Parameter | Definition or description |
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Lea–Catcheside time factor (46) | Radiation delivered at high dose rate is more biologically damaging than same dose delivered at low dose rate as a result of cells’ ability to repair sublethal damage over duration of irradiation. Modifying effect of repair has been modeled with Lea–Catcheside time factor, G(T): where D is total absorbed dose; is dose rate; μ is repair rate, assuming that probability of repair event decreases exponentially as function of time; w is time of first single-strand DNA break; t is time of second break; and T is duration of irradiation. For protracted irradiations such as those encountered in RPT, surviving fraction thus becomes . |

Biologically effective dose (47–49) | Variation in biologic response to same absorbed dose delivered at different dose rates or different numbers of fractions has led to concept of biologically effective dose (BED) (or extrapolated tolerance dose, ETD), the absorbed dose required to cause biologic effect if dose were delivered in infinitely small doses per fraction or, equivalently, at very low dose rates: and therefore . |

Equieffective dose (50,51) | Equieffective dose (EQDX in Gy) is a quantity that, like BED, is intended to account for differences in fractionation or dose rate; X in this notation refers to reference value of absorbed dose (Gy) per fraction d. It has been recommended that nomenclature for equieffective dose include α/β ratio as well as reference to X: . Newer notation for equieffective dose is thus EQDX_{α/β}, with recommended standard of EQD2_{α/β}, where 2 refers to reference 2-Gy daily fraction. BED is equivalent to EQD0 (52) and is thus particularly relevant to RPT. Low, continuous dose rates delivered by radiopharmaceuticals require modification of this equation to incorporate Lea–Catcheside time factor G(T = ∞) (53–55): |

Equivalent uniform dose (56–58) | Tumor therapeutic response and normal-tissue toxicity may not correlate with average absorbed doses even when based on individualized biodistribution and kinetic data because of spatial nonuniformity of dose (Fig. 2 (57)). A quantity has therefore been developed, equivalent uniform dose (EUD), that provides a single value weighted to account for surviving fraction of tumor cells, given spatial distribution of absorbed dose within tumor volume. For any dose distribution, corresponding EUD is absorbed dose (Gy), which, when distributed uniformly across target volume comprised of N voxels, achieves same survival fraction among clonogenic cells: . |

Equivalent uniform biologically effective dose (56–58) | EUD has been formulated as equivalent uniform biologic effective dose, EUBED), as first described by O’Donoghue (57). It is often expressed using only linear component of linear-quadratic model: . Solving for EUBED yields |