Applying the reciprocal dose principle to heterogeneous phantoms: practical experience from Monte Carlo studies

The reciprocity theorem states that for any pair of regions in a uniform isotropic or uniform scatterless model, the specific absorbed fraction (phi) is independent of which region is designated source and which is designated target. Although the conditions of these models are not met by phantoms heterogeneous in tissue composition and density, calculations with a Monte Carlo radiation transport code show that in many cases the reciprocal phi's from photon radiation are approximately equal. In these cases we may speak of the 'reciprocity principle'. Previous workers have estimated that the principle is valid within a factor of 2 (Snyder) or within about 20% (Mayneord and Clarke), except when one of the organs in the pair considered is the skeleton, where the reciprocal phi's may differ by as much as a factor of 4. We find that the principle holds within at least 10% when both organs are of near-unit-density. When one of the organs is near the tissue-vacuum boundary (skin, breasts, or testes), the reciprocal phi's may differ by as much as 10% or so at energies where scattering is marked. When one of the organs is the lungs or the whole body, a comparable error may occur at some energies. We conclude that more extensive use of the reciprocity principle in internal dose computations in heterogeneous phantoms is warranted.