Review and history of photon cross section calculations

Monte Carlo calculated photon interaction coefficients for several body tissues

Absorption of energy in body tissues because of radiation interactions may induce harmful outcomes such as cancer and hereditary effects due to a variety of damages in the integrity and activity of the cells. This study presents Monte Carlo calculated $\boldsymbol{\mu} /\boldsymbol{\rho}$, ${\boldsymbol{\mu}}_{\boldsymbol{en}}/\boldsymbol{\rho}$ and ${\boldsymbol{\mu}}_{\boldsymbol{tr}}/\boldsymbol{\rho}$ values of some common tissues and organs found in the human body (namely, adipose tissue, blood, bone-cortical, brain-grey/white matter, breast tissue, eye lens, lung tissue, muscle-skeletal, ovary, soft tissue and testes) as well as water for comparison purposes. The simulation model involves a monoenergetic point source producing a pencil beam where, depending on the parameter under study, particle flux, energy flux or absorbed dose from photon interactions are scored in the range of 10 keV to 20 MeV energy. The simulations were performed using the Monte Carlo package MCNP6.1 and provided $\boldsymbol{\mu} /\boldsymbol{\rho}$, ${\boldsymbol{\mu}}_{\boldsymbol{en}}/\boldsymbol{\rho}$ and ${\boldsymbol{\mu}}_{\boldsymbol{tr}}/\boldsymbol{\rho}$ values. The data produced in this study were compared with theoretical photon attenuation data from the XMUDAT database and demonstrated good agreement. The results, which are based on a simple model geometry and pure elemental compositions, indicate that this approach can be applied to evaluate $\boldsymbol{\mu} /\boldsymbol{\rho}$, ${\boldsymbol{\mu}}_{\boldsymbol{en}}/\boldsymbol{\rho}$ and ${\boldsymbol{\mu}}_{\boldsymbol{tr}}/\boldsymbol{\rho}$ in a broad energy range for any element, compound or mixture.

Relativistic impulse approximation-based compton component of mass energy absorption coefficients (cm2/g) for few materials of medical interest

Total, whole-atom, individual and integrated Compton scattering cross sections and Compton energy absorption scattering cross sections are evaluated for light elements, such as, H, C, N, O, P, and Ca, with relativistic impulse approximation methods. Most of the phantom materials composed of these elements, which are the basic constituents of biological soft-tissue and attenuation through them, provides potential source of information. Compton scattering cross-sections for few biological materials, such as, H2O, C2H4, C8H8, C5H8O2, C6H11NO, C16H14O3, C55H102O6, [Ca3(PO4)]3Ca (OH)2 of medical interest, have been evaluated with the use of double differential scattering cross-section based on impulse approximation. Utilized these values to evaluate the Compton energy absorption cross sections and Compton component of mass energy absorption coefficients (cm2/g) in the energy region from 0.005 to 10 MeV. The derived results are compared with the theoretical tabulations.

An experimental approach to determine the gamma radiation interaction mean free path and exposure buildup factor for biomolecules

This experimental approach was designed to understand the gamma interaction parameters for the essential biomolecules, including starch soluble, cholesterol, myristic acid, glucose, oxalic acid, dextrose, salicylic acid, ethyl cellulose and sucrose. The empirical determination of gamma interaction parameters, such as interaction mean-free-path (MFP), buildup factor, and effective atomic number (Zeff) was performed by measuring mass attenuation coefficient (μ/ρ) at energies of 356 keV, 511 keV, 662 keV, 1173 keV, 1275 keV and 1332 keV. This was achieved using weak radioactive sources and a NaI(Tl) scintillation spectrometer with collimated and non-collimated transmission geometry. The experimentally determined values of gamma-ray interaction parameters were obtained non-destructively and precisely agreeing with the expected values from simulations and codes. In addition, the research findings also revealed a novel trend in gamma interaction mean free path as a function of energy and variable buildup factors for the selected biomolecules. These research findings provide valuable insight into the process of gamma radiation interaction. This approach may fulfil the increasing demand of medical, technical and academic research laboratories for a cost-effective and reliable empirical methodology to understand gamma radiation interaction with matter.

A complex Gaussian approach to molecular photoionization

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by nonlinear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH₃ and H₂ O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.

