Segment‐averaged LET concept and analytical calculation from microdosimetric quantities in proton radiation therapy

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.

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.

The relation between microdosimetry and induction of direct damage to DNA by alpha particles

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

A Critical Review of LET-Based Intensity-Modulated Proton Therapy Plan Evaluation and Optimization for Head and Neck Cancer Management

In this review article, we review the 3 important aspects of linear-energy-transfer (LET) in intensity-modulated proton therapy (IMPT) for head and neck (H&N) cancer management. Accurate LET calculation methods are essential for LET-guided plan evaluation and optimization, which can be calculated either by analytical methods or by Monte Carlo (MC) simulations. Recently, some new 3D analytical approaches to calculate LET accurately and efficiently have been proposed. On the other hand, several fast MC codes have also been developed to speed up the MC simulation by simplifying nonessential physics models and/or using the graphics processor unit (GPU)–acceleration approach. Some concepts related to LET are also briefly summarized including (1) dose-weighted versus fluence-weighted LET; (2) restricted versus unrestricted LET; and (3) microdosimetry versus macrodosimetry. LET-guided plan evaluation has been clinically done in some proton centers. Recently, more and more studies using patient outcomes as the biological endpoint have shown a positive correlation between high LET and adverse events sites, indicating the importance of LET-guided plan evaluation in proton clinics. Various LET-guided plan optimization methods have been proposed to generate proton plans to achieve biologically optimized IMPT plans. Different optimization frameworks were used, including 2-step optimization, 1-step optimization, and worst-case robust optimization. They either indirectly or directly optimize the LET distribution in patients while trying to maintain the same dose distribution and plan robustness. It is important to consider the impact of uncertainties in LET-guided optimization (ie, LET-guided robust optimization) in IMPT, since IMPT is sensitive to uncertainties including both the dose and LET distributions. We believe that the advancement of the LET-guided plan evaluation and optimization will help us exploit the unique biological characteristics of proton beams to improve the therapeutic ratio of IMPT to treat H&N and other cancers.

A systematic review on the usage of averaged LET in radiation biology for particle therapy

Linear Energy Transfer (LET) is widely used to express the radiation quality of ion beams, when characterizing the biological effectiveness. However, averaged LET may be defined in multiple ways, and the chosen definition may impact the resulting reported value. We review averaged LET definitions found in the literature, and quantify which impact using these various definitions have for different reference setups. We recorded the averaged LET definitions used in 354 publications quantifying the relative biological effectiveness (RBE) of hadronic beams, and investigated how these various definitions impact the reported averaged LET using a Monte Carlo particle transport code. We find that the kind of averaged LET being applied is, generally, poorly defined. Some definitions of averaged LET may influence the reported averaged LET values up to an order of magnitude. For publications involving protons, most applied dose averaged LET when reporting RBE. The absence of what target medium is used and what secondary particles are included further contributes to an ill-defined averaged LET. We also found evidence of inconsistent usage of averaged LET definitions when deriving LET-based RBE models. To conclude, due to commonly ill-defined averaged LET and to the inherent problems of LET-based RBE models, averaged LET may only be used as a coarse indicator of radiation quality. We propose a more rigorous way of reporting LET values, and suggest that ideally the entire particle fluence spectra should be recorded and provided for future RBE studies, from which any type of averaged LET (or other quantities) may be inferred.

Experimental validation of an analytical microdosimetric model based on Geant4-DNA simulations by using a silicon-based microdosimeter

PURPOSE

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

METHODS AND MATERIAL

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

RESULTS

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

CONCLUSION

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

Clinical implications of variable relative biological effectiveness in proton therapy for prostate cancer

PURPOSE

To study the potential consequences of differences in the evaluation of variable versus uniform relative biological effectiveness calculations in proton radiotherapy for prostate cancer.

METHODS AND MATERIAL

Experimental data with proton beams suggest that relative biological effectiveness increases with linear energy transfer. This relation also depends on the α / β ratio, characteristic of a tissue and a considered endpoint. Three phenomenological models (Carabe et al., Wedenberg et al. and McNamara et al.) are compared to a mechanistic model based on microdosimetry (microdosimetric kinetic model) and to the current assumption of uniform relative biological effectiveness equal to 1.1 in a prostate case.

