Microdosimetric Measurements and Estimation of Human Cell Survival for Heavy-Ion Beams

Analysis of the Influence of Boron Distribution on Compound Biological Effectiveness Values in Boron Neutron Capture Therapy

PURPOSE

Boron neutron capture therapy (BNCT) is an innovative cancer treatment that uses the 10B(n,α)7Li reaction to selectively destroy cancer cells at the cellular level. In BNCT, the biological effectiveness of boron doses is typically assessed using the compound biological effectiveness (CBE) factor. This study analyzes the impact of boron distribution on CBE values based on the microdosimetric kinetic model and Monte Carlo simulations.

METHODS AND MATERIALS

Simulations were conducted on both macroscopic and microscopic scales. At the macroscopic level, the average dose absorbed by cells within tissues was modeled, whereas at the microscopic level, the microdosimetric lineal energy spectra and the microscopic dose absorbed by cell nuclei were simulated. The CBE values for various cells during BNCT were then derived from the Monte Carlo simulation data.

RESULTS

Results indicate that although macroscopic boron concentrations had no significant impact on CBE values, the distribution of boron at the cellular level played a crucial role; CBE values increased as boron moved closer to the cell nucleus.

CONCLUSIONS

This study proposes a method for calculating CBE values using Monte Carlo simulations, providing insights for evaluating CBE values and developing novel boron agents for BNCT.

Extending TOPAS with an analytical microdosimetric function: application and benchmarking with nBio track structure simulations

Microdosimetric distributions are important to accurately describe the biological impact of ionizing radiation, particularly in ion therapy. The computational demands of track structure simulations, a gold standard for modeling microscopic energy deposition, limit their practicality for large-scale or clinical applications. The analytical microdosimetric function (AMF) is a computationally efficient function that reproduces track structure simulation results. First introduced in the particle and heavy ion transport code system Monte Carlo code in 2006 and updated in 2023, the AMF offers a promising alternative for calculating microdosimetric spectra. This study implements the AMF within the Geant4-based Tool for Particle Therapy (TOPAS) platform, enabling efficient calculation of microdosimetric spectra and radiobiological metrics, including dose-mean lineal energy (y¯D) and relative biological effectiveness (RBE) using clinically relevant models, including the modified microdosimetric kinetic model and Mayo Clinic Florida MKM. Using OpenTOPAS (v4.0.0), the AMF extension was benchmarked against TOPAS-nBio track structure simulations for ions relevant to radiotherapy and space applications (1H,4He,7Li,12C,16O,20Ne,40Ar,56Fe). AMF results were further compared with TOPAS-nBio at different depths within the mixed radiation field of a carbon spread-out Bragg peak (SOBP). The AMF extension demonstrated reasonable agreement with TOPAS-nBio track structure simulations for most ions and energies. Microdosimetric spectra and derived metrics,y¯Dand RBE, showed average discrepancies under 10% for most cases. Deviations were largely attributed to differences in Monte Carlo stopping power models and ionization cross-sections. In an SOBP, the RBE calculated using TOPAS-nBio and AMF consistently agreed within 5%. Additionally, the AMF achieved significant computational efficiency, reducing simulation times by over 98% compared to TOPAS-nBio at discrete depths in an SOBP. The AMF extension in TOPAS provides a computationally efficient alternative to track structure simulations for microdosimetric analysis and RBE modeling. Its integration with advanced RBE models enables rapid, accurate calculations critical for particle therapy research and clinical treatment planning.

A biological optimization method for carbon therapy via iterative Jacobian-based linearization

Objective.Carbon ion radiotherapy (CIRT) can provide higher biological effectiveness and cause more damage to cancer cells compared to photon or proton radiotherapy, especially for radio-resistant tumors. The optimization of biological dose is essential for CIRT, to achieve the desirable tumoricidal dose while mitigating biological damage to normal tissues and organs at risk (OAR). However, the biological optimization for CIRT is mathematically challenging, due to the nonlinear nature of biological dose model, which can lead to computational inaccuracy and inefficiency. This work will develop an accurate and efficient biological optimization method for CIRT.Approach.The proposed method is called iterative Jacobian-based linearization (IJL). In IJL, the biological dose is modeled as the product of the physical dose and relative biological effect, which is based on the linear-quadratic model via the local effect model in this work, and the optimization objective consists of dose-volume histogram based biological dose objectives within clinical target volume and OAR. The optimization algorithm for IJL is through iterative convex relaxation, in which the nonlinear biological dose is iteratively linearized using Jacobian-based approximations and the linear subproblems are solved using alternating direction method of multipliers. To compare with IJL, the limited-memory quasi-Newton (QN) method (limited-memory version) is developed that directly solves the same nonlinear biological optimization problem.Main results.Compared to the QN, IJL demonstrated superior plan accuracy, e.g. better OAR sparing with the reduction of biological dose in the CTV-surrounding volume (PTV1cm) to 89.7%, 95.0%, 88.3% for brain, lung, and abdomen, respectively; IJL also had higher computational efficiency, with approximately 1/10 the computational time per iteration and continuously decreasing objectives (while being stagnated for QN after certain number of iterations).Significance.A novel optimization algorithm, IJL, incorporating iterative linearization of biological dose, is proposed to accurately and efficiently solve the biological optimization problem for CIRT. It demonstrates superior plan accuracy and computational efficiency compared to the direct nonlinear QN optimization method.

Impact of nuclear fragmentation and irradiation scenarios on the dose-averaged LET, the RBE, and their relationship for H, He, C, O, and Ne ions

BACKGROUND

Projectile and target fragmentation are nuclear phenomena that can influence the computation of the linear energy transfer (LET) and the relative biological effectiveness (RBE) in external radiotherapy with accelerated ions. Correlations between these two quantities are routinely established during radiobiological experiments to interpret the results and to develop and calibrate RBE models.

PURPOSE

This study systematically evaluates the impact of secondary fragments and irradiation scenarios on the dose-averaged LET, the RBE, and their correlation in the case of exposures to clinically relevant ion beams.

METHODS

57 600 microdosimetric lineal energy spectra and corresponding LET distributions were simulated with the Monte Carlo code PHITS across different scenarios, including track segment calculations, pristine, and spread-out Bragg peaks of 1H, 4He, 12C, 16O, and 20Ne ions within water phantoms. The LET distributions were analyzed to calculate the dose-average LET, both including or excluding the contribution of secondary ions of an element different from the primary beam. Similarly, the lineal energy distributions were processed in conjunction with the Mayo Clinic Florida microdosimetric kinetic model to compute the RBE for two theoretical cell lines (α/β = 2 and 10 Gy in the case of 6 MV x-rays). Correlations between the RBE and dose-averaged LET were established by analyzing the simulation results within water phantoms and then compared to the corresponding trends from the track segment calculations.

RESULTS

Excluding secondary fragments had a pronounced impact on the dose-averaged LET and the RBE, particularly in the entrance regions of proton beams and close to the distal edge of heavier ions. The correlations between the RBE and the dose-averaged LET were not universal, but highly dependent on the irradiation scenario. For proton beams only, the dose-averaged LET of hydrogen ions served as a practical first-order descriptor of the RBE. Track segment simulations, commonly used for calibrating and benchmarking RBE models, provided a reasonable approximation for low-energy beams but failed to fully capture the complexity of polyenergetic radiation fields.

CONCLUSIONS

Secondary fragments can substantially affect the dose-averaged LET and the RBE, even in proton beams. The dose-averaged LET, including or not the contributions from secondary fragments, was generally unable to adequately capture RBE variations across different scenarios. A more comprehensive approach, considering microdosimetric distributions, is necessary to accurately describe RBE variations in ion therapy.

A library of proton lineal energy spectra spanning the full range of clinically relevant energies

PURPOSE

In locations where the proton energy spectrum is broad, lineal energy spectrum-based proton biological effects models may be more accurate than dose-averaged linear energy transfer (LETd) based models. However, the development of microdosimetric spectrum-based biological effects models is hampered by the extreme computational difficulty of calculating microdosimetric spectra. Given a precomputed library of lineal energy spectra for monoenergetic protons, a weighted summation can be performed which yields the lineal energy spectrum of an arbitrary polyenergetic beam. Using this approach, lineal energy spectra can be rapidly calculated on a voxel-by-voxel level.

ACQUISITION AND VALIDATION METHODS

Monoenergetic proton tracks generated using Geant4-DNA were imported into SuperTrack, a GPU-accelerated software for calculation of microdosimetric spectra. Libraries of proton lineal energy spectra which span the energy range of 0-300 MeV were computed. The libraries were validated by comparison to Monte Carlo calculations in the literature, as well as lineal energy spectra measured experimentally with a tissue equivalent proportional counter.

DATA FORMAT AND USAGE NOTES

The lineal energy libraries have been made available in three data formats, two are plain-text, .csv and .les, and one binary encoded, root. Library files include the lineal energy bin abscissa in keV per micron and the unnormalized number of counts occurring within that bin. A computational technique for summation of the library files to yield the lineal energy of a polyenergetic beam is described in this work.

