Radiation Transport Theory Research Articles

Reflectance of Biological Turbid Tissues under Wide Area Illumination: Single Backward Scattering Approach

Various scenarios of light propagation paths in turbid media (single backward scattering, multiple backward scattering, banana shape) are discussed and their contributions to reflectance spectra are estimated. It has been found that a single backward or multiple forward scattering quasi-1D paths can be the major contributors to reflected spectra in wide area illumination scenario. Such a single backward scattering (SBS) approximation allows developing of an analytical approach which can take into account refractive index mismatched boundary conditions and multilayer geometry and can be used for real-time spectral processing. The SBS approach can be potentially applied for the distances between the transport and reduced scattering domains. Its validation versus the Kubelka-Munk model, path integrals, and diffusion approximation of the radiation transport theory is discussed.

Об эффективности методов максимального сечения в теории переноса излучения

Об эффективности методов максимального сечения в теории переноса излучения

Radiative transport theory for light propagation in luminescent media

We propose a generalization of radiative transport theory to account for light propagation in luminescent random media. This theory accounts accurately for the multiple absorption and reemission of light at different wavelengths and for anisotropic luminescence. To test this theory, we apply it to model light propagation in luminescent solar concentrators (LSCs). The source-iteration method is used in two spatial dimensions for LSCs based on semiconductor quantum dots and aligned nanorods. The LSC performance is studied in detail, including its dependence on particle concentration and the anisotropy of the luminescence. The computational results using this theory are compared with Monte Carlo simulations of photon transport and found to agree qualitatively. The proposed approach offers a deterministic methodology, which can be advantageous for analytic and computational modeling. This approach has potential for more efficient and cost-effective LSCs, as well as in other applications involving luminescent radiation.

Pulsatile blood flow in human bone assessed by laser-Doppler flowmetry and the interpretation of photoplethysmographic signals

Human bone blood flow, mean blood speed and the number of moving red blood cells were assessed (in arbitrary units), as a function of time, during one cardiac cycle. The measurements were obtained non-invasively on five volunteers by laser-Doppler flowmetry at large interoptode spacing. The investigated bones included: patella, clavicle, tibial diaphysis and tibial malleolus. As hypothesized, we found that in all bones the number of moving cells remains constant during cardiac cycles. Therefore, we concluded that the pulsatile nature of blood flow must be completely determined by the mean blood speed and not by changes in blood volume (vessels dilation). Based on these results, it is finally demonstrated using a mathematical model (derived from the radiative transport theory) that photoplethysmographic (PPG) pulsations observed by others in the literature, cannot be generated by oscillations in blood oxygen saturation, which is physiologically linked to blood speed. In fact, possible oxygen saturation changes during pulsations decrease the amplitude of PPG pulsations due to specific features of the PPG light source. It is shown that a variation in blood oxygen saturation of 3% may induce a negative change of ∼1% in the PPG signal. It is concluded that PPG pulsations are determined by periodic ‘positive’ changes of the reduced scattering coefficient of the tissue and/or the absorption coefficient at constant blood volume. No explicit experimental PPG measurements have been performed. As a by-product of this study, an estimation of the arterial pulse wave velocity obtained from the analysis of the blood flow pulsations give a value of 7.8 m s−1 (95% confidence interval of the sample mean distribution: [6.7, 9.5] m s−1), which is perfectly compatible with data in the literature. We hope that this note will contribute to a better understanding of PPG signals and to further develop the domain of the vascular physiology of human bone.

Tritium breeding control within liquid metal blankets

A key requirement for DEMO is the on-site breeding of tritium. In order to do this, a robust control system must be employed to ensure enough tritium is being bred to sustain the fusion reactor, whilst not breeding an amount which would exceed the plant's tritium inventory license. A tritium breeding method which is cost effective and reduces radioactive waste for disposal is that of the liquid metal breeder such as those based around LiPB and FLiBe. This paper focuses on the modeling of a simplified fusion reactor design with a LiPb blanket with linked radiation transport, nuclide burn-up and control theory. Two simple models were simulated using the FATI code which incorporated a PID (proportional integral derivative) controller that adjusted the Li6/Li7 ratio in order to increase/decrease tritium production based on the difference between the measured excess tritium inventory and the desired excess inventory. The modelling has initially demonstrated that a linear PID controller has the capability to manage tritium production within a LiPb liquid blanket.

