Range-energy Relation Research Articles

Dose estimation using in-beam positron emission tomography: Demonstration for 11C and 15O ion beams

Ion therapy has been well established for many decades owing to sharp depth-dose gradient and high cell-killing capability of ions. However, monitoring of the incident ions is needed to reduce ion range uncertainty for effective tumor treatment. Positron-emitting ion beams, known as radioactive ion (RI) beams, can be used as the optimal clinical approach for simultaneously treating and monitoring the incident ions using positron emission tomography (PET) imaging. The low intensity of RI beams, which previously was the main difficulty of their clinical use, was recently addressed by the development of accelerator technology. Since the quantity of interest in ion therapy is the dose and a direct comparison of planned and delivered doses is highly desirable, we focused on predicting the depth dose from PET images for RI beams in this work for the first time. We developed a method for predicting the depth dose of polyenergetic ion beams of 11C and 15O from PET images of these ion beams. The depth dose in water was measured for mono- and polyenergetic ion beams. The monoenergetic ion beams had a momentum acceptance (MA) of ±0.25%, while the polyenergetic beams had an MA of ±2.5%. PET imaging was performed during and shortly after irradiation of a polymethylmethacrylate (PMMA) phantom with mono- and polyenergetic radioactive ion beams. The energy distribution of each polyenergetic ion beam was obtained from the measured momentum distribution of that beam. A set of depth dose and PET profiles in PMMA was constructed for several monoenergetic ion beams using measured data of a monoenergetic ion beam and the range-energy relation. To estimate the depth dose for each polyenergetic beam, a linear combination of weighted PET profiles of monoenergetic beams was iteratively fitted to the measured PET profile of the polyenergetic beam, and the resulting weights were combined with the corresponding monoenergetic depth doses to predict the depth dose distribution. Significance. The depth doses of the polyenergetic ion beams were predicted with mean relative errors of 2.20% and 1.95% for 11C and 15O ion beams, respectively. These errors represent the mean value of the differences between the predicted and measured values, normalized to the maximum measured value. The predicted distal fall-off positions at 80% of the Bragg peak were within 0.13 mm of the measured values for both ion beams. The applicability of the method was demonstrated for a head phantom irradiated with 11C ion beams using Monte Carlo simulation and the predicted distal fall-off positions at 80% of the Bragg peak was within 0.08 mm of the simulated values.

Electron Absorbed Fractions and S Factors for Intermediate Size Target Volumes: Comparison of Analytic Calculations and Monte Carlo Simulations

The absorbed fraction and the S factor represent fundamental quantities in MIRD-based dosimetry of radiopharmaceutical therapy (RPT). Although Monte Carlo (MC) simulations represent the gold standard in RPT dosimetry, dose point kernels (DPK) obtained from analytic range–energy relations offer a more practical alternative for charged-particle dosimetry (β- or α-emitters). In this work, we perform DPK- and MC-based calculations of the self-absorbed fractions and S factors for monoenergetic electrons uniformly distributed in intermediate-size target volumes (~mm to cm) relevant to micrometastasis and disseminated disease. Specifically, the aim of the present work is as follows: (i) the development of an analytic range–energy relation, effective over a broad energy range (100 keV–20 MeV) covering most applications of radiotherapeutic interest; (ii) the application of the new formula to DPK-based calculations of the absorbed fraction and S factor and comparison against MC simulations (both published and present work data) as well as the MIRDcell V2.0.16 software, which uses a similar analytic methodology; and (iii) the study of the influence of simulation parameters (step-size, tracking/production cut-off energies, and ionization model) in Geant4-based calculations of S factors. It is shown that the present DPK-based calculations are in excellent agreement (within 1.5%) with the MIRDcell software, while also being in fair agreement with published MC data as well as with the new Geant4 simulations, with average differences of ~20% for the (sub) mm-sized volumes and ~10% for the cm-sized volumes. The effect of the choice of Geant4 simulation parameters was found to be negligible for the examined target volumes (~mm), except for the use of the Penelope ionization model, which may exhibit noticeable discrepancies (up to ~20%) against the Standard and Livermore models. The present work provides quantitative information that may be useful to both the MC- and DPK-based beta dosimetry of micrometastasis and disseminated disease, which represents an important field of application of RPT.