POTENTIAL APPLICATIONS

The lineal energy libraries can be used to rapidly determine the lineal energy spectra at the location of cell cultures for in-vitro experiments and in each voxel of a treatment plan for in-vivo outcome modelling. These libraries have already been incorporated into RayStation 2023B-IonPG for lineal energy spectra calculation and we anticipate they will be incorporated into further dose calculation engines and Monte Carlo toolkits.

Symbolic Regression: A Versatile Approach for Constructing Phenomenological Models of Radiobiological Effects

The development of quantitative models that correlate physical, chemical, and biological parameters with radiobiological effects is imperative in the domains of radiotherapy and radiation protection. Due to the challenges associated with quantifying underlying mechanisms, phenomenological models are frequently established in preference to mechanistic models. However, the lack of a universal methodology for constructing phenomenological models presents a significant challenge in the field. We employ symbolic regression as a method for constructing phenomenological models. We attempt to develop models for the survival fraction, microdosimetric parameters, the radiation oxygen effect, and the FLASH effect. Additionally, we compare the results obtained from our symbolic regression approach with existing formulas in the scientific literature to assess the efficacy and validity of our method. Symbolic regression yields multiple simple formulas for each modeling task undertaken. These formulas demonstrate a comparable ability to predict radiobiological effects as the formulas presented in previous scientific publications. Our findings propose that symbolic regression is an automated and flexible strategy for constructing phenomenological models of radiobiological effects. Additionally, they underscore that the interpretability of a model is as crucial as its goodness of fit, as symbolic regression can identify various distinct formulas that adequately fit the provided data points.

Heavy Ion Particle Therapy in Modern Day Radiation Oncology

Heavy ion radiotherapy is an emerging technology for treating radioresistant solid tumors. Unlike current low-linear energy transfer techniques, heavy ion radiotherapy, such as carbon ion radiotherapy, enhances the biologic effects related to cancer therapy. Prospective clinical evidence has demonstrated feasibility and efficacy in several disease sites, including head and neck, thoracic, central nervous system, gastrointestinal, pelvic tumors, and sarcomas. Although presently unavailable in the Americas, Mayo Clinic is constructing a heavy ion facility in the United States that is planned for clinical operation in 2028.

Investigation of factors related to treatment planning of x-ray SBRT and scanning carbon-ion radiation therapy for early-stage lung cancer patients

This study aimed to compare the treatment plans of x-ray SBRT and scanning carbon ion radiation therapy (CIRT) for localized lung tumors, and to evaluate the dose dependence of tumor size tumor-to-heart distance. For phantom verification, we used a chest phantom with a spherical simulated tumor. Treatment plans for 3-dimensional conformal radiation therapy (3D-CRT), volumetric modulated arc therapy (VMAT), and CIRT were created. GTVs were created in sizes ranging from 0.5 to 5 cm in diameter, and the dependence of the lung dose on GTV diameter was evaluated for each treatment plan. For patient validation, 30 cases of localized lung tumors were analyzed. 3D-CRT, VMAT, and CIRT treatment plans were developed, and DVH parameters were evaluated for each GTV size and GTV-to-heart distance. In both phantom and patient validations, the OAR doses were the lowest for CIRT. The lung dose increased with increasing GTV diameter for all three treatment plans. CIRT had the smallest ratio of lung dose increase to GTV diameter increase among the three treatment plans. Heart dose in CIRT was independent of GTV size and GTV-to-heart distance Conclusions: The results of the present study suggested that the use of scanning CIRT can reduce the OAR dose while guaranteeing the tumor dose compared to x-ray SBRT. In addition, it was suggested that CIRT can treat patients with large GTV sizes while maintaining low lung and heart dose.

Establishment of a practical methodology for evaluating equieffective dose of individual patients based on RT-PHITS

BACKGROUND

The RadioTherapy package based on PHITS (RT-PHITS) is an individual dosimetry system applicable to both targeted radionuclide therapy (TRT) and external radiotherapy. This study aims to establish a practical methodology for evaluating both absorbed doses and equieffective doses (EQDX) by improving RT-PHITS.

METHODS

We developed an Excel-based program, ExPORT-PHITS, which simplifies the conversion of the dose rates of specific organs and tumors calculated by RT-PHITS into corresponding absorbed doses and EQDX. ExPORT-PHITS offers two options for evaluating EQDX, each adopting a different type of microdosimetric kinetic model, to assess its dependence. The performance of the improved RT-PHITS, including ExPORT-PHITS, was evaluated using SPECT/CT images of two castration-resistant prostate cancer patients with bone metastases after the injection of 223RaCl2 and 99mTc-MDP.

RESULTS

Reasonable agreement was observed between absorbed doses calculated by RT-PHITS, IDAC Dose 2.1, and MIRDcalc, although absorbed doses in normal organs following the injection of 223RaCl2 were comparatively higher than those reported in other studies. Results for 223RaCl2 also showed that EQD2 tended to exceed the corresponding absorbed doses and RBE-weighted doses, while the relation was reversed for the injection of 99mTc-MDP.

CONCLUSIONS

These findings underscore RT-PHITS as a valuable tool for accurately modeling and optimizing individual TRT, especially for treatments involving α-ray emitters.

Rectal Gas-Induced Dose Changes in Carbon Ion Radiation Therapy for Prostate Cancer: An In Silico Study

PURPOSE

This study aims to determine dosimetric influence of rectal gas in carbon ion radiation therapy (CIRT) for prostate cancer and to establish a procedure for removal rectal gas in clinical scenarios.

MATERIALS AND METHODS

We analyzed 18 prostate cancer cases with bulky rectal gas. The dose distribution was recalculated on computed tomography (CT) with bulky rectal gas (gasCT) after creating the initial plan on a CT without bulky rectal gas, and the doses were transformed using a displacement vector field. This created a dose distribution simulation irradiated with the residual rectal gas. Among 12 fractions (fx) for prostate cancer CIRT, different residual rectal gas fx were used to develop 12 dose distributions, each of which was compared with that in the initial plan. Clinical target volume (Dmin, D99.5%), rectum, and rectal wall (V95%, V80%) parameters were assessed. We investigated the indicators associated with these dose changes using digital reconstruction radiograph (DRR) images.

RESULTS

The dosimetric changes in the clinical target volume were not significantly different from that in the initial treatment plan for both Dmin and D99.5%. Compared to the initial plan, the dose-volume histogram parameters showed changes exceeding 1 cm3 when residual rectal gas was present in the following number of fractions: 8 fx for V95% rectum, 5 fx for V80% rectum, 10 fx for V95% rectal wall, and 11 fx for V80% rectal wall. Changes in rectal and rectal wall parameters were highly correlated with the extent of rectal gas assessed on DRR images.

CONCLUSION

Rectal gas removal may not be necessary up to 4 fx. Moreover, indicators related to dose changes based on DRR images were highly correlated with dose changes, revealing the possibilities of estimating dose changes due to rectal gas from kV-x-ray images and using gas effect evaluation during CIRT irradiation.

In-vitroand microdosimetric study of proton boron capture therapy and neutron capture enhanced proton therapy

Objective.The clinical advantage of proton therapy, compared to other types of irradiations, lies in its reduced dose to normal tissue. Still, proton therapy faces challenges of normal tissue toxicity and radioresistant tumors. To combat these challenges, proton boron capture therapy (PBCT) and neutron capture enhanced particle therapy (NCEPT) were proposed to introduce high-LET radiation in the target volume.Approach. In this work, we performedin-vitroexperiments with a V79 cell line to validate PBCT and introduced a novel approach to use NCEPT in proton therapy. We quantified the effectiveness of PBCT and NCEPT with microdosimetric measurements, Monte-Carlo simulations and microdosimetric kinetic RBE model (MKM).Main results. No RBE increase was observed for PBCT. With the use of a tungsten spallation source, enough neutrons were generated in the incoming proton beam to measure significant neutron capture in the microdosimeter. However, no significant increase of RBE was detected when conventionalin vitroprotocol was followed. The resulting cell deactivation based RBE for NCEPT was found to be heavily dependent on which criteria was used to determine surviving colonies.Significance. PBCT and NCEPT are two proposed treatment modalities that may have the potential to expand the cases in which proton therapy can be beneficial. Understanding the scope of these treatment methods and developing measurement protocols to evaluate and understand their RBE impact are the first step to quantify their potential in clinical context.

Contribution of Nuclear Fragmentation to Dose and RBE in Carbon-Ion Radiotherapy

Variable relative biological effectiveness (RBE) of carbon radiotherapy may be calculated using several models, including the microdosimetric kinetic model (MKM), stochastic MKM (SMKM), repair-misrepair-fixation (RMF) model, and local effect model I (LEM), which have not been thoroughly compared. In this work, we compared how these four models handle carbon beam fragmentation, providing insight into where model differences arise. Monoenergetic and spread-out Bragg peak carbon beams incident on a water phantom were simulated using Monte Carlo. Using these beams, input parameters for each model (microdosimetric spectra, DNA double-strand break yield, kinetic energy spectra, physical dose fragment contributions) were calculated for each contributing carbon beam fragment (hydrogen, helium, lithium, beryllium, boron, secondary carbon, primary carbon, electrons, and "other"). Scored input parameters for each fragment were used to calculate linear (α) and quadratic (β) parameters according to each model, which were combined with reference α and β values and absorbed physical dose to calculate RBE. Contributions from secondary fragments were found to exceed 30% of the total physical dose. Using identical beam parameters, the four models produced not only different RBE values but also different RBE trends. In all models, RBE was highest for secondary carbon ions. Beyond secondary carbons, the RBE magnitude typically increased with the atomic number of the fragment, but RBE trends differed dramatically by model and beamline region (entrance, spread-out Bragg peak, and tail). Variations in fragment RBE were large enough to be apparent in biological dose predictions. This study demonstrated that fragmentation is a nonnegligible consideration in carbon radiotherapy. Our findings identified differences in RBE among specific fragments and the four models, contributing to variability in the total biological dose across models. Because these findings emphasize differences in how various models handle carbon beam fragments, greater care should be taken in characterization of secondary fragments in particle therapy.

