# Can OCT Angiography Be Made a Quantitative Blood Measurement Tool?
## 4 OCTA Algorithms
### Complex Signal-Based OCTA Algorithms  
Complex signal-based OCTA algorithms use \(\text{S}(\text{x},\text{z},\text{t})\), the complex field, which includes both the intensity/amplitude and phase in Equation (1). As both intensity and phase fluctuations (Figure 4B,C,E,F) arise from field fluctuations (Figure 4A,D), we assert that the complex field is more fundamental than either the intensity or phase. In particular, the static component can be readily handled in the complex domain (Figure 6). Also, unlike intensity-based OCTA, complex signal-based OCTA is sensitive to slow flow with only phase changes [60]. In 2007, [PERSON] et al. [61] demonstrated complex signal-based OCT angiography, also called optical microangiography (OMAG), for the first time, while interframe complex OCTA was introduced later [16; 62]. The most basic complex OCTA algorithm is based on subtraction,  
\[\Delta\text{S}(\text{x},\text{z},\text{t})=\left|\text{S}(\text{x},\text{z}, \text{t}+\text{T})-\text{S}(\text{x},\text{z},\text{t})\right|, \tag{10}\]  
where \(\text{S}(\text{x},\text{z},\text{t}+\text{T})\) and \(\text{S}(\text{x},\text{z},\text{t})\) are complex OCT signals acquired at the same position separated by a time lag T. This is a difference-based algorithm without normalization. Spatial or temporal averaging may be applied as needed. This expression may also be generalized as a variance calculation (or high-pass filter [16]) that eliminates static scattering:  
\[\Delta\text{S}(\text{x},\text{z})=\frac{1}{\text{N}}\sum_{\text{t}=0}^{( \text{N}-1)\text{T}}\left|\text{S}(\text{x},\text{z},\text{t})-\overline{ \text{S}(\text{x},\text{z})}\right|^{2}. \tag{11}\]  
This is a temporally averaged, variance-based algorithm without normalization. As static and dynamic scatterer fields add in the complex domain (Figure 6), the above expression correctly eliminates static scattering to quantify the dynamic scattering signal. Using a complex signal-based algorithm, several applications of OCTA are demonstrated here. Figure 7A,B shows OCTA graphing of the mouse brain vasculature in vivo. Longitudinal monitoring of recovery in the mouse brain, one week after an experimental ischemic stroke, is shown in Figure 7C. Note the presence of vascular remodeling (yellow arrows). Figure 8 shows OCTA of a rodent eye in vivo. Figure 9 presents OCTA of pig ear skin, including a cross-sectional intensity image (Figure 9A), cross-sectional angiogram image (Figure 9B), color-coded angiogram of superficial and deep vasculature (Figure 9C), and angiograms centered at different depths (Figure 9D-I). All figures employ a complex interframe subtraction algorithm for angiography. In 2014, [PERSON] et al. [63] proposed a complex differential variance (CDV) algorithm. This differential variance algorithm, applied to the OCT signal at a position \((\mathrm{x},\mathrm{z})\), is:  
\[\mathrm{CDV}(\mathrm{x},\mathrm{z})=\sqrt{1-\frac{\sum_{\mathrm{t}=0}^{( \mathrm{N}-2)\mathrm{T}}|\sum_{\mathrm{k}=-\mathrm{L}}^{\mathrm{L}}w_{\mathrm{ k}}\mathrm{S}(\mathrm{x},\mathrm{z}-\mathrm{k},\mathrm{t})\mathrm{S}^{*}( \mathrm{x},\mathrm{z}-\mathrm{k},\mathrm{t}+\mathrm{T})|}{\sum_{\mathrm{t}=0}^ {(\mathrm{N}-2)\mathrm{T}}\sum_{\mathrm{k}=-\mathrm{L}}^{\mathrm{L}}w_{ \mathrm{k}}\frac{1}{2}[\mathrm{I}(\mathrm{x},\mathrm{z}-\mathrm{k},\mathrm{t })+\mathrm{I}(\mathrm{x},\mathrm{z}-\mathrm{k},\mathrm{t}+\mathrm{T})]}}, \tag{12}\]  
where \(w_{\mathrm{k}}\) is a depth-dependent window function of length \(2\mathrm{L}+1\). Though it is referred to as a \"variance\" method, this algorithm is actually a spatially and temporally averaged, correlation-based method with normalization (see the discussion of variance versus correlation in Section 4.4). The correlation is estimated by averaging on a complex basis axially (in z) and a magnitude basis over time. Also note that the correlation definition is the complex conjugate of that used elsewhere in this paper, though due to the absolute value operation, this minor discrepancy has no effect on the final CDV.