A systematic approach for calibrating a Monte Carlo code to a treatment planning system for obtaining dose, LET, variable proton RBE and out-of-field dose

Objective. While integration of variable relative biological effectiveness (RBE) has not reached full clinical implementation, the importance of having the ability to recalculate proton treatment plans in a flexible, dedicated Monte Carlo (MC) code cannot be understated . Here we provide a step-wise method for calibrating dose from a MC code to a treatment planning system (TPS), to obtain required parameters for calculating linear energy transfer (LET), variable RBE and in general enabling clinical realistic research studies beyond the capabilities of a TPS. Approach. Initially, Pristine Bragg peaks (PBP) were calculated in both the Eclipse TPS and the FLUKA MC code. A rearranged Bortfeld energy-range relation was applied to the initial energy of the beam to fine-tune the range of the MC code at 80% dose level distal to the PBP. The energy spread was adapted by dividing the TPS range by the MC range for dose level 80%–20% distal to the PBP. Density and relative proton stopping power were adjusted by comparing the TPS and MC for different Hounsfield units. To find the relationship of dose per primary particle from the MC to dose per monitor unit in the TPS, integration was applied to the area of the Bragg curve. The calibration was validated for spread-out Bragg peaks (SOBP) in water and patient treatment plans. Following the validation, variable RBE were calculated using established models. Main results. The PBPs ranges were within ± mm threshold, and a maximum of 5.5% difference for the SOBPs was observed. The patient validation showed excellent dose agreement between the TPS and MC, with the greatest differences for the lung tumor patient. Significance. A procedure for calibrating a MC code to a TPS was developed and validated. The procedure enables MC-based calculation of dose, LET, variable RBE, advanced (secondary) particle tracking and more from treatment plans.

Comparison of methodologies for creating spread-out Bragg peaks in proton therapy using TOPAS and MCNP codes

In proton beam treatments, the superposition of several weighted Bragg curves with different incident energies is required to homogeneously irradiate a large tumor volume, creating a spread-out Bragg peak (SOBP). This paper confirms on the suitability of two different methods to create SOBPs – Bortfeld/Jette's and MCMC (Monte Carlo calculations and Matrix Computations), using Monte Carlo simulations performed with TOPAS and MCNP6.1. To generate the SOBPs, algorithms were developed for implementation of the two methods, which enabled to find the weights for thirty variations of SOBPs, categorized according to their width and maximum depths. The MCMC method used weight optimization in designing SOBPs to avoid negative values. In contrast, the Bortfeld/Jette's method yielded the SOBPs according to the variation of a power-law parameter (p) introduced by the range-energy relationship. Optimal values of p, from MCNP and TOPAS, were selected in order to retrieve SOBPs with the best smoothness and then related to those obtained from the literature. In comparing both methods and codes, dose homogeneity parameters (HOM) were used to examine the SOBP flatness and gamma analyses were employed to assess the dose deposition along its full extension. The results showed that the SOBPs designed using the MCMC method had better HOM values and computational performance for both codes when compared to the Bortfeld/Jette's method. The gamma analyses highlighted significant differences between the entrance doses comparing the two different methods, for SOBPs with intermediate and high depths and small width. This evaluation was not possible with the HOM values alone, which stresses the relevance of a broad analysis to avoid unintended doses in healthy tissues.

Annular energy and radial dose distributions study for a wide range of ions of different equal LET groups in water

Annular energy distribution, AED is a new concept deduced from radial dose, RDD that enables one to draw a map of energy-dose distribution around the ion's path at the nanometer scale better than the ordinary radial dose. The distribution of energy for different equal LET groups of ions of the same LET (keV/μm) were studied using this concept. Annular energy distributions, AEDs for 185 ions impeded in water medium were studied using Katz radial dose formula. AED was calculated using Butts-Katz and Tabata electron range-energy (R-E) relations and were compared. AED and shell annular energy distribution, SAED for those ions were mapping and confirming that energy distributions for ions of the same LET are not the same. AED growth with annular width r=0.1(nm)⟶Rmin(nm) showing a peak at the maximum annular energy width, rMAEW. Butts-Katz and Tabata show same annular energy distribution peaks of the same value, however, Tabata shows that energy is distributed over a wide range than Butts-Katz. Thus, Butts-Katz R-E relation is recommended and considered. AED for the studied 185 ions shows a peak at certain width called the maximum annular energy width, rMAEW. This rMAEW showed a monotonic increasing function with ion's β2. The total annular energy distribution, TAED for the different ions were determined and it shows a linear increasing function of the ion's (Z*/β)2.