Impact of photoelectric cross section data on systematic uncertainties for Monte Carlo breast dosimetry in mammography

Monte Carlo (MC) simulations are employed extensively in breast dosimetry studies. In the energy interval of interest in mammography energy deposition is predominantly caused by the photoelectric effect, and the corresponding cross sections used by the MC codes to model this interaction process have a direct influence on the simulation results. The present work compares two photoelectric cross section databases in order to estimate the systematic uncertainty, related to breast dosimetry, introduced by the choice of cross sections for photoabsorption. The databases with and without the so-called normalization screening correction are denoted as 'renormalized' or 'un-normalized', respectively. The simulations were performed with the PENELOPE/penEasy code system, for a geometry resembling a mammography examination. The mean glandular dose (MGD), incident air kerma (K_air), normalized glandular dose (DgN) and glandular depth-dose (GDD(z)) were scored, for homogeneous breast phantoms, using both databases. The AAPM Report TG-195 case 3 was replicated, and the results were included. Moreover, cases with heterogeneous and anthropomorphic breast phantoms were also addressed. The results simulated with the un-normalized cross sections are in better overall agreement with the TG-195 data than those from the renormalized cross sections; for MGD the largest discrepancies are 0.13(6)% and 0.74(5)%, respectively. The MGD,K_airand DgN values simulated with the two databases show differences that diminish from approximately 10%/3%/6.8% at 8.25 keV down to 1.5%/1.7%/0.4% at 48.75 keV, respectively. For polyenergetic spectra, deviations up to 2.5% were observed. The disagreement between the GDDs simulated with the analyzed databases increases with depth, ranging from -1% near the breast entrance to 4% near the bottom. Thus, the choice of photoelectric cross section database affects the MC simulation results of breast dosimetry and adds a non-negligible systematic uncertainty to the dosimetric quantities used in mammography.

Comparison between MCNP5, Geant4 and experimental data for gamma rays attenuation of PbO-BaO-B2O3 glasses

Monte Carlo simulations, MCNP5 and Geant4 codes were developed to investigate radiation shielding properties of xPbO-(50-x) BaO-50B2O3 (where 5 ≤ x ≤ 45 mol%) consider to be glass systems. The mass attenuation coefficients were evaluated for different PbO concentration in the glass samples for varies photon energies of 0.356, 0.662, 1.173 and 1.332 MeV. The obtained mass attenuation coefficient values used to calculate half-value layer, effective atomic number, and electron density. The simulation parameters were compared with experimental data. Results show that the simulation results of mass attenuation coefficients for all PbO concentrations were generally in good agreement with experimental results, however, mass attenuation coefficient values calculated using Geant4 were slightly lower than MCNP5 and experimental data on the low energy of 0.356 MeV. The results obtained from MCNP5 and Geant4 codes might be able to assessment mass attenuation for different glass systems. Furthermore, gamma ray, fast neutron and charged particle interaction for the glass systems were studied using buildup factors, fast neutron removal cross sections and ranges respectively.

Imaging of Biological Materials and Cells by X-ray Scattering and Diffraction

Cells and biological materials are large objects in comparison to the size of internal components such as organelles and proteins. An understanding of the functions of these nanoscale elements is key to elucidating cellular function. In this review, we describe the advances in X-ray scattering and diffraction techniques for imaging biological systems at the nanoscale. We present a number of principal technological advances in X-ray optics and development of sample environments. We identify radiation damage as one of the most severe challenges in the field, thus rendering the dose an important parameter when putting different X-ray methods in perspective. Furthermore, we describe different successful approaches, including scanning and full-field techniques, along with prominent examples. Finally, we present a few recent studies that combined several techniques in one experiment in order to collect highly complementary data for a multidimensional sample characterization.

Quantitative characterization of the X-ray beam at the Australian Synchrotron Imaging and Medical Beamline (IMBL)

A critical early phase for any synchrotron beamline involves detailed testing, characterization and commissioning; this is especially true of a beamline as ambitious and complex as the Imaging & Medical Beamline (IMBL) at the Australian Synchrotron. IMBL staff and expert users have been performing precise experiments aimed at quantitative characterization of the primary polychromatic and monochromatic X-ray beams, with particular emphasis placed on the wiggler insertion devices (IDs), the primary-slit system and any in vacuo and ex vacuo filters. The findings from these studies will be described herein. These results will benefit IMBL and other users in the future, especially those for whom detailed knowledge of the X-ray beam spectrum (or `quality') and flux density is important. This information is critical for radiotherapy and radiobiology users, who ultimately need to know (to better than 5%) what X-ray dose or dose rate is being delivered to their samples. Various correction factors associated with ionization-chamber (IC) dosimetry have been accounted for, e.g. ion recombination, electron-loss effects. A new and innovative approach has been developed in this regard, which can provide confirmation of key parameter values such as the magnetic field in the wiggler and the effective thickness of key filters. IMBL commenced operation in December 2008 with an Advanced Photon Source (APS) wiggler as the (interim) ID. A superconducting multi-pole wiggler was installed and operational in January 2013. Results are obtained for both of these IDs and useful comparisons are made. A comprehensive model of the IMBL has been developed, embodied in a new computer program named spec.exe, which has been validated against a variety of experimental measurements. Having demonstrated the reliability and robustness of the model, it is then possible to use it in a practical and predictive manner. It is hoped that spec.exe will prove to be a useful resource for synchrotron science in general, and for hard X-ray beamlines, whether they are based on bending magnets or insertion devices, in particular. In due course, it is planned to make spec.exe freely available to other synchrotron scientists.

