Biomedical Engineering Reference
In-Depth Information
Fig. 13.11
Example of a dose-response curve,
showing the incidence of an effect (e.g., certain
cancers per 100,000 population per year) as a
function of dose. Circles show measured
values with associated error bars. Solid line at
high doses is drawn to extrapolate linearly
(dashed curve A) to the level of normal
incidence at zero dose. Dashed curve B shows
a nonlinear extrapolation to zero dose. Dashed
curve C corresponds to having a threshold of
about 0.75 Gy.
response at low doses for high-LET radiation is shown in Fig. 13.12 by the curve
H
(which may even begin to decrease in slope at high doses).
For low-LET radiation, dose-response curves in many cases appear to bend up-
ward as the dose increases at low doses and low dose rates, as indicated by the
curve
L
1
in Fig. 13.12. Such behavior is consistent with a quadratic dependence of
the magnitude
E
(
D
) of the effect as a function of the dose
D
:
D
2
.
(13.13)
E
(
D
)
=
α
D
+
β
Here
α
and
β
are constants whose values depend on the biological effect under
study, the type of radiation, the dose rate, and other factors. This mathematical
form of response, which is commonly referred to as “linear-quadratic” (a mis-
nomer), has a theoretical basis in association with a requirement that
two
inter-
acting lesions are needed to produce the biological damage observed. (It dates back
to the 1930s, when it was employed to describe the dose response for some chromo-
some aberrations, which result from interactions between breaks in two separate
chromatids.) As with high-LET radiation, the effect at very low doses must be due
to individual tracks. As the dose is increased, the chance for two tracks to overlap
soon becomes appreciable at low LET. The response for two-track events should in-
crease as the square of the dose. The initial linear component of the dose-response
