Analytic function for predicting light fluence rate of circular fields on a semi-infinite turbid medium

Abstract

Accurate determination of in-vivo light fluence rate is critical for preclinical and clinical studies involving photodynamic therapy (PDT). The light fluence distribution in tissue depends on both the tissue optical properties and the incident field size. This study compares the longitudinal light fluence distribution inside biological tissue in the central axis of circular uniform light field with different radii for a range of in-vivo tissue optical properties (absorption coefficients (µ a ) between 0.01 and 1 cm −1 and reduced scattering coefficients (µ s ') between 2 and 40 cm −1 ). This was done using Monte-Carlo simulations for a semi-infinite turbid medium in an air-tissue interface. The end goal is to develop simple analytical expressions that would fit the results from the Monte Carlo simulation for circular beams with different radii. A 6-parameter model ( can be used to fit MC simulation. Each of these parameters (b, C 2 , C 3 , λ 1 , λ 2 , and λ 3 ) is expressed as a function of tissue optical properties and beam radius. These results can then be compared against the existing expressions in the literature for broad beam for analysis in both accuracy and applicable range. The analytical function can be used as rapid guide in PDT to calculate in vivo light fluence distribution for known tissue optical properties.

Evaluation of singlet oxygen explicit dosimetry for predicting treatment outcomes of benzoporphyrin derivative monoacid ring A-mediated photodynamic therapy

“…22 Based on a previous study, 23 an empirical six-parameter fitting equation was used to fit the Monte-Carlo (MC) calculated light fluence rate data 22 for a 1-cm diameter field, with μ a ¼ 0.52 to 0.80 cm −1 and μ 0 s ¼ 7.9 to 14.1 cm −1 . The equation is of the following form:…”

“…23 INV ¼ ½SSD∕ðSSD þ dÞ 2 , where the source-to-surface distance SSD ¼ 9.34 cm based on the measurement of light fluence rate in water for the same collimated beam as a function of depth and fit to the inverse-inverse square law Table 2 PDT parameters (σ, ξ, and g) obtained for four mice treated with in-air fluence of 160 J∕cm 2 and in-air fluence rate of ϕ air ¼ 80 mW∕cm 2 using individual fitting to ½ 3 O 2 ðt Þ and ½S 0 ðt Þ simultaneously (see Fig. 3).…”

“…(3), and published fitting parameters. 23 For each spatial location, ½S 0 ðtÞ and ½ 3 O 2 ðtÞ can be calculated by solving the coupled differential equations [Eqs. (4) and (5)] using the initial conditions for ½S 0 0 based on fluorescence measurement before PDT and its assumed spatial homogeneous, the initial ½ 3 O 2 0 value (e.g., 50 μM from Tables 1), and ϕðdÞ.…”

Analytic function for predicting light fluence rate of circular fields on a semi-infinite turbid medium: erratum

“…(15) in the original manuscript [1] does not converge to zero when circular beam diameter exceeded 3/µ eff for µ a > 0.1cm −1 , and one has to manually set the parameter C 3 to be zero to achieve the reported accuracy. The inclusion of C 3 term using the original Eq.…”

“…(15) along with Eqs. (11)-(16) from [1] have been tested for the range of optical properties studied in the manuscript and no revision in the text is required.…”