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Pencil beam described by a Gaussian
❑
Assuming small-angle multiple scattering approximation, an elementary
pencil beam penetrating a scattering medium is very nearly Gaussian in its
lateral spread at all depths. (
Fermi–Eyges
theory)
❑
Large-angle scattering events could cause deviations from a pure Gaussian
distribution, but their overall effect on dose distributions is considered to be
small. Can be considered via straggling corrections.
❑
The spatial dose distribution for a Gaussian pencil beam can be represented
as:
❑
Where is the dose contributed by the pencil beam at a point at a
radial distance
r
from its central axis and at depth
z
❑
is the axial dose, and is the mean square radial
displacement of electrons as a result of multiple coulomb scattering.
Dublin 2018
6
d
p
(
r
,
z
)
=
d
p
(0,
z
)
×
e
-
r
2
/
s
r
2
(
z
)
d
p
(
r
,
z
)
d
p
(0,
z
)
s
r
2
(
z
)