Biomedical Engineering Reference
In-Depth Information
Bragg peak is smeared out laterally much more than at shallow
depths. Since protons are not “lost” but, rather, are spread out, the
fluence at the end of range is of lower amplitude but of greater lateral
extent than at shallower depths, as indicated in Figure 10.12c.
For this
reason, a small proton beam is not well-suited to the treatment of very
small (e.g., a few mm diameter) but deep (e.g., many cm) target
volumes.
A broad beam can be considered to be made up of a superposition of
pencil beams, side by side. How is it that one can superpose pencil
beams with miniscule Bragg peaks and end up with a broad beam
with a large Bragg peak?
Figure 10.13 portrays a broad beam as being composed of a large
number of pencil beams, set side-by-side. Since the pencil beams are
very little spread
at small depths
,
the point P will receive dose from
probably only the one pencil
beam pointed directly at it. On
the other hand, since the pencil
beams are considerably spread
out
at large depths
, point Q near
the end of range will receive dose
not only from the pencil beam
pointed directly at it, but from
several adjacent pencil beams
pointed at laterally adjacent
points. The doses from all these
beams add up to a much greater
value than that which would be
due to the directly-pointing pencil
beam alone. Indeed, they add up
to the broad-beam value.
Figure 10.13. A broad beam
made up of an array of parallel
pencil beams. The dotted lines
in the graphs on the right hand
side are the sum of the doses
from all pencil beams (see text).
Having said all this, of what use are pencil beams? It is twofold.
First, the proton beams used for scanning, as discussed below, are
finite pencil beams. An understanding of the properties of pencil
beams is therefore essential for planning the delivery of a scanned
beam. Second, the pencil beam is a useful theoretical concept for
computing the dose delivered by a scattered broad beam within the
patient, since it can be thought of as being composed of a number of
pencil beams.
