Chemical and Biological Effects of Radiation - Atoms, Radiation, and-Radiation Protection - page 440

34. What interrelationships do the extrapolation number, the

magnitude of D 0 ,andthesizeoftheshoulderhaveina
multitarget, single-hit cell-survival model?

35. Why does survival in a multitarget, single-hit model become

exponential at high doses?

36. (a) Sketch a linear plot of the exponential survival curve from

Fig. 13.13.

(b) Sketch a linear plot for the multitarget, single-hit curve

from Fig. 13.14. What form of curve is it?

37. A multitarget, single-hit survival model requires hitting n

targets in a cell at least once each to cause inactivation. A
single-target, multihit model requires hitting a single target in
a cell n times to produce inactivation. Show that these two
models are inherently different in their response. (For example,
at high dose consider the probability that hitting a target will
contribute to the endpoint.)

38. One can describe the exponential survival fraction, S / S 0 ,by

writing S / S 0 =

e - pD , where D isthenumberof“hits”perunit
volume (proportional to dose) and p is a constant, having the
dimensions of volume. Show how p can be interpreted as the
target size (or, more rigorously, as an upper limit to the target
size in a single-hit model).

39. The cell-survival data in Table 13.9 fit a multitarget, single-hit

survival curve. Find the slope at high doses and the
extrapolation number. Write the equation that describes the
data.

40. Cell survival is described in a certain experiment by the

single-target, single-hit response function, S / S 0 = e -1.6 D , where
D is in Gy. At a dose of 1 Gy, what is the probability of there
being
(a) no hits

(b) exactly two hits in a given target?

Table 13.9 Data for Problem 39

Dose (Gy) Surviving Fraction

0.10 0.993

0.25 0.933

0.50 0.729

1.00 0.329

2.00 0.0458

3.00 0.00578

4.00 0.00072