Biomedical Engineering Reference
In-Depth Information
patient as possible. All this represents a juggling act and a suitable
compromise has to be made in practice.
Broad beams
A broad beam of protons may
either be formed physically from a
series of actual pencil beams, as in
beam scanning as discussed below,
or may be produced by scattering.
at Bragg peak
at Bragg peak
Figure 10.16 shows a lateral pro-
file of a broad beam, generated
at entrance
at entrance
by passive scattering techniques.
For large proton penetrations (e.g.,
≥
-2.0
-2.0
0
0
1.0
1.0
-1.0
-1.0
2.0
distance (cm)
2.0
distance (cm)
- 2
), the lateral penumbra
cm
near the end of range is dominated
by scattering in the target material.
By contrast, for small proton
penetrations (e.g.,
20 g
⋅
Figure 10.16. Lateral dose pro-
profile of a 160 MeV broad beam
at the entrance and at the top of
the Bragg peak. The beam was
formed using the double scatter-
ing process. Figure courtesy of
B. Gottschalk, HCL, USA.
-2
lateral penumbra is usually domi-
nated by blurring effects that occur
upstream of the patient as a result
of finite beam size, scattering in upstream material and so forth. In
between, the two effects are comparable.
≤
8 g
⋅
cm
), the
Typically, where multiple Coulomb scattering in the patient
predominates, the least sharp penumbra is at and near the end of range
and is approximately equal to a bit more than 3% of the range. Thus,
a beam penetrating 15 cm could have a lateral penumbra (80%
20%)
of about 5 mm. In practice, because of upstream scattering, it is more
likely to be about 6 mm. This compares favorably with the penumbra
of a linac-produced X-ray beam that is typically 6 to 9 mm (see
Figure 4.18 in Chapter 4). At depths above about 20 cm, the proton
penumbra becomes greater than that of a high energy photon beam.
−
A
LL
T
HINGS
C
ONSIDERED
…
Figure 10.17 sums up all the effects we have been discussing. In it
are indicated a number of points throughout and outside a broad
proton beam. The dominant contributions to the dose at those points
are shown in the panel on the right hand side. I recommend, as an
exercise, covering the panel on the right hand side of the figure, and
trying to identify the principal contributions for yourself.
