Biologically Effective Dose (BED) or Radiation Biological Effect (RBEf)?

The current radiosensitive studies are described with linear-quadratic (LQ) cell survival (S) model for one fraction with a dose d. As result of assuming all sublethally damaged cells (SLDCs) are completely repaired during the interfractions, that is, no presence of SLDCs, the survived cells are calculated for a n-fractionated regimen with the LQ S(n,D) model. A mathematically processed subpart of LQS(n,D) is the biologically effective dose (BED) that is used for evaluating a so-called “biological dose.” The interactions of ionizing radiation with a living tissue can produce partial death or sublethal damage from healthy or sublethally damaged cells. The proportions of the killed and sub-lethally damaged cells define the radiation biological effects (RBEfs). Computational simulations using RBEFs for fractionated regimens let calculating tumor control probability. While the derivation of the LQ S(n,D) considers a 100% cell repair, that is, 0% of sublethally damaged cells (SLDCs), the radiobiological simulators take into account the presence of SLDCs, as well as a cell repair <100% during the interfractions and interruption. Given “biological dose” does not exist, but RBEf, there was need for creating the BED. It is shown how some uses of BED, like the derivation of EQ2D expression, can be done directly with the LQ S(n,D).