This is the first of two papers on the quantitative measurement of light energy fluence rates in optical phantoms and in tissues, in vitro and in vivo. The theory discussed in the present paper will be used in a forthcoming experimental paper to quantitatively check measurements of light energy fluence rates. A simple multiple flux model, which is equivalent to the diffusion approximation, is derived from the equation of transfer in a plane as well as in a spherical geometry. The equations obtained are similar to those of the Kubelka-Munk and related heuristic models. This permits conclusions regarding the limitations of these models and the values of their constants. The heuristic models are equivalent to diffusion theory for diffuse incident light, but not for collimated incident light. We also present a simple calculation of the radiance as a function of direction in the diffusion domain. This, together with the effective attenuation coefficient, permits indirect experimental determination of both the albedo and the anisotropy factor (g) of the scattering function. Similarity relations are discussed, as they result from the so called delta-Eddington approximation, leading to the conclusion that far from boundaries and sources light propagation characteristics do not change very much when g and omega s are varied, provided omega s (1-g) is kept constant (omega s = scattering coefficient). Therefore, only two optical constants are required to approximately describe light propagation in homogeneous and isotropic media in the diffusion approximation.
Miniature light detectors with isotropic response (isotropic light probes) permit quantitative measurement of light energy fluence rates in turbid media such as biological tissues. These isotropic probes are, for example, applied in photodynamic therapy to correlate light fluence in tissue with (tumour) tissue response, in vitro and in vivo. After description of its construction, two methods of calibration of an isotropic probe in air are discussed, in collimated and in diffuse light. The probe was first calibrated in air in collimated light, after which its response to diffuse light was checked in a flat and in a spherical geometry. Subsequently, the probe's response to collimated light in clear media, for example, water or glycerine which have refractive indices larger than that of air, has been established experimentally. The diffusion approximation to the transport equation in a simple spherical geometry has been used to calculate the probe's response as a function of the refractive index of clear media. The extent of agreement between theory and experiment indicates that the physical mechanisms are understood and indirectly validates the theoretical models.
The light distribution during photodynamic therapy of the bronchial tree has been estimated by measuring the fluence rate in ex vivo experiments on dissected pig bronchi. The trachea was illuminated (630 nm) with a cylindrical diffuser and the fluence rate was measured with a fibre optic isotropic probe. The experiment with the diffuser on the central axis was also simulated with Monte Carlo techniques using the optical properties that were determined with a double-integrating-sphere set-up. The results from ex vivo experiments and the Monte Carlo simulations were found to agree within the error of measurement (15%), indicating that the Monte Carlo technique can be used to estimate the light distribution for varying geometries and optical properties. The results showed that the light fluence rate in the mucosa of the tracheal tract may increase by a factor of six compared to the fluence rate in air (in the absence of tissue). This is due to the scattering properties of the tissue and the multiple reflections within the cavity. Further ex vivo experiments showed that the positioning of the diffuser is critical for the fluence rate in the lesion to be treated. When the position of the diffuser was changed from the central axis to near the lesion, the fluence rate in the mucosa increased significantly by several orders of magnitude as compared to the initial (central) illumination. The inter- and intraspecimen variations in this increase were large (+/- 35%) because of variations in optical and geometrical properties and light source positioning, respectively. These variations might cause under- or overdosage resulting in either insufficient tumour necrosis or excessive normal tissue damage.
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