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