RESULTS AND CONCLUSIONS

Phenomenological models clearly predict higher relative biological effectiveness values compared to microdosimetric kinetic model, that seems to approach to the constant value of 1.1 adopted in the clinics, at least for low linear energy transfer values achieved in typical prostate proton plans. All models predict a higher increase of the relative biological effectiveness-weighted dose for the prostate tumor than for the rest of structures involved due to its lower α / β ratio, even when linear energy transfer is, in general, lower in the tumor than on the surroundings tissues. Prostate cancer is, therefore, a good candidate to take advantage of variable relative biological effectiveness, especially if linear energy transfer is enhanced within the tumor. However, the discrepancies among models hinder the clinical implementation of variable relative biological effectiveness.

RBE for proton radiation therapy - a Nordic view in the international perspective

BACKGROUND

This paper presents an insight into the critical discussions and the current strategies of the Nordic countries for handling the variable proton relative biological effectiveness (RBE) as presented at The Nordic Collaborative Workshop for Particle Therapy that took place at the Skandion Clinic on 14th and 15th of November 2019.

MATERIAL AND METHODS

In the current clinical practice at the two proton centres in operation at the date, Skandion Clinic, and the Danish Centre for Particle Therapy, a constant proton RBE of 1.1 is applied. The potentially increased effectiveness at the end of the particle range is however considered at the stage of treatment planning at both places based on empirical observations and knowledge. More elaborated strategies to evaluate the plans and mitigate the problem are intensely investigated internationally as well at the two centres. They involve the calculation of the dose-averaged linear energy transfer (LET_d) values and the assessment of their distributions corroborated with the distribution of the dose and the location of the critical clinical structures.

RESULTS

Methods and tools for LET_d calculations are under different stages of development as well as models to account for the variation of the RBE with LET_d, dose per fraction, and type of tissue. The way they are currently used for evaluation and optimisation of the plans and their robustness are summarised. A critical but not exhaustive discussion of their potential future implementation in the clinical practice is also presented.

CONCLUSIONS

The need for collaboration between the clinical proton centres in establishing common platforms and perspectives for treatment planning evaluation and optimisation is highlighted as well as the need of close interaction with the research academic groups that could offer a complementary perspective and actively help developing methods and tools for clinical implementation of the more complex metrics for considering the variable effectiveness of the proton beams.

Radiobiological effectiveness difference of proton arc beams versus conventional proton and photon beams

This paper aims to demonstrate the difference in biological effectiveness of proton monoenergetic arc therapy (PMAT) compared to intensity modulated proton therapy (IMPT) and conventional 6 MV photon therapy, and to quantify this difference when exposing cells of different radiosensitivity to the same experimental conditions for each modality. V79, H1299 and H460 cells were cultured in petri dishes placed in the central axis of a cylindrical and homogeneous solid water phantom of 20 cm in diameter. For the PMAT plan, cells were exposed to 13 mono-energetic proton beams separated every 15° over a 180° arc, designed to deliver a uniform dose of higher LET to the petri dishes. For the IMPT plans, 3 fields were used, where each field was modulated to cover the full target. Cells were also exposed to 6 MV photon beams in petri dishes to characterize their radiosensitivity. The relative biological effectiveness of the PMAT plans compared with those of IMPT was measured using clonogenic assays. Similarly, in order to study the quantity and quality of the DNA damage induced by the PMAT plans compared to that of IMPT and photons, γ-H2AX assays were conducted to study the relative amount of DNA damage induced by each modality, and their repair rate over time. The clonogenic assay revealed similar survival levels to the same dose delivered with IMPT or x-rays. However, a systematic average of up to a 43% increase in effectiveness in PMAT plans was observed when compared with IMPT. In addition, the repair kinetic assays proved that PMAT induces larger and more complex DNA damage (evidenced by a slower repair rate and a larger proportion of unrepaired DNA damage) than IMPT. The repair kinetics of IMPT and 6 MV photon therapy were similar. Mono-energetic arc beams offer the possibility of taking advantage of the enhanced LET of proton beams to increase TCP. This study presents initial results based on exposing cells with different radiosensitivity to other modalities under the same experimental conditions, but more extensive clonogenic and in-vivo studies will be required to confirm the validity of these results.

