Abstract: A method for tracking the movement of a particle through a geometric model so as to facilitate the development of a dosimetry plan includes providing a particle with a short mean free path length; providing a geometric model which has a boundary which separates regions of the geometric model having different densities and/or compositions; arranging a first plurality of substantially uniform volume elements having a predetermined size into the geometric model; and arranging a second plurality of substantially uniform volume elements having a predetermined size less than that of the first plurality of substantially uniform volume elements, and in overlaying relation relative to the first plurality of substantially uniform volume elements.