spectral fluence of incident photons and electrons in water around a gold NP under charged particle equilibrium conditions and (b) the density of ionization clusters produced on average as well as conditional on the occurrence of at least one interaction in the NP using Associated Volume Clustering. Absorbed dose was determined for comparison with a recent benchmark intercomparison. Reported quantities are normalized to primary fluence, allowing to establish a connection to macroscopic dosimetric quantities.Main results.The modification of the electron spectral fluence by the gold NP is minor and mainly occurs at low energies. The net fluence of electrons emitted from the NP is dominated by electrons resulting from photon interactions. Similar to the known dose enhancement, increased ionization clustering is limited to a distance from the NP surface of up to200nm. The number of clusters per energy imparted is increased at distances of up to150nm, and accordingly the enhancement in clustering notably surpasses that of dose enhancement. Smaller NPs cause noticeable peaks in the conditional frequency of clusters between50nm-100nmfrom the NP surface.Significance.This work shows that low energy electrons emitted by NPs lead to an increase of ionization clustering in their vicinity exceeding that of energy imparted. While the electron component of the radiation field plays an important role in determining the background contribution to ionization clustering and energy imparted, the dosimetric effects of NPs are governed by the interplay of secondary electron production by photon interaction and their ability to leave the NP.

Lithium inelastic cross-sections and their impact on micro and nano dosimetry of boron neutron capture

Objective.To present a new set of lithium-ion cross-sections for (i) ionization and excitation processes down to 700 eV, and (ii) charge-exchange processes down to 1 keV u-1. To evaluate the impact of the use of these cross-sections on micro a nano dosimetric quantities in the context of boron neutron capture (BNC) applications/techniques.Approach.The Classical Trajectory Monte Carlo method was used to calculate Li ion charge-exchange cross sections in the energy range of 1 keV u-1to 10 MeV u-1. Partial Li ion charge states ionization and excitation cross-sections were calculated using a detailed charge screening factor. The cross-sections were implemented in Geant4-DNA v10.07 and simulations and verified using TOPAS-nBio by calculating stopping power and continuous slowing down approximation (CSDA) range against data from ICRU and SRIM. Further microdosimetric and nanodosimetric calculations were performed to quantify differences against other simulation approaches for low energy Li ions. These calculations were: lineal energy spectra (yf(y) andyd(y)), frequency mean lineal energyyF-, dose mean lineal energyyD-and ionization cluster size distribution analysis. Microdosimetric calculations were compared against a previous MC study that neglected charge-exchange and excitation processes. Nanodosimetric results were compared against pure ionization scaled cross-sections calculations.Main results.Calculated stopping power differences between ICRU and Geant4-DNA decreased from 33.78% to 6.9%. The CSDA range difference decreased from 621% to 34% when compared against SRIM calculations. Geant4-DNA/TOPAS calculated dose mean lineal energy differed by 128% from the previous Monte Carlo. Ionization cluster size frequency distributions for Li ions differed by 76%-344.11% for 21 keV and 2 MeV respectively. With a decrease in theN1within 9% at 10 keV and agreeing after the 100 keV. With the new set of cross-sections being able to better simulate low energy behaviors of Li ions.Significance.This work shows an increase in detail gained from the use of a more complete set of low energy cross-sections which include charge exchange processes. Significant differences to previous simulation results were found at the microdosimetric and nanodosimetric scales that suggest that Li ions cause less ionizations per path length traveled but with more energy deposits. Microdosimetry results suggest that the BNC's contribution to cellular death may be mainly due to alpha particle production when boron-based drugs are distributed in the cellular membrane and beyond and by Li when it is at the cell cytoplasm regions.