Modelling Dose Effects from Space Irradiations: Combination of High-LET and Low-LET Radiations with a Modified Microdosimetric Kinetic Model

The Microdosimetric Kinetic Model (MKM) to predict the effects of ionizing radiation on cell colonies is studied and reformulated for the case of high-linear energy transfer (LET) radiations with a low dose. When the number of radiation events happening in a subnuclear domain follows a Poisson distribution, the MKM predicts a linear-quadratic (LQ) survival curve. We show that when few events occur, as for high-LET radiations at doses lower than the mean specific energy imparted to the nucleus, zF,n, a Poisson distribution can no longer be assumed and an initial pure linear relationship between dose and survival fraction should be observed. Predictions of survival curves for combinations of high-LET and low-LET radiations are produced under two assumptions for their comparison: independent and combined action. Survival curves from previously published articles of V79 cell colonies exposed to X-rays, α particles, Ar-ions, Fe-ions, Ne-ions and mixtures of X-rays and each one of the ions are predicted according to the modified MKM. We conclude that mixtures of high-LET and low-LET radiations may enhance the effect of individual actions due to the increase of events in domains provided by the low-LET radiation. This hypothesis is only partially validated by the analyzed experiments.

Proton monoenergetic arc therapy (PMAT) to enhance LETd within the target

We show the performance and feasibility of a proton arc technique so-called proton monoenergetic arc therapy (PMAT). Monoenergetic partial arcs are selected to place spots at the middle of a target and its potential to enhance the dose-averaged linear energy transfer (LETd) distribution within the target. Single-energy partial arcs in a single 360 degree gantry rotation are selected to deposit Bragg's peaks at the central part of the target to increase LETd values. An in-house inverse planning optimizer seeks for homogeneous doses at the target while keeping the dose to organs at risk (OARs) within constraints. The optimization consists of balancing the weights of spots coming out of selected partial arcs. A simple case of a cylindrical target in a phantom is shown to illustrate the method. Three different brain cancer cases are then considered to produce actual clinical plans, compared to those clinically used with pencil beam scanning (PBS). The relative biological effectiveness (RBE) is calculated according to the microdosimetric kinetic model (MKM). For the ideal case of a cylindrical target placed in a cylindrical phantom, the mean LETd in the target increases from 2.8 keV μm^-1 to 4.0 keV μm^-1 when comparing a three-field PBS plan with PMAT. This is replicated for clinical plans, increasing the mean RBE-weighted doses to the CTV by 3.1%, 1.7% and 2.5%, respectively, assuming an [Formula: see text] ratio equal to 10 Gy in the CTV. In parallel, LETd to OARs near the distal edge of the tumor decrease for all cases and metrics (mean LETd, L_D,2% and L_D,98%). The PMAT technique increases the LETd within the target, being feasible for the production of clinical plans meeting physical dosimetric requirements for both target and OARs. Thus, PMAT increases the RBE within the target, which may lead to a widening of the therapeutic index in proton radiotherapy that would be highlighted for low [Formula: see text] ratios and hyperfractionated schedules.

On the concepts of dose-mean lineal energy, unrestricted and restricted dose-averaged LET in proton therapy