Quantifying radiation damage in biomolecular small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) is an increasingly popular technique that provides low-resolution structural information about biological macromolecules in solution. Many of the practical limitations of the technique, such as minimum required sample volume, and of experimental design, such as sample flow cells, are necessary because the biological samples are sensitive to damage from the X-rays. Radiation damage typically manifests as aggregation of the sample, which makes the collected data unreliable. However, there has been little systematic investigation of the most effective methods to reduce damage rates, and results from previous damage studies are not easily compared with results from other beamlines. Here a methodology is provided for quantifying radiation damage in SAXS to provide consistent results between different experiments, experimenters and beamlines. These methods are demonstrated on radiation damage data collected from lysozyme, glucose isomerase and xylanase, and it is found that no single metric is sufficient to describe radiation damage in SAXS for all samples. The radius of gyration, molecular weight and integrated SAXS profile intensity constitute a minimal set of parameters that capture all types of observed behavior. Radiation sensitivities derived from these parameters show a large protein dependence, varying by up to six orders of magnitude between the different proteins tested. This work should enable consistent reporting of radiation damage effects, allowing more systematic studies of the most effective minimization strategies.

[Benchmark experiment to verify radiation transport calculations for dosimetry in radiation therapy]

Monte Carlo simulations are regarded as the most accurate method of solving complex problems in the field of dosimetry and radiation transport. In (external) radiation therapy they are increasingly used for the calculation of dose distributions during treatment planning. In comparison to other algorithms for the calculation of dose distributions, Monte Carlo methods have the capability of improving the accuracy of dose calculations - especially under complex circumstances (e.g. consideration of inhomogeneities). However, there is a lack of knowledge of how accurate the results of Monte Carlo calculations are on an absolute basis. A practical verification of the calculations can be performed by direct comparison with the results of a benchmark experiment. This work presents such a benchmark experiment and compares its results (with detailed consideration of measurement uncertainty) with the results of Monte Carlo calculations using the well-established Monte Carlo code EGSnrc. The experiment was designed to have parallels to external beam radiation therapy with respect to the type and energy of the radiation, the materials used and the kind of dose measurement. Because the properties of the beam have to be well known in order to compare the results of the experiment and the simulation on an absolute basis, the benchmark experiment was performed using the research electron accelerator of the Physikalisch-Technische Bundesanstalt (PTB), whose beam was accurately characterized in advance. The benchmark experiment and the corresponding Monte Carlo simulations were carried out for two different types of ionization chambers and the results were compared. Considering the uncertainty, which is about 0.7 % for the experimental values and about 1.0 % for the Monte Carlo simulation, the results of the simulation and the experiment coincide.

Experimental verification of the individual energy dependencies of the partial L-shell photoionization cross sections of Pd and Mo

An experimental method for the verification of the individually different energy dependencies of L(1)-, L(2)-, and L(3)- subshell photoionization cross sections is described. The results obtained for Pd and Mo are well in line with theory regarding both energy dependency and absolute values, and confirm the theoretically calculated cross sections by Scofield from the early 1970 s and, partially, more recent data by Trzhaskovskaya, Nefedov, and Yarzhemsky. The data also demonstrate the questionability of quantitative x-ray spectroscopical results based on the widely used fixed jump ratio approximated cross sections with energy independent ratios. The experiments are carried out by employing the radiometrically calibrated instrumentation of the Physikalisch-Technische Bundesanstalt at the electron storage ring BESSY II in Berlin; the obtained fluorescent intensities are thereby calibrated at an absolute level in reference to the International System of Units. Experimentally determined fixed fluorescence line ratios for each subshell are used for a reliable deconvolution of overlapping fluorescence lines. The relevant fundamental parameters of Mo and Pd are also determined experimentally in order to calculate the subshell photoionization cross sections independently of any database.

