scattering medium such as air, or in a strongly absorbing medium such lead, where the photon
flux usually is typically strongly angular dependent. In such situations, either a higher order
quadrature set (many directions) is required or some ray-effects remedies must be appliednl~l
(such as Taylor Projection techniques and adaptive differencing schemeS19). More discussion on
discretization and ray-effects are presented in Chapter 2.
1.4.2.2 Monte carlo versus deterministic SN methods
The most fundamental difference between the Monte Carlo methods and the deterministic
SN transport method is that the SN method solves the transport equation for the average particle
behavior throughout the problem phase space, while the Monte Carlo method, the terms of the
transport equation are solved statistically by simulating the individual particles and recording
some aspects (tallies) of their average behavior, but only at specific tally locations requested by
the user.
In the discrete ordinates method, the phase space is divided into many small meshes, in
which the cross section is assumed to be constant. In the medical physics applications, the model
geometry, in this case, the patient is represented using regular voxel-based grid generated from a
segmented CT scan data or other digital imaging technique. The types of grids can then be easily
represented in an input deck for the SN calculations, making both Monte Carlo methods and
deterministic techniques capable of representing the model of study accurately.
Another advantage of the MC methods is that they can easily utilize continuous energy
interaction data, whereas deterministic calculations use multigroup or energy group averaged
data. However, photon attenuation coefficients in the energy range of interest for radiotherapy
(RT) are quite smooth with little structure (in contrast to neutron cross sections); and are
accurately represented by multigroup data. Recent research we conducted has shown that
multi-group deterministic methods produce highly accurate absorbed dose distributions in photon