Track detector based discriminative thoron measurement – An optimization study through experiments and modelling

The wide difference in the diffusion lengths of 222Rn and 220Rn in air can be exploited to selectively measure the two isotopes using the solid state nuclear track detector (SSNTD) based passive technique. For selective thoron measurement, LR-115 films are mounted at two different distances. The farther film records tracks only due to radon and its progenies and this can be subtracted from the tracks on the nearer film to obtain the thoron contributed tracks. This scheme has been explored in a previous study reported in literature. Based on this, an optimization exercise has been taken up in the present study for selectively measuring the thoron exhaled from soil samples. The optimum distance at which the LR films have to be mounted for recording maximum tracks, is experimentally deduced and this exercise has been supported with simple Monte Carlo modelling inclusive of the alpha particle range-energy relation. The optimum source-detector distance (distance at which track density is maximum) predicted by the model agreed with the experimental result.

Distribution of radial dose in water at nanometer scale for ions of the same linear energy transfer: benefits of the concept of annular dose

Annular-dose AD is a new conception , based on the radial dose distribution, RDD, introduced by the present work. AD is the integrated dose for many shells around the ions and it is defined as the dose deposited in the shell volume perpendicular to the ion path of width length equal and thickness equal unity (1 nm). Thus, it integrates and maps the deposited dose due to ion in any medium at nanometer scale better than the ordinary radial dose. Katz and Awad radial dose formulae plus Butts-Katz and Tabata electron range-energy relations are composing three different approaches. These approaches were used for studying the AD for 30 ions forming 4 different equal LET groups and have energy at Bragg peak region from 1.5 to 24 MeV n−1. The annular dose, AD as a function of the shell width for the ions under investigation showed that dose distributions around the ions of same LET are not the same and a clear peak at certain shell width called the ion’s maximum annular dose width, r MADW was determined for the first time. The r MADW is the position where the maximum reachable dose is delivered by secondary electrons around the ion. The ion’s r MADW showed an increasing function with Z*β within the same LET group. Interestingly, it was found that r MADW behaves as an increasing monotonic function of the relative ion velocity, β using the three approaches considered in this work.

Pixel Image Analysis and Its Application with an Alcohol-Based Liquid Scintillator for Particle Therapy.

We synthesized an alcohol-based liquid scintillator (AbLS), and we implemented an auxiliary monitoring system with short calibration intervals using AbLS for particle therapy. The commercial liquid scintillator used in previous studies did not allow the user to control the chemical ratio and its composition. In our study, the chemical ratio of AbLS was freely controlled by simultaneously mixing water and alcohol. To make an equivalent substance to the human body, 2-ethoxyethanol was used. There was no significant difference between AbLS and water in areal density. As an application of AbLS, the range was measured with AbLS using an electron beam in an image analysis that combined AbLS and a digital phone camera. Given a range–energy relationship for the electron expressed as areal density, the electron beam range (cm) in water can be easily estimated. To date, no literature report for the direct comparison of a pixel image analysis and Monte Carlo (MC) simulation has been published. Furthermore, optical tomography of the inverse problem was performed with AbLS and a mobile phone camera. Analyses of optical tomography images provide deeper insight into Radon transformation. In addition, the human phantom, which is difficult to compose with semiconductor diodes, was easily implemented as an image acquisition and analysis system.

