The influence of the size of the grid used for dose calculation on the accuracy of dose estimation

The standard presentation of a dose distribution as an isodose map is based on interpolation between dose values calculated on a matrix of equally spaced points. We explored the question of how the spacing of the grid used for the dose matrix affects the error due to interpolating the dose at any point. We defined two types of errors: the dose error, which is the difference between the interpolated and true dose at a given point; and the position error, which is the distance between the point of interest and the nearest point which has, in fact, the dose value estimated for the point of interest. We examine the problem using both an analytical beam profile (a Fermi function) and measured 60Co, x-ray and proton beam profiles. Our analysis showed that the interpolation errors are proportional to the curvature of the dose distribution and are relatively high in regions on either side of, but not including, the steepest part of the penumbra. Our results showed how big an interpolation error one should expect for a given size of the calculation grid. The specification of accuracy should be cast in the form of a pair of requirements, one for dose and the other for position. At a given point, only one of the two requirements needs to be satisfied. The position requirement is almost always the less demanding in clinical practice and permits the use of a larger grid spacing than if only a dose requirement is applied.(ABSTRACT TRUNCATED AT 250 WORDS)