Mapping neutron biological effectiveness for DNA damage induction as a function of incident energy and depth in a human sized phantom

We present new developments for an ab-initio model of the neutron relative biological effectiveness (RBE) in inducing specific classes of DNA damage. RBE is evaluated as a function of the incident neutron energy and of the depth inside a human-sized reference spherical phantom. The adopted mechanistic approach traces neutron RBE back to its origin, i.e. neutron physical interactions with biological tissues. To this aim, we combined the simulation of radiation transport through biological matter, performed with the Monte Carlo code PHITS, and the prediction of DNA damage using analytical formulas, which ground on a large database of biophysical radiation track structure simulations performed with the code PARTRAC. In particular, two classes of DNA damage were considered: sites and clusters of double-strand breaks (DSBs), which are known to be correlated with cell fate following radiation exposure. Within a coherent modelling framework, this approach tackles the variation of neutron RBE in a wide energy range, from thermal neutrons to neutrons of hundreds of GeV, and reproduces effects related to depth in the human-sized receptor, as well as to the receptor size itself. Besides providing a better mechanistic understanding of neutron biological effectiveness, the new model can support better-informed decisions for radiation protection: indeed, current neutron weighting (ICRP)/quality (U.S. NRC) factors might be insufficient for use in some radiation protection applications, because they do not account for depth. RBE predictions obtained with the reported model were successfully compared to the currently adopted radiation protection standards when the depth information is not relevant (at the shallowest depth in the phantom or for very high energy neutrons). However, our results demonstrate that great care is needed when applying weighting factors as a function of incident neutron energy only, not explicitly considering RBE variation in the target. Finally, to facilitate the use of our results, we propose look-up RBE tables, explicitly considering the depth variable, and an analytical representation of the maximal RBE vs. neutron energy.

Comparative study of a microdosimetric biological weighting function for RBE10modeling in particle therapy with a solid state SOI microdosimeter

Objective:the recently developed V79-RBE10biological weighting function (BWF) model is a simple and robust tool for a fast relative biological effectiveness (RBE) assessment for comparing different exposure conditions in particle therapy. In this study, the RBE10derived by this model (through the particle and heavy ion transport code system (PHITS) simulatedd(y)spectra) is compared with values of RBE10using experimentally derivedd(y)spectra from a silicon-on-insulator (SOI) microdosimeter.Approach:experimentally measuredd(y)spectra are used to calculate an RBE10value utilizing the V79-RBE10BWF model as well as the modified microdosimetric kinetic model (MKM) to produce an RBE10-vs-yDtrend for a wide range of ions. In addition, a beamline specific PHITS simulation was conducted which replicated the exact experimental conditions that were used with the SOI microdosimeter at the heavy ion medical accelerator in Chiba biological beamline with12C ions.Main Results:the RBE10-vs-yDtrend for1H,4He,7Li,12C,14N,16O,20Ne,28Si,56Fe, and124Xe ions is examined with good agreement found between the SOI microdosimeter derived RBE10values with the V79-RBE10BWF model and MKM, as well as the PHITS simulations for1H,4He,7Li,12C,16O, and56Fe ions while some discrepancies were seen for14N,20Ne, and28Si ions. Deviations have been attributed to the difference in the derivation of thed(y) spectra based on the different methods utilized. Good agreement was found betweenyDvalues and an over estimation was observed for RBE10values for the beamline specific simulation of the12Cion beam.Significance:overall, this study shows that the SOI microdosimeter is a valuable tool that can be utilized for quick and accurate experimental derivation of thed(y) spectra, which can then be convoluted with the weighting function of the V79-RBE10BWF model to derive RBE10. The SOI microdosimeter is able to derive experimental values ofyDand RBE10for various ions in any irradiation condition utilizing other radiobiological models.

Prediction of normal tissue complication probability for rat spinal cord tolerance following ion irradiations

Objective.Currently, treatment planning in cancer hadrontherapy relies on dose-volume criteria and physical quantities constraints. However, incorporating biologically related models of tumor control probability and of normal tissue complication probability (NTCP) would help further minimizing adverse tissue reactions, and would allow achieving a more patient-specific strategy. The aim of this work was therefore the development of a mechanistic approach to predict NTCP for late tissue reactions following ion irradiation.Approach.A dataset on the tolerance of the rat spinal cord was considered, providing NTCP (for paresis of at least grade II) experimental data following irradiation by photons, protons, helium and carbon ions, under different fractionation schemes. The photon data were fit by a mechanistic NTCP model with four parameters, called Critical Element Model; this allowed fixing the two parameters that only depend on the tissue features. Afterwards, the two parameters depending on radiation quality were predicted by applying the BIophysical ANalysis of Cell death and chromosome Aberrations biophysical model, for each ion type and dose-averaged linear energy transfer value.Main results.The predicted NTCP curves for ion irradiation were tested against the ion experimental data, by Chi-Square andp-value calculations. The model passed a significance test at 1% for all the datasets, and 5% for 13 out of 16 datasets, thus showing a good predictive power. The Relative biological effectiveness (RBE) was also calculated and compared with the data for the endpoint of NTCP equal to 50%, and a considerable discrepancy with the commonly calculated RBE for cell survival was shown.Significance.This study highlights the importance of considering the endpoint of interest when computing the RBE, through the application of a NTCP model, and it represents a first step towards the development of an approach to improve treatment plan optimization in therapy. To this aim, the approach needs to be extended to other endpoints and to be applied to patients' data.

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.

Dose compensation for decreased biological effective dose due to intrafractional interruption during radiotherapy: integration with a commercial treatment planning system

Objective.While the biological effective dose (BED) has been used to estimate the damage to tumor cells in radiotherapy, BED does not consider intrafractional interruption (IFI) occurring during irradiation. We aim to develop a framework to evaluate the decrease in BED [ΔBED] and to create a plan compensating for the decrease by IFI.Approach.ΔBEDwas calculated using a model based on the microdosimetric kinetic model (MKM) for four brain tumor cases treated using a volumetric-modulated arc therapy. Four biologically compensated plans (BCPs) were created in the treatment planning system by a single-time optimization using a base plan consideringΔBEDcreated in in-house software and optimization objectives for the original clinically delivered plan to achieve a homogeneous BED distribution within the planning target volume (PTV). The BED-volume histogram was evaluated for non-compensated plan and BCP with different timepoint of interruption, a percentage of gantry rotation angle (GRA) before interruption in planned GRA,ηand duration of interruptionτ. Characteristics of the dose accumulation were analyzed for different collimator angle sets, Plan A (10°, 85°) and Plan B (45° and 315°), for the first case.Main Results.Hot spots in theΔBEDdistribution forη= 25%, 50%, and 75% were observed at superior-and-interior ends, central region, and peripheral region in PTV, respectively. These behaviors could be understood by characteristics of the MKM-based model producing maximumΔBEDat 50% of the dose accumulation.ΔBED50%ranged 4.5%-6.6%, 5.0%-7.3%, and 5.3%-7.7% forτ= 60, 90, and 120 min, respectively. Plan A showed fast dose accumulation at superior and inferior edges while slow on peripheries in the lateral dose profile. Plan B showed more homogeneous PD distributions than Plan A during irradiation.Significance.The developed framework successfully evaluated and compensated for the decreased BED distribution.

LET-based approximation of the microdosimetric kinetic model for proton radiotherapy

BACKGROUND

Phenomenological relative biological effectiveness (RBE) models for proton therapy, based on the dose-averaged linear energy transfer (LET), have been developed to address the apparent RBE increase towards the end of the proton range. The results of these phenomenological models substantially differ due to varying empirical assumptions and fitting functions. In contrast, more theory-based approaches are used in carbon ion radiotherapy, such as the microdosimetric kinetic model (MKM). However, implementing microdosimetry-based models in LET-based proton therapy treatment planning systems poses challenges.

PURPOSE

This work presents a LET-based version of the MKM that is practical for clinical use in proton radiotherapy.

METHODS

At first, we derived an approximation of the Mayo Clinic Florida (MCF) MKM for relatively-sparsely ionizing radiation such as protons. The mathematical formalism of the proposed model is equivalent to the original MKM, but it maintains some key features of the MCF MKM, such as the determination of model parameters from measurable cell characteristics. Subsequently, we carried out Monte Carlo calculations with PHITS in different simulated scenarios to establish a heuristic correlation between microdosimetric quantities and the dose averaged LET of protons.

