Linear-quadratic radiobiology model ($-\ln S=\alpha d+\beta d^2$)

A model for surviving fraction $S$ after radiation dose $d$. Independent fully repaired fractions add their logarithmic effects. For $N$ equal fractions and no repopulation, dividing the total log kill by $\alpha$ gives the biologically effective dose $Nd(1+d/(\alpha /\beta ))$. Comparing tissue types requires their own parameters and the same stated repair assumptions.