Biomedical Engineering Reference
In-Depth Information
D
is large,
e
-
D
/
D
0
is small, and one can use the binomial expansion
6)
to write, in
place of Eq. (13.17),
S
S
0
=
1-(1-
n
e
-
D
/
D
0
)
=
n
e
-
D
/
D
0
.
(13.18)
The straight line represented by this equation on a semilog plot intercepts the or-
dinate (
D
n
, which is called the extrapolation number. As
shown in Fig. 13.14, the number of cellular targets
n
is thus obtained by extrapo-
lating the linear portion of the survival curve back to zero dose.
Many experiments with mammalian cells yield survival curves with shoulders.
However, literal interpretation of such data in terms of the elements of a multi-
target, single-hit model is not necessarily warranted. Cells in a population are not
usually identical. Some might be in different stages of the cell cycle, with differ-
ent sensitivity to radiation. Repair of initial radiation damage can also lead to the
existence of a shoulder on a survival curve.
Still other models of cell survival have been investigated. The multitarget, single-
hit model can be modified by postulating that only any
m
<
n
of the cellular targets
need to be hit in order to produce inactivation. Single-target, multihit models have
been proposed, in which more than one hit in a single cellular target is needed for
killing. In addition to these target models, other theories of cell survival are based
on different concepts.
0) at the value
S
/
S
0
=
=
13.14
Factors Affecting Dose Response
Relative Biological Effectiveness
Generally, dose-response curves depend on the type of radiation used and on the
biological endpoint studied. As a rule, radiation of high LET is more effective bio-
logically than radiation of low LET. Different radiations can be contrasted in terms
of their relative biological effectiveness (RBE) compared with X rays. If a dose
D
of a given type of radiation produces a specific biological endpoint, then RBE is
defined as the ratio
D
x
D
,
RBE
=
(13.19)
where
D
x
is the X-ray dose needed under the same conditions to produce the same
endpoint. As an example, irradiation of
Tradescantia
(spiderwort) produces in sta-
men hairs pink mutant events that can be counted and scored quantitatively. In
experiments with 680-keV neutrons and 250-kVp X rays, it is observed that 0.030
pink events per hair (minus control) are produced by a dose of 16.5 mGy with the
=
6 rsm ll
x
,(1-
x
)
n
1-
nx
.
