Comments on `Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations'

The Editor, Sir, Due to historical reasons, conventional radiotherapy planning systems calculate absorbed dose to water (Dw). Monte Carlo (MC) dose engines, however, generally compute energy dose or dose to medium (Dmed). Therefore, a conversion method is necessary in order to compare both types of dose distributions. In the paper ‘Converting absorbed dose to medium to absorbed dose to water for Monte Carlo based photon beam dose calculations’ Siebers et al (2000) suggest such a conversion procedure. Their method allows for the mapping of Dmed → Dw and vice versa using an energy and density dependent correction factor sw,med. The density dependence of sw,med has been evaluated by dividing the whole Hounsfield number or mass density (given in g cm−3 units) range of human tissue into a few bins consisting of air [0–0.08], lung [0.08–0.5], ICRU tissue [0.5–1.1], soft bone [1.1–1.4] and cortical bone [1.4–2.5]. Within each bin the authors have calculated the stopping power ratio for a given density by scaling the stopping power ratio of the corresponding material. The result is shown in figure 4 and the maximum error of the correction factor has been estimated to be 1.3%. However, we would like to debate underestimation of this error, in particular when referring to the data of figure 4. This figure shows a discontinuous function with steps at the arbitrary material boundaries. What happens, for example, if there are areas in the patient volume with mass densities of about 1.4 g cm−3? The decision as to which correction factor must be used (about 1.1 for cortical bone or 1.04 for soft bone) depends on the present choice of the threshold density. Therefore, the maximum error of sw,med in this density range (∼0.06) has the same order of magnitude as the correction itself and is much larger than 1.3%. In contrast to the authors we conclude that sw,med should only be applied to the five or six investigated materials in a small region around the nominal density, especially if the density is larger than 1 g cm−3. In order to evaluate the whole density range from 0 to 2.5 g cm−3, sw,med must be calculated for more materials, e.g. the materials from ICRU Report 46 (1992). The result should be a formula similar to equation (19) and figure 3 in the paper by Kawrakow et al (1996) but extended to lower energies. Furthermore, from this it follows that we have to be careful if we perform patient Monte Carlo dose calculations and determine the material parameters (cross sections, stopping powers, etc.) by Hounsfield binning and density scaling. If the number of materials is too small, the calculated MC dose errors can be large. Therefore, an alternative approach has been used in the XVMC (X-ray Voxel Monte Carlo) code (Kawrakow et al 1996, Fippel 1999). This code is based on nonlinear but continuous material parameter interpolation functions calculating all cross sections directly from a given density distribution. The error of this method is expected to be small because these functions result from investigation of all materials from ICRU Report 46 (1992).