Signal properties of split-spectrum amplitude decorrelation angiography for quantitative optical coherence tomography-based velocimetry

: Split-spectrum amplitude-decorrelation angiography (SSADA) is a noninvasive and three-dimensional angiographic technique with a microscale spatial resolution based on optical coherence tomography. The SSADA signal is known to be correlated with the blood flow velocity and the quantitative velocimetry with SSADA has been expected; however, the signal properties of SSADA are not completely understood due to lack of comprehensive investigations of parameters related to SSADA signals. In this study, phantom experiments were performed to comprehensively investigate the relation of SSADA signals with flow velocities, time separations, particle concentrations, signal-to-noise ratios, beam spot sizes, and viscosities, and revealed that SSADA signals reflect the spatial commonality within a coherence volume between adjacent A-scans.


Introduction
Optical coherence tomography (OCT) is an imaging technique to visualize three-dimensional structures of biomedical tissues, by means of low coherent interferometry of broadband infrared light [1][2][3][4][5][6]. Because OCT is non-invasive measurements and has a microscale spatial resolution (1-15 µm), OCT has been applied in clinics such as for retinal diseases and skin diseases [3,4]. By recent developments of OCT with high temporal resolutions, i.e. spectral domain OCT (SD-OCT) [5] and swept-source OCT (SS-OCT) [6], various functional imaging techniques with OCT have been developed. Especially, Doppler OCT (DOCT) [7][8][9], which quantifies the blood flow velocity within the tissue, is one of the functional imaging techniques that has been studied in the early stage after the establishment of OCT [9]. DOCT detects Doppler shift frequencies due to blood flows along the optical axis (axial direction) and has been applied in manifold fields such as retina and skin [7,8]. However, its application is limited because Doppler shift frequencies are highly related to the angle between the incident light beam and vessel orientations. For example, the retina has many blood vessels running perpendicular to the incident light beam, therefore, large amounts of blood vessels are unable to be detected by DOCT.
OCT based-angiography (OCTA), another type of functional imaging based on OCT, is able to detect vascular networks in vivo without using extrinsic dyes [10][11][12][13][14][15][16][17][18][19]. OCTA can map vascular networks by analyzing temporal changes in intensities [12][13][14], phases [15,16], or both of them (complex signals) [17][18][19] of OCT signals caused by motion of red blood cells (RBCs) in the vessel. Specifically, displacements of RBCs within the same imaging location at different times cause larger temporal fluctuations in OCT signals within vessels than surrounding static tissues. Recent studies revealed that OCTA signal correlates with the absolute blood flow velocity and has negligibly small dependence on the angle between incident light beams and vessel orientations in contrast to DOCT [20]. Hence, several phantom experiments were performed to realize the quantitative velocimetry with OCTA [20][21][22][23]. Among various OCTA methods, split-spectrum amplitude-decorrelation angiography (SSADA), an intensity-based OCTA method, gained many interests because SSADA has identical flow sensitivity on all directions and is less susceptible to axial motion artifacts, by making the coherence volume broader and isotropic. Due to these advantages, SSADA has already been implemented in commercial OCT system [24,25]. Using SSADA, Tokayer and colleagues measured human blood flowing in a glass capillary for several flow velocity conditions with varying time separations (time interval of adjacent A-scans), and examined the changes in SSADA signals [20]. They found that (i) SSADA signal is proportional to the flow velocity while the SSADA signal saturates at a certain flow velocity, and (ii) an increase in SSADA signal per flow velocity is proportional to the time separation while the SSADA signal is saturated earlier as the time separation increases. Su and colleagues also examined the changes in SSADA signals against blood vessel sizes using a microchannel with diameters of 8 to 60 µm [21]. They found that (iii) the increase of SSADA signal per flow velocity and the saturation value of SSADA signal are proportional to the diameter of the microchannel. In this way, properties of SSADA signals have been progressively understood, however, these studies investigated only a few specific parameters related to SSADA signals, and there is no study that comprehensively investigates SSADA signals with multiple parameters. Furthermore, the beam spot size and the signal-to-noise (S/N) ratio, which are basic parameters to give the performance of OCT system, have never been experimentally investigated.