Nanodosimetric quantity-weighted dose optimization for carbon-ion treatment planning

Dose verification of treatment plans is an essential step in radiotherapy workflows. In this work, we propose a novel method of treatment planning based on nanodosimetric quantity-weighted dose (NQWD), which could realize biological representation using pure physical quantities for biological-oriented carbon ion-beam treatment plans and their direct verification. The relationship between nanodosimetric quantities and relative biological effectiveness (RBE) was studied with the linear least-squares method for carbon-ion radiation fields. Next, under the framework of the matRad treatment planning platform, NQWD was optimized using the existing RBE-weighted dose (RWD) optimization algorithm. The schemes of NQWD-based treatment planning were compared with the RWD treatment plans in term of the microdosimetric kinetic model (MKM). The results showed that the nanodosimetric quantity F3 - 10 had a good correlation with the radiobiological effect reflected by the relationship between RBE and F3 - 10. Moreover, the NQWD-based treatment plans reproduced the RWD plans generally. Therefore, F3 - 10 could be adopted as a radiation quality descriptor for carbon-ion treatment planning. The novel method proposed herein not only might be helpful for rapid physical verification of biological-oriented ion-beam treatment plans with the development of experimental nanodosimetry, but also makes the direct comparison of ion-beam treatment plans in different institutions possible. Thus, our proposed method might be potentially developed to be a new strategy for carbon-ion treatment planning and improve patient safety for carbon-ion radiotherapy.

Primary study of the relative and compound biological effectiveness model for boron neutron capture therapy based on nanodosimetry

BACKGROUND

The current radiobiological model employed for boron neutron capture therapy (BNCT) treatment planning, which relies on microdosimetry, fails to provide an accurate representation the biological effects of BNCT. The precision in calculating the relative biological effectiveness (RBE) and compound biological effectiveness (CBE) plays a pivotal role in determining the therapeutic efficacy of BNCT. Therefore, this study focuses on how to improve the accuracy of the biological effects of BNCT.

PURPOSE

The purpose of this study is to propose new radiation biology models based on nanodosimetry to accurately assess RBE and CBE for BNCT.

METHODS

Nanodosimetry, rooted in ionization cluster size distributions (ICSD), introduces a novel approach to characterize radiation quality by effectively delineating RBE through the ion track structure at the nanoscale. In the context of prior research, this study presents a computational model for the nanoscale assessment of RBE and CBE. We establish a simplified model of DNA chromatin fiber using the Monte Carlo code TOPAS-nBio to evaluate the applicability of ICSD to BNCT and compute nanodosimetric parameters.

RESULTS

Our investigation reveals that both homogeneous and heterogeneous nanodosimetric parameters, as well as the corresponding biological model coefficients α and β, along with RBE values, exhibit variations in response to varying intracellular 10B concentrations. Notably, the nanodosimetric parameterM 1 C 2 $M_1^{{{\mathrm{C}}}_2}$ effectively captures the fluctuations in model coefficients α and RBE.

CONCLUSION

Our model facilitates a nanoscale analysis of BNCT, enabling predictions of nanodosimetric quantities for secondary ions as well as RBE, CBE, and other essential biological metrics related to the distribution of boron. This contribution significantly enhances the precision of RBE calculations and holds substantial promise for future applications in treatment planning.

Ionization detail parameters and cluster dose: a mathematical model for selection of nanodosimetric quantities for use in treatment planning in charged particle radiotherapy

Objective. To propose a mathematical model for applying ionization detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP).Approach. Our model provides for selection of preferred ID parameters (Ip) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopicIpand macroscopic RTP. Selection ofIpis demonstrated using published cell survival measurements for protons through argon, comparing results for nineteenIp:Nk,k= 2, 3, …, 10, the number of ionizations in clusters ofkor more per particle, andFk,k= 1, 2, …, 10, the number of clusters ofkor more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation.Main results. The preferredIpwereN4andF5for aerobic cells,N5andF7for hypoxic cells. Significant differences were found in cell survival for beams having the same LET or the preferredNk. Conversely, there was no significant difference forF5for aerobic cells andF7for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for theseIphad the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert thatIpexist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation.Significance. Our model provides a practical means to select preferredIpfrom radiobiological data, and to convertIpto the macroscopic cluster dose for particle RTP.

