Biomedical Engineering Reference
In-Depth Information
In addition to having shorter ranges, lower energy proton beams
typically have narrower Bragg peaks, as can be seen in Figure 10.8.
Range straggling of the protons and energy spread in the beam, as just
mentioned, spread out the Bragg peak by some percentage of its
range, typically about 1.5%, more or less independent of the proton
energy. The Bragg peak is narrower at lower energies because the
near-constancy of the width of the Bragg peak relative to its range
translates into a smaller
absolute
broadening of the Bragg peak at
shorter ranges (i.e., at lower energies).
Lower energy beams have a higher peak-to-plateau dose ratio (the
ratio of the dose at the peak of the Bragg peak to that at near-zero
depth), as seen in Figure
10.8. This phenomenon is
driven by the just-discussed
narrower widths of the Bragg
peaks of lower energy
protons. No matter what the
incident proton energy may
be, just about the same
69
MeV
69
MeV
231
MeV
231
MeV
amount of energy is deposited
in, say, the last couple of
-2
a medium. Thus, a narrower
Figure 10.8. A series of Bragg peaks
of beams with energies of between 69
and 231 MeV. Figure courtesy of B.
Gottschalk, HCL, USA (Gottschalk,
2004).
g
⋅
cm
of a proton's path in
peak has to be higher in order
for the total energy in the
peak to be constant. In con-
sequence, lower energy beams, since they have narrower Bragg peaks,
have a higher peak-to-plateau dose ratio than higher energy beams.
At an energy of around 150 MeV, the value of the peak-to-plateau
ratio is about 3:1 in practice. At that energy and in water-equivalent
material, the width of the peak is typically about 6 mm at the 80%
dose level, and the distal falloff of dose from 80% to 20%
−
which is
the typical descriptor of “penumbra”
is about 4 mm. The distal fall-
off becomes less steep at higher energies, following the broadening of
the Bragg peak
−
and, conversely, becomes steeper as the energy is
reduced. Thus, the “distal penumbra” of a 200 MeV beam whose
range in water is 25.6 cm, as shown in Table 10.1, is a relatively
broad 7 mm, while that of a 70 MeV beam whose range in water is
4.0 cm is close to 1 mm.
−
