Stopping Power Calculations Research Articles

Proton radiography to improve proton therapy treatment

The quality of cancer treatment with protons critically depends on an accurate prediction of the proton stopping powers for the tissues traversed by the protons. Today, treatment planning in proton radiotherapy is based on stopping power calculations from densities of X-ray Computed Tomography (CT) images. This causes systematic uncertainties in the calculated proton range in a patient of typically 3–4%, but can become even 10% in bone regions [1,2,3,4,5,6,7,8]. This may lead to no dose in parts of the tumor and too high dose in healthy tissues [1]. A direct measurement of proton stopping powers with high-energy protons will allow reducing these uncertainties and will improve the quality of the treatment.Several studies have shown that a sufficiently accurate radiograph can be obtained by tracking individual protons traversing a phantom (patient) [4,6,10]. Our studies benefit from the gas-filled time projection chambers based on GridPix technology [2], developed at Nikhef, capable of tracking a single proton. A BaF2 crystal measuring the residual energy of protons was used. Proton radiographs of phantom consisting of different tissue-like materials were measured with a 30×30 mm2 150 MeV proton beam. Measurements were simulated with the Geant4 toolkit.First experimental and simulated energy radiographs are in very good agreement [3]. In this paper we focus on simulation studies of the proton scattering angle as it affects the position resolution of the proton energy loss radiograph. By selecting protons with a small scattering angle, the image quality can be improved significantly.

Double Differential Charged Particle Emission Cross Sections and Stopping Power Calculations for Structural Fusion Materials 58,60Ni

In this study, double differential light charged particle emission cross section, which is a fundamental data to determine nuclear heating and material damages in structural fusion material research, for 58,60Ni target nuclei have been calculated by the TALYS 1.6 code at 14.8 MeV neutron incident energy and compared with available experimental data in EXFOR library. While the compound nucleus formation process contribution was found as dominant in the emission of proton and alpha particles, pre-equilibrium contribution was existed in the deuteron emission and the direct reaction contribution also was seen as dominant in higher particle emission energies. Penetrating distance and stopping powers also have been calculated for the alphas, deuterons and protons in 58,60Ni using GEANT4 code and compared with previous works of 50,52Cr and 46,48Ti.

Accurate stopping power calculations for antiprotons and protons

SynopsisThe convergent close-coupling method is applied to calculate antiproton and proton stopping cross sections for atomic and molecular targets. Excellent agreement with experimental measurements is obtained for antiprotons in helium while unexpectedly large disagreement is found for the hydrogen molecule, which is inconsistent with very good agreement between our ionisation cross section and the experiment.

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.

Improved calibration of mass stopping power in low density tissue for a proton pencil beam algorithm

Dose distributions for proton therapy treatments are almost exclusively calculated using pencil beam algorithms. An essential input to these algorithms is the patient model, derived from x-ray computed tomography (CT), which is used to estimate proton stopping power along the pencil beam paths. This study highlights a potential inaccuracy in the mapping between mass density and proton stopping power used by a clinical pencil beam algorithm in materials less dense than water. It proposes an alternative physically-motivated function (the mass average, or MA, formula) for use in this region. Comparisons are made between dose-depth curves calculated by the pencil beam method and those calculated by the Monte Carlo particle transport code MCNPX in a one-dimensional lung model. Proton range differences of up to 3% are observed between the methods, reduced to <1% when using the MA function. The impact of these range errors on clinical dose distributions is demonstrated using treatment plans for a non-small cell lung cancer patient. The change in stopping power calculation methodology results in relatively minor differences in dose when plans use three fields, but differences are observed at the 2%–2 mm level when a single field uniform dose technique is adopted. It is therefore suggested that the MA formula is adopted by users of the pencil beam algorithm for optimal dose calculation in lung, and that a similar approach is considered when beams traverse other low density regions such as the paranasal sinuses and mastoid process.

Double Differential Cross Section and Stopping Power Calculations of Light Charged Particle Emission for the Structural Fusion Materials 50,52Cr

Double differential cross section is a fundamental value to determine nuclear heating and material damages in structural fusion material research. In this study, double differential light charged particle emission cross sections for 50,52Cr target nuclei have been calculated by the TALYS 1.6 code at 14.8 MeV incident neutron energy. Penetrating distance and stopping powers have been calculated for the alpha, deuteron and proton particles, taking into consideration all possible reactions in 50,52Cr for incident energies of 0.5–22.2 MeV using GEANT4 calculation code. The compound nucleus formation process dominates the emission of proton and alpha particles. Direct reaction contribution becomes dominant in higher particle emission energies. The calculated double differential cross sections have been compared with the available experimental data taken from the literature.

