Proton Bragg Curves Research Articles

Tuning the range-energy relationship parameter for Monte Carlo-based proton Bragg curve spreading in muscle, bone, and polymethylmethacrylate.

Determination of spread-out Bragg peak (SOBP) inside media other than water is important for research or clinical purposes. Current study aims to characterize the optimal "p" values needed for the simulation of proton SOBP inside some dosimetry media using MCNPX Monte Carlo code. Following the provided data by ICRU-49 and applying the Bortfeld and Jette recommendations, the "p" values were determined for muscle, compact bone, and PMMA. Then, "p" values were optimized to reach accurate weight fractions for the Monte Carlo simulation of SOBP curves. Obtained optimal "p" values can produce accurate proton weight fractions for flat SOBP simulation. The slope of the SOBP region was highly dependent on the "p" value, so small changes in this parameter can largely tilt up or down the SOBP. The tabulated optimal "p" values can be reliably used for proton weight fraction determination during the Monte Carlo simulation of the proton beam SOBP curve inside the investigated media.

Spread-out Bragg peak measurements using a compact quality assurance range calorimeter at the Clatterbridge cancer centre

Objective. The superior dose conformity provided by proton therapy relative to conventional x-ray radiotherapy necessitates more rigorous quality assurance (QA) procedures to ensure optimal patient safety. Practically however, time-constraints prevent comprehensive measurements to be made of the proton range in water: a key parameter in ensuring accurate treatment delivery. Approach. A novel scintillator-based device for fast, accurate water-equivalent proton range QA measurements for ocular proton therapy is presented. Experiments were conducted using a compact detector prototype, the quality assurance range calorimeter (QuARC), at the Clatterbridge cancer centre (CCC) in Wirral, UK for the measurement of pristine and spread-out Bragg peaks (SOBPs). The QuARC uses a series of 14 optically-isolated 100 × 100 × 2.85 mm polystyrene scintillator sheets, read out by a series of photodiodes. The detector system is housed in a custom 3D-printed enclosure mounted directly to the nozzle and a numerical model was used to fit measured depth-light curves and correct for scintillator light quenching. Main results. Measurements of the pristine 60 MeV proton Bragg curve found the QuARC able to measure proton ranges accurate to 0.2 mm and reduced QA measurement times from several minutes down to a few seconds. A new framework of the quenching model was deployed to successfully fit depth-light curves of SOBPs with similar range accuracy. Significance. The speed, range accuracy and simplicity of the QuARC make the device a promising candidate for ocular proton range QA. Further work to investigate the performance of SOBP fitting at higher energies/greater depths is warranted.

Visible proton Bragg curve imaging by colour centre photoluminescence in radiation detectors based on lithium fluoride films on silica

Passive solid-state radiation detectors, based on the visible photoluminescence (PL) of radiation-induced colour centres in optically transparent lithium fluoride (LiF), polycrystalline thin films are under investigation for proton beam advanced diagnostics. After proton exposure, the latent images stored in LiF as local formations of stable F2 and F3 + aggregate defects, are directly read with a fluorescence microscope under illumination in the blue spectral range. Adopting a suitable irradiation geometry, the energy density that protons deposit in the material can be recorded as a spatial distribution of these light-emitting defects, from which a luminous replica of the proton Bragg curve can be thereafter extracted and analysed to reconstruct the proton beam energy spectrum. Their peculiar properties, such as wide dynamic range and linearity of the spectrally-integrated PL response vs. dose, make the investigation of two-dimensional LiF film radiation detectors grown on several types of substrate highly attractive. Here, the case of a LiF thin film thermally evaporated on a silica substrate, irradiated at grazing incidence with a 35 MeV proton beam, is investigated and reported for the first time. A comparison of the measured photoluminescent Bragg curve with Monte Carlo simulations demonstrates that the Bragg peak in the film is located at the very same position that would be expected in the underlying silica substrate rather than in LiF. The film packing density is shown not to have a significant effect on the peak depth, while even small nonzero grazing angle of the impinging proton beam is able to significantly modify the shape of the Bragg curve. These findings are ascribed to the effects of multiple Coulomb scattering in both the film and the substrate and are interesting for proton beam diagnostics and dosimetry.