Characterization of Makrofol[formula omitted] DE 1-1 (bisphenol-A polycarbonate) as SSNTD and its application in the alpha particle detection

Makrofol® DE 1-1 (bisphenol-A polycarbonate) was characterized as a solid state nuclear track detector (SSNTD) as well as for alpha particle detection. The bulk etch rate of the Makrofol® DE 1-1, at different etchant concentrations and temperatures, was found to be homogenous. The visible light absorbance measurements of the etched Makrofol® DE 1-1 at different etching conditions indicated that the lowest visible light absorbance occurs at the etching conditions of 75% 6 N KOH+25% C2H5OH and a temperature of 50∘C. The bulk etch rate activation energy EB increased from (0.59±0.05) eV to (0.76±0.05) eV for Makrofol® DE 1-1 etched in KOH and 25% 6 N KOH+75% C2H5OH, respectively. Before alpha particle tracks overlapping, the alpha track density in Makrofol® DE 1-1 is linearly correlated with the exposure time to alpha particles. The alpha particles track diameter was found to be a non-monotonic function of the alpha particle energy. The range of alpha particles in Makrofol® DE 1-1, which is a monotonic function of alpha particle energy, was determined using the over-etched track technique. The range-energy relationship of a perpendicularly incident alpha particle in a Makrofol® DE 1-1 detector can be used for the determination of the alpha particle energy over a wider energy range than with the etch pit diameter-energy relationship.

Analysis of a Single-Λ Hypernuclear Event in KEK-PS E373 Nuclear Emulsion Experiment

The purpose of this research is to identify a single-Λ hypernucleus and its decay products which support to get more information about hyperon-nucleon interaction. Before performing the analysis of a single-Λ hypernucleus, first, we have deduced the density of emulsion by calibrating the range-energy relation using alpha decay events data from thorium series. It is very important for the mass reconstruction of hypernucleus events in nuclear emulsion. And we have reconstructed a single-Λ hypernucleus event by using the kinematical reconstruction for mesonic and non-mesonic decay modes. From the result of our analysis, we can uniquely identify that single-Λ hypernucleus is $ {}_\Lambda ^9 B $ and decay products are 4He,3He, proton and neutron.

Monte Carlo calculation of proton ranges in water phantom for therapeutic energies

Introduction: One crucial point when calculating the distribution of doses with ions is the uncertainty of the Bragg peak. The proton ranges in determined geometries like homogeneous phantoms and detector geometries can be calculated with a number of various parameterization models. Several different parameterizations of the range-energy relationship exist, with different levels of accuracy and complexity. For benchmarking purposes and calibration of proton range, it is consequential to have an accurate computation scheme between ranges and energies. In this setting, Monte Carlo simulations became important more and more in order to evaluating treatment plans and dose distributions. High-resolution energy-range tables are created using the PSTAR database. The aim of this study is to calculate proton range in the range of therapeutic energy in a cubic water phantom with a submillimeter accuracy. Materials and Methods: Various Monte Carlo packages are available today that are specifically developed for handling radiation transport problems. GATE (version8) was used in this study to model the geometry and composition of a phantom. Geometries dictated to the toolkit were a cubic water phantom (40*40*40 cm3), as the target sitting on the xy-plane with the z-axis as its axis of symmetry. The primary particle source, emitting protons, were in the proximity of the phantom base on the z-axis. Mono energetic proton pencil beams (50, 100, 150, 200 MeV) hit the phantom. Several physics lists are defined in the GATE that we used FTFP_BERT. The simulations were carried out for 106 proton histories that yielded better than 1% statistical errors. Results: In the current study, the results of the Bragg Peak Profile for the energy range of 5- 200 MeV has been obtained. The range-energy relation was obtained by fitting the FTFP_BERT physics data. So far, many similar studies have been done in this regard, such as a study by Bozkurt using the MCNPX code. However, we investigated the overall energy range used in proton therapy and obtained the fit model using a greater bunch of data. Conclusion: By comparing the results obtained for each energy with NIST data, and with using Shapiro-Wilk statistical test, we did not see any significant difference. It was also found by calculating the percentage difference obtained with the CSDA data available in the NIST library, with the highest difference of 0.5%.

Accuracy of parameterized proton range models; A comparison

An accurate calculation of proton ranges in phantoms or detector geometries is crucial for decision making in proton therapy and proton imaging. To this end, several parameterizations of the range-energy relationship exist, with different levels of complexity and accuracy. In this study we compare the accuracy of four different parameterizations models for proton range in water: Two analytical models derived from the Bethe equation, and two different interpolation schemes applied to range-energy tables. In conclusion, a spline interpolation scheme yields the highest reproduction accuracy, while the shape of the energy loss-curve is best reproduced with the differentiated Bragg-Kleeman equation.

