### Abstract

Purpose: To determine conditions under which hypofractionation could be favorable for a normal tissue-even if tumor [α/β] exceeds the normal tissue's [α/β]. Methods: The hypofractionation sufficiency condition (HSC) for an organ is defined as a dose conformality constraint such that, if satisfied, a family of tumor control probability isoeffective fractionation schemes will show decreasing normal tissue complication probability with decreasing number of fractions. Results: In the extended equivalent uniform dose (EUD) model [obtained by replacing dose with linear quadratic (LQ) 2 Gy equivalent dose], the HSC for a normal organ is proven to be satisfied if a suitably weighted average of the relative dose [hypofractionation sufficiency index (HSI)] is less than the ratio of normal tissue to tumor [α/β]. The HSI is determined solely by dose distribution and the normal tissue volume factor, " a." If the HSC is satisfied for every normal tissue of concern, then there is a therapeutic gain with hypofractionation. The corresponding multifractionation sufficiency condition (therapeutic gain with increasing number of fractions) and multifractionation sufficiency index (MSI) are also derived. A sample clinical case is presented. Conclusions: Within the context of the LQ/EUD models, conformality measures (HSI and MSI) can be used to inform fractionation decisions.

Original language | English |
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Pages (from-to) | 1799-1805 |

Number of pages | 7 |

Journal | Medical physics |

Volume | 38 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2011 |

### Keywords

- biologically effective dose
- equivalent uniform dose
- hypofractionated radiotherapy
- linear quadratic model
- radiotherapy conformality measures