Passive SOBP generation from a static proton pencil beam using 3D-printed range modulators for FLASH experiments

The University Proton Therapy facility in Dresden (UPTD), Germany, is equipped with an experimental room with a beamline providing a static pencil beam. High proton beam currents can be achieved at this beamline which makes it suitable for FLASH experiments. However, the established experimental setup uses only the entrance channel of the proton Bragg curve. In this work, a set of 3D-printed range modulators designed to generate spread out Bragg peaks (SOBPs) for radiobiological experiments at ultra-high dose rate at this beamline is described. A new method to optimize range modulators specifically for the case of a static pencil beam based on the central depth dose profile is introduced. Modulators for two different irradiation setups were produced and characterized experimentally by measurements of lateral and depth dose distributions using different detectors. In addition, Monte Carlo simulations were performed to assess profiles of the dose averaged linear energy transfer (LETD) in water. These newly produced range modulators will allow future proton FLASH experiments in the SOBP at UPTD with two different experimental setups.

Characterization and quenching correction for a 2D real time radioluminescent system in therapeutic proton and carbon charged beams

Two dimensional radioluminescence (RL) films were investigated for application in proton and carbon therapy dosimetry. The films are made of Al 2 O 3 :C,Mg micro powder in two sizes (38 µm and 7 µm) mixed with a water-equivalent binder. The films were irradiated behind different thicknesses of solid slabs and behind wedge shaped plastic absorbers. Bragg curves presented quenching effect attributed to the non-linear response of the RL signal as a function of proton linear energy transfer (LET). Experimental data and Monte Carlo simulations were utilized to acquire a quenching correction method, adapted from Birks’ formula, to restore the linear dose response for particle therapy beams. The method for quenching correction was applied, reaching an agreement at the Bragg peak of 3 % for films with 38 µm median grain size phosphor and 1.5 % for films with 7 µm median grain size phosphor for the proton beams; and 2 % for films with 38 µm median grain size phosphor and 3 % for films with 7 µm median grain size phosphor for the carbon charged particles. • Radioluminescence Al2O3:C,Mg films and a scientific camera. • Real time two-dimensional RL characterization along proton and carbon Bragg curves. • Films were irradiated behind different thicknesses of solid slabs and behind wedge shaped plastic absorbers. • The films present quenching with high LET. • A quenching correction was applied, good agreement along the Bragg curve.

Photoluminescent Bragg curves in lithium fluoride thin films on silicon substrates irradiated with a 35 MeV proton beam

Proton irradiation of lithium fluoride (LiF) crystals and thin films causes the formation of electronic defects, known as color centers, in the crystal lattice, some of which show photoluminescence in the visible range under blue-light excitation. With a suitable irradiation geometry, the energy density that protons deposit in the material can be recorded as a spatial distribution of these light-emitting color centers, from which a luminous replica of the proton Bragg curve can be thereafter extracted and analyzed in a fluorescence microscope. In this paper, the cases of two LiF thin films deposited on silicon substrates and of a LiF crystal, all of them transversally irradiated with a nominal 35 MeV proton beam, are considered. A comparison of the measured photoluminescent Bragg curves with Monte Carlo simulations demonstrates (i) that the Bragg peaks in the films are located at the very same positions that would be expected in the underlying silicon substrates rather than in LiF and (ii) that an even small grazing angle of the impinging proton beam is able to significantly modify the shape of the Bragg curve in the films. Both of these findings are ascribed to the effects of multiple Coulomb scattering in both the film and the substrate. The coincidence of the Bragg peak positions with those expected in the silicon substrates and the possibility of visualizing such peaks in the Bragg curves stored as latent fluorescence images in the LiF films allow one to regard them as information transducers for proton beam diagnostics and dosimetry.

Dosimetric Assessment of a High Precision System for Mouse Proton Irradiation to Assess Spinal Cord Toxicity.

