Three-dimensional electron beam dose calculations

The MDAH pencil-beam algorithm developed by Hogstrom et al (1981) has been widely used in clinics for electron beam dose calculations for radiotherapy treatment planning. The primary objective of this research was to address several deficiencies of that algorithm and to develop an enhanced version. Two enhancements have been incorporated into the pencil-beam algorithm; one models fluence rather than planar fluence, and the other models the bremsstrahlung dose using measured beam data. Comparisons of the resulting calculated dose distributions with measured dose distributions for several test phantoms have been made. From these results it is concluded (1) that the fluence-based algorithm is more accurate to use for the dose calculation in an inhomogeneous slab phantom, and (2) the fluence-based calculation provides only a limited improvement to the accuracy the calculated dose in the region just downstream of the lateral edge of an inhomogeneity. The source of the latter inaccuracy is believed primarily due to assumptions made in the pencil beam's modeling of the complex phantom or patient geometry.^ A pencil-beam redefinition model was developed for the calculation of electron beam dose distributions in three dimensions. The primary aim of this redefinition model was to solve the dosimetry problem presented by deep inhomogeneities, which was the major deficiency of the enhanced version of the MDAH pencil-beam algorithm. The pencil-beam redefinition model is based on the theory of electron transport by redefining the pencil beams at each layer of the medium. The unique approach of this model is that all the physical parameters of a given pencil beam are characterized for multiple energy bins. Comparisons of the calculated dose distributions with measured dose distributions for a homogeneous water phantom and for phantoms with deep inhomogeneities have been made. From these results it is concluded that the redefinition algorithm is superior to the conventional, fluence-based, pencil-beam algorithm, especially in predicting the dose distribution downstream of a local inhomogeneity. The accuracy of this algorithm appears sufficient for clinical use, and the algorithm is structured for future expansion of the physical model if required for site specific treatment planning problems. ^

Measurement of isotopic uranium in water for compliance monitoring by liquid scintillation counting with alpha/beta discrimination

A simple and inexpensive method is described for analysis of uranium (U) activity and mass in water by liquid scintillation counting using $\alpha$/$\beta$ discrimination. This method appears to offer a solution to the need for an inexpensive protocol for monitoring U activity and mass simultaneously and an alternative to the potential inaccuracy involved when depending on the mass-to-activity conversion factor or activity screen.^ U is extracted virtually quantitatively into 20 ml extractive scintillator from a 1-$\ell$ aliquot of water acidified to less than pH 2. After phase separation, the sample is counted for a 20-minute screening count with a minimum detection level of 0.27 pCi $\ell\sp{-1}$. $\alpha$-particle emissions from the extracted U are counted with close to 100% efficiency with a Beckman LS6000 LL liquid scintillation counter equipped with pulse-shape discrimination electronics. Samples with activities higher than 10 pCi $\ell\sp-1$ are recounted for 500-1000 minutes for isotopic analysis. Isotopic analysis uses events that are automatically stored in spectral files and transferred to a computer during assay. The data can be transferred to a commercially available spreadsheet and retrieved for examination or data manipulation. Values for three readily observable spectral features can be rapidly identified by data examination and substituted into a simple formula to obtain $\sp{234}$U/$\sp{238}$U ratio for most samples. U mass is calculated by substituting the isotopic ratio value into a simple equation.^ The utility of this method for the proposed compliance monitoring of U in public drinking water supplies was field tested with a survey of drinking water from Texas supplies that had previously been known to contain elevated levels of gross $\alpha$ activity. U concentrations in 32 samples from 27 drinking water supplies ranged from 0.26 to 65.5 pCi $\ell\sp{-1}$, with seven samples exceeding the proposed Maximum Contaminant Level of 20 $\mu$g $\ell\sp{-1}$. Four exceeded the proposed activity screening level of 30 pCi $\ell\sp{-1}$. Isotopic ratios ranged from 0.87 to 41.8, while one sample contained $\sp{234}$U activity of 34.6 pCi $\ell\sp{-1}$ in the complete absence of its parent, $\sp{238}$U. U mass in the samples with elevated activity ranged from 0.0 to 103 $\mu$g $\ell\sp{-1}$. A limited test of screening surface and groundwaters for contamination by U from waste sites and natural processes was also successful. ^