A new scanning system for alpha decay events as calibration sources for range-energy relation in nuclear emulsion

A new scanning system named “Vertex picker” has been developed to rapid collect alpha decay events, which are calibration sources for the range-energy relation in nuclear emulsion. A computer-controlled optical microscope scans emulsion layers exhaustively, and a high-speed and high-resolution camera takes their micrographs. A dedicated image processing picks out vertex-like shapes. Practical operations of alpha decay search were demonstrated by emulsion sheets of the KEK-PS E373 experiment. Alpha decays of nearly 28 events were detected in eye-check work on a PC monitor per hour. This yield is nearly 20 times more effective than that by the conventional eye-scan method. The speed and quality is acceptable for the coming new experiment, J-PARC E07.

Nuclear emulsion measuring the prompt fission neutron spectrum of 238U induced by 2.8 MeV neutrons

The spectra of neutrons emitted in fission of 238U induced by 2.8MeV neutrons were measured by N-4 nuclear emulsion. Details like the experimental layout and conditions, and the track data reading, processing and correction were described. Also the energy-range relation of recoil protons among the N-4 nuclear emulsion was derived by Monte Carlo simulation and fitting method for the first time. The experimental results were presented as relative yields and were compared to the calculations using Maxwell and Watt models. The results were approximately the same as the theoretical PFNS, especially for those 3–6MeV and 11–14MeV outgoing neutrons, and the availability of nuclear emulsion measurement in the high-energy part of PFNS was proved.

Formulae for the secondary electron yield and total stopping power from 0.8 keV to 10 keV for metals

Based on the range–energy relationship, the characteristics of secondary electron emission, some relationship between the secondary electron yield δ and experimental results, the universal formulae for δ 0.8−2 (the subscript indicates that the energy range of primary energy at the surface W po is from 0.8 keV to 2 keV) and δ 2−10 for metals were deduced. The δ 0.8−10 calculated with the universal formulae and the δ 0.8−10 measured experimentally were compared, and the scattering of δ for the same metal was analysed. Finally, we concluded that the formulae were universal for δ 0.8−10 for metals. On the basis of some relationship between parameters of δ, we deduce a formula for expressing total stopping power S 0.8−10 as a function of S 10−30, δ 0.8−10, δ 10−30, backscattered coefficient η 0.8−10, η 10−30 and W po. The calculated S 0.8−10 were compared with the values measured experimentally and it was concluded that the formula to estimate S 0.8−10 was universal for metals.

Formula for the total stopping power from 2 keV to 10 keV for a metal

On the basis of the range-energy relationship, the relationships (L 2–10) among the total stopping power from 2 keV to 10 keV for a metal (S 2–10), the energy exponent (n 2–10), the primary energy at the surface (W p0), and the parameter (A 2–10) were deduced. In addition, the relationships (L 10–30) among the total stopping power from 10 keV to 30 keV for a metal (S 10–30), the energy exponent (n 10–30), W p0 and the parameter (A 10–30) were obtained. According to some relationships between the parameters of the secondary electron yield from 2 keV to 10 keV for a metal (δ 2–10), the composition of the secondary electron yield from 10 keV to 30 keV for a metal (δ 10–30), L 2–10, and L 10–30, the universal formula for expressing S 2–10 as a function of S 10–30, δ 2–10, δ 10–30, the backscattered coefficient (η) from 2 keV to 10 keV, η from 10 keV to 30 keV and W p0 was deduced. The S 2–10 calculated from this universal formula and the S 2–10 measured experimentally were compared, and we conclude that the formula presented in this paper is universal for S 2–10.

