Dose Course 2018_Flipping book
6
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:
(0, z ) × e - r 2 / s r
2 ( z )
d p
( r , z ) = d p
d
( r , z )
❑ 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. p d p (0, z ) s r 2 ( z ) ❑
Dublin 2018
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