The uncertainty associated with the relative biological effectiveness (RBE) in proton therapy, particularly near the Bragg peak (BP), has led to the shift towards biological-based treatment planning. Proton RBE uncertainty has recently been reported as a possible cause for brainstem necrosis in pediatric patients treated with proton therapy. Despite this, in vivo studies have been limited due to the complexity of accurate delivery and absolute dosimetry. The purpose of this investigation was to create a precise and efficient method of treating the mouse spinal cord with various portions of the proton Bragg curve and to quantify associated uncertainties for the characterization of proton RBE. Mice were restrained in 3D printed acrylic boxes, shaped to their external contour, with a silicone insert extending down to mold around the mouse. Brass collimators were designed for parallel opposed beams to treat the spinal cord while shielding the brain and upper extremities of the animal. Up to six animals may be accommodated for simultaneous treatment within the restraint system. Two plans were generated targeting the cervical spinal cord, with either the entrance (ENT) or the BP portion of the beam. Dosimetric uncertainty was measured using EBT3 radiochromic film with a dose-averaged linear energy transfer (LETd) correction. Positional uncertainty was assessed by collecting a library of live mouse scans (n = 6 mice, two independent scans per mouse) and comparing the following dosimetric statistics from the mouse cervical spinal cord: Volume receiving 90% of the prescription dose (V90); mean dose to the spinal cord; and LETd. Film analysis results showed the dosimetric uncertainty to be ±1.2% and ±5.4% for the ENT and BP plans, respectively. Preliminary results from the mouse library showed the V90 to be 96.3 ± 4.8% for the BP plan. Positional uncertainty of the ENT plan was not measured due to the inherent robustness of that treatment plan. The proposed high-throughput mouse proton irradiation setup resulted in accurate dose delivery to mouse spinal cords positioned along the ENT and BP. Future directions include adapting the setup to account for weight fluctuations in mice undergoing fractionated irradiation.

Double-strand breaks measured along a 160 MeV proton Bragg curve using a novel FIESTA-DNA probe in a cell-free environment

Proton radiotherapy treatment planning systems use a constant relative biological effectiveness (RBE) = 1.1 to convert proton absorbed dose into biologically equivalent high-energy photon dose. This method ignores linear energy transfer (LET) distributions, and RBE is known to change as a function of LET. Variable RBE approaches have been proposed for proton planning optimization. Experimental validation of models underlying these approaches is a pre-requisite for their clinical implementation. This validation has to probe every level in the evolution of radiation-induced biological damage leading to cell death, starting from DNA double-strand breaks (DSB). Using a novel FIESTA-DNA probe, we measured the probability of double-strand break (P DSB) along a 160 MeV proton Bragg curve at two dose levels (30 and 60 Gy (RBE)) and compared it to measurements in a 6 MV photon beam. A machined setup that held an Advanced Markus parallel plate chamber for proton dose verification alongside the probes was fabricated. Each sample set consisted of five 10 μl probes suspended inside plastic microcapillary tubes. These were irradiated with protons to 30 Gy (RBE) at depths of 5–17.5 cm and 60 Gy (RBE) at depths of 10–17.2 cm with 1 mm resolution around Bragg peak. Sample sets were also irradiated using 6MV photons to 20, 40, 60, and 80 Gy. For the 30 Gy (RBE) measurements, increases in P DSB/Gy were observed at 17.0 cm followed by decreases at larger depth. For the 60 Gy (RBE) measurements, no increase in P DSB/Gy was observed, but there was a decrease after 17.0 cm. Dose-response for P DSB between 30 and 60 Gy (RBE) showed less than doubling of P DSB when dose was doubled. Proton RBE effect from DSB, RBEP,DSB, was <1 except at the Bragg peak. The experiment showed that the novel probe can be used to perform DNA DSB measurements in a proton beam. To establish relevance to clinical environment, further investigation of the probe’s chemical scavenging needs to be performed.

Algorithm for inversion of photoluminescent Bragg curves in lithium fluoride applied to the analysis of proton beam energy spectra

In a recent paper, an analytical expression for proton Bragg curves was introduced and utilized to best fit photoluminescent depth distributions of optically active F2 and F3+ color centers in lithium fluoride, with the purpose of evaluating the energy spectrum of a proton beam, assumed to consist of the superposition of Gaussian components. Here, an original alternative method is introduced by means of which the same energy spectrum analysis can be performed by iteratively applying a suitable mathematical operator to the photoluminescent depth distribution, no best fitting operation being needed.

