Calculation of the biological effective dose (BED) of a fractionated course of hadron particle radiation (e.g., protons or carbon ions) administered via a spread-out Bragg peak (SOBP) to a population of cells with heterogeneous radiosensitivity is described. The calculated BED has the important property that, if equal to that of a course of photon radiation, the particle course will result in the same fraction of cells of the exposed population that survive and can be expected to have the same clinical effect. The calculated BED provides a way to relate the effect of a planned treatment course with particle radiation to clinical experience of the effects of treatment with low-LET photon radiation.

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