In this study, to understand signal properties of SSADA and to realize quantitative velocimetry based on SSADA, we comprehensively investigated parameters related to SSADA signals with one OCT system. Relationships between SSADA signals and flow velocities, time separations, particle concentrations (associated with RBC concentrations), S/N ratios, beam spot sizes, and viscosities were investigated via phantom experiments.

Experimental system setup
We used SS-OCT system based on Mach-Zehnder interferometer (IV-2000, Santec Corp.; Fig. 1). The swept-source laser (HSL-2000, Santec Corp.) had the swept rate τ of 50 µs that determines A-scan rate of SS-OCT imaging, the center wavelength λ c of 1,334 nm with a full width at half maximum of 117 nm, and the average output power of 18.1 mW. The coherence length, which determines the axial spatial resolution, was 13.4 µm (in air). The light was irradiated to the sample through a collimator (beam diameter d = 7 mm) and an objective lens (focal length f = 60 mm), resulting in the beam spot size of 14.6 µm, which determines transverse spatial resolution. To imitate the scattering of blood flows, we used a lipid solution (Intralipos (IL); Intralipos injection 20%, Otsuka Pharmaceutical Co., Ltd.) [26,27]. The IL concentration was controlled by mixing with purified water. The IL solution was injected into a glass capillary having outer/inner diameters of 1.5/0.86 mm with a syringe pump (1235N, Atom Medical Corp.). The flow rates were ranged from 0 to 32 ml/h in 2 ml/h steps that are converted to the mean flow velocities (flow rate per cross-sectional area) of 0 to 15.3 mm/s in 0.96 mm/s steps in the glass capillary. The grass capillary was placed perpendicular to the OCT beam (axial direction) with a rotation stage.
To examine the relationship between SSADA signals and S/N ratios with one OCT system, neutral density (ND) filters were employed. The ND filters (transmittances T r of 50, 25, 12, and 6%; Asahi Spectra Co., Ltd.) were placed between the collimator and the objective lens in the sample arm ( Fig. 1) to restrict the incident light intensity on the sample and the backscattered light intensity from the sample. We investigated how the S/N ratio influences SSADA signals under five conditions with/without the ND filters (see Fig. S1 in the Supplement 1).
Also, to examine the relationship between SSADA signals and beam spot sizes, we employed handmade pinholes that were made with a belt punch set (TPO8S, Trusco Nakayama Corp.). The pinholes with diameters d ′ of 7, 5, 4, and 3 mm were placed between the collimator and the objective lens in the sample arm ( Fig. 1), and resulting beam spot sizes ∆x were estimated to 20.9, 27.6, 33.7, and 44.3 µm, respectively (see Fig. S2 in the Supplement 1) [28]. We investigated how the beam spot size influences SSADA signals under five conditions with/without the pinholes.

SSADA analysis
In order to investigate the time separation ∆t of 0.25, 0.50, 1.00, and 2.00 ms and to compare our results with the previous studies [20,21], multi-timescale SSADA shown in Eq. (1) was used [20,29,30], where z represents the axial position, A m n represents n-th OCT signal intensity obtained from m-th split spectrum, M represents the number of spectrum split, and N represents the number of A-scans at the same position (so-called M-scan). As described above, τ = 50 µs was the A-scan rate of our system, and thus we obtained SSADA signals D at ∆t of 0.25, 0.50, 1.00, and 2.00 ms by calculating decorrelations between n-th and n+5th, n-th and n+10th, n-th and n+20th, n-th and n+40th OCT signal intensities, respectively. The number of spectrum split M was fixed to 11 that covered the full spectrum for stable calculation of the SSADA signals D [31]. The Gaussian function was used to split the spectrum as a window function, and the widths of the Gaussian function were set to make the coherence volume (spatial resolutions along axial and transverse directions) isotropic. The number of A-scans at the same position N was 10,000 to stably calculate SSADA signals and to investigate a wide range of the time separations with the limited A-scan rate of 50 µs.