To calculate 3D distributions of microdosimetric-based restricted dose-averaged LET (LETd) and dose-mean lineal energy ([Formula: see text]) in order to explore their similarities and differences between each other and with the traditional unrestricted LETd. Additionally, a new expression for optimum restricted LETd calculation is derived, allowing for disregarding straggling-associated functions in the classical microdosimetric theory. Restricted LETd and [Formula: see text] for polyenergetic beams can be obtained by integrating previously developed energy-dependent microdosimetric functions over the energetic spectrum of these beams. This calculation is extended to the entire calculation volume using an algorithm to determine spectral fluence. Equivalently, unrestricted LETd can be obtained integrating the stopping power curve on the spectrum. A new expression to calculate restricted LETd is also derived. Results for traditional and new formulas are compared for a clinical 100 MeV proton beam. Distributions of unrestricted LETd, restricted LETd and [Formula: see text] are analyzed for a prostate case, for microscopic spherical sites of 1 µm and 10 µm in diameter. Traditional and new expressions for restricted LETd remarkably agree, being the mean differences 0.05  ±  0.04 keV µm^-1 for the 1 µm site and 0.05  ±  0.02 keV µm^-1 for the 10 µm site. In the prostate case, the ratio between the maximum and the central value for central axis (CAX) profiles is around 2 for all the quantities, being the highest for restricted LETd for 1 µm (2.17) and the lowest for [Formula: see text] for 1 µm (1.78). Unrestricted LETd, restricted LETd and [Formula: see text] can be analytically computed and compared for clinical plans. Two important consequences of the calculation of [Formula: see text] are: (1) its distribution can be verified by directly measuring it in clinical beams; and (2), optimization of proton treatments based on these quantities is enabled as well as future developments of RBE models based on them.

A kernel-based algorithm for the spectral fluence of clinical proton beams to calculate dose-averaged LET and other dosimetric quantities of interest

PURPOSE

To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose-averaged LET (LETd) in proton radiotherapy.

MATERIAL AND METHODS

A kernel-based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results.

RESULTS

Considering the nine energies simulated, fits for the functions modeling the fluence in-depth provide an average R 2 equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average R 2 of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average R 2 of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of -0.007 ± 0.008 keV/μm with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/μm including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/μm.

CONCLUSION

This new spectral fluence-based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.

Validation of linear energy transfer computed in a Monte Carlo dose engine of a commercial treatment planning system

The relative biological effectiveness (RBE) of protons is highly variable and difficult to quantify. However, RBE is related to the local ionization density, which can be related to the physical measurable dose weighted linear energy transfer (LET_D). The aim of this study was to validate the LET_D calculations for proton therapy beams implemented in a commercially available treatment planning system (TPS) using microdosimetry measurements and independent LET_D calculations (Open-MCsquare (MCS)). The TPS (RayStation v6R) was used to generate treatment plans on the CIRS-731-HN anthropomorphic phantom for three anatomical sites (brain, nasopharynx, neck) for a spherical target (Ø  =  5 cm) with uniform target dose to calculate the LET_D distribution. Measurements were performed at the University Medical Center Groningen proton therapy center (Proteus Plus, IBA) using a µ ⁺-probe utilizing silicon on insulator microdosimeters capable of detecting lineal energies as low as 0.15 keV µm^-1 in tissue. Dose averaged mean lineal energy [Formula: see text] depth-profiles were measured for 70 and 130 MeV spots in water and for the three treatment plans in water and an anthropomorphic phantom. The [Formula: see text] measurements were compared to the LET_D calculated in the TPS and MCS independent dose calculation engine. D · [Formula: see text] was compared to D · LET_D in terms of a gamma-index with a distance-to-agreement criteria of 2 mm and increasing dose difference criteria to determine the criteria for which a 90% pass rate was accomplished. Measurements of D · [Formula: see text] were in good agreement with the D · LET_D calculated in the TPS and MCS. The 90% passing rate threshold was reached at different D · LET_D difference criteria for single spots (TPS: 1% MCS: 1%), treatment plans in water (TPS: 3% MCS: 6%) and treatment plans in an anthropomorphic phantom (TPS: 6% MCS: 1%). We conclude that D · LET_D calculations accuracy in the RayStation TPS and open MCSquare are within 6%, and sufficient for clinical D · LET_D evaluation and optimization. These findings remove an important obstacle in the road towards clinical implementation of D · LET_D evaluation and optimization of proton therapy treatment plans. Novelty and significance The dose weighed linear energy transfer (LET_D) distribution can be calculated for proton therapy treatment plans by Monte Carlo dose engines. The relative biological effectiveness (RBE) of protons is known to vary with the LET_D distribution. Therefore, there exists a need for accurate calculation of clinical LET_D distributions. Previous LET_D validations have focused on general purpose Monte Carlo dose engines which are typically not used clinically. We present the first validation of mean lineal energy [Formula: see text] measurements of the LET_D against calculations by the Monte Carlo dose engines of the Raystation treatment planning system and open MCSquare.