An analytical approximation of proton Bragg curves in lithium fluoride for beam energy distribution analysis

An analytical model that approximates Bragg curves due to protons in water is extended to lithium fluoride (LiF), both in bulk and lower-density homogeneous thin film form. To that purpose, Monte Carlo simulations of proton range for energies from 5 to 65 MeV are best fitted so that optimal values of the model parameters are deduced for LiF. Tests are performed by comparing analytically computed Bragg curves with corresponding ones simulated by Monte Carlo software in LiF, bulk and lower density, at two example proton energies and energy-straggling widths. The model is then applied to the reconstruction of the energy spectra of proton beams by best fitting experimental Bragg profiles due to visible photoluminescence of optically-active F2 and F3+ color centers created in LiF crystals by the ionizing interaction of protons with the material.

Validation of new 2D ripple filters in proton treatments of spherical geometries and non-small cell lung carcinoma cases

A ripple filter (RiFi) is a passive energy modulator used in scanned particle therapy to broaden the Bragg peak, thus lowering the number of accelerator energies required for homogeneous target coverage, which significantly reduces the irradiation time. As we have previously shown, a new 6 mm thick RiFi with 2D groove shapes produced with 3D printing can be used in carbon ion treatments with a similar target coverage and only a marginally worse planning conformity compared to treatments with in-use 3 mm thick RiFis of an older 1D design. Where RiFis are normally not used with protons due to larger scattering and straggling effects, this new design would be beneficial in proton therapy too.Measurements of proton Bragg curves and lateral beam profiles were carried out for different RiFi designs and thicknesses as well as for no RiFi at the Heidelberg Ionenstrahl-Therapiezentrum. Base data for proton treatment planning were generated with the Monte Carlo code SHIELD-HIT12A with and without the 2D 6 mm RiFi. Plans on spherical targets in water were calculated with TRiP98 for a systematic RiFi performance analysis and for comparisons with carbon ion plans for the same respective energy depth step sizes. Plans for 9 stage I static non small cell lung cancer patients were calculated with Eclipse 13.7.15. Dose-volume-histograms, spatial dose distributions and dosimetric indexes were used for plan evaluation.Measurements confirm the functionality of the new 2D RiFi design, which reduces the beam spot size compared to 1D RiFis of the same thickness. Planning studies show that a 6 mm thick 2D RiFi could be used in proton therapy to lower the irradiation time. Although slightly worse planning conformity and dose homogeneity were found for plans with the RiFi compared to plans without, satisfactory results within the planning objective were obtained for all cases.

Dose build-up effects induced by delta electrons and target fragments in proton Bragg curves—measurements and simulations

Dose build-up effects in the entrance channel of proton Bragg curves were investigated in detail by means of simulations and experiments. There are two relevant dose build-up effects. Firstly, the δ-electron build-up effect which takes place in the first few millimeters of the tissue until an equilibrium state of the forward-scattered δ-electrons is reached. Secondly, the target fragment build-up effect that covers the first centimeters in the entrance channel of the proton Bragg curve. These target fragments are created in inelastic interactions of the beam protons with the target nuclei and partially have low kinetic energies and/or high atomic numbers compared to the incident beam protons. Consequently, the target fragments possess high LET values and thus an increased RBE. However, the production cross sections relevant for target fragmentation in ion beam therapy still have large uncertainties. Therefore, in this work target fragmentation was investigated indirectly by measuring low-noise proton Bragg curves with the focus placed on their build-up regions. The measurements clearly show the magnitude and shape of the two different build-up effects. Additionally, with the application of a magnetic filter, it was possible to separate the measurement of the target fragment build-up effect from the δ-electron build-up effect. Corresponding FLUKA Monte Carlo simulations were carried out for the experimental setup. A comparison of the experimental results with the FLUKA predictions enabled the assessment of the precision of FLUKA models, e.g. the δ-electron production models and the nuclear event generators which are responsible for target fragmentation reactions. It could be shown that the relevant models worked well to reproduce both build-up effects.

