Incorporating geometric uncertainties into dose calculations with convolution: the effect of spatial invariance

Convolution methods have been incorporated into dose calculations to model the effect of geometric uncertainties on the dose received. These methods assume spatial invariance of the dose distribution, although it is known that this is violated in practice. The magnitudes of the resulting errors are not well documented. The authors specifically address the issue of spatial invariance due to tissue inhomogeneities and surface contours. They accomplished this by comparing two approaches. First, the uncertainty in beam positioning was modeled with a Gaussian distribution. A static dose distribution (with surface and inhomogeneity corrections) was calculated and was convolved with the Gaussian to yield a "blurred" dose distribution incorporating the uncertainties. Second, the dose was calculated using a finite number of spatially displaced individual beams (each calculated with surface and inhomogeneity corrections) weighted by the same Gaussian for their displacement from the static beam position. The difference between the results of the two methods indicates the error in the convolution method. This analysis was performed for four phantoms with various surface curvature and internal inhomogeneities. Significant differences are observed due to the effect of surface curvature, while the errors due to internal inhomogeneities appear to be minor. It is concluded that for convolution algorithms to be of clinical use, the inaccuracy due to the effect of surface curvature needs to be addressed.