Investigation of the relation between SSADA signals and flow velocities
The relation between SSADA signals and flow velocities was analyzed in the following steps. First, SSADA signals were obtained from 10,000 A-scans at the center of the glass capillary, and SSADA signals within the glass capillary were extracted ( Fig. 2(a), red dashed line). Next, theoretical flow velocities along the axial direction u(r) shown in Fig. 2(b) were calculated by an equation, where r andū represent a normalized radius ranged from -1 to 1 and the mean flow velocity in the glass capillary, respectively. This equation is well-known formula to give the velocity distribution for the laminar flow through a circular pipe. In our experiments, the flow rate was up to 32 ml/h. Assuming that the viscosity of IL solution is equivalent to that of the water (1.0 × 10 −6 m 2 /s), Reynolds number R e at the flow rate of 32 ml/h was 13 that satisfied the laminar flow condition (R e ≪ 2000), and thus all experiments were thought to be performed under laminar flow states. Finally, SSADA signals and theoretically calculated flow velocities obtained from 17 flow conditions were plotted into a scatter diagram (Fig. 2(c), top), and then the scatter diagram was binned with a bin size of 1 mm/s and the median values of the SSADA signals for each bin were plotted with the first (25%) and the third (75%) quantiles. (Figure 2(c), bottom). Note that non-linearity and large variation in the curves of SSADA signals were often seen in the flow velocities around 0 to 10 mm/s probably because the theoretical flow velocity distribution calculated from Eq. (2) does not always matched with the actual flow distribution in such slow velocity range, but these would not so affect in obtaining characteristics of the curve such as slopes and intercepts.

Dependence of particle concentrations (IL concentrations)
At first, we examined the dependence of particle concentrations on SSADA signals, which correspond to the dependence of the hematocrit level, by using IL solutions with four different concentrations, 0.5, 1.0, 2.0, and 4.0%. Figure 3(a) shows relations between SSADA signals and flow velocities at four different time separations for four IL concentrations. The SSADA signals were saturated at around 0.215 regardless of the time separation while larger time separation led the saturation of SSADA signals at smaller flow velocities. These results are consistent with previous studies [20,21]. However, the intercepts, which are the values of SSADA signals at the flow velocity of 0 mm/s, were increased as the time separation increased, whereas the previous study reported that the intercepts had no changes against the time separation (see Discussions) [20].
On the other hand, IL concentrations seemed not to affect SSADA signals for any flow velocities and time separations. To facilitate the comparison between SSADA signals for different IL concentrations, we focused on four parameters: the flow velocity at which SSADA signals saturate (saturation flow velocity), the slope, the intercept, and the variation of the curves. The saturation flow velocity was defined as a flow velocity that the value of SSADA signals reaches to 95% of 0.215. The slope and the intercept were obtained by a linear-fitting of the curve in a range from 0 mm/s to the saturation flow velocity for each condition. The variation was evaluated with the median of the ranges of SSADA signals between 25% and 75% quantiles for each flow velocity (median of the variation). Figure 3(b-e) shows these parameters against the IL concentrations. As expected from Fig. 3(a), the saturation flow velocity, the slope, the intercept, and the variation were not changed by IL concentrations. The slope for the time separation of 2.00 ms were unstable across IL concentrations probably because data points used for the linear-fitting were too small due to small saturation flow velocities ( Fig. 3(b,c)). Additionally, increase of the time separation ∆t tended to make the slopes increased as ∆t smaller than 1.00 ms in this case, whereas the previous study reported that the slope was proportional to the time separation (see Discussions) [20]. The variations tended to be larger as IL concentration increased or as the time separation decreased (Fig. 3(e)), but these changes could be negligibly small as referring to the following results (see Figs. 4(e) and 5(e)). From these results, SSADA signals were found to be independent on IL concentrations, i.e. particle concentrations. Thus, in the further analyses below we used the datasets obtained from IL solutions with a fixed concentration.