RESULTS

A simple allometric function was found able to describe the relationship between the dose-averaged LET of protons and the dose-mean lineal energy, which includes the contributions of secondary particles. The LET-based MKM was used to model the in vitro clonogenic survival RBE of five human and rodent cell lines (A549, AG01522, CHO, T98G, and U87) exposed to pristine and spread-out Bragg peak (SOBP) proton beams. The results of the LET-based MKM agree well with the biological data in a comparable or better way with respect to the other models included in the study. A sensitivity analysis on the model results was also performed.

CONCLUSIONS

The LET-based MKM integrates the predictive theoretical framework of the MCF MKM with a straightforward mathematical description of the RBE based on the dose-averaged LET, a physical quantity readily available in modern treatment planning systems for proton therapy.

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.

Incorporating boron distribution variations in microdosimetric kinetic model-based relative biological effectiveness calculations for boron neutron capture therapy

This study introduces the MKM_B model, an approach derived from the MKM model, designed to evaluate the biological effectiveness of Boron Neutron Capture Therapy (BNCT) in the face of challenges from varying microscopic boron distributions. The model introduces a boron compensation factor, allowing for the assessment of compound Biological Effectiveness (CBE) values for different boron distributions. Utilizing the TOPAS simulation platform, the lineal energy spectrum of particles in BNCT was simulated, and the sensitivity of the MKM_B model to parameter variations and the influence of cell size on the model were thoroughly investigated. The CBE values for 10B-boronphenylalanine (BPA) and 10B-sodium (BSH) were determined to be 3.70 and 1.75, respectively. These calculations were based on using the nucleus radius of 2.5 μm and the cell radius of 5 μm while considering a 50% surviving fraction. It was observed that as cell size decreased, the CBE values for both BPA and BSH increased. Additionally, the model parameter rd was identified as having the most significant impact on CBE, with other parameters showing moderate effects. The development of the MKM_B model enables the accurate prediction of CBE under different boron distributions in BNCT. This model offers a promising approach to optimize treatment planning by providing increased accuracy in biological effectiveness.

Linear Energy Transfer Measurements and Estimation of Relative Biological Effectiveness in Proton and Helium Ion Beams Using Fluorescent Nuclear Track Detectors

PURPOSE

Our objective was to develop a methodology for assessing the linear energy transfer (LET) and relative biological effectiveness (RBE) in clinical proton and helium ion beams using fluorescent nuclear track detectors (FNTDs).

METHODS AND MATERIALS

FNTDs were exposed behind solid water to proton and helium (4He) ion spread-out Bragg peaks. Detectors were imaged with a confocal microscope, and the LET spectra were derived from the fluorescence intensity. The track- and dose-averaged LET (LETF and LETD, respectively) were calculated from the LET spectra. LET measurements were used as input on RBE models to estimate the RBE. Human alveolar adenocarcinoma cells (A549) were exposed at the same positions as the FNTDs. The RBE was calculated from the resulting survival curves. All measurements were compared with Monte Carlo simulations.

RESULTS

For protons, average relative differences between measurements and simulations were 6% and 19% for LETF and LETD, respectively. For helium ions, the same differences were 11% for both quantities. The position of the experimental LET spectra primary peaks agreed with the simulations within 9% and 14% for protons and helium ions, respectively. For the RBE models using LETD as input, FNTD-based RBE values ranged from 1.02 ± 0.01 to 1.25 ± 0.04 and from 1.08 ± 0.09 to 2.68 ± 1.26 for protons and helium ions, respectively. The average relative differences between these values and simulations were 2% and 4%. For A549 cells, the RBE ranged from 1.05 ± 0.07 to 1.47 ± 0.09 and from 0.89 ± 0.06 to 3.28 ± 0.20 for protons and helium ions, respectively. Regarding the RBE-weighted dose (2.0 Gy at the spread-out Bragg peak), the differences between simulations and measurements were below 0.10 Gy.

CONCLUSIONS

This study demonstrates for the first time that FNTDs can be used to perform direct LET measurements and to estimate the RBE in clinical proton and helium ion beams.

Modelling Cellular Response to Ionizing Radiation: Mechanistic, Semi-Mechanistic, and Phenomenological Approaches - A Historical Perspective

Radiation research is a multidisciplinary field, and among its many branches, mathematical and computational modelers have played a significant role in advancing boundaries of knowledge. A fundamental contribution is modelling cellular response to ionizing radiation as that is the key to not only understanding how radiation can kill cancer cells, but also cause cancer and other health issues. The invention of microdosimetry in the 1950s by Harold Rossi paved the way for brilliant scientists to study the mechanism of radiation at cellular and sub-cellular scales. This paper reviews some snippets of ingenious mathematical and computational models published in microdosimetry symposium proceedings and publications of the radiation research community. Among these are simulations of radiation tracks at atomic and molecular levels using Monte Carlo methods, models of cell survival, quantification of the amount of energy required to create a single strand break, and models of DNA-damage-repair. These models can broadly be categorized into mechanistic, semi-mechanistic, and phenomenological approaches, and this review seeks to provide historical context of their development. We salute pioneers of the field and great teachers who supported and educated the younger members of the community and showed them how to build upon their work.

Correlation between dose-volume parameters and rectal bleeding after 12 fractions of carbon ion radiotherapy for prostate cancer

BACKGROUND

Carbon ion radiotherapy (CIRT) is currently used to treat prostate cancer. Rectal bleeding is a major cause of toxicity even with CIRT. However, to date, a correlation between the dose and volume parameters of the 12 fractions of CIRT for prostate cancer and rectal bleeding has not been shown. Similarly, the clinical risk factors for rectal bleeding were absent after 12 fractions of CIRT.

AIM

To identify the risk factors for rectal bleeding in 12 fractions of CIRT for prostate cancer.

METHODS

Among 259 patients who received 51.6 Gy [relative biological effectiveness (RBE)], in 12 fractions of CIRT, 15 had grade 1 (5.8%) and nine had grade 2 rectal bleeding (3.5%). The dose-volume parameters included the volume (cc) of the rectum irradiated with at least x Gy (RBE) (Vx) and the minimum dose in the most irradiated x cc normal rectal volume (Dx).

RESULTS

The mean values of D6cc, D2cc, V10 Gy (RBE), V20 Gy (RBE), V30 Gy (RBE), and V40 Gy (RBE) were significantly higher in the patients with rectal bleeding than in those without. The cutoff values were D6cc = 34.34 Gy (RBE), D2cc = 46.46 Gy (RBE), V10 Gy (RBE) = 9.85 cc, V20 Gy (RBE) = 7.00 cc, V30 Gy (RBE) = 6.91 cc, and V40 Gy (RBE) = 4.26 cc. The D2cc, V10 Gy (RBE), and V20 Gy (RBE) cutoff values were significant predictors of grade 2 rectal bleeding.

CONCLUSION

The above dose-volume parameters may serve as guidelines for preventing rectal bleeding after 12 fractions of CIRT for prostate cancer.

Evaluation of relative biological effectiveness for diseases of the circulatory system based on microdosimetry

In the next decade, the International Commission on Radiological Protection (ICRP) will issue the next set of general recommendations, for which evaluation of relative biological effectiveness (RBE) for various types of tissue reactions would be needed. ICRP has recently classified diseases of the circulatory system (DCS) as a tissue reaction, but has not recommended RBE for DCS. We therefore evaluated the mean and uncertainty of RBE for DCS by applying a microdosimetric kinetic model specialized for RBE estimation of tissue reactions. For this purpose, we analyzed several RBE data for DCS determined by past animal experiments and evaluated the radius of the subnuclear domain best fit to each experiment as a single free parameter included in the model. Our analysis suggested that RBE for DCS tends to be lower than that for skin reactions, and their difference was borderline significant due to large variances of the evaluated parameters. We also found that RBE for DCS following mono-energetic neutron irradiation of the human body is much lower than that for skin reactions, particularly at the thermal energy and around 1 MeV. This tendency is considered attributable not only to the intrinsic difference of neutron RBE between skin reactions and DCS but also to the difference in the contributions of secondary γ-rays to the total absorbed doses between their target organs. These findings will help determine RBE by ICRP for preventing tissue reactions.

Evaluation of the availability of single-position treatment with a rotating gantry and the validity of deformable image registration dose assessment for pancreatic cancer carbon-ion radiotherapy

BACKGROUND

This study aimed to evaluate the clinical acceptability of rotational gantry-based single-position carbon-ion radiotherapy (CIRT) to reduce the gastrointestinal (GI) dose in pancreatic cancer. We also evaluated the usefulness of the deformable image registration (DIR)-based dosimetry method for CIRT.

MATERIAL AND METHODS

Fifteen patients with pancreatic cancer were analyzed. The treatment plans were developed for four beam angles in the supine (SP plan) and prone (PR plan) positions. In the case of using multiple positions, the treatment plan was created with two angles for each of the supine and prone position (SP + PR plan). Dose evaluation for multiple positions was performed in two ways: by directly adding the values of the DVH parameters for each position treatment plan (DVH sum), and by calculating the DVH parameters from the accumulative dose distribution created using DIR (DIR sum). The D2cc and D6cc of the stomach and duodenum were recorded for each treatment plan and dosimetry method and compared.

