Theoretical prediction of the source-detector separation distance suited   to the application of the spatially resolved spectroscopy from the   near-infrared attenuation data cube of tissues
  The modified Beer-Lambert law (MBL) and the spatially resolved spectroscopy are used to measure the tissue oxidation in muscles and brains by the continuous wave near-infrared spectroscopy. The spatially resolved spectroscopy predicts the change in the concentration of the absorber by measuring the slope of attenuation data according to the separation and calculating the absorption coefficients of tissue on the basis of the slop in attenuation at the separation distance satisfying the linearity of this slop. This study analyzed the appropriate source-detector separation distance by using the diffuse approximation resolution for photon migration when predicting the absorption coefficient by the spatially resolved spectroscopy on the basis of the reflective image of the tissue. We imagine the 3 dimensional attenuation image with the absorption coefficient, reduced scattering coefficient and separation distance as its axes and obtained the attenuation data cube by calculating the attenuation on a certain interval of coordinate on the basis of the diffuse approximation expression. We predicted the separation distance appropriate for the application of the spatially resolved spectroscopy by calculating and analyzing the first derivatives and second derivatives of attenuation with respect to the coordinates and also doing the differential pathlength factors and first derivatives of the attenuation with respect to the absorption coefficient from the attenuation data cube. When analyzing the hemoglobin derivatives in tissues, the appropriate separation distances are 3-5cm and the value of its corresponding differential pathlength factors are from 3.5 to 5. These data agree with the preceding experimental data. 
Yong-Wu Ri, Sung-Hu Jong, Song-Jin Im
physics.optics