Mean Excitation Energy Research Articles

On the Need for the Mean Excitation Energies of Polyatomic Ionic Systems

There are many cases where energy is deposited by fast hadrons into a gaseous target consisting of a variety of components. Examples include, but are not restricted to, planetary atmospheres [1], reactor plasmas [2,3], liquid crystals [4], and intergalactic space [5]. In all of these systems, although they differ widely in density (n), the incoming projectile will deposit energy into some mixture of atoms, molecules, their ions, and electrons.

Dose to ‘water-like’ media or dose to tissue in MV photons radiotherapy treatment planning: still a matter of debate

The difference between Monte Carlo Treatment Planning (MCTP) based on the assumption of ‘water-like’ tissues with densities obtained from CT procedures, or on tissue compositions derived from CT-determined densities, have been investigated. Stopping powers and electron fluences have been calculated for a range of media and body tissues for 6 MV photon beams, including changes in their physical data (density and stopping powers). These quantities have been used to determine absorbed doses using cavity theory. It is emphasized that tissue compositions given in ICRU or ICRP reports should not be given the standing of physical constants as they correspond to average values obtained for a limited number of human-body samples.It has been shown that mass stopping-power ratios to water are more dependent on patient-to-patient composition differences, and therefore on their mean excitation energies (I-values), than on mass density. Electron fluence in different media are also more dependent on media composition (and their I-values) than on density. However, as a consequence of the balance between fluence and stopping powers, doses calculated from their product are more constant than what the independent stopping powers and fluence variations suggest.Additionally, cancelations in dose ratios minimize the differences between the ‘water-like’ and ‘tissue’ approaches, yielding practically identical results except for bone, and to a lesser extent for adipose tissue. A priori, changing from one approach to another does not seem to be justified considering the large number of approximations and uncertainties involved throughout the treatment planning tissue segmentation and dose calculation procedures. The key issue continues to be the composition of tissues and their I-values, and as these cannot be obtained for individual patients, whatever approach is selected does not lead to significant differences from a water reference dose, the maximum of these being of the order of 5% for bone tissues. Considering, however, current developments in advanced dose calculation methods, planning in terms of dose-to-tissue should be the preferred choice, under the expectancy that progress in the field will gradually improve some of the crude approximations included in MCTP and numerical transport methods.The small differences obtained also show that a retrospective conversion from dose-to-tissue to dose-to-water, based on a widely used approach, would mostly increase the final uncertainty of the treatment planning process. It is demonstrated that, due to the difference between electron fluence distributions in water and in body tissues, the conversion requires an additional fluence correction that has so far been neglected. An improved expression for the conversion and data for the fluence correction factor are provided. These will be necessary even in a dose-to-tissue environment, for the normalization of the treatment plan to the reference dosimetry of the treatment unit, always calibrated in terms of absorbed dose to water.

WE‐D‐BRF‐05: Quantitative Dual‐Energy CT Imaging for Proton Stopping Power Computation

Purpose:To extend the two‐parameter separable basis‐vector model (BVM) to estimation of proton stopping power from dual‐energy CT (DECT) imaging.Methods:BVM assumes that the photon cross sections of any unknown material can be represented as a linear combination of the corresponding quantities for two bracketing basis materials. We show that both the electron density (ρe) and mean excitation energy (Iex) can be modeled by BVM, enabling stopping power to be estimated from the Bethe‐Bloch equation. We have implemented an idealized post‐processing dual energy imaging (pDECT) simulation consisting of monogenetic 45 keV and 80 keV scanning beams with polystyrene‐water and water‐CaCl2 solution basis pairs for soft tissues and bony tissues, respectively. The coefficients of 24 standard ICRU tissue compositions were estimated by pDECT. The corresponding ρe, Iex, and stopping power tables were evaluated via BVM and compared to tabulated ICRU 44 reference values.Results:BVM‐based pDECT was found to estimate ρe and Iex with average and maximum errors of 0.5% and 2%, respectively, for the 24 tissues. Proton stopping power values at 175 MeV, show average/maximum errors of 0.8%/1.4%. For adipose, muscle and bone, these errors result range prediction accuracies less than 1%.Conclusion:A new two‐parameter separable DECT model (BVM) for estimating proton stopping power was developed. Compared to competing parametric fit DECT models, BVM has the comparable prediction accuracy without necessitating iterative solution of nonlinear equations or a sample‐dependent empirical relationship between effective atomic number and Iex. Based on the proton BVM, an efficient iterative statistical DECT reconstruction model is under development.

