Utility of normal tissue-to-tumor α/β ratio when evaluating isodoses of isoeffective radiation therapy treatment plans

Purpose: To achieve a better understanding of the effect of the number of fractions on normal tissue sparing for equivalent tumor control in radiation therapy plans by using equivalent biologically effective dose (BED) isoeffect calculations. Methods and Materials: The simple linear quadratic (LQ) model was assumed to be valid up to 10 Gy per fraction. Using the model, we formulated a well-known mathematical equality for the tumor prescription dose and probed and solved a second mathematical problem for normal tissue isoeffect. That is, for a given arbitrary relative isodose distribution (treatment plan in percentages), 2 isoeffective tumor treatment regimens (N fractions of the dose D and n fractions of the dose d) were denoted, which resulted in the same BED (corresponding to 100% prescription isodose). Given these situations, the LQ model was further exploited to mathematically establish a unique relative isodose level, z (%), for the same arbitrary treatment plan, where the BED to normal tissues was also isoeffective for both fractionation regimens. Results: For the previously stated problem, the relative isodose level z (%), where the BEDs to the normal tissue were also equal, was defined by the normal tissue α/β ratio divided by the tumor α/β times 100%. Fewer fractions offers a therapeutic advantage for those portions of the normal tissue located outside the isodose surface, z, whereas more fractions offer a therapeutic advantage for those portions of the normal tissue within the isodose surface, z. Conclusions: Relative isodose-based treatment plan evaluations may be useful for comparing isoeffective tumor regimens in terms of normal tissue effects. Regions of tissues that would benefit from hypofractionation or standard fractionation can be identified.