## 2 Methods
### Mesh-Based Monte Carlo for Optical Coherence Tomography (MMC-OCT)  
Throughout the simulation of this paper, a fast mesh-based Monte Carlo (MMC) photon migration algorithm for imaging in 3D complex tissue was used [16; 17], and a schematic that clearly illustrates the simulation process is shown in Figure 3. Before proceeding with the steps described in Figure 3,  
Figure 2: Wavelength dependence of oxyhemoglobin and deoxyhemoglobin absorption (blue and green, respectively) [22], whole blood scattering (red) [22], and water absorption (black) [20]. the \"MMCLAB\" package needs to be downloaded [30], which contains all the MATLAB m-files mentioned in Figure 3.  
In simulations, the light source was a pencil beam, and a circular detector with a radius of 10 \(\upmu\)m was placed at the same position as the emission position of the photon packet. The initial set number of photons and \(\theta_{\max}\) were \(5\times 10^{13}\) and \(3^{\circ}\), respectively. After running Monte Carlo MATLAB program \"mmclab\", the parameters _nscat_, _ppath_, v, and \(z_{\max}\) of each detected photon are obtained. It should be noted that the mesh of the tissue is subdivided in the depth direction in order to obtain the depth coordinates at which the scattering event occurs. Then, according to the condition \(\left|sum(ppath)-2z\right|<l_{c}/2\), the photons within the collecting angle \(\theta_{\max}\) are divided into different depths \(z\) having a thickness of \(l_{c}\). To classify the photon further, on satisfaction of \(\left|sum(ppath)-2z_{\max}\right|<l_{c}/2\), the photon is recorded as a class I photon, otherwise it is recorded as a class II photon [10; 13]. We directly obtained the backscattered field of the tissue detected by the OCT system represented as Equation (3) through the above steps, without simulating the complete imaging process of the OCT. The resolution of \(z\)-space is equal to \(l_{c}\), which is determined by the spectral bandwidth of the light source, and \(\mu_{t}\) is the average extinction coefficients of the tissue within the spectral bandwidth. Similarly, for the analysis of functional imaging of FD-OCT, the depth-resolved spectrum \(H\) (\(z\), \(k_{n}\)) represented by Equation (4) was directly obtained. From Equation (4), we found that the effect of window function \(g\) in the STFT is equivalent to that of a light source with a narrower spectral width. Therefore, we controlled the \(z\)-space resolution by setting \(l_{c}\), and the expression of \(l_{c}\) is \(\Delta z=\lambda^{2}/(2\Delta\lambda)\)[21]. \(\mu_{t}\) is the extinction coefficient of the tissue over the spectral bandwidth of the window function. Figure 3: Flow chart describing the simulation process of mesh-based Monte Carlo optical coherence tomography (MMC-OCT). \(\mu_{u}\) and \(g\) are the absorption coefficient and anisotropy factor, respectively; \(\theta_{i}\) is the angle between the emission direction of the detected photon and \(z\) axis; \(\theta_{\max}\) is the collecting angle; \(l_{c}\) is axial resolution (i.e., the coherence length); \(z\) is the probing depth; \(sum\) (_nscat_) and \(sum\) (_prpath_) represent the sum of scattering events and the sum of path lengths in all media, respectively. \(N_{\rm I}\) (\(z\)) and \(N_{\rm II}\) (\(z\)) are the numbers of class I photon and class II photon that are reflected/backscattered at the \(z\)-depth, respectively. All simulations were run using a desktop computer with an Intel Core 3-GHz 64-bit processor (Intel Corporation, Santa Clara, CA, USA) and 16 GB of RAM running the Windows operating system. It, however, has to be pointed out that the simulation time of MMC-OCT is long. Simulation of a \(300\times 300\times 500\)\(\upmu\)m gray matter (discretized using a mesh of 15,720 nodes and 87,996 elements) for \(5\times 10^{11}\) photons took approximately 2.5 h per A-scan. However, the simulation time can be greatly reduced by improving the program.