Dose-averaged LET calculation for proton track segments using microdosimetric Monte Carlo simulations.

There is an increasing interest in calculating linear energy transfer (LET) distributions for proton therapy treatments in order to assess the influence of this quantity in biological terms. Microdosimetric Monte Carlo (MC) simulations are useful tools to calculate dose-averaged LET, as this has been broadly proposed as the most adequate quantity to characterize these biological effects. However, a straightforward uniform sampling of the scoring site turns out to be computationally unaffordable. In contrast, some issues have been pointed out with the more efficient weighted sampling approach, frequently used in literature. Here, we address the issues associated with the latter method and propose adequate corrections to achieve reliable calculations of dose-averaged LET values from microdosimetry. Proton track structures have been simulated with Geant4-DNA considering two different approaches. One version employs a uniform sampling for placing the spherical site and is used as the reference. The other one uses a weighted sampling by considering the spatial distribution of transfer points. Some corrections are proposed for calculating a dose-averaged LET comparable to the reference case. An additional MC approach is proposed to obtain the weighted mean of the energy imparted per electronic collision of the proton within the site, the δ 2 function, related to the straggling distribution, as an intermediate step in the LET calculation. Energy imparted per event distributions are different when employing either sampling methods, due to the different geometrical randomness. We have found an agreement below (0.15 ± 0.05) keV/μm in the worst case for uniform and weighted methods in dose-averaged LET values when the weighted sampling results are corrected according to our proposal. Our analysis is restricted to spherical sites of 1 and 10 μm diameter and monoenergetic beams in the range from 2 to 90 MeV. This work shows a reliable and computational-efficient method to perform calculations of track segment dose-averaged LET using MC simulations for proton therapy beams, including the necessary considerations for obtaining the straggling distribution characteristics. The validity of this approach remains as long as the stopping power of the proton can be considered as constant along its track within the site.

Bertolet A ，Baratto-Roldán A ，Barbieri S ，Baiocco G ，Carabe A ，Cortés-Giraldo MA ... -  《-》

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

This work introduces the concept of segment-averaged linear energy transfer (LET) as a new approach to average distributions of LET of proton beams based on a revisiting of microdosimetry theory. The concept of segment-averaged LET is then used to generate an analytical model from Monte Carlo simulations data to perform fast and accurate calculations of LET distributions for proton beams. The distribution of energy imparted by a proton beam into a representative biological structure or site is influenced by the distributions of (a) LET, (b) segment length, which is the section of the proton track in the site, and (c) energy straggling of the proton beam. The distribution of LET is thus generated by the LET of each component of the beam in the site. However, the situation when the LET of each single proton varies appreciably along its path in the site is not defined. Therefore, a new distribution can be obtained if the particle track segment is decomposed into smaller portions in which LET is roughly constant. We have called "segment distribution" of LET the one generated by the contribution of each portion. The average of that distribution is called segment-averaged LET. This quantity is obtained in the microdosimetry theory from the average and standard deviation of the distributions of energy imparted to the site, segment length, and energy imparted per collision. All this information is calculated for protons of clinically relevant energies by means of Geant4-DNA microdosimetric simulations. Finally, a set of analytical functions is proposed for each one of the previous quantities. The presented model functions are fitted to data from Geant4-DNA simulations for monoenergetic beams from 100 keV to 100 MeV and for spherical sites of 1, 5, and 10 μm in diameter. The average differences along the considered energy range between calculations based on our analytical models and MC for segment-averaged dose-averaged restricted LET are -0.2 ± 0.7 keV/μm for the 1 μm case, 0.0 ± 0.9 keV/μm for the 5 μm case, and -0.3 ± 1.1 keV/μm for the 10 μm case, respectively. All average differences are below the average standard deviation (1σ) of the MC calculations. A new way of averaging LET for a proton beam is performed to incorporate the effects produced by the variation of stopping power of each individual proton along microscopic biological structures. An analytical model based on MC simulations allows for fast and accurate calculations of segment-averaged dose-averaged restricted LET for proton beams, which otherwise would need to be calculated from exhaustive MC simulations of clinical plans.

Bertolet A ，Baratto-Roldán A ，Cortés-Giraldo MA ，Carabe-Fernandez A ... -  《-》

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

Guan F ，Peeler C ，Bronk L ，Geng C ，Taleei R ，Randeniya S ，Ge S ，Mirkovic D ，Grosshans D ，Mohan R ，Titt U ... -  《-》

An analytical dose-averaged LET calculation algorithm considering the off-axis LET enhancement by secondary protons for spot-scanning proton therapy.

To evaluate the biological effects of proton beams as part of daily clinical routine, fast and accurate calculation of dose-averaged linear energy transfer (LETd ) is required. In this study, we have developed the analytical LETd calculation method based on the pencil-beam algorithm (PBA) considering the off-axis enhancement by secondary protons. This algorithm (PBA-dLET) was then validated using Monte Carlo simulation (MCS) results. In PBA-dLET, LET values were assigned separately for each individual dose kernel based on the PBA. For the dose kernel, we employed a triple Gaussian model which consists of the primary component (protons that undergo the multiple Coulomb scattering) and the halo component (protons that undergo inelastic, nonelastic and elastic nuclear reaction); the primary and halo components were represented by a single Gaussian and the sum of two Gaussian distributions, respectively. Although the previous analytical approaches assumed a constant LETd value for the lateral distribution of a pencil beam, the actual LETd increases away from the beam axis, because there are more scattered and therefore lower energy protons with higher stopping powers. To reflect this LETd behavior, we have assumed that the LETs of primary and halo components can take different values (LETp and LEThalo ), which vary only along the depth direction. The values of dual-LET kernels were determined such that the PBA-dLET reproduced the MCS-generated LETd distribution in both small and large fields. These values were generated at intervals of 1 mm in depth for 96 energies from 70.2 to 220 MeV and collected in the look-up table. Finally, we compared the LETd distributions and mean LETd (LETd,mean ) values of targets and organs at risk between PBA-dLET and MCS. Both homogeneous phantom and patient geometries (prostate, liver, and lung cases) were used to validate the present method. In the homogeneous phantom, the LETd profiles obtained by the dual-LET kernels agree well with the MCS results except for the low-dose region in the lateral penumbra, where the actual dose was below 10% of the maximum dose. In the patient geometry, the LETd profiles calculated with the developed method reproduces MCS with the similar accuracy as in the homogeneous phantom. The maximum differences in LETd,mean for each structure between the PBA-dLET and the MCS were 0.06 keV/μm in homogeneous phantoms and 0.08 keV/μm in patient geometries under all tested conditions, respectively. We confirmed that the dual-LET-kernel model well reproduced the MCS, not only in the homogeneous phantom but also in complex patient geometries. The accuracy of the LETd was largely improved from the single-LET-kernel model, especially at the lateral penumbra. The model is expected to be useful, especially for proper recognition of the risk of side effects when the target is next to critical organs.

Hirayama S ，Matsuura T ，Ueda H ，Fujii Y ，Fujii T ，Takao S ，Miyamoto N ，Shimizu S ，Fujimoto R ，Umegaki K ，Shirato H ... -  《-》

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

Bertolet A ，Cortés-Giraldo MA ，Carabe-Fernandez A 《-》