Implementation of the microdosimetric kinetic model using analytical microdosimetry in a treatment planning system for proton therapy.

PURPOSE: To implement RBE calculations in treatment planning systems based on the Microdosimetric Kinetic Model (MKM) upon analytical calculations of dose-mean lineal energy (yD). MKM relies on the patterns of energy deposition in sub-nuclear structures called domains, whose radii are cell-specific and need to be determined. METHODS AND MATERIAL: The radius of a domain (rd) can be determined from the linear-quadratic (LQ) curves from clonogenic experiments for different cell lines exposed to X-ray and proton beams with known yD. In this work, LQ parameters for two different human lung cell lines (H1299 and H460) are used, and yD among cells is calculated through an analytical algorithm. Once rd is determined, MKM-based calculations of RBE are implemented in a treatment planning system (TPS). Results are compared to those produced by phenomenological models of RBE, such as Carabe and McNamara. RESULTS: Differences between model-based predictions and experimentally determined RBE are analyzed for yD=5 keV/µm. For the H1299 line, mean differences in RBE are 0.13, -0.29 and -0.27 for our MKM-based calculation, Carabe and McNamara models, respectively. For the H460 line, differences become -0.044, -0.091 and -0.048, respectively. RBE is computed for these models in a simple plan, showing MKM the best agreement with the experimentally obtained RBE, keeping deviations below 0.08. CONCLUSIONS: Microdosimetry calculations at the TPS-level provide tools to improve predictions of RBE using the MKM with actual values of yD instead of LET. The radius of the characteristic domain needs to be determined to tailor the RBE prediction for each cell or tissue.

Organic generation of real-world real-time data for clinical evidence in radiation oncology.

PURPOSE: We introduce a system devoted to automatically produce structured data in radiotherapy to: (i) relate clinical outcomes with any variable; and (ii) optimize resources and procedures. METHODS AND MATERIAL: We have designed a detailed workflow for a patient to follow during radiotherapy treatments. Four elements of Oncology Information Systems (OISs) can be mainly interrelated in our system: (a) task lists to be accomplished by the staff; (b) forms to fill in at each step of the workflow; (c) generation of reports; and (d) a system to trigger new tasks, forms or reports when an needed, either automatically or manually. We handle the data dumped into reports with Visual Basic for Word code to store structured data for patients in electronic medical records (EMRs). These EMRs can be further analyzed, generating clinical real-world data in real time, i.e., at any step of the process. RESULTS: Our system was implemented about the beginning of 2019, producing a database filled with a pool of 1,184 patients in a year. Although one year is not long enough to produce statistically clinical outcomes, we show our results for cancer by anatomical location so far to meet the first goal stated above. With respect to the second goal, we here (1) show the distribution of times taken for the whole radiotherapy process divided by anatomical locations for, (2) study the fractionations schemes used throughout 2019, and (3) evaluate the number of missed sessions of treatment in our institution. Our system also leads to better communication among staff members, dramatically reducing misunderstandings because of the centralization of the information. CONCLUSIONS: We present an integrated customization of an OIS, yet adaptable to others, that makes possible an optimized performance of the department by driving an automatized paperless workflow; and allows for an automatized and effortless collection of structured data throughout the radiotherapy process.

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 for y ¯ F and y ¯ 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% for y ¯ F and 1.17% for y ¯ 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 clinical y ¯ D with our analytical method.

An Analytical Microdosimetric Model for Radioimmunotherapeutic Alpha Emitters.

In this work, we present a methodology to analytically determine microdosimetric quantities in radioimmunotherapy and targeted radiotherapy with alpha particles. Monte Carlo simulations using the Geant4-DNA toolkit, which provides interaction models at the microscopic level, are performed for monoenergetic alpha particles traversing spherical sites with diameters of 1, 5 and 10 µm. An analytical function is fitted against the data in each case to model the energy imparted by monoenergetic particles to the site, as well as the variance of the distribution of energy imparted. Those models allow us to obtain the mean and dose-mean values of specific energy (z) and lineal energy (y) for polyenergetic arrangements of alpha particles. The energetic spectrum is estimated by considering the distance that each particle needs to travel to reach the sensitive target. We apply this methodology to a simple case in radioimmunotherapy: a spherical cell that has its membrane uniformly covered by 211At, an alpha emitter, with a spherical target representing the nucleus, placed at the center of the cell. We compare the results of our analytical method with calculations using Geant4-DNA of this specific setup for three nucleus sizes corresponding to our three functions. For nuclei with diameter of 1 µm and 5 µm, all mean and dose-mean quantities for y and z were in an agreement within 4% to Geant4-DNA calculations. This agreement improves to approximately 1% for dose-mean lineal energy and dose-mean specific energy. For the 10-µm-diameter case, discrepancies scale to approximately 9% for mean values and 3% for dose-mean values. Dose-mean values are within Geant4-DNA uncertainties in all cases. Our method provides accurate analytical calculations of dose-mean quantities that may be further employed to characterize radiobiological effectiveness of targeted radiotherapy. The spatial distributions of sources and targets are required to calculate microdosimetric-relevant quantities.

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 / ß 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 / ß 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.

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, LD,2% and LD,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.

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.

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.

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

PURPOSE: 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. METHODS AND MATERIALS: 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. RESULTS: 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. CONCLUSIONS: 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.

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

PURPOSE: 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. METHODS AND MATERIAL: 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. RESULTS: 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. CONCLUSIONS: 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.