We used MCS as the foundation to determine reliable values of $\beta HbO,j$, $\beta HbR,j$, $\beta b,j$, and $\beta a,k$. The simulation model used here consisted of a single layer of cortical tissue, in which $\mu a(\lambda )$ and $\mu s\u2032(\lambda )$ are homogeneously distributed. The absorption coefficients $\mu a(\lambda )$ converted from the concentrations $CHbO$ and $CHbR$ and the reduced scattering coefficient $\mu s\u2032(\lambda )$ deduced by the coefficient $a$ and the exponent $b$ were provided as inputs to the simulation, whereas the diffuse reflectance spectrum $r(\lambda )$ was derived as output. The input values of $CHbO$, $CHbR$, $a$, and $b$ and the output reflectance spectra are useful as the data set in statistically determining the values of $\beta HbO,i$, $\beta HbR,i$, $\beta b,i$, and $\beta a,j$ for determining the absolute values of $CHbO$, $CHbR$, $a$, and $b$. The five different values of 60,258, 80,344, 100,430, 120,516, and 180,774 were calculated by multiplying the typical value^{40} of $a$ by 0.5, 0.75, 1.0, 1.25, and 1.5, respectively, whereas the five values of 1.2442, 1.31332, 1.3824, 1.45156, and 1.52068 were calculated by multiplying the typical value^{40} of $b$ by 0.5, 0.75, 1.0, 1.25, and 1.5, respectively. The reduced scattering coefficients $\mu s\u2032(\lambda )$ of the cortical tissue with the 25 different values were derived using Eq. (15). The sum of the absorption coefficients of oxyhemoglobin and deoxyhemoglobin $\mu a,HbO(\lambda )+\mu a,HbR(\lambda )=\mu a,HbT(\lambda )$ for $CHbT=4.652$, 23.26, and $116.3\u2009\u2009\mu M$ was used as input to the cortical tissue in the simulation. Tissue oxygen saturation StO_{2} was determined by $\mu a,HbO(\lambda )/\mu a,HbT(\lambda )$, and values of 0%, 20%, 40%, 60%, 80%, and 100% were used for the simulation. The above values were also used for the refractive index of the cortical layer. In total, 450 diffuse-reflectance spectra at $\lambda =500$, 520, 540, 560, 570, 580, 600, 730, and 760 nm were simulated under the various combinations of $CHbO$, $CHbR$, $a$, and $b$. The MRA1 analysis for each simulated spectrum based on Eq. (16) generated the 450 sets of vector $\alpha 1$ and concentrations $CHbO$ and $CHbR$ and exponent $b$, and the 450 sets of vector $\alpha 2$ and coefficient $a$. The coefficient vectors $\beta HbO$, $\beta HbR$, and $\beta b$ were statistically determined by performing MRA2, whereas the coefficient vector $\beta HbO$ was determined statistically by performing MRA3. Once $\beta HbO$, $\beta HbR$, $\beta b$, and $\beta a$ were obtained, $CHbO$, $CHbR$, $a$, and $b$ were calculated from $\alpha HbO$, $\alpha HbR$, and $\alpha 0$, which were derived from MRA1 for the measured reflectance spectrum, without the MCS, as shown in Fig. 1(b). Therefore, the spectrum of the reduced scattering coefficient $\mu s\u2032(\lambda )$ and that of the absorption coefficient $\mu a(\lambda )$ were reconstructed by Eqs. (12) and (15), respectively, from the measured reflectance spectrum.