Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation

Background and Objective: Surface laser irradiation of tissue often produces a fluence rate that varies only with depth. Modeling of laser- induced fluorescence involves an expression for the fraction of fluorescence emitted per unit depth that escapes from the medium. We present accurate expressions for fluence rate and escape function for the one-dimensional case based upon Monte Carlo simulation results. Study Design/Material and Methods: Expressions were proposed for fluence rate, φ(z)/E₀ = C₁exp(-k₁z/δ)- C₂exp(-k₂z/δ), and escape function, G(z) = C₃exp(-k₃z/δ), that varied solely with depth relative to effective penetration depth, z/δ. The scalar (C) and exponential (k) coefficient values were found by curve fitting the expressions to Monte Carlo simulation results. Results: The coefficients varied as smooth functions of diffuse reflectance, R(d), for the range R(d) = 0.01-0.8, and were independent of scattering anisotropy in the range g = 0.7- 0.9. Simple expressions approximated the relationship of each coefficient to Rd. Conclusion: The proposed expressions have accuracy comparable to Monte Carlo simulations, over an essentially unrestricted range of diffuse reflectance values. The expressions may be combined accurately to portray laser-induced fluorescence measurements of a turbid medium.