Biomedical Engineering Reference
In-Depth Information
n
=
n
e
−
μ
.
d
where
n
0
is the number of incident photons,
n
is the number of
photons at depth
d
, and
0
is a physical constant characteristic of the
target material and a function of the photon energy, termed the linear
attenuation coefficient. The property of exponential attenuation
expresses a very important physical principle which applies in many
other areas too, such as in radioactive decay. Exponential behavior
occurs when:
μ
there is a set of a large number of objects (e.g., photons or radio-
active atoms) each of which can experience some process (e.g.,
an interaction or a decay);
once an object experiences the process in question, it is removed
from the set of objects;
the probability of a process occurring is independent of the
occurrence of previous processes.
These conditions are only partially met in a photon beam, as we
shall see. If we assume that the deposition of dose at a point is
proportional to the number of photons at that point, and that
exponential attenuation is taking place, then the dose distribution
would be as schematically depicted in Figure 4.12a.
Figure 4.12. Schematic representation of the depth-dose distribution of
a photon beam with dose plotted logarithmically. (a) First order
approximation; (b) with build-up; and (c) with beam hardening and
other effects (see text).
However, dose is
not
proportional to the number of photons at a point
but, rather, to the energy deposited by the secondary electrons. You
will remember that the secondary electrons travel of the order of 1 cm
beyond the interaction point of, say, a 4 MeV photon - and, that they
tend to travel in the forward direction. The number of secondary
electrons builds-up below the surface of the irradiated medium,
giving rise to dose distributions such as are illustrated in Figure 4.12b.
