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Table 1 Formula by Dale describing the linear quadratic model

From: Radiation necrosis after a combination of external beam radiotherapy and iodine-125 brachytherapy in gliomas

BED for fractionated therapy for late-reacting tissue

N × d × (1 + [d/3 Gy]) − K × T

BED for protracted therapy for late-reacting tissue

R × T × (1 + [2R]/[µ × 3 Gy]) − K × T

BED for fractionated therapy for tumor tissue

N × d × (1 + [d/10 Gy]) − K × T

BED for protracted therapy for tumor tissue

R × T × (1 + [2R]/[µ × 10 Gy]) − K × T

  1. BED biologically effective dose (total dose × relative effectiveness − repopulation factor), N number of fractions, d fraction dose (Gy), K repopulation factor 0.6 (Gy × day–1), T treatment time (days), R dose rate (Gy × h–1), µ recovery half-life 0.46 (h –1)