Applications of dual-energy CT in urologic imaging: an update

This article discusses modern dual-energy computed tomography (DECT) and the unique material-specific information these scanners can provide. A description of the technical aspects of the various DECT techniques is provided. Specific clinical applications in urologic imaging, including chemical composition of urolithiasis, evaluation of renal masses, detection of urothelial neoplasms, and adrenal adenoma imaging, are discussed. The unique postprocessed image sets, including virtual noncontrast, iodine overlay, and stone composition, are described.

Population growth dynamics of carbon nanotubes

Understanding the population growth behavior of filamentary nanostructures, such as carbon nanotubes (CNTs), is hampered by the lack of characterization techniques capable of probing statistical variations with high spatial resolution. We present a comprehensive methodology for studying the population growth dynamics of vertically aligned CNT forests, utilizing high-resolution spatial mapping of synchrotron X-ray scattering and attenuation, along with real-time height kinetics. We map the CNT alignment and dimensions within CNT forests, revealing broadening and focusing of size distributions during different stages of the process. Then, we calculate the number density and mass density of the CNT population versus time, which are true measures of the reaction kinetics. We find that the mass-based kinetics of a CNT population is accurately represented by the S-shaped Gompertz model of population growth, although the forest height and CNT length kinetics are essentially linear. Competition between catalyst activation and deactivation govern the rapid initial acceleration and slow decay of the CNT number density. The maximum CNT density (i.e., the overall catalyst activity) is limited by gas-phase reactions and catalyst-surface interactions, which collectively exhibit autocatalytic behavior. Thus, we propose a comprehensive picture of CNT population growth which combines both chemical and mechanical cooperation. Our findings are relevant to both bulk and substrate-based CNT synthesis methods and provide general insights into the self-assembly and collective growth of filamentary nanostructures.

The minimum crystal size needed for a complete diffraction data set

In this work, classic intensity formulae were united with an empirical spot-fading model in order to calculate the diameter of a spherical crystal that will scatter the required number of photons per spot at a desired resolution over the radiation-damage-limited lifetime. The influences of molecular weight, solvent content, Wilson B factor, X-ray wavelength and attenuation on scattering power and dose were all included. Taking the net photon count in a spot as the only source of noise, a complete data set with a signal-to-noise ratio of 2 at 2 A resolution was predicted to be attainable from a perfect lysozyme crystal sphere 1.2 microm in diameter and two different models of photoelectron escape reduced this to 0.5 or 0.34 microm. These represent 15-fold to 700-fold less scattering power than the smallest experimentally determined crystal size to date, but the gap was shown to be consistent with the background scattering level of the relevant experiment. These results suggest that reduction of background photons and diffraction spot size on the detector are the principal paths to improving crystallographic data quality beyond current limits.

Quantitative imaging of element composition and mass fraction using dual-energy CT: three-material decomposition

In principle, dual-energy CT can only accurately decompose a mixture into two materials. To decompose a mixture into three constitute materials using dual-energy CT measurements, a third criteria must be provided to solve for three unknowns with only two spectral measurements. One solution is to assume that the sum of the volumes of three constituent materials is equivalent to the volume of the mixture (i.e., volume conservation), but this is not always true. A more generalized solution is to use the principle of mass conservation, which assumes that the sum of the masses of the three constituent materials is equivalent to the mass of the mixture. In this article, a mass-conservation based, three-material decomposition dual-energy CT algorithm is described and experimental validation of the accuracy of the technique presented. The results demonstrate that the proposed method can accurately measure elemental concentrations under low noise imaging conditions. Clinically, this may be applied to measure the mass fraction of any chemical element in a three-material mixture of solutions without the requirement of volume conservation.

Parameters and computer software for the evaluation of mass attenuation and mass energy-absorption coefficients for body tissues and substitutes

The mass attenuation and energy-absorption coefficients (radiation interaction data), which are widely used in the shielding and dosimetry of X-rays used for medical diagnostic and orthovoltage therapeutic procedures, are strongly dependent on the energy of photons, elements and percentage by weight of elements in body tissues and substitutes. Significant disparities exist in the values of percentage by weight of elements reported in literature for body tissues and substitutes for individuals of different ages, genders and states of health. Often, interested parties are in need of these radiation interaction data for body tissues or substitutes with percentage by weight of elements and intermediate energies that are not tabulated in literature. To provide for the use of more precise values of these radiation interaction data, parameters and computer programs, MUA_T and MUEN_T are presented for the computation of mass attenuation and energy-absorption coefficients for body tissues and substitutes of arbitrary percentage-by-weight elemental composition and photon energy ranging between 1 keV (or k-edge) and 400 keV. Results are presented, which show that the values of mass attenuation and energy-absorption coefficients obtained from computer programs are in good agreement with those reported in literature.