A stoichiometric calibration method for dual energy computed tomography

The accuracy of radiotherapy dose calculation relies crucially on patient composition data. The computed tomography (CT) calibration methods based on the stoichiometric calibration of Schneider et al (1996 Phys. Med. Biol. 41 111–24) are the most reliable to determine electron density (ED) with commercial single energy CT scanners. Along with the recent developments in dual energy CT (DECT) commercial scanners, several methods were published to determine ED and the effective atomic number (EAN) for polyenergetic beams without the need for CT calibration curves. This paper intends to show that with a rigorous definition of the EAN, the stoichiometric calibration method can be successfully adapted to DECT with significant accuracy improvements with respect to the literature without the need for spectrum measurements or empirical beam hardening corrections. Using a theoretical framework of ICRP human tissue compositions and the XCOM photon cross sections database, the revised stoichiometric calibration method yields Hounsfield unit (HU) predictions within less than ±1.3 HU of the theoretical HU calculated from XCOM data averaged over the spectra used (e.g., 80 kVp, 100 kVp, 140 kVp and 140/Sn kVp). A fit of mean excitation energy (I-value) data as a function of EAN is provided in order to determine the ion stopping power of human tissues from ED–EAN measurements. Analysis of the calibration phantom measurements with the Siemens SOMATOM Definition Flash dual source CT scanner shows that the present formalism yields mean absolute errors of (0.3 ± 0.4)% and (1.6 ± 2.0)% on ED and EAN, respectively. For ion therapy, the mean absolute errors for calibrated I-values and proton stopping powers (216 MeV) are (4.1 ± 2.7)% and (0.5 ± 0.4)%, respectively. In all clinical situations studied, the uncertainties in ion ranges in water for therapeutic energies are found to be less than 1.3 mm, 0.7 mm and 0.5 mm for protons, helium and carbon ions respectively, using a generic reconstruction algorithm (filtered back projection). With a more advanced method (sinogram affirmed iterative technique), the values become 1.0 mm, 0.5 mm and 0.4 mm for protons, helium and carbon ions, respectively. These results allow one to conclude that the present adaptation of the stoichiometric calibration yields a highly accurate method for characterizing tissue with DECT for ion beam therapy and potentially for photon beam therapy.

Use of the BIPM calorimetric and ionometric standards in megavoltage photon beams to determine Wair and Ic

The BIPM graphite calorimeter standard for absorbed dose to water has been used in conjunction with an ionization chamber of known volume and with Monte Carlo simulations of these arrangements to determine the value for Wair in 60Co radiation and in accelerator photon beams up to 25 MV. The results show no evidence for a variation in Wair at the 0.2% level over this energy range. Taking the constancy of Wair as established, the best estimate is Wair = 34.03 eV with a standard uncertainty of 0.21%. Consistent with this analysis, and assuming the use of the grain density in evaluating the stopping power of graphite, is the value Ic = 81.1 eV for the mean excitation energy for graphite, with standard uncertainty 1.8 eV.

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 Mean Excitation Energy of Materials for Projectile Stopping Power

Determination of the Mean Excitation Energy of Materials for Projectile Stopping Power

Accurate evaluation of pressure effects on the electronic stopping cross section and mean excitation energy of atomic hydrogen beyond the Bethe approximation

Atomic hydrogen is used as a fundamental reference target system to explore pressure effects on the electronic stopping cross section, Se, of swift bare ions such as protons and α-particles. This is achieved by considering the hydrogen atom under pressure as a padded spherically-confined quantum system. Within this scheme, Se is calculated rigorously in the first Born approximation taking into account the full target excitation spectrum and momentum transfer distribution for different confinement conditions (pressures) and fixed projectile charge states. Pressure effects on the target mean excitation energy, I, are also formally calculated and compared with corresponding accurate calculations based on the Local Plasma Approximation (LPA). Even though atomic hydrogen is the simplest target system, its accurate treatment to account for the role of pressure in the stopping dynamics is found to provide useful means to understand the behavior of more complex systems under similar conditions. It is found that: (i) the region of projectile velocities for which the Bethe approximation remains valid is shifted towards higher values as pressure increases; (ii) shell corrections are enhanced relative to the free-atom case as pressure increases, and (iii) the LPA seems to underestimate I as pressure is increased. The results of this work for atomic hydrogen may serve as accurate benchmark reference values for studies of pressure effects on Se and I using different methodologies.