RESULTS

There were no significant differences among any of the treatment planning and dosimetry methods (p > 0.05). The DVH parameters for the stomach and duodenum were higher in the PR plan and SP plan, respectively, and DVH sum tended to be between the SP and PR plans. DVH sum and DIR sum, DVH sum tended to be higher for D2cc and DIR sum tended to be higher for D6cc.

CONCLUSION

There were no significant differences in the GI dose, which suggests that treatment with a simple workflow performed in one position should be clinically acceptable. In CIRT, DIR-based dosimetry should be carefully considered because of the potential for increased uncertainty due to the steep dose distributions.

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.

A comparative study on the dose-effect of low-dose radiation based on microdosimetric analysis and single-cell sequencing technology

The biological mechanisms triggered by low-dose exposure still need to be explored in depth. In this study, the potential mechanisms of low-dose radiation when irradiating the BEAS-2B cell lines with a Cs-137 gamma-ray source were investigated through simulations and experiments. Monolayer cell population models were constructed for simulating and analyzing distributions of nucleus-specific energy within cell populations combined with the Monte Carlo method and microdosimetric analysis. Furthermore, the 10 × Genomics single-cell sequencing technology was employed to capture the heterogeneity of individual cell responses to low-dose radiation in the same irradiated sample. The numerical uncertainties can be found both in the specific energy distribution in microdosimetry and in differential gene expressions in radiation cytogenetics. Subsequently, the distribution of nucleus-specific energy was compared with the distribution of differential gene expressions to guide the selection of differential genes bioinformatics analysis. Dose inhomogeneity is pronounced at low doses, where an increase in dose corresponds to a decrease in the dispersion of cellular-specific energy distribution. Multiple screening of differential genes by microdosimetric features and statistical analysis indicate a number of potential pathways induced by low-dose exposure. It also provides a novel perspective on the selection of sensitive biomarkers that respond to low-dose radiation.

Biological dose optimization incorporating intra-tumoural cellular radiosensitivity heterogeneity in ion-beam therapy treatment planning

Objective.Treatment plans of ion-beam therapy have been made under an assumption that all cancer cells within a tumour equally respond to a given radiation dose. However, an intra-tumoural cellular radiosensitivity heterogeneity clearly exists, and it may lead to an overestimation of therapeutic effects of the radiation. The purpose of this study is to develop a biological model that can incorporate the radiosensitivity heterogeneity into biological optimization for ion-beam therapy treatment planning.Approach.The radiosensitivity heterogeneity was modeled as the variability of a cell-line specific parameter in the microdosimetric kinetic model following the gamma distribution. To validate the developed intra-tumoural-radiosensitivity-heterogeneity-incorporated microdosimetric kinetic (HMK) model, a treatment plan with H-ion beams was made for a chordoma case, assuming a radiosensitivity heterogeneous region within the tumour. To investigate the effects of the radiosensitivity heterogeneity on the biological effectiveness of H-, He-, C-, O-, and Ne-ion beams, the relative biological effectiveness (RBE)-weighted dose distributions were planned for a cuboid target with the stated ion beams without considering the heterogeneity. The planned dose distributions were then recalculated by taking the heterogeneity into account.Main results. The cell survival fraction and corresponding RBE-weighted dose were formulated based on the HMK model. The first derivative of the RBE-weighted dose distribution was also derived, which is needed for fast biological optimization. For the patient plan, the biological optimization increased the dose to the radiosensitivity heterogeneous region to compensate for the heterogeneity-induced reduction in biological effectiveness of the H-ion beams. The reduction in biological effectiveness due to the heterogeneity was pronounced for low linear energy transfer (LET) beams but moderate for high-LET beams. The RBE-weighted dose in the cuboid target decreased by 7.6% for the H-ion beam, while it decreased by just 1.4% for the Ne-ion beam.Significance.Optimal treatment plans that consider intra-tumoural cellular radiosensitivity heterogeneity can be devised using the HMK model.

Investigation of the Impact of Temporal Dose Delivery Patterns of Ion Irradiation with the Local Effect Model

We present an extension of the Local Effect Model (LEM) to include time-dose relationships for predicting effects of protracted and split-dose ion irradiation at arbitrary LET. With this kinetic extension, the spatial and temporal induction and processing of DNA double strand breaks (DSB) in cellular nuclei can be simulated for a wide range of ion radiation qualities, doses and dose rates. The key concept of the extension is based on the joint spatial and temporal coexistence of initial DSB, leading to the formation of clustered DNA damage on the µm scale (as defined e.g., by the size scale of Mbp chromatin loops), which is considered to have an increased cellular lethality as compared to isolated, single DSB. By simulating the time dependent induction and repair of DSB and scoring of isolated and clustered DSB upon irradiation, the impact of dose rate and split dose on the cell survival probability can be computed. In a first part of this work, we systematically analyze the predicted impact of protraction in dependence of factors like dose, LET, ion species and radiosensitivity as characterized by the photon LQ-parameters. We establish links to common concepts that describe dose rate effects for low LET radiation. We also compare the model predictions to experimental data and find agreement with the general trends observed in the experiments. The relevant concepts of our approach are compared to other models suitable for predicting time effects. We investigate an apparent analogy between spatial and temporal concentration of radiation delivery, both leading to increased effectiveness, and discuss similarities and differences between the general dependencies of these clustering effects on their impacting factors. Finally, we conclude that the findings give additional support for the general concept of the LEM, i.e. the characterization of high LET radiation effects based on the distinction of just two classes of DSB (isolated DSB and clustered DSB).

Sacral-Nerve-Sparing Planning Strategy in Pelvic Sarcomas/Chordomas Treated with Carbon-Ion Radiotherapy

To minimize radiation-induced lumbosacral neuropathy (RILSN), we employed sacral-nerve-sparing optimized carbon-ion therapy strategy (SNSo-CIRT) in treating 35 patients with pelvic sarcomas/chordomas. Plans were optimized using Local Effect Model-I (LEM-I), prescribed DRBE|LEM-I|D50% (median dose to HD-PTV) = 73.6 (70.4-76.8) Gy (RBE)/16 fractions. Sacral nerves were contoured between L5-S3 levels. DRBE|LEM-I to 5% of sacral nerves-to-spare (outside HD-CTV) (DRBE|LEM-I|D5%) were restricted to <69 Gy (RBE). The median follow-up was 25 months (range of 2-53). Three patients (9%) developed late RILSN (≥G3) after an average period of 8 months post-CIRT. The RILSN-free survival at 2 years was 91% (CI, 81-100). With SNSo-CIRT, DRBE|LEM-I|D5% for sacral nerves-to-spare = 66.9 ± 1.9 Gy (RBE), maintaining DRBE|LEM-I to 98% of HD-CTV (DRBE|LEM-I|D98%) = 70 ± 3.6 Gy (RBE). Two-year OS and LC were 100% and 93% (CI, 84-100), respectively. LETd and DRBE with modified-microdosimetric kinetic model (mMKM) were recomputed retrospectively. DRBE|LEM-I and DRBE|mMKM were similar, but DRBE-filtered-LETd was higher in sacral nerves-to-spare in patients with RILSN than those without. At DRBE|LEM-I cutoff = 64 Gy (RBE), 2-year RILSN-free survival was 100% in patients with <12% of sacral nerves-to-spare voxels receiving LETd > 55 keV/µm than 75% (CI, 54-100) in those with ≥12% of voxels (p < 0.05). DRBE-filtered-LETd holds promise for the SNSo-CIRT strategy but requires longer follow-up for validation.

Calculation of biological effectiveness of SOBP proton beams: a TOPAS Monte Carlo study

Objective.This study aims to investigate the biological effectiveness of Spread-Out Bragg-Peak (SOBP) proton beams with initial kinetic energies 50-250 MeV at different depths in water using TOPAS Monte Carlo code.Approach.The study modelled SOBP proton beams using TOPAS time feature. Various LET-based models and Repair-Misrepair-Fixation model were employed to calculate Relative Biological Effectiveness (RBE) for V79 cell lines at different on-axis depths based on TOPAS. Microdosimetric Kinetic Model and biological weighting function-based models, which utilize microdosimetric distributions, were also used to estimate the RBE. A phase-space-based method was adopted for calculating microdosimetric distributions.Main results.The trend of variation of RBE with depth is similar in all the RBE models, but the absolute RBE values vary based on the calculation models. RBE sharply increases at the distal edge of SOBP proton beams. In the entrance region of all the proton beams, RBE values at 4 Gy i.e. RBE(4 Gy) resulting from different models are in the range of 1.04-1.07, comparable to clinically used generic RBE of 1.1. Moving from the proximal to distal end of the SOBP, RBE(4 Gy) is in the range of 1.15-1.33, 1.13-1.21, 1.11-1.17, 1.13-1.18 and 1.17-1.21, respectively for 50, 100, 150, 200 and 250 MeV SOBP beams, whereas at the distal dose fall-off region, these values are 1.68, 1.53, 1.44, 1.42 and 1.40, respectively.Significance.The study emphasises application of depth-, dose- and energy- dependent RBE values in clinical application of proton beams.

