factors that were derived from the relative photon/electron density in the path through tissue as
compared to that in water4'5. These methods, at their best, were useful for obtaining depth dose
information in the center of a broad beam, for a medium consisting of homogeneous layers. Even
then, these approaches do not account for the fact that photons interact not only with electrons,
but also with the nucleus. For example, the elastic scattering cross section depends on the atomic
number of the material. The clinical implication of this is that not all materials behave like
scaled-density water; real bone, for example, scatters photons to greater extent than water of
equivalent bone density due to the presence of Ca and other high Z elements not found in liquid
water. The effect of this was better addressed in the "Pencil Beam" method.
1.3 Pencil Beam Transport.
The Pencil Beam method sums the dose distribution from individual small diameter rays
called pencil beams. A pencil beam is made up of particles which pass through a differential
cross sectional area, 3x~y The off-axis dependence of the dose distribution for each pencil
beam is described by thick-target multiple scattering'. The on-axis dose information is obtained
from measured depth-dose data.
The calculation of absorbed dose assumes that the patient or phantom can be represented
by a stack of slabs of different material types. Each individual slab is homogeneous and infinite
in lateral extent. Assuming a single pencil beam has normal incidence on such geometry, the
absorbed dose at a position (x, y, z) can be expressed as
D(x, y, z) = f (x, y, z)g(z) (1-1)
where the first factor is the off-axis term, and the second factor is the central-axis term. The off-
axis term may be represented by a Gaussian of the form