Dependence of S/N ratios
As far as we know, there was no study that investigated the relation between SSADA signals and S/N ratios. By employing ND filters as shown in Fig. 1 to restrict the light in the sample arm, for the first time, we controlled S/N ratio and examined how the relation between SSADA signals and flow velocities are changed against the S/N ratio. We used IL solution with a concentration of 1% whose S/N ratio was 37.7 dB without using ND filters (transmittance T r = 100%), while the background level of the OCT intensity was set to 0 dB. The ND filters with transmittances T r of 50, 25, 12, and 6% changed the S/N ratios to 30.0, 22.4, 16.0, and 11.4 dB, respectively (see Fig. S1 in the Supplement 1). Figure 4(a) shows the curves of SSADA signals and flow velocities for each S/N ratio. The curves for T r of 50 and 25% coincided well with those for T r of 100% regardless of the time separations. In contrast, the curves for T r of 12 and 6% showed smaller slopes and larger  intercepts than the others that were clearly observed as the time separation was getting smaller. The saturation values of SSADA signals seemed to be the same across all conditions. To facilitate the comparison, we evaluated the saturation flow velocity, the slope, the intercept, and the variation against the transmittance of the ND filters ( Fig. 4(b-e)). As expected from Fig. 4(a), these parameters for T r of 50 and 25% were almost consistent with those for T r of 100%. In the cases of T r of 12 and 6%, the saturation flow velocities and the slopes were slightly smaller, and the intercepts were larger compared to those for T r of 100%. The amount of these changes for T r of 6% were larger than those for T r of 12%. The variations for time separations of 0.25 and 0.50 ms also tended to be larger than those for T r of 100%. These changes were not surprising because SSADA quantifies the temporal variation of OCT intensities as the decorrelation coefficient [14], and small S/N ratios are expected to give low temporal correlations, i.e. high decorrelations, of OCT intensities, leading to large variation of SSADA signals. Hence, the baselines of SSADA signals that corresponds to the intercept were increased by small S/N ratios, and the slope were also changed with the changes of baselines. Therefore, SSADA signals were found to be dependent on S/N ratios when the S/N ratios are smaller than a certain value. In our OCT system, SSADA signals were not affected when the S/N ratio was 22.4 dB (T r = 25%) but were affected when the S/N ratio was 16.0 dB (T r = 12%), so that adaptive calibration curves are required to quantify the flow velocity with our system if the S/N ratio is smaller than around 20 dB.

Dependence of beam spot sizes
In order to investigate the dependence of the beam spot size on SSADA signals for the first time as well as the S/N ratio, the pinholes were employed to control the beam spot size, and the relation between SSADA signals and flow velocities against the beam spot size was examined. The pinholes with diameters of 7, 5, 4, and 3 mm changed the beam spot size to 20.9, 27.6, 33.7, and 44.3 µm, respectively, while the beam spot size was 14.6 µm without using any pinholes (see Figs. S2 and S3 in the Supplement 1). Figure 5(a) shows SSADA signals against the flow velocities for each beam spot size. The saturation values of SSADA signals were the same across all beam spot sizes. The saturation flow velocity and the variation were getting larger as the beam spot size became larger, and the slope was getting smaller as the beam spot size became larger. To facilitate the comparison, the saturation flow velocity, the slope, the intercept, and the variation were calculated (Fig. 5(b-e)). The saturation flow velocities seemed to have positive correlations with the beam spot sizes for each time separation (Fig. 5(b)). This would be because SSADA signal does not saturate when the same moving particles are included within a coherence volume of analyzed adjacent A-scans, and large beam spot sizes provide large coherence volumes, resulting in the positive correlations between the saturation flow velocity and the beam spot size. With this increase of the saturation flow velocity, the slopes were getting smaller as the beam spot sizes become larger, showing negative correlations (Fig. 5(c)). The intercepts seemed not to be affected by the beam spot size, whereas the SSADA signal at the time separation of 0.25 ms for the beam spot size of 44.3 µm was slightly larger than the others. This was because of the S/N ratio rather than due to the beam spot size. The small diameter of the pinhole results in small S/N ratios since the pinhole restricts the power of the incident light to the sample, and actually employing the pinhole with d ′ of 3 mm (∆x = 44.3 µm) largely decreased the S/N ratios (Fig. S3 in the Supplement 1). The variations were also getting larger as the beam spot sizes became larger, showing positive correlations. Especially for d ′ of 4 and 3 mm in Fig. 5(a), large variations were observed in a high flow velocity range (12 to 30 mm/s) that were not observed in the others. It is considered that changes in spatial pattern of the moving particles within the coherence volume affect the temporal stability of SSADA signals and the large coherence volume, i.e. the large beam spot size, is more sensitive to the changes than the small coherence volume. From these results, we found that SSADA signals largely depend on the beam spot size and suggested that changes in spatial pattern of the moving particles within the coherence volume between adjacent A-scans contribute the changes of SSADA signals.