GEANT4-DNA simulation of temperature-dependent and pH-dependent yields of chemical radiolytic species

Objective.GEANT4-DNA can simulate radiation chemical yield (G-value) for radiolytic species such as the hydrated electron (eaq-) with the independent reaction times (IRT) method, however, only at room temperature and neutral pH. This work aims to modify the GEANT4-DNA source code to enable the calculation ofG-values for radiolytic species at different temperatures and pH values.Approach.In the GEANT4-DNA source code, values of chemical parameters such as reaction rate constant, diffusion coefficient, Onsager radius, and water density were replaced by corresponding temperature-dependent polynomials. The initial concentration of hydrogen ion (H+)/hydronium ion (H3O+) was scaled for a desired pH using the relationship pH = -log10[H+]. To validate our modifications, two sets of simulations were performed. (A) A water cube with 1.0 km sides and a pH of 7 was irradiated with an isotropic electron source of 1 MeV. The end time was 1μs. The temperatures varied from 25 °C to 150 °C. (B) The same setup as (A) was used, however, the temperature was set to 25 °C while the pH varied from 5 to 9. The results were compared with published experimental and simulated work.Main results.The IRT method in GEANT4-DNA was successfully modified to simulateG-values for radiolytic species at different temperatures and pH values. Our temperature-dependent results agreed with experimental data within 0.64%-9.79%, and with simulated data within 3.52%-12.47%. The pH-dependent results agreed well with experimental data within 0.52% to 3.19% except at a pH of 5 (15.99%) and with simulated data within 4.40%-5.53%. The uncertainties were below ±0.20%. Overall our results agreed better with experimental than simulation data.Significance.Modifications in the GEANT4-DNA code enabled the calculation ofG-values for radiolytic species at different temperatures and pH values.

Track Structure of Light Ions: The Link to Radiobiology

It is generally recognized that the biological response to irradiation by light ions is initiated by complex damages at the DNA level. In turn, the occurrence of complex DNA damages is related to spatial and temporal distribution of ionization and excitation events, i.e., the particle track structure. It is the aim of the present study to investigate the correlation between the distribution of ionizations at the nanometric scale and the probability to induce biological damage. By means of Monte Carlo track structure simulations, the mean ionization yield M1 and the cumulative probabilities F1, F2, and F3 of at least one, two and three ionizations, respectively, were calculated in spherical volumes of water-equivalent diameters equal to 1, 2, 5 and 10 nm. When plotted as a function of M1, the quantities F1, F2 and F3 are distributed along almost unique curves, largely independent of particle type and velocity. However, the shape of the curves depends on the size of the sensitive volume. When the site size is 1 nm, biological cross sections are strongly correlated to combined probabilities of F2 and F3 calculated in the spherical volume, and the proportionality factor is the saturation value of biological cross sections.

Application of a simple DNA damage model developed for electrons to proton irradiation

Proton beam therapy allows irradiating tumor volumes with reduced side effects on normal tissues with respect to conventional x-ray radiotherapy. Biological effects such as cell killing after proton beam irradiations depend on the proton kinetic energy, which is intrinsically related to early DNA damage induction. As such, DNA damage estimation based on Monte Carlo simulations is a research topic of worldwide interest. Such simulation is a mean of investigating the mechanisms of DNA strand break formations. However, past modellings considering chemical processes and DNA structures require long calculation times. Particle and heavy ion transport system (PHITS) is one of the general-purpose Monte Carlo codes that can simulate track structure of protons, meanwhile cannot handle radical dynamics simulation in liquid water. It also includes a simple model enabling the efficient estimation of DNA damage yields only from the spatial distribution of ionizations and excitations without DNA geometry, which was originally developed for electron track-structure simulations. In this study, we investigated the potential application of the model to protons without any modification. The yields of single-strand breaks, double-strand breaks (DSBs) and the complex DSBs were assessed as functions of the proton kinetic energy. The PHITS-based estimation showed that the DSB yields increased as the linear energy transfer (LET) increased, and reproduced the experimental and simulated yields of various DNA damage types induced by protons with LET up to about 30 keV μm−1. These results suggest that the current DNA damage model implemented in PHITS is sufficient for estimating DNA lesion yields induced after protons irradiation except at very low energies (below 1 MeV). This model contributes to evaluating early biological impacts in radiation therapy.

