Discussion
The novel aspect of this dissertation is that both anisotropic
scattering and mismatched boundary conditions are included in
light transport models. These phenomena significantly affect
light transport and have not been included in tissue models previously.
Three different light transport models (the Monte Carlo, the
adding-doubling, and the delta-Eddington) have been presented.
A method for measuring the phase function of a tissue has been
introduced, as well as an indirect method for measuring the optical
properties of tissue. The measurement methods and the calculation
models are complementary: light transport cannot be modeled
without knowing the optical properties of the tissue and the
optical properties cannot be determined without an optical model
for converting reflection and transmission measurements into
optical properties.
Mismatched boundary conditions have a strong influence on fluence
rates. For example, in Figure 4.1 the fluence rate at a mismatched
surface is twice that for a matched surface. Careful implementation
of the boundary conditions in the delta-Eddington model, indicates
that this approximation is not particularly good for calculating
fluences near mismatched boundaries. This results from using
only the first two moments of the radiance distribution to model
internal reflection. At the boundaries, highly anisotropic radiance
distributions make higher order radiance moments comparable to
the lower order moments and the accuracy of the delta-Eddington
model suffers accordingly. Consequenly, fluences rates for tissues
with mismatched boundaries and high anisotropies should not be
estimated with the delta-Eddington approximation
Anisotropic scattering also affects the fluence rate in tissue
(Figure 4.2). Both the adding-doubling and the Monte Carlo methods
are capable of accommodating an arbitrary scattering phase function.
Unfortunately, the phase function has not been measured at wavelengths
besides 633nm. The phase function needs to be measured at other
wavelengths before accurate light transport calculations may
be made.
The adding-doubling method should be used when one-dimensional
calculations are needed. Approximate methods like the delta-Eddington
approximation should be avoided whenever possible. In particular,
it would be desirable to replace the delta-Eddington method with
the adding-doubling in the iteration technique of Chapter 6.
Preliminary work indicates that the adding-doubling method yields
accurate values for reflection and transmission with as few as
four quadrature points. Calculations with such a model are only
10-100 times slower than delta-Eddington calculations, and do
not suffer from the approximations of the delta-Eddington model.
Finally, the Monte Carlo method cannot be recommended highly
enough. This method allows modelling of complex structures without
approximation. Perhaps most importantly, the Monte Carlo method
is the only reliable method for calculating fluence rates in
tissue for finite beam irradiances. In particular, the convolution
formulas derived in Chapter 2 allow fluence rate calculation
for finite beams to be made quickly, once an impulse response
has been calculated. These fluence rates may then be used in
a thermal model to calculate tissue damage or ablation.
| 
