Dose to tissue medium or water cavities as surrogate for the dose to cell nuclei at brachytherapy photon energies

It has been suggested that modern dose calculation algorithms should be able to report absorbed dose both as dose to the local medium, D(m,m,) and as dose to a water cavity embedded in the medium, D(w,m), using conversion factors from cavity theory. Assuming that the cell nucleus with its DNA content is the most important target for biological response, the aim of this study is to investigate, by means of Monte Carlo (MC) simulations, the relationship of the dose to a cell nucleus in a medium, D(n,m,) to D(m,m) and D(w,m), for different combinations of cell nucleus compositions and tissue media for different photon energies used in brachytherapy. As D(n,m) is very impractical to calculate directly for routine treatment planning, while D(m,m) and D(w,m) are much easier to obtain, the questions arise which one of these quantities is the best surrogate for D(n,m) and which cavity theory assumptions should one use for its estimate. The Geant4.9.4 MC code was used to calculate D(m,m,) D(w,m) and D(n,m) for photon energies from 20 (representing the lower energy end of brachytherapy for ¹⁰³Pd or ¹²⁵I) to 300 keV (close to the mean energy of (¹⁹²Ir) and for the tissue media adipose, breast, prostate and muscle. To simulate the cell and its nucleus, concentric spherical cavities were placed inside a cubic phantom (10 × 10 × 10 mm³). The diameter of the simulated nuclei was set to 14 µm. For each tissue medium, three different setups were simulated; (a) D(n,m) was calculated with nuclei embedded in tissues (MC-D(n,m)). Four different published elemental compositions of cell nuclei were used. (b) D(w,m) was calculated with MC (MC-D(w,m)) and compared with large cavity theory calculated D(w,m) (LCT-D(w,m)), and small cavity theory calculated D(w,m) (SCT-D(w,m)). (c) D(m,m) was calculated with MC (MC-D(m,m)). MC-D(w,m) is a good substitute for MC-D(n,m) for all photon energies and for all simulated nucleus compositions and tissue types. SCT-D(w,m) can be used for most energies in brachytherapy, while LCT-D(w,m) should only be considered for source spectra well below 50 keV, since contributions to the absorbed dose inside the nucleus to a large degree stem from electrons released in the surrounding medium. MC-D(m,m) is not an appropriate substitute for MC-D(n,m) for the lowest photon energies for adipose and breast tissues. The ratio of MC-D(m,m) to MC-D(n,m) for adipose and breast tissue deviates from unity by 34% and 15% respectively for the lowest photon energy (20 keV), whereas the ratio is close to unity for higher energies. For prostate and muscle tissue MC-D(m,m) is a good substitute for MC-D(n,m). However, for all photon energies and tissue types the nucleus composition with the highest hydrogen content behaves differently than other compositions. Elemental compositions of the tissue and nuclei affect considerably the absorbed dose to the cell nuclei for brachytherapy sources, in particular those at the low-energy end of the spectrum. Thus, there is a need for more accurate data for the elemental compositions of tumours and healthy cells. For the nucleus compositions and tissue types investigated, MC-D(w,m) is a good substitute to MC-D(n,m) for all simulated photon energies. Whether other studied surrogates are good approximations to MC-D(n,m) depends on the target size, target composition, composition of the surrounding tissue and photon energy.

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