Applications of nanodosimetry in particle therapy planning and beyond

This topical review summarizes underlying concepts of nanodosimetry. It describes the development and current status of nanodosimetric detector technology. It also gives an overview of Monte Carlo track structure simulations that can provide nanodosimetric parameters for treatment planning of proton and ion therapy. Classical and modern radiobiological assays that can be used to demonstrate the relationship between the frequency and complexity of DNA lesion clusters and nanodosimetric parameters are reviewed. At the end of the review, existing approaches of treatment planning based on relative biological effectiveness (RBE) models or dose-averaged linear energy transfer are contrasted with an RBE-independent approach based on nandosimetric parameters. Beyond treatment planning, nanodosimetry is also expected to have applications and give new insights into radiation protection dosimetry.

Geant4-DNA modeling of nanodosimetric quantities in the Jet Counter for alpha particles

The purpose of this work was to validate the calculation accuracy of nanodosimetric quantities in Geant4-DNA track structure simulation code. We implemented the Jet Counter (JC) nanodosimeter geometry in the simulation platform and quantified the impact of the Geant4-DNA physics models and JC detector performance on the ionization cluster size distributions (ICSD). ICSD parameters characterize the quality of radiation field and are supposed to be correlated to the complexity of the initial DNA damage in nanoscale and eventually the response of biological systems to radiation. We compared Monte Carlo simulations of ICSD in JC geometry performed using Geant4-DNA and PTra codes with experimental data collected for alpha particles at 3.8 MeV. We investigated the impact of simulation and experimental settings, i.e., three Geant4-DNA physics models, three sizes of a nanometer sensitive volume, gas to water density scaling procedure, JC ion extraction efficiency and the presence of passive components of the detector on the ICSD and their parameters. We found that ICSD in JC geometry obtained from Geant4-DNA simulations in water correspond well to ICSD measurements in nitrogen gas for all investigated settings, while the best agreement is for Geant4-DNA physics option 4. This work also discusses the accuracy and robustness of ICSD parameters in the context of the application of track structure simulation methods for treatment planning in particle therapy.

First measurements of ionization cluster-size distributions with a compact nanodosimeter

PURPOSE

A nanodosimeter is a type of detector which measures single ionizations in a small gaseous volume in order to obtain ionization cluster size probability distributions for characterization of radiation types. Working nanodosimeter detectors are usually bulky machines which require a lot of space. In this work, the authors present a compact ceramic nanodosimeter detector and report on first measurements of cluster size distributions of 5 MeV alpha particles.

METHODS

Single ionization measurements are achieved by applying a weak electric field to collect positive ions in a hole in a ceramic plate. Inside the ceramic plate, due to a strong electric field, the ions are accelerated and produce impact-ionizations. The resulting electron avalanche is detected in a read-out electrode. A Bayesian unfolding algorithm is then applied to the experimentally obtained cluster size distributions to reconstruct the true cluster size distributions.

RESULTS

Experimentally obtained cluster size distributions by the compact nanodosimeter detector are presented. The reconstructed cluster size distributions agreed well with Monte Carlo simulated cluster size distributions for small volumes (diameter = 2.5 nm). For larger volumes, discrepancies between the reconstructed cluster size distributions and cluster size distributions from Monte Carlo simulations were observed.

CONCLUSIONS

For the first time, ionization cluster size probability distributions could be obtained by a small and compact nanodosimeter detector. This signifies the achievement of a critical step toward the wide application of nanodosimetric characterization of radiation types including in clinical environments.

Independent reaction times method in Geant4-DNA: Implementation and performance

PURPOSE

The simulation of individual particle tracks and the chemical stage following water radiolysis in biological tissue is an effective means of improving our knowledge of the physico-chemical contribution to the biological effect of ionizing radiation. However, the step-by-step simulation of the reaction kinetics of radiolytic species is the most time-consuming task in Monte Carlo track-structure simulations, with long simulation times that are an impediment to research. In this work, we present the implementation of the independent reaction times (IRT) method in Geant4-DNA Monte Carlo toolkit to improve the computational efficiency of calculating G-values, defined as the number of chemical species created or lost per 100 eV of deposited energy.

