Estimation of Maximum Obtainable RBE ‘Turnover-Points’ (LETU) for Accelerated Ions Based on a Nuclear Charge Radius Hypothesis to Obtain Iso-Effective LET and RBE Values

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Purpose: The purpose of this study is to analyze the relationship between nuclear charge (Z), atomic mass (A), LET (linear energy transfer for maximal relative biological effectiveness (RBE)) for accelerated ions based on the hypothesis that for each ion, LETU is related to their nuclear radius. Methods: Published LETU data for proton, helium, carbon, neon, silicon, argon, and iron ions and their Z and A numbers are fitted by a power law function (PLF) and compared with PLF based on atomic cross-sections and nuclear dimensions for spherical or spheroidal atomic nuclei. The PLF allows for isoeffective RBE estimations for different ions at any value of LET based on the LETU estimations. For any two ions, A and B, and a specified bioeffect obtained at LETA, the equivalent isoeffective LETB, is estimated using LETB=LETA.LETU[B]LETU[A]. Results: The data-fitting program provided the following results: 𝐿𝑈 = 78.1. 𝐴0.26, and 𝐿𝑈 = 86.6. 𝑍0.29, where 78.1 and 86.6 keV.μm−1 are the proton LET U values (i.e., without proton cellular range limit considerations). Goodness-of-fit tests are similar for each model, but the proton estimations differ. These exponents are lower than 0.66 and 0.33 (those for nuclear cross-sections and spherical nuclear radii, respectively), but suggest prolate nuclear shapes in most of the ions studied. Worked examples of estimating isoeffective LET values for two differentions are provided. Conclusions: The fitted power law relationships between LETU and Z or A are broadly equivalent and compatible with prolate nuclear shapes. These models may offer a more rational basis for future ion-beam radiobiology research.