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

Microdosimetric characterization of a clinical proton therapy beam: comparison between simulated lineal energy distributions in spherical water targets and experimental measurements with a silicon detector

Objective Treatment planning based on computer simulations were proposed to account for the increase in the relative biological effectiveness (RBE) of proton radiotherapy beams near to the edges of the irradiated volume. Since silicon detectors could be used to validate the results of these simulations, it is important to explore the limitations of this comparison. Approach Microdosimetric measurements with a MicroPlus Bridge V2 silicon detector (thickness = 10 µm) were performed along the Bragg peak of a clinical proton beam. The lineal energy distributions, the dose mean values, and the RBE calculated with a biological weighting function were compared with simulations with PHITS (microdosimetric target = 1 µm water sphere), and published clonogenic survival in vitro RBE data for the V79 cell line. The effect of the silicon-to-water conversion was also investigated by comparing three different methodologies (conversion based on a single value, novel bin-to-bin conversions based on SRIM and PSTAR). Main results Mainly due to differences in the microdosimetric targets, the experimental dose-mean lineal energy and RBE values at the distal edge were respectively up to 53% and 28% lower than the simulated ones. Furthermore, the methodology chosen for the silicon-to-water conversion was proven to affect the dose mean lineal energy and the RBE10 up to 32% and 11% respectively. The best methodology to compensate for this underestimation was the bin-to-bin silicon-to-water conversion based on PSTAR. Significance This work represents the first comparison between PHITS-simulated lineal energy distributions in water targets and corresponding experimental spectra measured with silicon detectors. Furthermore, the effect of the silicon-to-water conversion on the RBE was explored for the first time. The proposed methodology based on the PSTAR bin-to-bin conversion appears to provide superior results with respect to commonly used single scaling factors and is recommended for future studies.

Correlation of LET With MRI Changes in Brain and Potential Implications for Normal Tissue Complication Probability for Patients With Meningioma Treated With Pencil Beam Scanning Proton Therapy

PURPOSE

This study aimed to investigate the correlation between imaging changes in brain normal tissue and the spatial distribution of linear energy transfer (LET) for a cohort of patients with meningioma treated with scanned proton beams. Then, assuming imaging changes are induced by cell lethality, we studied the correlation between normal tissue complication probability and LET.

METHODS AND MATERIALS

Magnetic resonance imaging T2/fluid attenuated inversion recovery acquired at different intervals after proton radiation were coregistered with the planning computed tomography (CT) images from 26 patients with meningioma with abnormalities after proton radiation therapy. For this purpose, the T2/fluid attenuated inversion recovery areas not on the original magnetic resonance images were contoured, and the LET values for each voxel in the patient geometry were calculated to investigate the correlation between the position of imaging changes and the LET at those positions. To separate the effect of the dose as the inductor of these changes, we compared the LET in these areas with a sample of voxels matching the dose distributions across the image change areas. Patients with a higher LET in image change areas were grouped to verify whether they shared common characteristics.

RESULTS

Eleven of the patients showed higher dose-averaged LET (LETd) in imaging change regions than in the group of voxels with the same dose. This group of patients had significantly shallower targets for their treatment than the other 15 and used fewer beams and angles.

CONCLUSIONS

This study points toward the possibility that areas with imaging change are more likely to occur in regions with high dose or in areas with lower dose but increased LETd. The effect of LETd on imaging changes seems to be more relevant when treating superficial lesions with few nonopposed beams. However, most patients did not show a spatial correlation between their image changes and the LETd values, limiting the cases for the possible role of high LET as a toxicity inductor.

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.

Microdosimetry of a therapeutic proton beam with a mini-TEPC and a MicroPlus-Bridge detector for RBE assessment

Proton beams are widely used worldwide to treat localized tumours, the lower entrance dose and no exit dose, thus sparing surrounding normal tissues, being the main advantage of this treatment modality compared to conventional photon techniques. Clinical proton beam therapy treatment planning is based on the use of a general relative biological effectiveness (RBE) of 1.1 along the whole beam penetration depth, without taking into account the documented increase in RBE at the end of the depth dose profile, in the Bragg peak and beyond. However, an inaccurate estimation of the RBE can cause both underdose or overdose, in particular it can cause the unfavourable situation of underdosing the tumour and overdosing the normal tissue just beyond the tumour, which limits the treatment success and increases the risk of complications. In view of a more precise dose delivery that takes into account the variation of RBE, experimental microdosimetry offers valuable tools for the quality assurance of LET or RBE-based treatment planning systems. The purpose of this work is to compare the response of two different microdosimetry systems: the mini-TEPC and the MicroPlus-Bridge detector. Microdosimetric spectra were measured across the 62 MeV spread out Bragg peak of CATANA with the mini-TEPC and with the Bridge microdosimeter. The frequency and dose distributions of lineal energy were compared and the different contributions to the spectra were analysed, discussing the effects of different site sizes and chord length distributions. The shape of the lineal energy distributions measured with the two detectors are markedly different, due to the different water-equivalent sizes of the sensitive volumes: 0.85 μm for the TEPC and 17.3 μm for the silicon detector. When the Loncol's biological weighting function is applied to calculate the microdosimetric assessment of the RBE, both detectors lead to results that are consistent with biological survival data for glioma U87 cells. Both the mini-TEPC and the MicroPlus-Bridge detector can be used to assess the RBE variation of a 62 MeV modulated proton beam along its penetration depth. The microdosimetric assessment of the RBE based on the Loncol's weighting function is in good agreement with radiobiological results when the 10% biological uncertainty is taken into account.

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.

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.