METHODS

The computational efficiency of IRT, as implemented, is compared to that from available Geant4-DNA step-by-step simulations for electrons, protons and alpha particles covering a wide range of linear energy transfer (LET). The accuracy of both methods is verified using published measured data from fast electron irradiations for ^• OH and e aq - for time-dependent G-values. For IRT, simulations in the presence of scavengers irradiated by cobalt-60 γ-ray and 2 MeV protons are compared with measured data for different scavenging capacities. In addition, a qualitative assessment comparing measured LET-dependent G-values with Geant4-DNA calculations in pure liquid water is presented.

RESULTS

The IRT improved the computational efficiency by three orders of magnitude relative to the step-by-step method while differences in G-values by 3.9% at 1 μs were found. At 7 ps, ^• OH and e aq - yields calculated with IRT differed from recent published measured data by 5% ± 4% and 2% ± 4%, respectively. At 1 μs, differences were 9% ± 5% and 6% ± 7% for ^• OH and e aq - , respectively. Uncertainties are one standard deviation. Finally, G-values at different scavenging capacities and LET-dependent G-values reproduced the behavior of measurements for all radiation qualities.

CONCLUSION

The comprehensive validation of the Geant4-DNA capabilities to accurately simulate the chemistry following water radiolysis is an ongoing work. The implementation presented in this work is a necessary step to facilitate performing such a task.

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.

Nanodosimetric quantities and RBE of a clinically relevant carbon-ion beam

PURPOSE

Although carbon-ion therapy is becoming increasingly attractive to the treatment of tumors, details about the ionization pattern formed by therapeutic carbon-ion beam in tissue have not been fully investigated. In this work, systematic calculations for the nanodosimetric quantities and relative biological effectiveness (RBE) of a clinically relevant carbon-ion beam were studied for the first time.

METHODS

The method combining both track structure and condensed history Monte Carlo (MC) simulations was adopted to calculate the nanodosimetric quantities. Fragments and energy spectra at different positions of the radiation field of a clinically relevant carbon-ion pencil beam were generated by means of MC simulations in water. Nanodosimetric quantities such as mean ionization cluster size ( M 1 ), the first moment of conditional cluster size ( M 1 C 2 ), cumulative probability ( F 2 ), and conditional cumulative probability ( F 3 C 2 ) at these positions were then acquired based on the spectra and the pre-calculated nanodosimetric database created by track structure MC simulations. What's more, a novel approach to calculate RBE based on the said nanodosimetric quantities was introduced. The RBE calculations were then conducted for the carbon-ion beam at different water-equivalent depths.

RESULTS

Lateral distributions at various water-equivalent depths of both the nanodosimetric quantities and RBE values were obtained. The values of M 1 , M 1 C 2 , F 2 , and F 3 C 2 were 1.49, 2.67, 0.30, and 0.38 at the plateau at the beam central axis and maximized at 2.79, 5.69, 0.47, and 0.68 at the depths around the Bragg peak, respectively. At a given depth, M 1 and F 2 decreased laterally with increasing the distance to the beam central axis while M 1 C 2 and F 3 C 2 remained nearly unchanged at first and then decreased except for M 1 C 2 at the rising edge of the Bragg peak. The calculated RBE values were 1.07 at the plateau and 3.13 around the Bragg peak. Good agreement between the calculated RBE values and experimental data was obtained.

CONCLUSIONS

Different nanodosimetric quantities feature the track structure of therapeutic carbon-ion beam in different manners. Detailed ionization patterns generated by carbon-ion beam could be characterized by nanodosimetric quantities. Moreover the combined method adopted in this work to calculate nanodosimetric quantities is not only valid but also convenient. Nanodosimetric quantities are significantly helpful for the RBE calculations in carbon-ion therapy.

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.