Minimal dielectric polarization stopping power in white dwarfs

In this paper, we investigate the energy loss of ions by arbitrarily degenerate electron fluid, in the framework of hydrodynamic model by incorporating the generalized relativistic degeneracy pressure, Wigner–Seitz cell Coulomb interactions, and electron spin-exchange pressures for a wide range of electron number-density regimes relevant to the solid density (SD), inertial confinement fusion (ICF), warm dense matter (WDM), and super-dense astrophysical objects, such as white dwarf (WD) stars. It is found that the use of non-relativistic degeneracy pressure for electron fluid, instead of the exact Chandrasekhar relativistic degeneracy pressure, for the ICF density regime and beyond can introduce significant relative error to the stopping power calculation. Therefore, current study may introduce a significant change to the ICF scheme of super-compressed fuel. It is further revealed that the relativistic degeneracy parameter, R0, and the atomic number of constituent ions, Z, significantly affect the maximum stopping power velocity of ions. We also discover that the velocity-averaged energy loss function becomes minimal in electron number density typical of white dwarf stars, n0≃2×1030 cm−3. It is found that the characteristic density for the minimal ion beam energy loss does not depend on the value of other plasma parameters, such as the ion–electron collision rate and the ion temperature or its atomic number. The latter finding, in particular, may help in better understanding of fusion-burning waves in dense compact stars and their cooling mechanisms.

Quantum Dynamics Simulation of Electrons in Materials on High-Performance Computers

Advancement in high-performance computing allows us to calculate properties of increasingly complex materials with unprecedented accuracy. At the same time, to take full advantage of modern leadership-class supercomputers, the calculations need to scale well on hundreds of thousands of processing cores. We demonstrate such high scalability of our recently developed implementation of Ehrenfest non-adiabatic electron-ion dynamics up to 1 million floating-point processing units on two different leadership-class computing architectures. As a representative example of material properties that derive from quantum dynamics of electrons, we demonstrate the accurate calculation of electronic stopping power, which characterizes the rate of energy transfer from a high-energy particle to electrons in materials. We discuss the specific case of crystalline gold with a hydrogen atom as the high-energy particle, and we illustrate detailed scientific insights that can be obtained from the quantum dynamics simulation at the electronic structure level. Please note that two animation videos of the time evolution for Figure 3 are available as Web extras at http://youtu.be/WxiMZ2DVBbM and http://youtu.be/bAcaxF9ARzM.

Conversion of Magnetic Energy of Runaway Electrons During Disruption Termination

AbstractA substantial portion of poloidal magnetic energy stored in the RE beam could dissipate in the first wall (FW) armor due to ohmic dissipation of inductive current. Relatively small part of magnetic energy can also be converted into heat during a direct impact of the RE beam on the FW due to the ohmic dissipation of a return current, induced by penetration of the RE beam into a metal in the skin time scale. The observed increase of temperature at a spot on the JET dump plate upon increasing the RE current can be explained by assuming that 50 % of the RE energy, predominantly magnetic energy, is converted into heat. Calculations of the RE stopping power (SP) onto the ITER FW Be bulk armor predict strong erosion. While the threshold energy for beryllium melting is about 5 MJ/m2, the RE heat deposition is expected to be almost twice as large. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Simulation of the direct production of 99mTc at a small cyclotron

Usually 99mTc is produced indirectly through generator 99Mo/99mTc. In the present study, the direct production of this radioisotope by charged particle irradiation was investigated using Monte Carlo method. After scouting of the reactions that produce 99mTc, excitation functions of these reactions were predicted by optical model components in the TALYS-1.6 code. Suitable energy range of projectile for this production was selected by spotting of maximum cross section and minimum impurity due to other emission channels. Then target geometry was designed based on stopping power calculation by the SRIM code. Thick target yield of 100Mo(p,2n)99mTc, 98Mo(p,γ)99mTc and natMo(p,x)99mTc reactions was predicted by the result of excitation function and stopping power calculations. Finally, 100Mo(p,2n)99mTc reaction was selected as a primary reaction for the direct production of 99mTc and its process was simulated by employing the MCNPX code to calculate the energy distribution of proton in the 100Mo target body and estimation of residual nuclei during irradiation. Good agreement was obtained between the experimental, the theoretical, and the simulation-based (analytical and directly) production yields. This study demonstrated that Monte Carlo provides a method for the design and optimization of targets for the radionuclide production purposes.