Neonization method for stopping, mean excitation energy, straggling, and for total and differential ionization cross sections of CH4, NH3, H2O and FH by impact of heavy projectiles

We propose a neonization method to deal with molecules composed by hydrides of the second row of the periodic table of elements: CH4, NH3, OH2 and FH. This method describes these ten-electron molecules as dressed atoms in a pseudo-spherical potential. We test it by covering most of the inelastic collisional magnitudes of experimental interest: ionization cross sections (total, single and double differential), stopping power, energy-loss straggling and mean excitation energy. To this end, the neonization method has been treated with different collisional formalisms, such as the continuum-distorted-wave–eikonal-initial-state, the first order Born, and the shell-wise local plasma approximations. We show that the present model reproduces the different empirical values with high reliability in the intermediate to high-energy region. We also include the expansion of the spherical wave functions in terms of Slater-type orbitals and the analytic expression for the spherical potentials. This makes it possible in the future to tackle present neonization strategy with other collisional models.

Coupled cluster calculations of mean excitation energies of the noble gas atoms He, Ne and Ar and of the H2 molecule

Using an asymmetric Lanczos chain algorithm for the calculation of the coupled cluster linear response functions at the coupled cluster singles and doubles (CCSD) and coupled cluster singles and approximate iterative doubles (CC2) levels of approximation, we have calculated the mean excitation energies of the noble gases He, Ne and Ar, and of the hydrogen molecule (H2). Convergence with respect to the one-electron basis set was investigated in detail for families of correlation-consistent basis sets including both augmentation and core-valence functions. We find that the electron correlation effects at the CCSD level change the mean excitation energies obtained at the uncorrelated Hartree–Fock level by about 1%. For the two-electron systems He and H2, our CCSD results (for a Lanczos chain length equal to the full excitation space), I0 = 42.28 eV (helium) and I0 = 19.62 eV (H2), correspond to full configuration interaction results and are therefore the exact, non-relativistic theoretical values for the mean excitation energy of these two systems within the Bethe theory for the chosen basis set and, in the case of H2, at the experimental equilibrium geometry.

Calculations of stopping powers and inelastic mean free paths for 20 eV–20 keV electrons in 11 types of human tissue

Systematic calculations are performed for determining the stopping powers (SP) and inelastic mean free paths (IMFP) for 20eV–20keV electrons in 11 types of human tissue. The calculations are based on a dielectric model, including the Born−Ochkur exchange correction. The optical energy loss functions (OELF) are empirically evaluated, because of the lack of available experimental optical data for the 11 tissues under consideration. The evaluated OELFs are examined by the f-sum rule expected from the dielectric response theory, and by calculation of the mean excitation energy. The calculated SPs are compared with those for PMMA (polymethylmethacrylate, a tissue equivalent material) and liquid water. The SP and IMFP data presented here are the results for the 11 human tissues over the energy range of 20eV–20keV, and are of importance in radiotherapy planning and for studies of various radiation effects on human tissues.

Extrapolation of the Bethe equation for electron stopping powers to intermediate and low electron energies by empirical simulation of target effective mean excitation energy and atomic number

A series of simple stopping power (SP) formulas, modified from the relativistic Bethe equation, is presented that is based on the concepts of target effective atomic number and mean excitation energy (MEE). The analytical model function is constructed to approximate experimental or calculated SPs at low electron energies and tend asymptotically to the relativistic Bethe function at high energies. The energy dependencies of our effective values, in contrast with theoretical approaches, are defined empirically by parametrization with tuning parameters. A least-squares fitting routine based on the Levenberg–Marquardt algorithm was developed. We utilize the material parameters and numerical calculations of SPs from optical data using the full Penn-algorithm. Our formula is thought to be applicable for energies above 60eV. Our simulations of SPs for 41 elemental solids are found to be in good agreement with published numerical results. The flexibility of a general empirical formula is shown. Shortened formulas were developed that are applicable for particular energy ranges, and effective MEEs are proposed that differ from previously recommended values. The presented formulas may be used for analytical calculation of SPs over a broad projectile energy region.

