Empirical relationship between Kubelka-Munk and radiative transfer coefficients for extracting optical parameters of tissues in diffusive and nondiffusive regimes

Arindam Roy; Rajagopal Ramasubramaniam; Harshavardhan A. Gaonkar

doi:10.1117/1.JBO.17.11.115006

8 November 2012 Empirical relationship between Kubelka-Munk and radiative transfer coefficients for extracting optical parameters of tissues in diffusive and nondiffusive regimes

Arindam Roy, Rajagopal Ramasubramaniam, Harshavardhan A. Gaonkar

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Journal of Biomedical Optics, Vol. 17, Issue 11, 115006 (November 2012). https://doi.org/10.1117/1.JBO.17.11.115006

Abstract

Kubelka-Munk (K-M) theory is a phenomenological light transport theory that provides analytical expressions for reflectance and transmittance of diffusive substrates such as tissues. Many authors have derived relations between coefficients of K-M theory and that of the more fundamental radiative transfer equations. These relations are valid only in diffusive light transport regime where scattering dominates over absorption. They also fail near boundaries where incident beams are not diffusive. By measuring total transmittance and total reflectance of tissue phantoms with varying optical parameters, we have obtained empirical relations between K-M coefficients and the radiative transport coefficients for integrating sphere-based spectrophotometers that use uniform, nondiffusive incident beams. Our empirical relations show that the K-M scattering coefficients depend only on reduced scattering coefficient (μ′_s), whereas the K-M absorption coefficient depends on both absorption (μ_a) and reduced scattering (μ′_s) coefficients of radiative transfer theory. We have shown that these empirical relations are valid in both the diffusive and nondiffusive regimes and can predict total reflectance within an error of 10%. They also can be used to solve the inverse problem of obtaining multiple optical parameters such as chromophore concentration and tissue thickness from the measured reflectance spectra with a maximum accuracy of 90% to 95%.

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Arindam Roy, Rajagopal Ramasubramaniam, and Harshavardhan A. Gaonkar "Empirical relationship between Kubelka-Munk and radiative transfer coefficients for extracting optical parameters of tissues in diffusive and nondiffusive regimes," Journal of Biomedical Optics 17(11), 115006 (8 November 2012). https://doi.org/10.1117/1.JBO.17.11.115006

Published: 8 November 2012

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