  Monte Carlo simulations using the code PENELOPE have been performed to test a
simplified model of the source channel geometry of the Leksell
GammaKnife$^{\circledR}$. The characteristics of the radiation passing through
the treatment helmets are analysed in detail. We have found that only primary
particles emitted from the source with polar angles smaller than 3$^{\rm o}$
with respect to the beam axis are relevant for the dosimetry of the Gamma
Knife. The photons trajectories reaching the output helmet collimators at
$(x,y,z=236 {\rm mm})$, show strong correlations between $\rho=(x^2+y^2)^{1/2}$
and their polar angle $\theta$, on one side, and between $\tan^{-1}(y/x)$ and
their azimuthal angle $\phi$, on the other. This enables us to propose a
simplified model which treats the full source channel as a mathematical
collimator. This simplified model produces doses in excellent agreement with
those found for the full geometry. In the region of maximal dose, the relative
differences between both calculations are within 3%, for the 18 and 14 mm
helmets, and 10%, for the 8 and 4 mm ones. Besides, the simplified model
permits a strong reduction (larger than a factor 15) in the computational time.
