Calculation of clinical dose distributions in proton therapy from microdosimetry

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.

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.

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.