Evaluating Geant4 platform for nuclear well-logging problems

The results presented in this paper are based on computational experiments aimed at modeling nuclear well-logging tools. Well-logging services require not only development and characterization of nuclear logging tools but also development of algorithms for interpreting measured data with inclusion of various environmental corrections. For nuclear tools, the only feasible way of accomplishing those tasks is using computer simulations based on the radiation transport theory and Monte Carlo methods. Commonly, nuclear well-logging community uses the Monte Carlo N-Particle transport code (MCNP) for such modeling. However, MCNP is not universally available. Therefore, as an alternative, we consider the Geant4 platform developed under the auspices of European Organization for Nuclear Research (CERN) for modeling high-energy physics experiments. Computations aimed at solving nuclear well-logging problems revealed several discrepancies between Geant4 and MCNP5 results. To enhance the accuracy of Geant4 in low-energy radiation transport, some numerical models used in this software were modified. The results of various benchmarks of the amended version of Geant4 against MCNP5 are presented. These results clearly indicate that the modified version of Geant4 is capable of solving nuclear geophysics problems with the same accuracy as MCNP.

Eigenvalues of the Anisotropic Transport Equation in a Slab

The critical eigenvalues of the transport equation play an important role in the description of the dynamics of transport problems both in nuclear physics as well as in radiative transport theory. This article treats the problem of calculating numerically the critical spectrum of the transport equation with semireflecting boundary conditions. The eigenvalue problem is solved using spectral methods and numerical results are presented. The scattering kernel is considered to be one of three types, namely, isotropic, linearly anisotropic, or Rayleigh scattering, even although more general kernels could be considered.

Implications of the visual appearance of ball lightning for luminosity mechanisms

Observations of ball lightning continue to pose one of the more difficult unsolved problems in atmospheric physics. Lack of quantitative data has frustrated attempts to explain how the objects emit light. We examine three leading theories for the immediate cause of light emission: excitation of plasma, small hot individual particles suspended in air, and hot fractal clusters of small particles. Using radiative transport theory, we find quantitative values for the ranges of particle density and temperature required to produce luminous intensities consistent with the bulk of reported observations, as well as estimates of power requirements for each mechanism. We conclude that all of these mechanisms are consistent with many ball-lightning observations, and that more than one of them may be involved in the luminosity of ball lightning.

