Parameterising microdosimetric distributions of mono-energetic proton beams for fast estimates of y D and y*

Track Structure Components: Characterizing Energy Deposited in Spherical Cells from Direct and Peripheral HZE Ion Hits

To understand the biological effects of radiation, it is important to determine how ionizing radiation deposits energy in micrometric targets. The energy deposited in a target located in an irradiated tissue is a function of several factors such as the radiation type and the irradiated volume size. We simulated the energy deposited by energetic ions in spherical targets of 1, 2, 4, and 8 µm radii encompassed in irradiated parallelepiped volumes of various sizes using the stochastic radiation track structure code Relativistic Ion Tracks (RITRACKS). Because cells are usually part of a tissue when they are irradiated, electrons originating from radiation tracks in neighboring volumes also contribute to energy deposition in the target. To account for this contribution, we used periodic boundary conditions in the simulations. We found that the single-ion spectra of energy deposition in targets comprises two components: the direct ion hits to the targets, which is identical in all irradiation conditions, and the contribution of hits from electrons from neighboring volumes, which depends on the irradiated volume. We also calculated an analytical expression of the indirect hit contributions using the local effect model, which showed results similar to those obtained with RITRACKS.

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.

Microdosimetric measurements as a tool to assess potential in-field and out-of-field toxicity regions in proton therapy

Relative biological effectiveness (RBE) variations are thought to be one of the primary causes of unexpected normal-tissue toxicities during tumor treatments with charged particles. Unlike carbon therapy, where treatment planning is optimized on the basis of the RBE-weighted dose, a constant RBE value of 1.1 is currently used in proton therapy. Assuming a uniform value can lead to under- or over-dosage, not just to the tumor but also to surrounding normal tissue. RBE changes have been linked with dose/fraction, the biological endpoint and beam properties. Understanding radiation quality and the associated RBE can improve the prediction of normal-tissue toxicities. In this study, we exploited microdosimetry for characterizing radiation quality in proton therapy in-field, and off-beam at 20 (beam edge), 50 (close out-of-field) and 100 (far out-of-field) mm from the beam center. We measured the lineal energy y spectra in a water phantom irradiated with 152 MeV protons, from which beam quality as well as the physical dose could be obtained. Taking advantage of the linear quadratic model and a modified version of the microdosimetric kinetic model, the microdosimetric data were combined with radiobiological parameters (α and β) of human salivary gland tumor cells for assessing cell survival RBE and RBE-weighted dose. The results indicate that if a dose of 60 Gy is delivered to the peak, the beam edge receives up to 6 Gy while the close and far out-of-field regions receive doses on the order of 10^-3 Gy and 10^-4 Gy, respectively. The RBE estimate in-beam shows large variations, ranging from 1.0 ± 0.2 at the entrance channel to 2.51 ± 0.15 at the tail. The beam edge follows a similar trend but the RBE calculated at the Bragg peak depth is 2.27 ± 0.17, i.e. twice the RBE in-beam (1.05 ± 0.15). Out-of-field, the estimated RBE is always significantly higher than 1.1 and increases with increasing lateral distance, reaching the overall highest value of 3.4 ± 0.3 at a depth of 206 mm and a lateral distance of 10 mm. The combination of RBE and dose into the biological dose points to the beam edge and the end-of-range in-beam as the areas with the highest risk of potential toxicities.

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.