Stopping power of 1H and 4He in lithium niobate

Lithium niobate is an important material for applications in bulk optoelectronics and integrated optics devices. Ion beam analysis methods are often used to study this material. However, to our knowledge a single study has been presented in 1996 on measurement of stopping powers in LiNbO3 at velocities usual in ion beam analysis, for protons and deuterons near the stopping power maximum. The results were 15% lower than the values calculated from the elemental Li, Nb and O stopping powers then available together with the Bragg rule. In practice, all ion beam analysis studies of LiNbO3 still use the Bragg rule. We have used a bulk method, previously developed by us and applied successfully to other systems, to determine experimentally the stopping power of lithium niobate for 1H and 4He ions in the energy range 0.3–2.3MeV. The results of our measurements and bulk method analysis are presented and discussed in the context of currently available stopping power calculations.

Energy deposition of H and He ion beams in hydroxyapatite films: a study with implications for ion-beam cancer therapy.

Ion-beam cancer therapy is a promising technique to treat deep-seated tumors; however, for an accurate treatment planning, the energy deposition by the ions must be well known both in soft and hard human tissues. Although the energy loss of ions in water and other organic and biological materials is fairly well known, scarce information is available for the hard tissues (i.e., bone), for which the current stopping power information relies on the application of simple additivity rules to atomic data. Especially, more knowledge is needed for the main constituent of human bone, calcium hydroxyapatite (HAp), which constitutes 58% of its mass composition. In this work the energy loss of H and He ion beams in HAp films has been obtained experimentally. The experiments have been performed using the Rutherford backscattering technique in an energy range of 450-2000 keV for H and 400-5000 keV for He ions. These measurements are used as a benchmark for theoretical calculations (stopping power and mean excitation energy) based on the dielectric formalism together with the MELF-GOS (Mermin energy loss function-generalized oscillator strength) method to describe the electronic excitation spectrum of HAp. The stopping power calculations are in good agreement with the experiments. Even though these experimental data are obtained for low projectile energies compared with the ones used in hadron therapy, they validate the mean excitation energy obtained theoretically, which is the fundamental quantity to accurately assess energy deposition and depth-dose curves of ion beams at clinically relevant high energies. The effect of the mean excitation energy choice on the depth-dose profile is discussed on the basis of detailed simulations. Finally, implications of the present work on the energy loss of charged particles in human cortical bone are remarked.

Determination of the maximum energy loss for electron stopping power calculations and its effect on backscattering electron yield in Monte-Carlo simulations applying continuous slowing-down approximation

The maximum energy loss for electron stopping power calculations by the full Penn algorithm within the dielectric formalism is determined with taking into account the contribution of electron and plasmon excitations. Use of these calculated electron stopping powers in Monte Carlo simulations applying continuous slowing down approximation gives the backscattering electron yields in much better agreement with experimental data than previous other theoretical results. The muffin-tin model is used to describe the electron elastic scattering by atom bound in solids with taking into account the exchange correlation and polarization effect.

Semi empirical formula for electronic stopping power determination of 24Mg, 27Al and 28Si ions crossing Formvar foil in the ion energy domain of LSS theory

We have determined continuous stopping power of heavy ions in thin Formvar foil for 28Si, 27Al and 24Mg ions over an energy range of (0.1–0.5)MeV/nucleon. Heavy Ions Elastic Recoil Detection Analysis (HI-ERDA) technique coupled with time of flight (ToF) spectrometer has been used to measure energy loss of charged particles in this thin absorber. Lindhard, Scharff and Schiott (LSS) theory compared with the corresponding determined stopping values in Formvar, shows significantly large deviations. However, a novel semi empirical expression has been proposed here and tested for better stopping power calculations at low velocity in the ion energy domain of LSS theory for 28Si, 27Al and 24Mg ions crossing thin Formvar foil. The results were compared to the obtained experimental stopping power data, predictions of LSS theory and also to those generated by SRIM-2010 computer code. The obtained results exhibit good agreement with experimental data.