An analytical solution to proton Bragg peak deflection in a magnetic field

The role of MR imaging for image-guided radiation therapy (IGRT) is becoming more and more important thanks to the excellent soft tissue contrast offered by MRI. Hybrid therapy devices with integrated MRI scanners are under active development for x-ray therapy. The combination of proton therapy with MRI imaging has only been investigated at the theoretical or conceptual level. Of concern is the deflection of the proton beam in the homogeneous magnetic field. A previous publication has come to the conclusion that the impact of a 0.5 T magnetic field on the dose distribution for proton therapy is very small and lateral deflections stay well below 2 mm. The purpose of this study is to provide new insights into the effects of magnetic fields on a proton beam coming to rest in a patient. We performed an analytical calculation of the lateral deflection of protons with initial energies between 50 MeV and 250 MeV, perpendicular to the beam direction and the magnetic field. We used a power-law range-energy relationship and the Lorentz force in both relativistic and non-relativistic conditions. Calculations were done for protons coming to rest in water or soft tissue, and generalized to other uniform and non-uniform media. Results were verified by comparisons with numerical calculations and Monte Carlo simulations. A key result of our calculations is that the maximum lateral deflection at the end of range is proportional to the third power of the initial energy. Accordingly, due to the strong dependence on the energy, even a relatively small magnetic field of 0.5 T will cause a deflection of the proton beam by 1 cm at the end of range of a 200 MeV beam. The maximum deflection at 200 MeV is more than 10 times larger than that of a 90 MeV beam. Relativistic corrections of the deflection are generally small but they can become non-negligible at higher energies around 200 MeV and above. Contrary to previous findings, the lateral deflection of a proton beam can be significant (1 cm and above) even in relatively small magnetic fields of 0.5 T. However, the curved path of a proton beam in a magnetic field is easily predictable and it should be possible to account for this in treatment planning.

SU-E-T-14: Modeling of 3D Positron Emission Activity Distributions Induced by Proton Irradiation: A Semi-Empirical Method.

to present and validate a method for modeling three-dimensional positron emission (PE) activity distributions induced by proton beam irradiation for PET/CT delivery verification studies in homogeneous media. the method relies on modeling the 3D proton flux distribution by combining the analytical expression for the depth reduction of proton flux with the empirically obtained lateral distribution. The latter is extracted from the corresponding dose distribution under the assumption that the projectile energy is nearly constant in the lateral plane. The same assumption allows calculating the 3D induced activity distributions from proton flux distributions by parameterizing the energy-dependent activation cross-sections in terms of depth via the energy-range relation. Results of this modeling approach were validated against experimental PET/CT data from three phantom deliveries: unmodulated (pristine) beam, spread-out Bragg peak (SOBP) delivery without a range compensator, and SOBP with a range compensator. BANG3-Pro2 polymer gel was used as a phantom material because of its elemental soft-tissue equivalence. the agreement between modeled and measured activity distributions was evaluated using 3D gamma index analysis method, which, despite being traditionally reserved for dose distribution comparisons, is sufficiently general to be applied to other quantities. The evaluation criteria were dictated by limitations of PET imaging and were chosen to correspond to count rate uncertainty (6% value difference) and spatial resolution (4 mm distance to agreement). With these criteria and the threshold of 6%, the fraction of evaluated voxels passing the gamma evaluation was 97.9% for the pristine beam, 98.9% for the SOBP without compensator, and 98.5% for SOBP with compensator. results of gamma evaluation indicate that the activity distributions produced by the model are consistent with experimental data within the uncertainties of PET imaging for clinical proton beams deliveries. This work was supported by the Bankhead-Coley Florida Biomedical Research Program under Grant No. 1BD10-34212.

Radial dose distributions for ions in arbitrary matter

The radial dose distribution in water and silicon for ions with a wide range of energies, and the energy dissipation of normally incident electrons of energies 0.025, 0.1, 1 and 10 MeV in C, Al, Cu, Sn and Pb have been calculated on the basis of classical collision dynamics and a general logarithmic polynomial range-energy relationship. The results of the present work almost agree well with Monte Carlo calculations and measured data.

A range-based method to calibrate a magnetic spectrometer measuring the energy spectrum of the backward electron beam of a plasma focus

The electron beam emitted from the back of plasma focus devices is being studied as a radiation source for intraoperative radiation therapy applications. A plasma focus device is being developed for this purpose, and there is a need for characterizing its electron beam, particularly, insofar as the energy spectrum is concerned. The instrument used is a magnetic spectrometer. To calibrate this spectrometer, a procedure relying on the energy-range relation in Mylar® has been devised and applied. By measuring the transmission through increasing thicknesses of the material, electron energies could be assessed and compared to the spectrometer readings. Thus, the original calibration of the instrument has been extended to higher energies and also to better accuracy. Methods and results are presented.