Some statistical characteristics of the rough surface of human skin

The statistical properties of the skin surface have been described with the use of two approaches. The first approach is based on the probabilistic description of the skin topology at a given distribution density of rough surface heights and its correlation function. The Gaussian and quasi-periodic surfaces, whose parame- ters were estimated from the literature data, have been considered. The second approach is based on the ap- plication of the directional distribution function of microsurfaces of the skin. In the approximation of geometric optics, the shadowing effects of surface relief elements, as applied to the human skin, have been in- vestigated. The changes in the probability density of heights and slopes of parts of the surface irradiated with a directed beam due to the shadow regions have been estimated. The influence of shadowings on the electro- magnetic-field-quadratic photometric characteristics of the scattered light has been investigated. The results obtained are of interest for solving direct and inverse problems of biomedical optics — for analyzing the ra- diation fields in the biotissue and recovering its parameters by optical methods. Introduction. At the present time in medical practice various methods of irradiation of biological tissues and their diagnostics with the help of light are used widely. Of special value thereby are noninvasive methods realized through the skin because they are painless, cheap, and used in real time. Examples are photodynamic (1, 2) and low- intensity (3, 4) laser therapy of near-surface parts of the tissue, the determination of the structural and biophysical pa- rameters of the medium by the energy (5, 6) or polarization (6) characteristics of scattered light, and the investigation of the penetration depth of light into the tissue (7). The optical part of biomedical investigations and practical appli- cations is based on the methods of spectroscopy and optics of scattering media, and the radiation transport theory used for any absorbing and scattering media. In terms of theory, numerical (8) (mainly the Monte Carlo method) and ana- lytic (7, 9-11) approaches to the description of light fields inside and outside of biotissues have been well developed. In a particular realization of algorithms and computer programs, it is necessary to take into account the influ- ence of the structure of the skin surface on the radiation characteristics in such media. As a rule, the surface is as- sumed to be smooth (6, 8, 10, 11). This assumption is justified by a number of factors. First, the solution of the problem of the radiation transport in the medium is thus simplified considerably. At the same time, from general physical considerations it is clear that such an assumption may lead to errors in the calculation of the characteristics of the light fields in the medium. For example, in (2), the influence of the degree of roughness of the interface be- tween two media on the scattered radiation characteristics under different illumination conditions was estimated. It was shown that the coefficients of reflection and transmission of light under directed illumination of smooth and rough sur- faces may differ from one another by a factor of 1.5-2 or more. It is clear that for many optical problems these dif- ferences are very great. Second, there is a tangible lack of experimental data on the roughness characteristics of the skin surface which could form the basis for the statistical description of its structure. In other words, at present perti- nent initial physical data are absent. This is due to the wide variation of surface properties with the type of skin, am- bient conditions, age of a person, his/her physical and physiological condition, and many other factors. Third, to study the laws of scattering (reflection and transmission) of light by a statistically rough surface of any medium (including skin), special methods and algorithms are required.

TU‐A‐BRB‐03: Realization of the Unit of Absorbed Dose to Water for I‐125 Interstitial Brachytherapy Sources

Purpose: To establish a primary standard for I‐125 interstitial brachytherapy sources in terms of absorbed dose to water and thereby to improve the accuracy and effectiveness of the dosimetry for brachytherapy. Methods: The primary standard is a large, air‐filled, parallel‐plate extrapolation chamber in a phantom of water‐equivalent material (RW1). The thickness of the entrance plate defines the measurement depth within the water phantom and the inner side of the front plate the reference plane of the chamber. The method of evaluation was derived analytically based on radiation transport theory. A conversion factor has to be applied to the difference of ionization charges measured at two plate separations. This factor is composed of quotients of kerma values calculated for different plate separations in the chamber. In a recent publication it has been shown that this conversion factor is robust against uncertainties of database and spectra in comparison to conversion factors needed to convert the Reference Air Kerma Rate (RAKR) into Dw. With this measure the relative uncertainties of the conversion into Dw could be reduced from 10% to 1 %. Results: Dw and RAKR of four ‘BEBIG Symmetra I25.S16’‐ seeds were determined by means of primary standards. With this an experimentally determined dose rate constant was obtained, which could be compared to literature data. The uncertainty of the experimentally determined dose‐rate constant results to 1.6% as the uncertainties of the determination of Dw is 1.3% and of the RAKR is 0.9%. The mean value of the determined dose rate constants amounts to 1.021×10−4 m‐2 and is in good agreement with the TG‐43 consensus value of 1.012×10−4 m‐2. Conclusions: A primary standard was developed which is able to determine the absorbed dose to water for I‐125 interstitial brachytherapy sources with an uncertainty of 1.3%. The research within this EURAMET joint research project leading to these results has received funding from the European Community's Seventh Framework Programme, ERA‐NET Plus, under Grant Agreement No. 217257.

