Chemical and Biological Effects of Radiation - Atoms, Radiation, and-Radiation Protection - page 428

Fig. 13.13 Semilogarithmic plot of surviving fraction S / S 0 as a
function of dose D , showing exponential survival characterized
by straight line.

mean lethal dose; D 0 is therefore the average dose absorbed by each cell before it
is killed. The surviving fraction when D

= D 0 is, from Eq. (13.14),

S
S 0 =

e -1 = 0.37.

(13.15)

For this reason, D 0 is also called the “D-37” dose.
Exponential behavior can be accounted for by a “single-target,” “single-hit” model
of cell survival. We consider a sample of S 0 identical cells and postulate that each
cell has a single target of cross section σ . We postulate further that whenever ra-
diation produces an event, or “hit,” in a cellular target, then that cell is inactivated
and does not survive. The biological target itself and the actual physical event that
is called a hit need not be specified explicitly. On the other hand, one is free to
associate the target and its size with cellular DNA or other components and a hit
with an energy-loss event in the target, such as a neutron collision or traversal by a
charged particle. When the sample of cells is exposed uniformly to radiation with
fluence ϕ , then the total number of hits in cellular targets is ϕ

S 0 σ . Dividing by the
number of cells S 0 gives the average number of hits per target in the cellular pop-
ulation: k

= ϕσ . The distribution of the number of hits per target in the population
is Poisson (Problem 27). The probability of there being exactly k hits in the target
of a given cell is therefore P k = k k e - k / k ! . The probability that a given cell survives
the irradiation is given by the probability that its target has no hits: P 0 = e - k

= e - ϕσ .