Photon Transport Model Research Articles

Limiting values of backscatter factors for low-energy x-ray beams

Models for the calculation of upper and lower limiting values to the backscatter factor (BSF) are presented. The upper limit is obtained from Monte Carlo simulations of infinite parallel beams incident on semi-infinite phantoms with the dose contributions from all orders of photon scatter considered. The lower limits are calculated using an analytical photon transport model which considers only the primary dose and the scatter dose from photons that have undergone single scattering interactions in the phantom. The limiting values can be used to evaluate measured and modelled BSF values for x-ray beams with photons of 150 keV. A parametrization of the limiting values in terms of photon energy and irradiation field size is presented so that results determined for monoenergetic beams can be extended to polyenergetic spectra. The utility of the limits is illustrated by comparisons made with BSFs from the literature.

Time-resolved optical imaging of a solid tissue-equivalent phantom

A solid plastic phantom has been developed with optical properties that closely match those of human breast tissue at near-IR wavelengths. The phantom is a 54-mm-thick slab containing four small cylinders of contrasting scatter and absorption. A detailed description of the phantom is followed by an account of an attempt to image the phantom by a time-resolved imaging technique. Images generated with transmitted light with the shortest flight times revealed the embedded cylinders with greater visibility than images obtained with continuous light transillumination. However, images corresponding to flight times of less than ~700 ps were severely degraded from a lack of detected photons. An attempt was made to overcome this degradation by extrapolating the measured temporal distributions with an analytic model of photon transport. Results suggest that subcentimeter resolution imaging of low-contrast tumors in the breast is scientifically possible. Our phantom is available to any other research groups wishing to evaluate their systems.

A simple model of photon transport

In this paper I describe a simple model of photon transport. This simple model includes: tabulated cross sections and average expected energy losses for all elements between hydrogen ( Z = 1) and fermium ( Z = 100) over the enrgy range 10 eV to 1 GeV, simple models to analytically describe coherent and incoherent scattering, and a simple model to describe fluorescence. This is all of the data that is required to perform photon transport calculations.

Recursive recovery of a family of Markov transition probabilities from boundary value data

Recent developments in optical imaging inspired the model of photon transport discussed below. (Infrared radiation is used to image relatively soft and homogeneous tissue.) The difficulty of solving Maxwell’s equations, or even linear transport equations, led to this ‘‘diffuse tomographic’’ model. A recursive scheme for solving the two-dimensional problem is sketched and the first recursive step is detailed.

The spatial resolution performance of a time-resolved optical imaging system using temporal extrapolation

Optical imaging methods are being explored as a potential means of screening for breast cancer. Previous investigations of time-resolved imaging techniques have suggested that due to the lack of photons with sufficiently small pathlengths, the spatial resolution achievable through a human breast would be unlikely to be better than a centimeter. Experimental results presented here indicate, however, that higher resolution may be achieved by extrapolating the measured temporal distribution of transmitted photons. This is performed using a least-squares fit between data and an analytic model of photon transport. The spatial resolution of a time-resolved imaging system was evaluated by measuring the edge response produced by an opaque mask embedded in the center of a 51-mm-thick, very highly scattering medium. The limiting spatial resolution was improved from about 13 mm to about 5 mm.

Enhanced time-resolved imaging with a diffusion model of photon transport

Imaging through highly scattering media with transmitted photons with the shortest flight times is limited ultimately by the available number of photons with sufficiently short paths. A method is described that enhances the performance of the time-resolved imaging technique. A least-squares fit was obtained between the measured temporal distributions of transmitted light and a model of photon transport based on the diffusion approximation to the radiative transfer theory. Images constructed from the model estimates of short-path-length photon intensities provide information on internal structure, with a significantly improved signal-to-noise ratio compared with those that would be obtained directly from the data.

Generalized dual-energy-window scatter compensation in spatially varying media for SPECT

The detection of scattered photons in the photopeak energy window hinders accurate activity estimation in single-photon-emission computed tomography (SPECT). To compensate for photons scattered in spatially varying media, a framework for generalized dual-energy-window scatter subtraction has been developed. Generalized scatter subtraction factors are introduced, and these factors are decomposed into terms dependent on the uniform (average) and spatially varying components of the source activity distribution. The variation of these factors with projection pixel location and gamma camera position is analysed for a simulated myocardial perfusion study with a 99Tcm source radionuclide and a non-uniform thorax model. Monte Carlo methods are used to model photon transport and detection. The application of pixel-dependent scatter subtraction factors for scatter compensation is evaluated in an image reconstruction experiment for this simulated myocardial perfusion study. Generalized matrix inverses with noise-dependent regularization are used for image reconstruction. For this simulation, use of a pixel-dependent scatter subtraction factor and a constant scatter subtraction factor are effective for scatter compensation. Activity estimates within the left ventricular myocardium for these two methods are practically the same as those obtained from image reconstructions where the detection of Compton-scattered photons is included in the system matrix.

A vectorized Monte Carlo code for modeling photon transport in SPECT.