Stopping Powers of Protons in Biological Human Body Substances

In this paper we present a simple method for the calculation of mass stopping power (in MeV cm 2 /g) of protons from 0.5 Mev to 200 MeV energy range in biological human body substances such as water, bone, muscle and tissue. The proposed relations have been described in terms of energy of proton and mean ( ) of atomic number (Z) and atomic weight (A). A fairly good agreement has been found between our simplified values for mass stopping power of protons for water, bone, muscle and tissue and that of Mukherjee calculated values.

Stopping power and CSDA range calculations for incident electrons and positrons in breast and brain tissues

The stopping power in some biological compounds for electrons and positrons was calculated over the energy range from 100 eV to 1 GeV. Total stopping power was obtained by summing the electronic (collisional) and radiative stopping power of the target materials and then employing the continuous slowing down approximation (CSDA) to calculate the path length of incident particles in the target. An effective charge approximation was used for the calculation of collisional stopping power, and an analytical expression for the radiation length was applied to obtain the radiative stopping power. Calculations of stopping power and CSDA range were based mostly on analytical expressions, to allow for an easy calculation of these parameters. The results were tabulated and compared with available data.

The influence of silicone oil used in ophthalmology on the proton therapy of uveal melanomas

In ocular proton therapy the important parameters range and modulation of the proton field are calculated by a simple geometric ray tracking. Due to the assumed homogeneous eye tissue, the relative-to-water proton stopping power is nearly constant within the radiation field. In cases when silicone oil tamponades are used, this will no longer hold. CT-data which are necessary to estimate the path length of protons within the oil show bigger attenuation of x-rays then in eye tissue. The use of a CT-calibration curve to deduce the relative-to-water electron density for proton stopping power calculation would be misleading giving a value of 1.05 and thus a higher proton stopping power. In reality the relative-to-water electron density is smaller, namely 0.95, leading to a proton range prolonged by about 11% of the path length within the silicone oil, if the demand for the range adjustment would not be recognized (missing information from ophthalmologists or no CT data). This finding is congruent in analytical and Monte Carlo calculations as well as in experimental investigations, being presented here. The misleading result of the CT calibration curve is explained and therapeutic consequences are demonstrated. Multiple Coulomb scattering in silicone oil does not affect the size of the planed irradiation field.

Electronic stopping cross sections for protons in Al2O3: an experimental and theoretical study

The electronic stopping cross section (SCS) of Al2O3 for proton beams is studied both experimentally and theoretically. The measurements are made for proton energies from 40 keV up to 1 MeV, which cover the maximum stopping region, using two experimental methods, the transmission technique at low energies (~40–175 keV) and the Rutherford backscattering at high energies (≈190–1000 keV). These new data reveal an increment of 16% in the SCS around the maximum stopping with respect to older measurements. The theoretical study includes electronic stopping power calculations based on the dielectric formalism and on the transport cross section (TCS) model to describe the electron excitations of Al2O3. The non-linear TCS calculations of the SCS for valence electrons together with the generalized oscillator strengths (GOS) model for the core electrons compare well with the experimental data in the whole range of energies considered.

A study on the calculation of stopping power and CSDA Range for incident positrons

In this work, we have given a new method to calculate stopping power for incident positrons in a number of different targets. Our method are based on the Gümüş’s method for incident electrons. We have calculated the collisional and radiative stopping power and then found the total stopping power of targets. For collisional stopping power, we used Gümüş’s method for electrons but adapted it to the positrons. Tsai’s method has been used to calculate the radiative stopping power and after the founding the total stopping power with these two values, we used the Continuous Slowing Down Approximation to obtain the range values. Calculation was done for Al, Si, Ag, LiF, CaF 2 and H 2O targets and results were compared with the ICRU 37 report and Penelope 2005 code and found that agreement is less than 10%.

Energy loss of keV fluorine ions scattered off a missing-row reconstructed Au(110) surface under grazing incidence

A joint experimental and theoretical study of energy loss is presented for 1-to-4-keV fluorine negative ions in grazing scattering on a missing-row reconstructed Au(110) surface. Measurements of energy losses for various azimuthal orientations of the crystal have been performed by means of a time-of-flight method with a pulsed beam. The dependence of the fraction of surviving negative ions on azimuthal angles, was determined. Our energy-loss data are discussed in light of trajectory and stopping-power calculations, where the explicit inclusion of the nonuniform electron density at the surface provides good agreement with the experimental data. The simulation allows us to delineate various trajectory classes that correspond to different contributions in the energy-loss spectra for various azimuthal orientations of the surface.