Evaluation of slowing down of proton and deuteron beams in CH2, LiH, and Al partially ionized plasmas

In this work, proton and deuteron stopping due to free and bound electrons in partially ionized plasma targets is evaluated. The stopping of target free electrons is calculated using the dielectric formalism, well described in our previous works. In the case of target bound electrons, a short expression to calculate their contribution to the stopping is used, where mean excitation energies are obtained by means of the Hartree-Fock method. Experiments with different kinds of plasmas are analyzed. For LiH plasma, estimated plasma stopping fits experimental data very well, within the error bars, recognizing the well-known enhanced plasma stopping. In the case of CH_{2} plasma, we obtain, from estimated ionization, that total stopping power increases when target electron density does. Our estimations are very similar to experimental data which show the same behavior with target free and bound electron density. Finally, in Al plasma, we compare directly our calculations with experimental data finding a very close agreement, where both stoppings have the same dependence on target ionicity. All these comparisons verify our theoretical model which estimates the proton or deuteron energy loss in partially ionized plasmas.

Universal scaling behavior of molecular electronic stopping cross section for protons colliding with small molecules and nucleobases

The electronic stopping cross section and mean excitation energy for molecules and 5 nucleobases have been calculated within the first Born approximation in terms of an orbital decomposition to take into account the molecular structure. The harmonic oscillator (HO) description of the stopping cross section together with a Floating Spherical Gaussian Orbital (FSGO) model is implemented to account for the chemical composition of the target. This approach allows us to use bonds, cores, and lone pairs as HO basis to describe the ground state molecular structure. In the HO model, the orbital angular frequency is the only parameter that connects naturally with the mean excitation energy. As a result, we obtain a simple expression for the equivalent mean excitation energy in terms of the orbital radius parameter, as well as an analytical expression of the stopping cross section. For gas phase molecular targets, we provide HO based orbital mean excitation energies to describe any molecule containing C, N, O, H, and P atoms. We present results for protons colliding with H2, N2, O2, H2O, CO2, propylene (C3H6), methane (CH4), ethylene (C2H4) and the nucleobases – guanine (C5H5N5O), cytosine (C4H5N2O2), thymine (C5H6N2O2), adenine (C5H5N5) and uracil (C4H4N2O2). The results for the stopping cross section are compared with available experimental and theoretical data showing good to excellent agreement in the region of validity of the model. The HO approach allows us to obtain a universal stopping cross section formula to describe a universal scaling behavior for the energy loss process. The universal scaled curve is confirmed by the experimental data.

Spencer–Attix water/medium stopping-power ratios for the dosimetry of proton pencil beams

This paper uses Monte Carlo simulations to calculate the Spencer–Attix water/medium stopping-power ratios (sw, med) for the dosimetry of scanned proton pencil beams. It includes proton energies from 30 to 350 MeV and typical detection materials such as air (ionization chambers), radiochromic film, gadolinium oxysulfide (scintillating screens), silicon and lithium fluoride. Track-ends and particles heavier than protons were found to have a negligible effect on the water/air stopping-power ratios (sw, air), whereas the mean excitation energy values were found to carry the largest source of uncertainty. The initial energy spread of the beam was found to have a minor influence on the sw, air values in depth. The water/medium stopping-power ratios as a function of depth in water were found to be quite constant for air and radiochromic film—within 2.5%. Also, the sw, med values were found to have no clinically relevant dependence on the radial distance—except for the case of gadolinium oxysulfide and proton radiography beams. In conclusion, the most suitable detection materials for depth-dose measurements in water were found to be air and radiochromic film active layer, although a small correction is still needed to compensate for the different sw, med values between the plateau and the Bragg peak region. Also, all the detection materials studied in this work—except for gadolinium oxysulfide—were found to be suitable for lateral dose profiles and field-specific dose distribution measurements in water.