Effects of cellular radioresponse on therapeutic helium-, carbon-, oxygen-, and neon-ion beams: a simulation study

Objective. Helium, oxygen, and neon ions in addition to carbon ions will be used for hypofractionated multi-ion therapy to maximize the therapeutic effectiveness of charged-particle therapy. To use new ions in cancer treatments based on the dose-fractionation protocols established in carbon-ion therapy, this study examined the cell-line-specific radioresponse to therapeutic helium-, oxygen-, and neon-ion beams within wide dose ranges.Approach. Response of cells to ions was described by the stochastic microdosimetric kinetic model. First, simulations were made for the irradiation of one-field spread-out Bragg peak beams in water with helium, carbon, oxygen, and neon ions to achieve uniform survival fractions at 37%, 10%, and 1% for human salivary gland tumor (HSG) cells, the reference cell line for the Japanese relative biological effectiveness weighted dose system, within the target region defined at depths from 90 to 150 mm. The HSG cells were then replaced by other cell lines with different radioresponses to evaluate differences in the biological dose distributions of each ion beam with respect to those of carbon-ion beams.Main results. For oxygen- and neon-ion beams, the biological dose distributions within the target region were almost equivalent to those of carbon-ion beams, differing by less than 5% in most cases. In contrast, for helium-ion beams, the biological dose distributions within the target region were largely different from those of carbon-ion beams, more than 10% in several cases.Significance.From the standpoint of tumor control evaluated by the clonogenic cell survival, this study suggests that the dose-fractionation protocols established in carbon-ion therapy could be reasonably applied to oxygen- and neon-ion beams while some modifications in dose prescription would be needed when the protocols are applied to helium-ion beams. This study bridges the gap between carbon-ion therapy and hypofractionated multi-ion therapy.

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.

Sensitivity of a mini-TEPC to radiation quality variations in clinical proton beams

PURPOSE

This work aims at studying the sensitivity of a miniaturized Tissue-Equivalent Proportional Counter to variations of beam quality in clinical radiation fields, to further investigate its performances as radiation quality monitor.

METHODS

Measurements were taken at the CATANA facility (INFN-LNS, Catania, Italy), in a monoenergetic and an energy-modulated proton beam with the same initial energy of 62 MeV. PMMA layers were placed in front of the detector to measure at different depths along the depth-dose profile. The frequency- and dose-mean lineal energy were compared to the track- and dose-averaged LET calculated by Monte Carlo simulations. A microdosimetric evaluation of the Relative Biological Effectiveness (RBE) was performed and compared with cell survival experiments.

RESULTS

Microdosimetric distributions measured at identical depths in the two beams show spectral differences reflecting their different radiation quality. Discrepancies are most evident at depths corresponding to the Spread-Out Bragg Peak, while spectra at the entrance and in the dose fall-off regions are similar. This can be explained by the different energy components that compose the pristine and spread-out peaks at each depth. The trend of microdosimetric mean values matches that of calculated LET averages along the entire penetration depth, and the microdosimetric estimation of RBE is consistent with radiobiological data not only at 2 Gy but also at lower dose levels, such as those absorbed by healthy tissues.

CONCLUSIONS

The mini-TEPC is sensitive to differences in radiation quality resulting from different modulations of the proton beam, confirming its potential for beam quality monitoring in proton therapy.

Exploring Helium Ions' Potential for Post-Mastectomy Left-Sided Breast Cancer Radiotherapy

Proton therapy presents a promising modality for treating left-sided breast cancer due to its unique dose distribution. Helium ions provide increased conformality thanks to a reduced lateral scattering. Consequently, the potential clinical benefit of both techniques was explored. An explorative treatment planning study involving ten patients, previously treated with VMAT (Volumetric Modulated Arc Therapy) for 50 Gy in 25 fractions for locally advanced, node-positive breast cancer, was carried out using proton pencil beam therapy with a fixed relative biological effectiveness (RBE) of 1.1 and helium therapy with a variable RBE described by the mMKM (modified microdosimetric kinetic model). Results indicated that target coverage was improved with particle therapy for both the clinical target volume and especially the internal mammary lymph nodes compared to VMAT. Median dose value analysis revealed that proton and helium plans provided lower dose on the left anterior descending artery (LAD), heart, lungs and right breast than VMAT. Notably, helium therapy exhibited improved ipsilateral lung sparing over protons. Employing NTCP models as available in the literature, helium therapy showed a lower probability of grade ≤ 2 radiation pneumonitis (22% for photons, 5% for protons and 2% for helium ions), while both proton and helium ions reduce the probability of major coronary events with respect to VMAT.

Modeling for predicting survival fraction of cells after ultra-high dose rate irradiation

Objective. FLASH radiotherapy (FLASH-RT) with ultra-high dose rate (UHDR) irradiation (i.e. > 40 Gy s-1) spares the function of normal tissues while preserving antitumor efficacy, known as the FLASH effect. The biological effects after conventional dose rate-radiotherapy (CONV-RT) with ≤0.1 Gy s-1have been well modeled by considering microdosimetry and DNA repair processes, meanwhile modeling of radiosensitivities under UHDR irradiation is insufficient. Here, we developed anintegrated microdosimetric-kinetic(IMK)model for UHDR-irradiationenabling the prediction of surviving fraction after UHDR irradiation.Approach.TheIMK model for UHDR-irradiationconsiders the initial DNA damage yields by the modification of indirect effects under UHDR compared to CONV dose rate. The developed model is based on the linear-quadratic (LQ) nature with the dose and dose square coefficients, considering the reduction of DNA damage yields as a function of dose rate.Main results.The estimate by the developed model could successfully reproduce thein vitroexperimental dose-response curve for various cell line types and dose rates.Significance.The developed model would be useful for predicting the biological effects under the UHDR irradiation.

Variable RBE in proton radiotherapy: a comparative study with the predictive Mayo Clinic Florida microdosimetric kinetic model and phenomenological models of cell survival

Objectives. (1) To examine to what extent the cell- and exposure- specific information neglected in the phenomenological proton relative biological effectiveness (RBE) models could influence the computed RBE in proton therapy. (2) To explore similarities and differences in the formalism and the results between the linear energy transfer (LET)-based phenomenological proton RBE models and the microdosimetry-based Mayo Clinic Florida microdosimetric kinetic model (MCF MKM). (3) To investigate how the relationship between the RBE and the dose-mean proton LET is affected by the proton energy spectrum and the secondary fragments.Approach. We systematically compared six selected phenomenological proton RBE models with the MCF MKM in track-segment simulations, monoenergetic proton beams in a water phantom, and two spread-out Bragg peaks. A representative comparison within vitrodata for human glioblastoma cells (U87 cell line) is also included.Main results. Marked differences were observed between the results of the phenomenological proton RBE models, as reported in previous studies. The dispersion of these models' results was found to be comparable to the spread in the MCF MKM results obtained by varying the cell-specific parameters neglected in the phenomenological models. Furthermore, while single cell-specific correlation between RBE and the dose-mean proton LET seems reasonable above 2 keVμm-1, caution is necessary at lower LET values due to the relevant contribution of secondary fragments. The comparison within vitrodata demonstrates comparable agreement between the MCF MKM predictions and the results of the phenomenological models.Significance. The study highlights the importance of considering cell-specific characteristics and detailed radiation quality information for accurate RBE calculations in proton therapy. Furthermore, these results provide confidence in the use of the MCF MKM for clonogenic survival RBE calculations in proton therapy, offering a more mechanistic approach compared to phenomenological models.

Microdosimetry-based investigation of biological effectiveness of252Cf brachytherapy source: TOPAS Monte Carlo study

Objective.To investigate biological effectiveness of252Cf brachytherapy source using Monte Carlo-calculated microdosimetric distributions.Approach.252Cf source capsule was placed at the center of the spherical water phantom and phase-space data were scored as a function of radial distance in water (R= 1-5 cm) using TOPAS Monte Carlo code. The phase-space data were used to calculate microdosimetric distributions at 1μm site size. Using these distributions, Relative Biological Effectiveness (RBE), mean quality factor (Q̅) and Oxygen Enhancement Ratio (OER) were calculated as a function ofR.Main results.The overall shapes of the microdosimetric distributions are comparable at all the radial distances in water. However, slight variation in the bin-wise yield is observed withR. RBE,Q̅and OER are insensitive to R over the range 1-5 cm. Microdosimetric kinetic model based RBE values are about 2.3 and 2.8 for HSG tumour cells and V79 cells, respectively, whereas biological weighting function-based RBE is about 2.8. ICRP 60 and ICRU 40 recommendation-basedQ̅values are about 14.5 and 16, respectively. Theory of dual radiation action based RBE is 11.4. The calculated value of OER is 1.6.Significance.This study demonstrates the relative insensitivity of RBE,Q̅and OER radially away from the252Cf source along the distances of 1-5 cm in water.

