Pencil Beam Dose Distributions Research Articles

Dosimetric evaluation of a two-dimensional, arc electron, pencil-beam algorithm in water and PMMA

The accuracy of dose calculations from a pencil-beam algorithm developed specifically for arc electron beam therapy was evaluated at 10 and 15 MeV. Mid-arc depth-doses were measured for 0' and 90' arcs using 12 and 15 cm radius cylindrical water phantoms. Calculated depth-doses for the 90' arced beams in the build-up region were as much as 3% less than measured values. Calculated values of output (dose per monitor unit) at the depth of the maximum calculated dose were compared with measured values. Isodose contours for a 90' arc were also measured in a 15 cm radius PMMA phantom. At the depth of maximum dose the algorithm predicted doses in the penumbral regions, both with and without collimation, which agreed within a few per cent of measured values. Differences between measurement and calculation are not believed to be clinically significant and are believed to be primarily due to the fact that the algorithm models neither large-angle scattering nor the effects of range straggling on the pencil-beam dose distribution.

Use of fast Fourier transforms in calculating dose distributions for irregularly shaped fields for three-dimensional treatment planning.

In three-dimensional radiation treatment planning, essentially all fields are irregular and compensated. Consequently, it is important to predict accurately dose for such fields to ensure adequate coverage of the target region and sparing of healthy tissues. Traditional approaches, namely, those involving scatter integration and extended source and those utilizing negatively weighted fields, are inaccurate, especially near the boundaries defined by blocks and collimators. In the method presented in this paper, dose distributions for arbitrarily shaped beams are calculated by two-dimensional convolution of the relative primary photon fluence distributions and kernels representing the cross-sectional profiles of a pencil beam at a series of depths. The pencil beam dose distributions are computed, once and for all, with the Monte Carlo method for photon energy spectrum for each treatment machine. The finite size of the source, which is important for cobalt machines, is also taken into account using convolution of the source with the relative primary fluence distribution. Convolutions are performed using fast Fourier transforms on an array processor. Results of calculations are in excellent agreement with measured data. While no data are presented for fields modified by compensators, the method of calculation should apply at least as well for such fields since the variations in fluence distribution for compensated fields are not as sharp as for points near the block boundaries.

Calculation of electron beam dose distributions for arbitrarily shaped fields

The method described enables isodose distributions and output factors of treatment fields can be predicted with good accuracy, without the need for any dose measurement in the actual field. A Gaussian pencil beam model is employed with two different pencil beams for each electron beam energy. The values of the parameters of the pencil beam dose distributions are determined from a set of measurements of broad beam distributions; in this way the influence of electrons scattering by the applicator walls is taken into account. The dose distribution of electrons scattered from high atomic number metal frames, which define the treatment field contour at the skin, is calculated separately and added. This calculation is based on experimentally derived data. The method has been tested for beams with 6, 10, 14 and 20 MeV electron energy. The distance between calculated and measured isodose lines with values between 10 and 90% is under 0.3 cm. The difference between calculated and measured output factors does not exceed 2%.

Electron beam dose calculations

Electron beam dose distributions in the presence of inhomogeneous tissue are calculated by an algorithm that sums the dose distribution of individual pencil beams. The off-axis dependence of the pencil beam dose distribution is described by the Fermi-Eyges theory of thick-target multiple Coulomb scattering. Measured square-field depth-dose data serve as input for the calculations. Air gap corrections are incorporated and use data from 'in-air' measurements in the penumbra of the beam. The effective depth, used to evaluate depth-dose, and the sigma of the off-axis Gaussian spread against depth are calculated by recursion relations from a CT data matrix for the material underlying individual pencil beams. The correlation of CT number with relative linear stopping power and relative linear scattering power for various tissues is shown. The results of calculations are verified by comparison with measurements in a 17 MeV electron beam from the Therac 20 linear accelerator. Calculated isodose lines agree nominally to within 2 mm of measurements in a water phantom. Similar agreement is observed in cork slabs simulating lung. Calculations beneath a bone substitute illustrate a weakness in the calculation. Finally a case of carcinoma in the maxillary antrum is studied. The theory suggests an alternative method for the calculation of depth-dose of rectangular fields.