Discussions
We explored the signal properties of SSADA to realize OCT-based velocimetry using SSADA. The relation of SSADA signals with flow velocities and time separations was almost consistent with the previous studies. However, there were two inconsistent results [20]: Tokayer and colleagues showed that (i) the intercepts in the curves of SSADA signals and flow velocities did not depend on the time separation, and (ii) the slope of the curve was proportional to the time separation, but these were not the case for our experiments. This former inconsistency would be because the range of the time separations was largely different between their and our experiments (∆t = 0.056 to 0.280 ms for them and ∆t = 0.25 to 2.00 ms for us). The value of SSADA signals at the flow velocity of 0 mm/s (baseline SSADA signals) has been thought to reflect to the displacement of moving particles due to Brownian motion [20,21,32]. Hence, large time separations as in our experiments will lead to large displacements by Brownian motion that make the increase of baseline SSADA signals not negligible. In order to confirm this hypothesis, we tested how the curves of SSADA signals and flow velocities are changed against the viscosity, which is a factor to determine the displacements of moving particles by Brownian motion (Fig. 6). The IL solutions with a concentration of 1% were used, and their viscosities were changed by adding a viscosity modifier, carboxymethyl cellulose (CMC; see Fig. S4 in the Supplement 1). As expected, Fig. 6(d) showed that the intercepts decreased as the viscosities (CMC concentrations) increased since Brownian motion was prevented due to the increase of the viscosity. This is clear evidence that Brownian motion determines the baseline SSADA signals, and is the reason why the intercept in our results was not consistent with the previous study. The latter inconsistency would be also because of difference in the range of the time separation, meaning that the slope was considered to be proportional to the time separation only in their small range of the time separation (∆t = 0.056 to 0.280 ms). In other word, the slope would not be proportional to the time separation in nature. Focusing on Fig. 6(c), the slope for time separation of 2.00 ms was larger than that of 1.00 ms under CMC concentration of 0.05 and 0.07%, whereas all other results showed the slopes for time separation of 2.00 ms were smaller than that of 1.00 ms (for CMC concentration of 0 and 0.02% in Fig. 6(c), Figs. 3(c), 4(c), and 5(c)). By taking these results into account, the slope is thought to be passively determined by connecting the baseline SSADA signal (the intercept) and the SSADA signal at the saturation flow velocity. This hypothesis can explain that high viscosities (CMC concentrations of 0.05 and 0.07% in Fig. 6(c)) made the baseline SSADA signals for the time separation of 2.00 ms small enough to give higher slopes than those for 1.00 ms. In addition, SSADA signal saturates at a certain value and thus both baseline SSADA signal and saturation flow velocity cannot be proportional to the time separation (see Fig. S5 in the Supplement 1). Therefore, we would conclude that the slope is not proportional to the time separation.
