Sampling techniques using randomly distributed points and regular Cartesian grids were compared for the evaluation of volume, dose-volume histogram, tumor control, and normal tissue complication probabilities in radiation treatments. Particularly, the uncertainties associated with each sampling technique in estimating the dose-volume histograms for several dose distributions are analyzed in detail. It is found that the estimation of these parameters using sampling points on a regular Cartesian grid is, in general, significantly more efficient than using random points. This finding is different from other published results. The choice of grid size for sampling was analyzed according to the AAPM recommended uncertainty on the dose delivered to the patient. It was concluded that when grid sampling is used, a grid size of 0.5 cm is adequate for most plans to meet the guidelines.

Non-water solid phantoms are often used in the determination of absorbed dose to water for electron beams. Protocols have been established and widely accepted. In these procedures, several assumptions in addition to the Spencer-Attix conditions are required, and several correction factors are needed. A direct approach, in which the conversion is carried out in a single step using a modified Spencer-Attix formula, is studied in this paper. The approach is consistent with the protocols for water phantom, and the conversion factors can be calculated using Monte Carlo simulation. The behavior of the conversion factors is described by comparing the results from the AAPM protocol and experiment data for three electron energies (6, 12, and 16 MeV). This study demonstrates that for beam calibration at dmax, the results from the new approach agree with those from the protocol with a maximum discrepancy of 1% for PMMA and 1.3% for polystyrene. For the depth dose measurement from near the surface to R80, the agreement is within 1.5% for PMMA, 2.5% for polystyrene, and 2.8% for electron solid water. It also demonstrates that for electron solid water, the new approach provides better agreement with experiment data for the beam calibration at d(max).