Planning Strategy to Optimize the Dose-Averaged LET Distribution in Large Pelvic Sarcomas/Chordomas Treated with Carbon-Ion Radiotherapy

To improve outcomes in large sarcomas/chordomas treated with CIRT, there has been recent interest in LET optimization. We evaluated 22 pelvic sarcoma/chordoma patients treated with CIRT [large: HD-CTV ≥ 250 cm3 (n = 9), small: HD-CTV < 250 cm3 (n = 13)], DRBE|LEM-I = 73.6 (70.4-73.6) Gy (RBE)/16 fractions, using the local effect model-I (LEM-I) optimization and modified-microdosimetric kinetic model (mMKM) recomputation. We observed that to improve high-LETd distribution in large tumors, at least 27 cm3 (low-LETd region) of HD-CTV should receive LETd of ≥33 keV/µm (p < 0.05). Hence, LETd optimization using 'distal patching' was explored in a treatment planning setting (not implemented clinically yet). Distal-patching structures were created to stop beams 1-2 cm beyond the HD-PTV-midplane. These plans were reoptimized and DRBE|LEM-I, DRBE|mMKM, and LETd were recomputed. Distal patching increased (a) LETd50% in HD-CTV (from 38 ± 3.4 keV/µm to 47 ± 8.1 keV/µm), (b) LETdmin in low-LETd regions of the HD-CTV (from 32 ± 2.3 keV/µm to 36.2 ± 3.6 keV/µm), (c) the GTV fraction receiving LETd of ≥50 keV/µm, (from <10% to >50%) and (d) the high-LETd component in the central region of the GTV, without significant compromise in DRBE distribution. However, distal patching is sensitive to setup/range uncertainties, and efforts to ascertain robustness are underway, before routine clinical implementation.

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections.

Evaluation of the Yield of DNA Double-Strand Breaks for Carbon Ions Using Monte Carlo Simulation and DNA Fragment Distribution

PURPOSE

The aim of this work was to provide a method to evaluate the yield of DNA double-strand breaks (DSBs) for carbon ions, overcoming the bias in existing methods due to the nonrandom distribution of DSBs.

METHODS AND MATERIALS

A previously established biophysical program based on the radiation track structure and a multilevel chromosome model was used to simulate DNA damage induced by x-rays and carbon ions. The fraction of activity retained (FAR) as a function of absorbed dose or particle fluence was obtained by counting the fraction of DNA fragments larger than 6 Mbp. Simulated FAR curves for the 250 kV x-rays and carbon ions at various energies were compared with measurements using constant-field gel electrophoresis. The doses or fluences at the FAR of 0.7 based on linear interpolation were used to estimate the simulation error for the production of DSBs.

RESULTS

The relative difference of doses at the FAR of 0.7 between simulation and experiment was -8.5% for the 250 kV x-rays. The relative differences of fluences at the FAR of 0.7 between simulations and experiments were -17.5%, -42.2%, -18.2%, -3.1%, 10.8%, and -14.5% for the 34, 65, 130, 217, 2232, and 3132 MeV carbon ions, respectively. In comparison, the measurement uncertainty was about 20%. Carbon ions produced remarkably more DSBs and DSB clusters per unit dose than x-rays. The yield of DSBs for carbon ions, ranging from 10 to 16 Gbp-1Gy-1, increased with linear energy transfer (LET) but plateaued in the high-LET end. The yield of DSB clusters first increased and then decreased with LET. This pattern was similar to the relative biological effectiveness for cell survival for heavy ions.

CONCLUSIONS

The estimated yields of DSBs for carbon ions increased from 10 Gbp-1Gy-1 in the low-LET end to 16 Gbp-1Gy-1 in the high-LET end with 20% uncertainty.

Extension of matRad with a modified microdosimetric kinetic model for carbon ion treatment planning: Comparison with Monte Carlo calculation

BACKGROUND

Treatment planning is essential for in silico particle therapy studies. matRad is an open-source research treatment planning system (TPS) based on the local effect model, which is a type of relative biological effectiveness (RBE) model.

PURPOSE

This study aims to implement a microdosimetric kinetic model (MKM) in matRad and develop an automation algorithm for Monte Carlo (MC) dose recalculation using the TOPAS code. In addition, we provide the developed MKM extension as open-source tool for users.

METHODS

Carbon beam data were generated using TOPAS MC pencil beam irradiation. We parameterized the TOPAS MC beam data with a double-Gaussian fit and modeled the integral depth doses and lateral spot profiles in the range of 100-430 MeV/u. To implement the MKM, the specific energy data table for Z = 1-6 and integrated depth-specific energy data were acquired based on the Kiefer-Chatterjee track structure and TOPAS MC simulation, respectively. Generic data were integrated into matRad, and treatment planning was performed based on these data. The optimized plan parameters were automatically converted into MC simulation input. Finally, the matRad TPS and TOPAS MC simulations were compared using the RBE-weighted dose calculation results. A comparison was made for three geometries: homogeneous water phantom, inhomogeneous phantom, and patient.

RESULTS

The RBE-weighted dose (DRBE ) distribution agreed with TOPAS MC within 1.8% for all target sizes for the homogeneous phantom. For the inhomogeneous phantom, the relative difference in the range of 80% of the prescription dose in the distal fall-off region (R80) between the matRad TPS and TOPAS MC was 0.6% (1.1 mm). DRBE between the TPS and the MC was within 4.0%. In the patient case, the difference in the dose-volume histogram parameters for the target volume between the TPS and the MC was less than 2.7%. The relative difference in R80 was 0.7% (1.2 mm).

CONCLUSIONS

The MKM was successfully implemented in matRad TPS, and the RBE-weighted dose was comparable to that of TOPAS MC. The MKM-implemented matRad was released as an open-source tool. Further investigations with MC simulations can be conducted using this tool, providing a good option for carbon ion research.

GPU-accelerated calculation of proton microdosimetric spectra as a function of target size, proton energy, and bounding volume size

Objective.Shortcomings of dose-averaged linear energy transfer (LETD), the quantity which is most commonly used to quantify proton relative biological effectiveness, have long been recognized. Microdosimetric spectra may overcome the limitations of LETDbut are extremely computationally demanding to calculate. A systematic library of lineal energy spectra for monoenergetic protons could enable rapid determination of microdosimetric spectra in a clinical environment. The objective of this work was to calculate and validate such a library of lineal energy spectra.Approach. SuperTrack, a GPU-accelerated CUDA/C++ based application, was developed to superimpose tracks calculated using Geant4 onto targets of interest and to compute microdosimetric spectra. Lineal energy spectra of protons with energies from 0.1 to 100 MeV were determined in spherical targets of diameters from 1 nm to 10μm and in bounding voxels with side lengths of 5μm and 3 mm.Main results.Compared to an analogous Geant4-based application, SuperTrack is up to 3500 times more computationally efficient if each track is resampled 1000 times. Dose spectra of lineal energy and dose-mean lineal energy calculated with SuperTrack were consistent with values published in the literature and with comparison to a Geant4 simulation. Using SuperTrack, we developed the largest known library of proton microdosimetric spectra as a function of primary proton energy, target size, and bounding volume size.Significance. SuperTrack greatly increases the computational efficiency of the calculation of microdosimetric spectra. The elevated lineal energy observed in a 3 mm side length bounding volume suggests that lineal energy spectra determined experimentally or computed in small bounding volumes may not be representative of the lineal energy spectra in voxels of a dose calculation grid. The library of lineal energy spectra calculated in this work could be integrated with a treatment planning system for rapid determination of lineal energy spectra in patient geometries.

Formulation of Time-Dependent Cell Survival with Saturable Repairability of Radiation Damage

This study aims to provide a model that compounds historically proposed ideas regarding cell survival irradiated with X rays or particles. The parameters used in this model have simple meanings and are closely related to cell death-related phenomena. The model is adaptable to a wide range of doses and dose rates and thus can consistently explain previously published cell survival data. The formulas of the model were derived by using five basic ideas: 1. "Poisson's law"; 2. "DNA affected damage"; 3. "repair"; 4. "clustered affected damage"; and 5. "saturation of reparability". The concept of affected damage is close to but not the same as the effect caused by the double-strand break (DSB). The parameters used in the formula are related to seven phenomena: 1. "linear coefficient of radiation dose"; 2. "probability of making affected damage"; 3. "cell-specific repairability", 4. "irreparable damage by adjacent affected damage"; 5. "recovery of temporally changed repairability"; 6. "recovery of simple damage which will make the affected damage"; 7. "cell division". By using the second parameter, this model includes cases where a single hit results in repairable-lethal and double-hit results in repairable-lethal. The fitting performance of the model for the experimental data was evaluated based on the Akaike information criterion, and practical results were obtained for the published experiments irradiated with a wide range of doses (up to several 10 Gy) and dose rates (0.17 Gy/h to 55.8 Gy/h). The direct association of parameters with cell death-related phenomena has made it possible to systematically fit survival data of different cell types and different radiation types by using crossover parameters.

A systematic analysis of the particle irradiation data ensemble in the key of the microdosimetric kinetic model: Should clonogenic data be used for clinical relative biological effectiveness?

PURPOSE

To perform a systematic analysis of the Particle Irradiation Data Ensemble (PIDE) database for clonogenic survival assays in the context of the Microdosimetric Kinetic Model (MKM).

METHODS AND MATERIAL

Our study used data from the PIDE database containing data on various cell lines and radiation types. Two main parameters of the MKM were determined experiment-wise: the domain radius, which accounts for the increase of the linear parameter as a function of LET or lineal energy, and the nucleus radius, which accounts for the overkilling effect at LET high enough. We used experiments with LET less and more than 75 keV/μm to determine domain and nucleus radius, respectively. Experiments with cells in asynchronous phase of the cell cycle and monoenergetic beams were considered, and data from 294 out of 461 available experiments with protons, alpha, and carbon beams were used.