Eventually, the signal properties of SSADA were investigated on flow velocities, time separations, particle concentrations, S/N ratios, beam spot sizes, and viscosities. As the results, we validated that the curve of SSADA signals and flow velocities depends on the time separation, and found that the curve also depends on the S/N ratio, the beam spot size, and the viscosity while does not depend on the particle concentration. Specifically, the decrease of S/N ratios increased the baseline SSADA signals (the intercepts) and the variation of SSADA signals if the S/N ratio was smaller than a certain value, which was 20 dB for our system. The increase of viscosities also decreased the baseline SSADA signals. The increase of beam spot sizes increased the saturation flow velocity and the variation, and there was the positive correlation between beam spot sizes and the saturation flow velocities. In fact, this positive correlation was predicted in previous studies [20,21] but was experimentally validated for the first time. To further investigate this positive correlation, the relation between saturation flow velocities and ratios of beam spot sizes and time separations ∆x/∆t were calculated (Fig. 7). A statistically significant positive correlation was obtained, and the ratios of the saturation flow velocity and ∆x/∆t were almost consistent across all conditions (0.658 ± 0.112). These results suggest that the dynamic range of the flow velocity quantified by SSADA signals is determined by α∆x/∆t, i.e. a velocity of particles to travel a certain ratio α of the coherence volume (∆x) in a period for adjacent A-scans (∆t). Overall, we propose that the signal properties of SSADA can be qualitatively understood with a model showing the commonality of spatial patterns of moving particles within a coherence volume (Fig. 8). Suppose that spatial patterns of particles within a coherence volume are changed as the particles travel in a period for adjacent A-scans (t and t + ∆t). The dependence of flow velocities and time separations on SSADA signals is explained to reflect to the spatial commonality between adjacent A-scans ( Fig. 8(a)): the orange regions in Fig. 8 indicate regions commonly existed in adjacent A-scans, and the SSADA signal D decreases as the area of the orange region increases. The particle concentration does not affect the area of orange regions if the displacement between adjacent A-scans is the same, resulting in the independence of particle concentrations on SSADA signals (Fig. 8(b)). The dependence of S/N ratio on SSADA signals is explained by Fig. 8(c) where the decrease of S/N ratio makes precise detection of the spatial commonality difficult. The beam spot size changes the size of a coherence volume and thus the spatial commonality is changed even if the displacements between adjacent A-scans are the same (Fig. 8(d)), resulting in the changes of the saturation flow velocity. Although we did not perform the experiment, this model can explain the dependence of vessel sizes found by Su and colleagues [21]. They showed that SSADA signals depend on the vessel size, and the value that SSADA signals saturate D sat is getting smaller as the vessel size decreases. Their results are explained by thinking of static tissues within a coherence volume that secure the spatial commonality within the coherence volume between adjacent A-scans, and the secured spatial commonality makes the value that SSADA signals saturate decrease (Fig. 8(e)). The blue dots represent spatial patterns of static tissues that do not change over time. The orange regions indicate the spatial commonality between adjacent A-scans (t and t + ∆t). D, SSADA signal. D sat , the value that SSADA signals saturate.
Finally, we mention differences between our phantom experiment and actual in vivo SSADA imaging and possible difficulties of quantifying the blood flow velocity with SSADA in vivo, focusing on (i) particle sizes, (ii) capillary sizes, (iii) wavelengths, and (iv) time separations. For the particle size, IL was used in our experiments, but the particle size of IL (sub-micron order) is largely different from the sizes of RBC (micron order), meaning that in the actual in vivo SSADA imaging, only a few particles (RBCs) should be included within a coherence volume for typical OCTs. Hence, by thinking of the model shown in Fig. 8, the spatial commonality between adjacent A-scans for RBCs will be difficult to detect when OCTs with a typical spatial resolution are used, compared with IL particles. This difficulty would lead to changes in SSADA signals seen in small S/N ratios such as the decrease of saturation flow velocities and the increase of baseline SSADA signals (the intercepts) ( Fig. 4(b,d)). Actually, previous studies that investigated SSADA signals with RBCs showed small saturation flow velocities against the beam spot sizes [20,21]. The ratio of the saturation flow velocity and ∆x/∆t was around 0.658 for our study but was around 0.03 for Tokayer's study. Furthermore, particle sizes also affect light scattering properties. IL contains isotropic particles that have sub-micron order size, leading to small scattering anisotropy, while RBC is biconcave and has micron order particle size, leading to strong forward scattering [33][34][35]. The strong forward scattering might also change the saturation flow velocity and ∆x/∆t, and leads to projection artifacts [34,36]. Although several methods to remove the projection artifacts have been developed [37], we need further investigation how the artifact removal influences SSADA signals to quantify the blood flow velocity. On the other hand, Bernucci and colleagues found that the projection artifact can be eliminated by injecting IL as a contrast agent [34]. Since our result showed that SSADA signals are not affected by IL concentration (Fig. 3), the use of contrast agents such as IL can be a future way to quantify the blood flow velocity without being affected by the projection artifact.
