Restricted Stopping Research Articles

On the calculation of mean restricted collision stopping powers.

An analytical method for the calculation of ratios of mean restricted collision stopping powers (L/rho)(g)m averaged over the charged particle spectra and the photon spectrum that is accurate to first order has been developed, and it has been explored whether a moderate change in the photon fluence spectrum with field size has an effect on the mean restricted collision stopping power ratio in high-Z materials. The results of this study indicate that for the case of a miniphantom, moderate changes in the photon fluence spectrum have only a weak effect on the ratios of mean restricted collision stopping powers.

A Spatial Characteristic Scheme for Multigroup Discrete Ordinates Electron Energy Deposition in Two Dimensions

AbstractEnergy deposition calculations are performed due to an incident source of electrons in rectangular slab geometry using the method of discrete ordinates for directions and the multigroup treatment in energy. Using the restricted stopping power formalism to distinguish between large energy loss collisions (catastrophic) and small energy loss collisions (continuous), coupled with a second‐order differencing scheme in energy, an improved model of electron energy loss is incorporated in our computational model. Results are presented for isotropic and normal incident sources and compared with available results.

Photon field quantities and units for kernel based radiation therapy planning and treatment optimization

The problem of choosing radiation quantities and units for energy deposition kernels and their associated kernel densities is treated with the aim of making them consistent with related classical radiation quantities and units such as restricted mass stopping powers and mass attenuation coefficients. It is shown that it is very useful to define the kernels, h(r), in terms of the quotient of the mean specific energy imparted to the medium by the radiant energy incident on a volume element centred at the origin of the kernel. The basic building block used to generate these kernels is the point energy deposition kernel, hp, describing the spatial distribution of the energy imparted by a photon interacting at a point in a medium. This will allow the kernels to be regarded as generalizations of the traditional mass stopping and attenuation coefficients, which in detail describe the spatial distribution of the mean energy deposition around an interaction site. As a consequence, the irradiation of kernel density, f(r), should be expressed in terms of the radiant energy incident per unit volume of the medium. It is shown that the kernel density is equal to minus the divergence of the incident unattenuated vectorial energy fluence, and it therefore acts as an irradiation density for the incident vectorial energy fluence.

Restricted collision stopping power of tissue substitutes for electrons.

Restricted collision stopping power of tissue substitutes for electrons.

The role of Monte Carlo simulation of electron transport in radiation dosimetry

A brief overview is given of the role in radiation dosimetry of electron transport simulations using the Monte Carlo technique. Two areas are discussed in some detail. The first is the calculation of stopping-power ratios for use in ion chamber dosimetry. The uncertainty in stopping-power ratios is discussed with attention being drawn to the fact that the relative uncertainty in restricted collision stopping powers is greater than that in unrestricted stopping powers if the major source of uncertainty is the density effect correction. Using ICRU Report 37 stopping powers and electron spectra calculated in a small cylinder of graphite, the value of the Spencer—Attix graphite to air stopping-power ratio in a 60Co beam is found to be 1.0021 for an assumed graphite density of 1.70 g/cm 3 and 0.23% less for an assumed density of 2.26 g/cm 3. The second area discussed is the feasibility of using Monte Carlo techniques to calculate dose patterns in a patient undergoing electron beam radiotherapy.

Output calibration in solid water for high energy photon beams

The AAPM Protocol recommends the use of water, polystyrene or acrylic media for measuring the output of high energy photon beams. It provides the appropriate restricted mass stopping powers and mass energy absorption coefficients for converting the dose to these media to dose to water. A water-equivalent solid has been developed for dosimetric applications [C. Constantinou, F. Attix, and B. Paliwal, Med. Phys. 9, 436 (1982)]. Calculated values for the restricted mass stopping powers and mass energy absorption coefficients have been published for this material [A. Ho and B. Paliwal, Med. Phys. 13, 403 (1986)]. The accuracy of these calculations was investigated by making output measurements, following the Protocol, with a Farmer type chamber in four materials for Co-60, 4, 6, 10, 18, and 24 MV photon beams. The results show that the scaled dose to water for the different media agree to better than 1%, and the analysis supports the methodology of the Protocol for obtaining the dose to water from the different media.

Stopping-power and mass energy-absorption coefficient ratios for Solid Water.

The AAPM Task Group 21 protocol provides tables of ratios of average restricted stopping powers and ratios of mean energy-absorption coefficients for different materials. These values were based on the work of Cunningham and Schulz. We have calculated these quantities for Solid Water (manufactured by RMI), using the same x-ray spectra and method as that used by Cunningham and Schulz. These values should be useful to people who are using Solid Water for high-energy photon calibration.

Nuclear stopping power for particles transmitted through thin foils in the beam direction

The restricted nuclear stopping power, S n ∗ , experienced by particles transmitted through a thin foil in the forward direction has been examined by the Monte Carlo program TRIM [1]. A comparison is made with a calculation of Besenbacher et al. [2], revealing increasing deviations for decreasing target thickness. A new algorithm is proposed to evaluate S n ∗ from a formula derived by Fastrup et al. [3], showing agreement with the TRIM calculations within ± 20%.

Conversion factors for calculating mass stopping power ratios.

In order to use an air-filled ionisation chamber for dosimetry of a photon or electron beam in a material, it is necessary to know the restricted (Spencer-Attix) mass stopping power ratio of the material, relative to air. A method is described in which a conversion factor, k, is derived by comparing unrestricted stopping power ratios of various materials (relative to air) with those for water (relative to air). Provided that the material does not differ too greatly in effective atomic number from that of water, this ratio is independent of energy and is a constant for any material both for unrestricted and restricted stopping powers. Values of k have been calculated for 31 materials and application of any one such factor to the restricted mass stopping power ratio of water relative to air allows the appropriate restricted mass stopping power of the material, relative to air, to be derived.

Muon shielding around high-energy electron accelerators: Part II. Experimental investigation

This paper describes and presents results of an experiment measuring the fluence and absorbed dose delivered by electron accelerator-produced muons penetrating thick iron shields. The experiment was designed to check the theoretical calculations described in the preceding paper. Nuclear track emulsions and scintillation counters were used to measure fluence and 7LiF was used for the dose measurements. It is shown that the absorbed dose can be calculated from the fluence data by using a restricted stopping power. The results of the measurements indicate that the theoretical calculation accurately predicts the muon fluence and absorbed dose at small angles (< 30 mrad) but underestimates both at large angles by an order of magnitude or more. Several possible explanations for this effect are discussed.

Optimal Stopping of a Markov Process

Optimal Stopping of a Markov Process