A vectorized Monte Carlo computer code has been developed for modeling photon transport in single photon emission computed tomography (SPECT). The code models photon transport in a uniform attenuating region and photon detection by a gamma camera. It is adapted from a history-based Monte Carlo code in which photon history data are stored in scalar variables and photon histories are computed sequentially. The vectorized code is written in FORTRAN77 and uses an event-based algorithm in which photon history data are stored in arrays and photon history computations are performed within DO loops. The indices of the DO loops range over the number of photon histories, and these loops may take advantage of the vector processing unit of our Stellar GS1000 computer for pipelined computations. Without the use of the vector processor the event-based code is faster than the history-based code because of numerical optimization performed during conversion to the event-based algorithm. When only the detection of unscattered photons is modeled, the event-based code executes 5.1 times faster with the use of the vector processor than without; when the detection of scattered and unscattered photons is modeled the speed increase is a factor of 2.9. Vectorization is a valuable way to increase the performance of Monte Carlo code for modeling photon transport in SPECT.

A standard timing benchmark for EGS4 Monte Carlo calculations.

A Fortran 77 Monte Carlo source code built from the EGS4 Monte Carlo code system has been used for timing benchmark purposes on 29 different computers. This code simulates the deposition of energy from an incident electron beam in a 3-D rectilinear geometry such as one would employ to model electron and photon transport through a series of CT slices. The benchmark forms a standalone system and does not require that the EGS4 system be installed. The Fortran source code may be ported to different architectures by modifying a few lines and only a moderate amount of CPU time is required ranging from about 5 h on PC/386/387 to a few seconds on a massively parallel supercomputer (a BBN TC2000 with 512 processors).

Mathematical Modeling of a Gravel-Pack Logging Tool

Summary This report discusses a sophisticated mathematical model of a gravel-pack logging tool that has a gamma ray source and a single gamma ray detector. We use a generalized Monte Carlo computer code, called MCNP, to model photon transport in three-dimensional (3D) geometries. Our approach includes a technique called variance reduction, which both reduces computational time and increases the precision of the results. The mathematical model is verified by comparison of calculated results with measurements made in laboratory simulations of gravel-pack completions. Laboratory measurements reported previously1 included a wide selection of fluids of various materials and densities, several screens, tubings, and two casing sizes. Comparison of the modeling results with experimental data reveals excellent agreement, giving a high level of confidence to the model. This study had three major objectives: (1) to expand our understanding of the physical processes involved, (2) to verify and to interpret the laboratory data, and (3) to provide a method by which tool responses can be obtained for a variety of borehole and gravel-pack conditions not measured in the laboratory. Thus, we were able to develop a generalized interpretation method that predicts downhole conditions as a function of tool response. A field example showing this interpretation procedure is presented.

Some observations on skin and organ doses during X-ray fluoroscopic examinations.

Knowledge of the skin dose from radiodiagnostic investigations enables the calculation of doses to other organs. The measurement of skin doses and their subsequent translation to organ doses by application of appropriate organ-to-skin dose ratios is less cumbersome, more generally applicable, and more acceptable to the patient than direct estimations of organ dose using intracavitary measurements. Although organ doses can alternatively be calculated from recorded beam characteristics in conjunction with tissue-air ratios, or by employing Monte Carlo photon transport models, it is not always possible to obtain all the necessary physical data for such calculations during fluoroscopy using equipment with automatic brightness control, or with falling-load generators. Actual dose measurement is indicated in such situations.

Energy imparted to water slabs by photons in the energy range 5-300 keV. Calculations using a Monte Carlo photon transport model

In diagnostic examinations of the trunk and head, the energy imparted to the patient is related to the radiation risk. In this work, the energy imparted to laterally infinite, 10-300 mm thick water slabs by 5-300 keV photons is calculated using a Monte Carlo photon transport model. The energy imparted is also derived for energy spectra of primary photons relevant to diagnostic radiology. In addition to values of energy imparted, values of backscattered and transmitted energies, quantities primarily obtained in the transport calculations, are reported. Assumptions about coherent scattering are shown to be important for values of backscattered and transmitted energies but unimportant with respect to values of energy imparted. Comparisons are made with other Monte Carlo results from the literature. Discrepancies of 10-20% in some calculated quantities can be traced back to the use of different tabulation of interaction cross-sections by various authors.

An examination of classical coupling of laser light to thin, dense plasma layers

Classical coupling, i. e. net absorption by inverse bremsstrahlung, of laser radiation in thin layers of dense (n >> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) plasmas is described by Eqs. (19) and (26) according to a wave description of the radiation field and a simple hydrodynamic model of the plasma and by Eqs. (29) and (47) according to a photon transport model. Though it appears that neither of these descriptions can be explored further without computer assistance, their implications seem to be quite discrepant. Equation (28) implies that the Maxwell-hydrodynamic model leads to high reflectivity of thin, dense plasma layers. Equation (47), on the other hand, implies - because of the smallness of Γ ~ υ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ei</sub> /w ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> - 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> - that any plasma layer is extremely absorptive in the density region for which n ~ n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . Though this discrepancy is, so far, based only upon qualitative arguments, it nevertheless appears real.