Biomedical Engineering Reference
In-Depth Information
infinite slab, but in the shadow of the edges of the sliver there would
be a dose perturbation
typical of that seen in
the shadow of the edge
of a semi-infinite slab. The
question is, what happens
when the sliver is thin?
How do these perturba-
tions add up? Does the
sliver pull-back the pene-
tration of the protons in
its geometric shadow, or
does scattering outside the
Figure 11.4. Monte Carlo calculation of
shadow of the sliver fill in
the dose along the central axis of the
the dose behind the sliver?
Figure 11.4 shows the
beam through a sliver of high density
material (Teflon) embedded in water for
various thicknesses of the sliver. Repro-
of a Monte Carlo calcula-
duced with permission from Goitein
and Sisterson (1978).
3
tion
for this situation, for
3
A Monte Carlo calculation, in the context of a physics problem (e.g. the
calculation of the dose distribution of a proton beam), is one in which a
series of “histories” (e.g., of a proton traversing matter) are simulated. In
each history, various physical processes are experienced (e.g., the proton
interactions listed in Chapter 10) and are simulated in a computer program.
Some quantity or quantities of interest (e.g., the dose) can then be
estimated from the cumulative contribution of the histories (e.g., the sum
of the doses deposited in a volume element from each incident proton's
history). The technique gets its somewhat risqué name from the fact that
the starting values for the histories, and the physical effects that are
simulated, are all picked at random (by the throw of the computer-
equivalent of a Monte Carlo croupier's dice) from the theoretically known
distribution of possibilities. Even if the physics of the interactions is
perfectly well-known, there will be statistical uncertainties in the results.
The more histories that are followed, the smaller those uncertainties will be
(reducing approximately as the square root of the number of histories). As
a result, a very large number of histories is needed; ten million histories
would not be at all unusual in calculating the dose distribution of a proton
beam to
±
2% accuracy (SD), for example. This makes Monte Carlo
calculations quite slow. However, they are intrinsically quite accurate
−
as
accurate as the knowledge of the physical processes allows.