RESULTS

Domain and nucleus radii were determined for 32 cell lines as the median among cell-specific experiments after filtering experiments using protons, α-particles, and carbon ions, including 28 human cells and 12 rodent cells. The median values found for domain radii were 380 nm for normal human cells, 390 nm for tumor human cells, 295 nm for normal rodent cells, and 525 nm for tumor rodent cells (only one experiment with rodent tumor cells) with large variability across cell lines and across experiments on each cell line.

CONCLUSIONS

Large inter-experiment variabilities were found for the same cell lines, based on enormous experimental uncertainties and different experimental conditions. Our analysis raises questions about how convenient is to use clonogenic data to feed RBE models to be utilized in the clinical practice in particle therapy.

Validation of robust radiobiological optimization algorithms based on the mixed beam model for intensity-modulated carbon-ion therapy

Currently, treatment planning systems (TPSs) that can compute the intensities of intensity-modulated carbon-ion therapy (IMCT) using scanned carbon-ion beams are limited. In the present study, the computational efficacy of the newly designed IMCT algorithms was analyzed for the first time based on the mixed beam model with respect to the physical and biological doses; moreover, the validity and effectiveness of the robust radiobiological optimization were verified. A dose calculation engine was independently generated to validate a clinical dose determined in the TPS. A biological assay was performed using the HSGc-C5 cell line to validate the calculated surviving fraction (SF). Both spot control (SC) and voxel-wise worst-case scenario (WC) algorithms were employed for robust radiobiological optimization followed by their application in a Radiation Therapy Oncology Group benchmark phantom under homogeneous and heterogeneous conditions and a clinical case for range and position errors. Importantly, for the first time, both SC and WC algorithms were implemented in the integrated TPS platform that can compute the intensities of IMCT using scanned carbon-ion beams for robust radiobiological optimization. For assessing the robustness, the difference between the maximum and minimum values of a dose-volume histogram index in the examined error scenarios was considered as a robustness index. The relative biological effectiveness (RBE) determined by the independent dose calculation engine exhibited a -0.6% difference compared with the RBE defined by the TPS at the isocenter, whereas the measured and the calculated SF were similar. Regardless of the objects, compared with the conventional IMCT, the robust radiobiological optimization enhanced the sensitivity of the examined error scenarios by up to 19% for the robustness index. The computational efficacy of the novel IMCT algorithms was verified according to the mixed beam model with respect to the physical and biological doses. The robust radiobiological optimizations lowered the impact of range and position uncertainties considerably in the examined scenarios. The robustness of the WC algorithm was more enhanced compared with that of the SC algorithm. Nevertheless, the SC algorithm can be used as an alternative to the WC IMCT algorithm with respect to the computational cost.

Event-by-event approach to the oxygen-effect-incorporated stochastic microdosimetric kinetic model for hypofractionated multi-ion therapy

An oxygen-effect-incorporated stochastic microdosimetric kinetic (OSMK) model was previously developed to estimate the survival fraction of cells exposed to charged-particle beams with wide dose and linear energy transfer (LET) ranges under various oxygen conditions. In the model, hypoxia-induced radioresistance was formulated based on the dose-averaged radiation quality. This approximation may cause inaccuracy in the estimation of the biological effectiveness of the radiation with wide variation in energy deposited to a sensitive volume per event, such as spread-out Bragg peak (SOBP) beams. The purpose of this study was to apply an alternative approach so as to consider the energy depositions on an event-by-event basis. The production probability of radiation-induced lesions per energy was formulated with oxygen partial pressure to account for the hypoxia-induced radioresistance. The reduction in the oxygen enhancement ratio for high-LET radiations was modeled by reducing the sensitive-volume size and increasing the saturation energy in microdosimetry. The modified OSMK model was tested against the reported survival data of three cell lines exposed to six species of ions with wide dose and LET ranges under aerobic and hypoxic conditions. The model reasonably reproduced the reported cell survival data. To evaluate the event-by-event approach, survival distributions of Chinese hamster ovary cells exposed to SOBP beams were estimated using the original and modified OSMK models. The differences in the estimated survival distributions between the models were marginal even under extreme hypoxia. The event-by-event approach improved the theoretical validity of the OSMK model. However, the original OSMK model can still provide an accurate estimation of the biological effectiveness of therapeutic radiations.

The complexity of DNA damage by radiation follows a Gamma distribution: insights from the Microdosimetric Gamma Model

Introduction

DNA damage is the main predictor of response to radiation therapy for cancer. Its Q8 quantification and characterization are paramount for treatment optimization, particularly in advanced modalities such as proton and alpha-targeted therapy.

Methods

We present a novel approach called the Microdosimetric Gamma Model (MGM) to address this important issue. The MGM uses the theory of microdosimetry, specifically the mean energy imparted to small sites, as a predictor of DNA damage properties. MGM provides the number of DNA damage sites and their complexity, which were determined using Monte Carlo simulations with the TOPAS-nBio toolkit for monoenergetic protons and alpha particles. Complexity was used together with a illustrative and simplistic repair model to depict the differences between high and low LET radiations.

Results

DNA damage complexity distributions were were found to follow a Gamma distribution for all monoenergetic particles studied. The MGM functions allowed to predict number of DNA damage sites and their complexity for particles not simulated with microdosimetric measurements (yF) in the range of those studied.

Discussion

Compared to current methods, MGM allows for the characterization of DNA damage induced by beams composed of multi-energy components distributed over any time configuration and spatial distribution. The output can be plugged into ad hoc repair models that can predict cell killing, protein recruitment at repair sites, chromosome aberrations, and other biological effects, as opposed to current models solely focusing on cell survival. These features are particularly important in targeted alpha-therapy, for which biological effects remain largely uncertain. The MGM provides a flexible framework to study the energy, time, and spatial aspects of ionizing radiation and offers an excellent tool for studying and optimizing the biological effects of these radiotherapy modalities.

Validation of the relative biological effectiveness of active-energy scanning carbon-ion radiotherapy on a commercial treatment planning system with a microdosimetic kinetic model

BACKGROUND

The study objective was to validate the relative biological effectiveness (RBE) calculated by the modified microdosimetric kinetic model in RayStation (Ray-MKM) for active-energy scanning carbon-ion radiotherapy.

METHODS

The Ray-MKM was benchmarked using a spread-out Bragg-peak (SOBP) plan, which was suggested in literature from the National Institute of Radiobiological Science (NIRS) in Japan. The residual RBE differences from the MKM at NIRS (NIRS-MKM) were derived using several SOBP plans with different ranges, SOBP widths, and prescriptions. To investigate the origins of the differences, we compared the saturation-corrected dose-mean specific energy [Formula: see text] of the aforementioned SOBPs. Furthermore, we converted the RBE-weighted doses with the Ray-MKM to those with local effect model I (LEM doses). The purpose was to investigate whether the Ray-MKM could reproduce the RBE-weighted conversion study.

RESULTS

The benchmark determined the value of the clinical dose scaling factor, [Formula: see text], as 2.40. The target mean RBE deviations between the Ray-MKM and NIRS-MKM were median: 0.6 (minimum: 0.0 to maximum: 1.69) %. The [Formula: see text] difference in-depth led to the RBE difference in-depth and was remarkable at the distal end. The converted LEM doses from the Ray-MKM doses were comparable (the deviation being - 1.8-0.7%) to existing literature.

CONCLUSION

This study validated the Ray-MKM based on our active-energy scanning carbon-ion beam via phantom studies. The Ray-MKM could generate similar RBEs as the NIRS-MKM after benchmarking. Analysis based on [Formula: see text] indicated that the different beam qualities and fragment spectra caused the RBE differences. Since the absolute dose differences at the distal end were small, we neglected them. Furthermore, each centre may determine its centre-specific [Formula: see text] based on this approach.

Creation, evolution, and future challenges of ion beam therapy from a medical physicist's viewpoint (Part 2). Chapter 2. Biophysical model, treatment planning system and image guided radiotherapy

When an ion beam penetrates deeply into the body, its kinetic energy decreases, and its biological effect increases due to the change of the beam quality. To give a uniform biological effect to the target, it is necessary to reduce the absorbed dose with the depth. A bio-physical model estimating the relationship between ion beam quality and biological effect is necessary to determine the relative biological effectiveness (RBE) of the ion beam that changes with depth. For this reason, Lawrence Berkeley Laboratory, National Institute of Radiological Sciences (NIRS) and GSI have each developed their own model at the starting of the ion beam therapy. Also, NIRS developed a new model at the starting of the scanning irradiation. Although the Local Effect Model (LEM) at the GSI and the modified Microdosimetric Kinetic Model (MKM) at the NIRS, the both are currently used, can similarly predict radiation quality-induced changes in surviving fraction of cultured cell, the clinical RBE-weighted doses for the same absorbed dose are different. This is because the LEM uses X-rays as a reference for clinical RBE, whereas the modified MKM uses carbon ion beam as a reference and multiplies it by a clinical factor of 2.41. Therefore, both are converted through the absorbed dose. In PART 2, I will describe the development of such a bio-physical model, as well as the birth and evolution of a treatment planning system and image guided radiotherapy.