The normalized total dose (NTD), or the isoeffective dose in 2 Gy fractions, was calculated using the Withers formula [11]:

where D is the total physical dose, d is the dose per fraction, and α/β is the tissue-specific ratio. In this work we assumed an α/β ratio of 3 Gy for late-responding normal tissues (lung), 3.4 Gy for late change in breast appearance, 4.6 Gy [8] and 10 Gy for tumor control and 10 Gy for skin (considering early reaction). To take into account the different overall treatment time the NTD was corrected in NTDT according with the formula [12]: where “”T”" is the overall treatment time (in days) for the schedule under consideration that delivered a normalized total dose NTD; “”t”" is the overall treatment time of a conventionally fractionated scheme (2 Gy/fraction, five fractions/week) that would PD98059 molecular weight deliver a radiation dose equal to “”NTDt”". “”t”" was calculated as follows: t = ((NTD/2) × (7/5), subtracting 2 days for the weekend if necessary. The find more difference (t -T) has positive values for treatment abbreviation and indicates the days of acceleration. Dprolif is the dose recovered per day due to proliferation, to compensate for rapid cell repopulation. For cancer a Dprolif value of 0.7 Gy/d was considered, as a mean value in the range 0.5 – 0.9 estimated for most tumours from a review of studies in literature [12, 13]. For

normal tissues, a Dprolif value of 0.2 Gy/d was adopted as reported by other authors [14, 15]. In Table 2 the results of the radiobiological calculation are summarised. Thus, correcting differences in overall treatment time, our schedule of 34 Gy in 10 fractions plus a boost of 8 Gy in one fraction delivered within 19 days is biologically equivalent to 59-70 Gy in 2 Gy/fr, considering the tumour bed volume, according to the α/β values of 10 and 4.6 Gy, respectively. Table 2 Radiobiological

equivalence of schedule used in this study. Treatment   Breast Tumor bed Schedule d(Gy) × (n. fr) 3.4 × 10 3.4 × 10 plus 8 × 1   Total physical dose (Gy) 34 42   Treatment time (days) 12 19 Normal tissue – late effect Lung (α/β = 3 Gy) NTD2 (Gy) 43.5 61.1   Acceleration (days) * Dprolif 18 * 0.2 24 * 0.2   NTDT (Gy) 47.1 Ceramide glucosyltransferase 65.9 Normal breast (α/β = 3.4 Gy) NTD2 (Gy) 42.8 59.7   Acceleration (days) * Dprolif 17 * 0.2 21 * 0.2   NTDT (Gy) 46.2 63.9 Tumor Breast Tumor (α/β = 4.6 Gy) NTD2 (Gy) 41.2 56.5   Acceleration (days) * Dprolif 17 * 0.7 19 * 0.7   NTDT (Gy) 53.1 69.8 Cancer cells (α/β = 10 Gy) NTD2 (Gy) 38 50   Acceleration (days) * Dprolif 13 * 0.7 14 * 0.7   NTDT (Gy) 47.1 59.8 Abbreviations: NTD2 is the normalized total dose at 2 Gy fraction, NTDT is the normalized total dose at 2 Gy fraction corrected for time acceleration (see text). Acceleration indicates the difference (t -T) respect to the conventional treatment.