Benchmarking multilevel, 2-D cylindrical radiation transport in a high energy density plasma environment

In modeling optically thick, high energy density plasmas (HEDP), radiation transport is of comparable importance to atomic physics, hydrodynamics, and other transport processes. Radiation transport theory is the framework for calculating radiation output based on atomic kinetics, and is thus critical to designing and diagnosing experiments in which radiation production is significant. Starting in the 1960s, the astrophysics community established benchmarks for computational radiation transport, based on a parameterized two-level-atom, and mostly applicable to media with very high optical depths and low collisional quenching of radiative transitions. The purpose of the work reported here is to establish a similar computational radiation transport benchmark that is more relevant to a laboratory HEDP environment. Our model consists of 8 levels of mostly K-shell Al ions, ranging from the ground state of Li-like Al to its bare nucleus. Rates connecting the levels are given by well-known, readily reproducible analytic prescriptions. The results presented consist of level populations as a function of position within the cylindrical medium, and emitted line profiles. For the plasma conditions considered, the magnitudes and spatial variations of the populations are a sensitive indicator of the accuracy of the radiation transport model, and are critical in calculating experimentally relevant quantities such as radiative powers and line ratios.

Diffusion of Polarized Light

We study partially polarized light propagation in random media governed by the theory of radiative transport. In particular, we derive a diffusion approximation when scattering is strong and absorption is weak. This diffusion approximation is substantially easier to solve than the vector radiative transport equation because it requires only the solution of a scalar problem. Included in this analysis is the derivation of a boundary layer solution that corrects the diffusion approximation near the boundaries and provides the means to derive boundary conditions for the diffusion approximation. We give an explicit solution for this boundary layer solution in terms of plane wave solutions that we calculate numerically using the discrete ordinate method. We evaluate the effectiveness of this diffusion approximation through comparison with the numerical solution of the full problem.

Realisation of the absorbed dose to water for I-125 interstitial brachytherapy sources

A large air-filled parallel-plate extrapolation chamber in a phantom of water-equivalent material is used as a primary standard measuring device for low-energy interstitial brachytherapy sources from which the unit of absorbed dose to water can be derived. The chamber is suitable for low-energy photons with energies up to 50keV. The method to determine the absorbed dose to water was newly developed based on radiation transport theory. It offers a clear analytical expression to determine Dw. A conversion factor C(xi,xi+1) has to be applied to the difference of ionization charges measured at two plate separations xi and xi+1.The details of the method are presented. The determination of Dw of an I-125 seed is demonstrated by the measurement of a ‘BEBIG Symmetra I25.S16’ – seed. Additional measurements of the reference air kerma rate with the PTB primary standard chamber GROVEX I allow to determine experimentally the dose rate constant of an I-125 seed by means of primary standards for the first time. Good agreement was found between the obtained dose rate constant and the published data.

Energy propagation in nonlinear internal wave ducts from radiative transport theory.

Nonlinear internal waves have 3‐D random variability arising from smaller scale physical oceanographic processes. Internal wave fronts form acoustic waveguides, and we examine propagation in directions nearly parallel to the fronts. Intensity fluctuations arising from the variability are treated by 3‐D radiative transport methods, which provide insight into the parametric dependence on waveguide randomness. We focus on situations where the frozen field approximation applies, the acoustic modes represent the vertical energy distribution in the waveguide, and the modes propagate adiabatically. Under these conditions, horizontal modal variations are specified by 2‐D radiative transport equations. With additional assumptions, the transport equations simplify to diffusion‐type equations. An alternative energy scattering interpretation describes the duct in terms of a 2‐D Galton’s box, assuming discrete scattering events occur as modes propagate down the duct. The resulting equations also reduce to diffusion‐type equations in the continuous limit. We use appropriate spatial variability scales from the SW06 experiment to investigate properties of acoustic intensity. [Work supported by the ONR.]

Stochastic radiative transfer in Markovian mixtures: Past, present, and future

The Markovian approach, originally suggested in the early 1900s, has widespread practical use in many of our present-day studies and allows one to build bridges between diverse research areas such as statistical physics, astronomy, and computational science. This overview takes a broad sweep of several important examples with the emphasis on the stochastic radiative transfer in a cloudy atmosphere. In particular, the overview (i) highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics and (ii) illustrates that ideas and tools introduced by these two distinguished scientists are gaining increasing impact and recognition in the atmospheric science.

