Motivation
The laser as a tool is becoming available to a growing number of
physicians, but before the doctor can use this tool he must select a laser, a beam
power, a spot size, and an irradiation time. Since small differences in any of
these parameters can determine whether an application is efficacious or
disastrous, some a priori knowledge about the effects of each parameter is
needed. This information is usually provided by mathematical models.
Any model of a laser treatment--photochemical, thermal, or ablative--is
based on the distribution of light in the tissue. For example, in thermal and
ablative applications, the light distribution is directly proportional to the heat
source used in the thermal model. In photochemical applications involving
hematoporphyrin derivative, the release of singlet oxygen is proportional to the
light distribution. Since photodynamic, thermal, and ablative models are only as
good as the optical model they are based on, it unfortunate that current
biomedical light transport models are approximate (e.g., the diffusion
approximation) or heuristic (Kubelka-Munk). The paint, paper, photographic,
and plastic industries; meteorology; oceanography; astrophysics; analytic
chemistry; and biology have all used exact optical models; however, these
methods have heretofore not been utilized in biomedical applications.
Accurate models are needed because approximate models fail near tissue
boundaries. In many applications, the distribution of light immediately beneath
the point of irradiation is critical. In these regions the assumptions made in the
approximate models are worst. For example, in the Kubelka-Munk
approximation the distribution of light immediately subsurface is assumed
isotropic. Since light must undergo several scattering events before an isotropic
profile is reached this approximation is poorest near the surface.
The optical properties of some tissues have been measured, but often in
the context of the heuristic Kubelka-Munk model and consequently, these
parameters should only be used with the Kubelka-Munk theory. Existing
methods are impractical for measurement of optical properties as a function of
wavelength. Current methods are ill-suited because they require diffuse light
[64], many sample thicknesses [70], or
goniophotometric measurements [13]. A practical method for
measurement of optical properties as a function of wavelength is needed. The
single scattering phase function (defined below) characterizing a tissue must
also be measured. Recent attempts to measure the phase function
[5,13] have not generated quantitative expressions that may
be used in more complete models.
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