SU‐F‐T‐144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water

Purpose:Semi‐empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water.Methods:The FLUKA, Monte Carlo (MC) general‐purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld's closed form equation approximating proton Bragg Curves as a basis, we derived the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld's fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld's equation to describe fragmentation tail. This term accounts for the pre‐peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion‐ Ablation fragmentation model.Results:The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm‐1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%).Conclusion:The derived semi‐empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi‐empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.

Degradation of proton depth dose distributions attributable to microstructures in lung-equivalent material.

The purpose of the work reported here was to investigate the influence of sub-millimeter size heterogeneities on the degradation of the distal edges of proton beams and to validate Monte Carlo (MC) methods' ability to correctly predict such degradation. A custom-designed high-resolution plastic phantom approximating highly heterogeneous, lung-like structures was employed in measurements and in Monte Carlo simulations to evaluate the degradation of proton Bragg curves penetrating heterogeneous media. Significant differences in distal falloff widths and in peak dose values were observed in the measured and the Monte Carlo simulated curves compared to pristine proton Bragg curves. Furthermore, differences between simulations of beams penetrating CT images of the phantom did not agree well with the corresponding experimental differences. The distal falloff widths in CT image-based geometries were underestimated by up to 0.2 cm in water (corresponding to 0.8-1.4 cm in lung tissue), and the peak dose values of pristine proton beams were overestimated by as much as ˜35% compared to measured curves or depth-dose curves simulated on the basis of true geometry. The authors demonstrate that these discrepancies were caused by the limited spatial resolution of CT images that served as a basis for dose calculations and lead to underestimation of the impact of the fine structure of tissue heterogeneities. A convolution model was successfully applied to mitigate the underestimation. The results of this study justify further development of models to better represent heterogeneity effects in soft-tissue geometries, such as lung, and to correct systematic underestimation of the degradation of the distal edge of proton doses.

Experimental depth dose curves of a 67.5 MeV proton beam for benchmarking and validation of Monte Carlo simulation.

To measure depth dose curves for a 67.5 ± 0.1 MeV proton beam for benchmarking and validation of Monte Carlo simulation. Depth dose curves were measured in 2 beam lines. Protons in the raw beam line traversed a Ta scattering foil, 0.1016 or 0.381 mm thick, a secondary emission monitor comprised of thin Al foils, and a thin Kapton exit window. The beam energy and peak width and the composition and density of material traversed by the beam were known with sufficient accuracy to permit benchmark quality measurements. Diodes for charged particle dosimetry from two different manufacturers were used to scan the depth dose curves with 0.003 mm depth reproducibility in a water tank placed 300 mm from the exit window. Depth in water was determined with an uncertainty of 0.15 mm, including the uncertainty in the water equivalent depth of the sensitive volume of the detector. Parallel-plate chambers were used to verify the accuracy of the shape of the Bragg peak and the peak-to-plateau ratio measured with the diodes. The uncertainty in the measured peak-to-plateau ratio was 4%. Depth dose curves were also measured with a diode for a Bragg curve and treatment beam spread out Bragg peak (SOBP) on the beam line used for eye treatment. The measurements were compared to Monte Carlo simulation done with geant4 using topas. The 80% dose at the distal side of the Bragg peak for the thinner foil was at 37.47 ± 0.11 mm (average of measurement with diodes from two different manufacturers), compared to the simulated value of 37.20 mm. The 80% dose for the thicker foil was at 35.08 ± 0.15 mm, compared to the simulated value of 34.90 mm. The measured peak-to-plateau ratio was within one standard deviation experimental uncertainty of the simulated result for the thinnest foil and two standard deviations for the thickest foil. It was necessary to include the collimation in the simulation, which had a more pronounced effect on the peak-to-plateau ratio for the thicker foil. The treatment beam, being unfocussed, had a broader Bragg peak than the raw beam. A 1.3 ± 0.1 MeV FWHM peak width in the energy distribution was used in the simulation to match the Bragg peak width. An additional 1.3-2.24 mm of water in the water column was required over the nominal values to match the measured depth penetration. The proton Bragg curve measured for the 0.1016 mm thick Ta foil provided the most accurate benchmark, having a low contribution of proton scatter from upstream of the water tank. The accuracy was 0.15% in measured beam energy and 0.3% in measured depth penetration at the Bragg peak. The depth of the distal edge of the Bragg peak in the simulation fell short of measurement, suggesting that the mean ionization potential of water is 2-5 eV higher than the 78 eV used in the stopping power calculation for the simulation. The eye treatment beam line depth dose curves provide validation of Monte Carlo simulation of a Bragg curve and SOBP with 4%/2 mm accuracy.

