after irradiation, and cell killing is minimal, which is due to very limited
radiation damage to the cell.
D 0 is determined from the slope of the straight line portion of the sur-
vival curve. It is the dose that kills 63% of the total number of cells. The
value of D 0 is a measure of radiosensitivity of a given type of cell. For
example, a large value of D 0 for a type of cell means that the cells are less
radiosensitive and vice versa.
The extrapolation number nis obtained by extrapolating the straight line
portion of the survival curve back to the Y-axis. Its value depends on the
width of the shoulder of the survival curve, that is, the quasithreshold value,
Dq. Its value for mammalian cells varies between 1 and 10.
Although Eq. (15.1) has some merit in expressing cell killing by radia-
tion, the linear-quadratic modelprovides a more accurate description of the
radiation-induced cell killing. This model is mathematically expressed as
S=e−aD−bD^2 (15.2)where Sis the survival fraction of the cells irradiated with dose Dand a
and bare constants. For low-LET radiations,bD^2 is negligible at low doses,
and the cell survival is proportional to the dose only, making the survival
curve linear (Fig. 15.12). At higher doses, the cell survival is proportional to
the square of the dose, and the curve tends to bend becoming concave
downward (Fig. 15.12). For high-LET radiations,bis zero, and so the sur-
vival curve becomes linear.
240 15. Radiation Biology
Fig. 15.12. Cell survival curves based on linear-quadratic model. The initial slope of
the linear-logarithmic plot gives cell killing proportional to e−aDand the latter part
to e−bD^2 which bends at higher doses. With high-LET radiations,bis zero, and the
curve is exponentially expressed simply by e−aD.