For the capillary size, we used a glass capillary with an inner diameter of 0.86 mm in the phantom experiments and suggested the feasibility to quantify the blood flow velocity with SSADA if the capillary size is enough larger than the coherence volume. However, a major advantage of OCTA including SSADA is detecting small capillaries (∼10 µm), which cannot be detected by other methods such as DOCT, and thus quantifying the blood flow velocity with SSADA is also required to apply to such small capillaries. Typically, those small capillaries are smaller than the coherence volume, which corresponds to the situation shown in Fig. 8(e). Our model suggests that quantifying the blood flow velocity is not impossible even in the situation shown in Fig. 8(e), but we will need complex calibration because the saturation flow velocity and the baseline SSADA signal will depend on the capillary size. For example, we have to examine changes of SSADA signals against blood flow velocities, capillary sizes, and time separations, estimate a capillary size from multi-timescale analysis of SSADA signals as shown in Fig. S5, and finally obtain the blood flow velocity from a calibration curve corresponding to the estimated capillary size. However, since it is impossible to perform calibration experiments with infinite capillary sizes, we will need another method such as machine learning to estimate quantitative blood flow velocities from finite calibration results.
For the wavelength of OCT, we used 1,300 nm light, whereas in vivo retinal imaging has typically employed 800 or 1,000 nm light [24,25]. According to the model shown in Fig. 8, the difference between these wavelengths will not affect signal properties of SSADA. However, the light scattering anisotropy, the scattering coefficient, and the absorption coefficient depend on the wavelength. The scattering anisotropy increases in lower wavelength, but compared with the difference between particle sizes described above, the difference in the scattering anisotropy would not affect SSADA signals [33]. Also, the dependency of the scattering coefficient on wavelengths will not affect SSADA signals since the difference in the scattering coefficient of tissues is negligibly small in the near infrared waveband [38]. On the other hand, differences in the absorption coefficient of tissues such as water and lipid are not negligible [38][39][40]. Especially in in vivo retinal imaging, the water absorption will decrease S/N ratios of OCT since the eyes contain a lot of water. The baseline SSADA signals will increase if the S/N ratio is smaller than a certain value (Fig. 4), and thus 800 or 1,000 nm light would be the better choice when quantifying the blood flow velocity in vivo.
For the time separation of OCT, we investigated SSADA signals for ∆t of 0.25 to 2.00 ms. However, the time separations for commercial OCT systems are not so fast (typically, ∆t > 2 ms) [25], which leads to small saturation flow velocity (Fig. S5(a)). One way to make the time separation faster is to change the scanning protocol. Typically, SSADA signals are calculated from multiple B-scan OCT images at the same B-scan position. Thus, the time separation is given by the multiplication of the A-scan rate and the A-line number, resulting in a large time separation. On the other hand, it is possible that multiple A-scans are performed at one location, and the location is moved to the next to construct a cross-sectional image. In principle, this protocol will make the time separation equal to the A-scan rate without changing total recording time, although motion artifacts such as discontinuity along the transverse axis in OCT image would be inevitable. Another way to improve the time separation is the use of megahertz OCT (MHz-OCT), which is OCT with A-scan rate faster than 1 MHz. For example, Optores GmbH (Germany) has sold a MHz-OCT (OMES 4D MHz-OCT System) that has A-scan rate of 1.5 MHz, and Kim and colleagues reported a MHz-OCT with A-scan rate of 9.4 MHz [41]. These MHz-OCTs can realize the time separation faster than 1ms. In the near future, MHz-OCT will be applied to SSADA imaging, which increases the feasibility of quantifying the blood flow velocity with SSADA in vivo.
In this study, to realize quantitative blood flow velocimetry with SSADA, we performed phantom experiments and obtained a clear idea to understand signal properties of SSADA for IL by comprehensively analyses of SSADA signals. Although further investigations are needed for in vivo quantitative blood flow velocimetry as described above, our results will help understanding in vivo signal properties of SSADA.

Conclusion
In order to explore signal properties of SSADA, the relations of SSADA signals with flow velocities, time separations, particle concentrations, S/N ratios, beam spot sizes, and viscosities were experimentally investigated. The phantom experiments revealed that the signal properties of SSADA can be explained by the spatial commonality within a coherence volume between adjacent A-scans. Our findings will give helpful insight to increase the feasibility of in vivo quantitative blood flow velocimetry with SSADA.