  The Monte Carlo method is widely used in the Gamma Knife dose distribution
calculations. In this study, Monte-Carlo simulation with Geant4 was applied to
determine Leksell Gamma Knife dose distribution for homogeneous solid water and
heterogeneous brain phantoms, and primarily focused on the differences arising
from the effects of inhomogeneity. The relative dose graphs were displayed for
different collimator diameters. The dose values from the maximal interval
regions were determined and compared. It seen that when the collimator size was
4mm, the mean maximum relative dose point was at 47mm for water phantom and at
44mm for the brain. The difference found was about 6.38%. The differences among
the results determined for water and brain were ranged from 2 to 17%. As a
result, the inhomogeneity effect should be considered in dose calculation in
Gamma Knife planning system.
  Keywords: Radiosurgery, Gamma Knife, {\gamma}-Rays, Inhomogeneity, Brain