The clinical impact of uncertainties in the mean excitation energy of human tissues during proton therapy

Uncertainties in the estimated mean excitation energies (I-values) needed for calculating proton stopping powers can be in the order of 10–15%, which introduces a fundamental limitation in the accuracy of proton range determination. Previous efforts have quantified shifts in proton depth dose distributions due to I-value uncertainties in water and homogenous tissue phantoms. This study is the first to quantify the clinical impact of I-value uncertainties on proton dose distributions within patient geometries. A previously developed Geant4 based Monte Carlo code was used to simulate a proton treatment plan for three patients (prostate, pancreases, and liver) with varying tissue I-values. A uniform variation study was conducted in which the tissue I-values were varied by ±5% and ±10% of the nominal values as well as a probabilistic variation study in which the I-values were randomly sampled according to a normal distribution with the mean equal to the nominal I-value and a standard deviation of 5 and 10% of the nominal values. Modification of tissue I-values impacted both the proton range and SOBP width. R90 range shifts up to 7.7 mm (4.4.%) and R80 range shifts up to 4.8 mm (1.9%) from the nominal range were recorded. Modulating the tissue I-values by 10% the nominal value resulted in up to a 3.5% difference mean dose in the target volumes and organs at risk compared to the nominal case. The range and dose differences were the largest for the deeper-seated prostate and pancreas cases. The treatments that were simulated with randomly sampled I-values resulted in range and dose differences that were generally within the upper and lower bounds set by the 10% uniform variations. This study demonstrated the impact of I-value uncertainties on patient dose distributions. Clearly, sub-millimeter precision in proton therapy would necessitate a reduction in I-value uncertainties to ensure an efficacious clinical outcome.

電子に対する制限質量衝突阻止能の計算・検索ソフトウェアの開発

In external radiotherapy, the absorbed doses are measured using an ionization process in a gas-filled ionization chamber and estimated by the extended cavity theory. The calculation requires both the W-value of cavity gas and the restricted mass collision stopping powers (L/ρ) for the gas and medium. ICRU Report 37 gives us the data regarding the mass collision stopping powers (S/ρ) for several elements and chemical compounds or mixtures. However, there are no detailed data for L/ρ. In this study, we developed an in-house program to calculate the L/ρ for arbitrary substances by the use of the equation described in ICRU Report 37. With this program, we can search the calculated L/ρ easily. When we calculated L/ρ for chemical compounds and mixtures with implementation of Bragg's additivity rule, a large error of density effect corrections was observed. Therefore, our program adopted both the mean excitation energy and density effect correction obtained by ESTAR, which was developed by Berger et al. With adoption of these values, the calculation accuracy of our program was improved. Our program is useful to search L/ρ for radiation dosimetry in radiotherapy.

Energy Deposition by Swift Hadrons in Mixed Gas Targets: The Mean Excitation Energy of Planetary Atmospheres

Energy Deposition by Swift Hadrons in Mixed Gas Targets: The Mean Excitation Energy of Planetary Atmospheres

Vibrational excitation of a molecule by a resonance current

Correct expressions are obtained for calculating a tunnel-resonance current through molecules. The participation of molecular vibrations in the resonance charge transfer through a molecule and vibrational excitation of the molecule are determined by the reorganization energy Er of the vibrational system depending on the displacement of the equilibrium position of vibrational modes in passing from the neutral molecule to the resonance state of a molecular ion. The mean excitation energy of the molecule during the propagation of an elementary charge changes from Er at the voltage across electrodes close to the threshold up to 2Er at voltages considerably exceeding the threshold voltage. An expression is obtained for the stationary vibrational temperature of the molecule, which is proportional to the resonance current.

Role of surfaces and interfaces in ion-beam energy deposition processes in layered and nanolayered materials

The role of surfaces and interfaces in the inelastic energy deposition rate of swift ions traversing a layered material is analyzed in terms of quantum confinement effects on the atomic mean excitation energies for target atoms close to a physical limiting boundary. Noticeable differences in energy deposition rates at surfaces and interfaces relative to the bulk values are predicted depending on the projectile energy. The results of this study suggest that quantum confinement effects on the energy deposition process in nanolayered materials should be properly accounted for in any stopping theory.