Calculation of the radiological depth

The concept of the radiological depth is central to all algorithms which calculate radiation dose in a heterogeneous medium. For a discrete heterogeneous medium, consisting of regions of inhomogeneity, the radiological depth is usually presented as the sum over segments of the product of the segment length and the inhomogeneity density of the region corresponding to the segment. This paper illustrates that the usual formulation is inefficient because it requires the solution of the topological problem of which region corresponds to each segment. For simple heterogeneity problems involving just three regions of inhomogeneity, it is found that the topological problem constitutes at least 85% of the time required to calculate the radiological depth. It is shown in this paper that formulating the radiological depth as a sum over regions rather than as a sum over segments allows one to avoid this topological problem entirely.