## 3 Results and Discussions
### Simulation Results of Brain Functional Sensing  
As we mentioned in the introduction, the application of spectroscopic OCT in brain functional sensing is usually to quantify three parameters: total hemoglobin concentration \(C\), blood oxygen saturation \(Y\), and scattering coefficient \(S\). After obtaining the OCT signals of different wavelengths using MMC-OCT, \(C\), \(Y\), and \(S\) can be calculated using the quantitative method introduced in Section 2.1. In this section, we studied brain functional sensing through theoretical analysis and MMC-OCT \begin{table}
\begin{tabular}{c c c c} \hline
**Tissue Type** & **Thickness (mm)** & \(\mu_{a}\) **(mm\({}^{-1}\))** & \(\mu_{s}\) **(mm\({}^{-1}\))** \\ \hline \multicolumn{4}{c}{**Hierarchical Structure**} \\ \hline Skull & 7 (0.15) & 0.019 & 7.8 \\ CSF & 2 (0.05) & 0.004 & 0.009 \\ Gray matter & 4 (0.1) & 0.02 & 9 \\ White matter & 34 (0.2) & 0.08 & 40.9 \\ \hline \multicolumn{4}{c}{**Vessel Structure**} \\ \hline Medium (Gray matter) & 0.5 & 0.02 & 9 \\ Vessel & 0.1 (Diameter) & 0.28 & 88.55 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters and optical parameters of simulated tissues at 630 nm wavelength. Figure 5: **(a,b)** 3D volumetric finite-element (FE) mesh of simulated tissue, in which \(R\) and \(O\) are the radius and center of the blood vessel, respectively. **(d)** Backscattered signal of the vessel tissue. **(c,e)** show the backscattered signal of the compressed and uncompressed hierarchical structures, respectively. simulation. Specifically, we explored factors that affect the quantitative accuracy of \(C\), \(Y\), and \(S\) using three wavelengths. In the visible light waveband (500-600 nm), the absorption coefficient of hemoglobin is much larger than that in the near-infrared waveband, as shown in Figure 2, so functional sensing is very advantageous. Therefore, we chose a visible waveband to simulate functional sensing of the brain tissue. To obtain parameters \(C\), \(Y\), and \(S\), we usually need to solve the following three-variable linear equations:  
\[\begin{array}{l}C[\varepsilon_{1D}+Y(\varepsilon_{1O}-\varepsilon  
approximately 100 \(\upmu\)m [19]. Here, for convenience, we assumed that \(\mu_{t1}\) had error d\(\mu_{t1}\), and \(\mu_{t2}\) and \(\mu_{t3}\) had no errors. In Figure 6a, when \(d\mu_{t1}\) is 0.1 mm\({}^{-1}\), \(dC/C=0\) and \(dS/S=0.028\), while \(dY/Y\) is up to 0.9. In Figure 6b, when \(d\mu_{t1}\) is 0.1 mm\({}^{-1}\), \(dC/C=3.3\) and \(dS/S=1.16\), while \(dY/Y\) is only 0.2. Therefore, we can choose the appropriate wavelengths to solve the scattering and absorption parameters according to the actual needs. Next, functional sensing of brain tissue was simulated using MMC-OCT. The most popular components of brain tissue for researchers are often the cerebral cortex (i.e., gray matter) and blood vessels, so we obtained backscattered signals at different wavelengths of vascular tissue. The blood vessel had a diameter of 50 \(\upmu\)m and was embedded in the gray matter tissue with a depth of 150 \(\upmu\)m. Firstly, the appropriate wavelengths were selected based on the spectral data shown in Figure 2. We set a light source with a center wavelength of 570 nm and a spectral width of 50 nm. The window function of the STFT has a width in the spectral domain of 15 nm, and there is no overlap between the window functions at the two adjacent wavelengths. Between 540 nm and 600 nm, we used Equations (12)-(14) to calculate the theoretical error of the three parameters obtained using different wavelength combinations, and each combination consists of three wavelengths with an interval of 15 nm. The error for each \(\mu_{t}\) is a random number within 0-0.1 mm\({}^{-1}\); \(Y=0.7\), \(C=2\) mmol, and \(S=70\) mm\({}^{-1}\). The curve in Figure 7a shows the sum of the errors of the three parameters calculated using different wavelength combinations, and the abscissa is the minimum of the three wavelengths. The number of calculations is 200.