Analytical expression of the β coefficient of cell survival curves predicted by the NanOx model in the low‐energy range

We derived in this work an analytical expression for the fast calculation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>β</mml:mi> <mml:annotation>$\beta$</mml:annotation></mml:semantics> </mml:math> coefficient for ion irradiations. Although the analytical expression resulted from the NanOx model, it can be also applied to any model used to compute <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>α</mml:mi> <mml:annotation>$\alpha$</mml:annotation></mml:semantics> </mml:math> . Overall, the approach presented in this work may provide a reasonable description of the behavior of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>β</mml:mi> <mml:annotation>$\beta$</mml:annotation></mml:semantics> </mml:math> with LET despite the large spread observed in experimental data.