Propagation and Scattering of Spherical Wave Pulses in Vegetation Using Scalar Transport Theory

A high frequency theoretical model of propagation and scattering in vegetation is presented which uses scalar radiative transport theory. The specific problem analyzed is that of a periodic sequence of Gaussian pulses incident from free space into a forest region (vegetation). The incident pulse train is taken to be a spherical wave that is restricted to a specified solid angle, which is characteristic of radiation produced by a microwave or mm-wave antenna. The forest is modeled as a half-space of randomly distributed particles that scatter and absorb electromagnetic energy. In the forest, strong forward scattering occurs and the theory allows for a comprehensive characterization of the effect of vegetation on the propagation and scattering of spherical wave pulses: their attenuation, their angular spread, their distortion due to pulse broadening.

Infinite integrals of Whittaker and Bessel functions with respect to their indices

We obtain several new closed-form expressions for the evaluation of a family of infinite-domain integrals of the Whittaker functions Wκ,μ(x) and Mκ,μ(x) and the modified Bessel functions Iμ(x) and Kμ(x) with respect to the index μ. The new family of definite integrals is useful in a variety of contexts in mathematical physics. In particular, the integral involving Kμ(x) represents a new example of the Kontorovich–Lebedev transform. We discuss the relationship between the results derived here and the previously known integrals of Whittaker and Bessel functions. In some cases, we obtain entirely new expressions, and in other cases, we generalize previously known results. An application to time-dependent radiation transport theory is also discussed.

Thermal Damage Analysis in Biological Tissues Under Optical Irradiation: Application to the Skin

The use of optical sources in medical praxis is increasing nowadays. In this study, different approaches using thermo-optical principles that allow us to predict thermal damage in irradiated tissues are analyzed. Optical propagation is studied by means of the radiation transport theory (RTT) equation, solved via a Monte Carlo analysis. Data obtained are included in a bio-heat equation, solved via a numerical finite difference approach. Optothermal properties are considered for the model to be accurate and reliable. Thermal distribution is calculated as a function of optical source parameters, mainly optical irradiance, wavelength and exposition time. Two thermal damage models, the cumulative equivalent minutes (CEM) 43 °C approach and the Arrhenius analysis, are used. The former is appropriate when dealing with dosimetry considerations at constant temperature. The latter is adequate to predict thermal damage with arbitrary temperature time dependence. Both models are applied and compared for the particular application of skin thermotherapy irradiation.

Using polarization to find a source in a turbid medium

We study multiple scattering of partially polarized light using the theory of radiative transport. In particular, we study the light that exits a half-space composed of a uniform absorbing and scattering medium due to an unpolarized, isotropic, and continuous planar source. We assume that Rayleigh scattering applies. Using only angular integrals of the two orthogonal polarization components of the intensity exiting the half-space, we recover the depth and the strength of this source in two stages. First, we recover the depth of the source through the solution of a one-dimensional nonlinear equation. Then we recover the strength of the source through the solution of a linear least-squares problem. This method is limited to sources located at depths on the order of a transport mean-free path or less. Beyond that depth, these data do not contain sufficient polarization diversity for this inversion method to work. In addition, we show that this method is sensitive to instrument noise. We present numerical results to validate these results.

Evaluation of failure probabilities of mechanical systems under seismic action by the Monte-Carlo simulation method

Direct Monte-Carlo simulation method plays an important role in modern computational methods. For a large class of multidimensional problems of radiative transport theory, the procedure is the only available method allowing the consideration of all varieties of geometric and physical presumptions. This gives rise to computational investigation of actual and practical problems such as neutron-transport problem, reactor shielding, and impurity diffusion in random fields. The method enables the determination of the first-passage probability that the system response exceeds prescribed safe domain. In this paper, the failure probabilities of a plate subjected to seismic load are determined using this simulation method. For the purpose of reliability analysis, the von Mises criterion is used to determine the limit state failure. For the seismic load, the statistical model of earthquake-induced ground acceleration proposed by Ruiz and Penzien is used.