TH‐A‐19A‐05: Modeling Physics Properties and Biologic Effects Induced by Proton and Helium Ions

Purpose:Currently, proton and carbon ions are used for cancer treatment. More recently, other light ions including helium ions have shown interesting physical and biological properties. The purpose of this work is to study the biological and physical properties of helium ions (He‐3) in comparison to protons.Methods:Monte Carlo simulations with FLUKA, GEANT4 and MCNPX were used to calculate proton and He‐3 dose distributions in water phantoms. The energy spectra of proton and He‐3 beams were calculated with high resolution for use in biological models. The repair‐misrepairfixation (RMF) model was subsequently used to calculate the RBE.Results:The proton Bragg curve calculations show good agreement between the three general purpose Monte Carlo codes. In contrast, the He‐3 Bragg curve calculations show disagreement (for the magnitude of the Bragg peak) between FLUKA and the other two Monte Carlo codes. The differences in the magnitude of the Bragg peak are mainly due to the discrepancy in the secondary fragmentation cross sections used by the codes. The RBE for V79 cell lines is about 0.96 and 0.98 at the entrance of proton and He‐3 ions depth dose respectively. The RBE increases to 1.06 and 1.59 at the Bragg peak of proton and He‐3 ions. The results demonstrated that LET, microdosimetric parameters (such as dose‐mean lineal energy) and RBE are nearly constant along the plateau region of Bragg curve, while all parameters increase within the Bragg peak and at the distal edge for both proton and He‐3 ions.Conclusion:The Monte Carlo codes should revise the fragmentation cross sections to more accurately simulate the physical properties of He‐3 ions. The increase in RBE for He‐3 ions is higher than for proton beams at the Bragg peak.

TH-E-BRC-05: Dosimetric Effects of Tissue Heterogeneity and Small Field Size in Proton Therapy - a Monte Carlo Study

Purpose: Proton beams have finite range and a potential to deliver a more conformal dose to the treatment target while sparing surrounding healthy tissues. To fully take advantage of the dosimetric advantage of proton beams, accurate dose calculation and range determination, especially for heterogeneous tissue and small fields, are important. The purpose of this work is to study the dosimetric effects of tissue density change and small field size in proton therapy plans using Monte Carlo methods. Methods: Using Monte Carlo code MCNPX 2.5.0, we simulated the proton dose distribution for the following cases: 1) a water phantom with heterogeneity inserts of various densities; 2) a water phantom using various beam sizes from 0.1, 0.25, 0.5, 2.0, 4.0 and 8.0 cm), 3) a phantom of low density (from 0.4 to 0.9 g/cm3 with 0.1 g/cm3 density interval) with proton beam energy at 150 MeV and 250 MeV respectively. Results: Proton penetration range and dose distributions changed significantly with inserts of various densities. Proton Bragg curves degraded when small beam with beam radius at several mm range. Proton Bragg curves degraded also when high energy proton beam irradiated to low density material. For high energy proton beam and small size beam, the Bragg curves degraded more significantly. For high energy proton beam and low density tissue, the Bragg curves degraded more significantly. Comparison of dose distributions between Monte Carlo simulation and treatment planning system calculations is underway. Conclusion: Accurate proton dose calculations are challenging in protontreatment planning for heterogeneous tissues. For low density tissue and small field size beams, proton Bragg curves degrades significantly and needs to take into account in protontreatment planning. By simulating detailed particle transport and energy deposition, Monte Carlo simulations provide accurate dose calculations in inhomogeneous tissues and for small field size beams.

Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

The well-known Bragg-Kleeman rule R CSDA = A ⋅ E has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range R CSDA of approximately monoenergetic protons with initial energy E 0 in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z(0 ≦ z ≦ R CSDA). A relativistic extension of the generalized Langevin equation yields the formula R CSDA = A ⋅ (E 0 + E/2M ⋅ c 2)p. The initial energy of therapeutic protons satisfies E 0 ≪ 2M ⋅ c 2(M ⋅ c 2 = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of R CSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations. Based on statistical quantum mechanics, an analysis of the Gaussian convolution and the Landau-Vavilov distribution function is carried out to describe these fluctuations. The Landau tail is derived as Hermite polynomial corrections of a Gaussian convolution. It is experimentally confirmed that proton Bragg curves with E 0 ≧ 120 MeV show a buildup, which increases with the proton energy. This buildup is explained by a theoretical analysis of impinging proton beamlets. In order to obtain a complete dose calculation model for proton treatment planning, some further aspects have to be accounted for: the decrease of the fluence of the primary protons due to nuclear interactions, the transport of released secondary protons, the dose contribution of heavy recoil nuclei, the inclusion of lateral scatter of the primary and secondary protons based on Molière’s multiple-scatter theory, and the scatter contributions of collimators. This study also presents some results which go beyond proton dose calculation models; namely, the application of the relativistic generalization of the Bragg-Kleeman rule to electrons and, in an appendix, a method to determine inelastic cross-sections of therapeutic protons in media of therapeutic interest.

Inverse problem of linear combinations of Gaussian convolution kernels (deconvolution) and some applications to proton/photon dosimetry and image processing

The deconvolution of a single Gaussian kernel is extended to a sum of Gaussian kernels with positive coefficients (case 1) and to a Mexican hat (case 2). In case 1 the normalization requires the sum of the normalized Gaussian kernels to be always 1, i.e. c0 + c1 + c2 + ⋅⋅⋅ = 1. Each coefficient satisfies ck > 0. In case 2 (Mexican hat) the properties c0 + c1 = 1 with c0 > 1and c1 < 0 hold; c1 = 1 − c0 has to be accounted for the normalization. We discuss examples of the deconvolution of both cases. Case 1 is considered in an analysis of transverse profiles (protons and photons) and in the deconvolution of CT images to eliminate scatter. Case 2 is applied to a proton Bragg curve measured by an ionization chamber and a diode detector. In the domain of the Bragg peak there is a different physical behavior between both measurement methods.

SU-FF-T-325: On the Role of Landau Tails in Buildup Effects of Bragg Curves for Proton Energies Beyond 140 MeV

Purpose: An improved version of the spot/raster scanning algorithm is being implemented in the proton dose model in ECLIPSE (Varian). Since the beam‐line of this treatment modality is rather different from other modalities using wheels and nozzles, measured Bragg curves also significantly differ in the initial plateau, resulting from an energy spectrum with a manifest Landau tail, if the initial proton energy is E ⩾ 140 MeV (in particular, if E ⩾ 200 MeV). Method and Materials:Proton Bragg curves have been delivered by different vendors and therapy centers, which show a significant buildup effect in the plateau region. The computational procedure is based on an analytical integration of Bethe‐Bloch equation and on the inelastic cross‐section of oxygen and some other materials (the transport of secondary protons is rigorously accounted for). The energy/range straggling of proton pencil beams used in scanning methods is described by a generalization of the composite Gaussian convolution kernel containing Landau tails in dependence of the energy (analytical representation of a Vavilov distribution function).Results: The experimental data obtained by scanning methods can excellently be explained by the generalized convolution model, which is only a composite Gaussian convolution for proton energies E ⩽ 140 MeV. The buildup effect in the initial plateau region is accurately described. Proton beam‐lines using range shifters provide Bragg curves with only very small indication of buildup effects, if E ⩾ 200 MeV. Conclusion: An accurate description of Bragg curves including buildup effects is an important feature of therapy planning systems, since the calculation of SOBP and monitor units (MU, absolute dosimetry) are incorrectly described by fitting curves neglecting Landau tails. Conflict of Interest: Varian Medical Systems.