The retina is an ideal tissue for vascular research due to the access granted to nonsuperficial vessels by the ocular media. Microscopic details in the living retina may be visualized with the aid of adaptive optics (AO) [1]. Although originally applied to imaging the photoreceptors, AO is now actively being used to explore the flow of blood constituents in the retina through small arterioles and venules [2,3] and through individual capillaries [4–8].

Recent developments allow direct visualization of every blood cell flowing through small areas of the para-foveal retinal capillary bed [8]. In some capillaries, the red cells appear bright and are separated by darker plasma, while in other capillaries the red cells are dark and the plasma bright. This reversal in contrast is observed even along single capillaries, such that the same red cell may transition from black to white in appearance as it moves downstream [8]. Ambiguity in the appearance of blood constituents is apparent in other AO modalities, with differences in imaging parameters evidently altering red cell appearance from bright [2] to dark [6,7]. While white blood cells are larger, less deformable, and less numerous than other blood constituents [9], there are no such simple criteria to divorce red cells from plasma and so automatically determine red cell statistics. This ambiguity may also occur in other modalities, where measurement of capillary hematocrit requires fluorescent labels but measurement of capillary velocity does not [10,11].

To investigate the appearance of blood constituents in retinal capillaries, we acquired high spatiotemporal resolution retinal image sequences from two healthy human subjects, using our flood-based AO ophthalmoscope described previously [8]. Imaging light was $593\pm 10\mathrm{nm}$ (FWHM), which we have previously observed to provide high vessel contrast [8]. Exposure time was 1.25 ms. Field of view was 1.25° horizontally, and was limited to 0.4° vertically to achieve imaging at 400 fps with our sCMOS science camera. This allows us to capture cellular flow through the capillaries without temporal aliasing [8].

In each subject, we selected a location of high capillary density in which all capillaries were close to focus (subject PB: 2° inferior, 1° nasal to fixation; subject JZ: 1° superior, 1° temporal). We determined the initial plane of the best subjective focus and then systematically varied the defocus component of the AO correction from $-0.20$ to $+0.20\mathrm{D}$ in 0.05 D steps. This step size approaches the limit that can be faithfully reproduced by our system given fluctuations in tear film, eye movements, and accommodation; it also approaches the limit to which quality of focus can be judged with our 7.5 mm imaging pupil. For each defocus condition, we acquired three sequences of 200 ms duration (80 frames).

Motion contrast was used to generate an initial image of the vasculature [12] over which vessels were traced manually in Photoshop before being reduced to a single pixel in width. For each defocus condition, skeletonized vessel segments were triaged according to whether moving corpuscles appeared bright, dark, or ambiguous. Figure 1 depicts the results for both subjects. The nature of the motion is best appreciated in the actual sequences, samples of which can be viewed in Media 1 (PB) and Media 2 (JZ). Negative powers correspond to a more anterior plane of focus; this was associated with bright moving corpuscles (white segments in Fig. 1). As the plane of focus shifted posteriorly (positive powers), moving corpuscles became darker (black segments in Fig. 1). Inversion of contrast from bright to dark was observed over shifts of only 0.05 D. Corpuscle identification was ambiguous in some vessels due to low contrast (gray segments in Fig. 1). This may occur due to blur, proximity to branches/crossings, or proximity to the edge of the imaged field. We also believe poor contrast to (paradoxically) result when the vessel is close to focus, following our observations and the discussion presented below regarding defocusing microscopy. We also note that some vessels took on a mixed appearance; that is, bright and dark regions on the same corpuscle.

 

Fig. 1. Intensity of corpuscles in capillary segments as a function of defocus. Black: dark corpuscles; white: bright corpuscles; gray: ambiguous corpuscles (e.g., due to loss of contrast). Bars indicate proportion of vessel pixels in each state (black, gray, or white). Representative sequences shown in Media 1 (PB, 2° inferior, 1° nasal) and Media 2 (JZ, 1° superior, 1° temporal). Scale: each panel is $410\times 190\mathrm{\mu m}$.

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The defocus-induced inversion of contrast noted above is consistent with a framework developed recently based on phase-contrast microscopy [13]. Phase differences in the imaged light field introduced by objects displaced from focus generate interference contrast in proportion to the curvature of the object, the difference in refractive index with the surrounding medium, and the distance of the object from the plane of focus. When this latter distance exceeds the system depth of field, the contrast rapidly diminishes, as expected. This has been termed “defocusing microscopy” [13].

This framework has in fact been applied to the study of isolated red blood cells with optical microscopy [14], including the observation that red cell contrast becomes inverted when the sign of defocus is reversed. Our data confirm these observations in red cells in vivo, with a similar trend operating in counterphase for the intervening plasma gaps. That is, plasma is bright when red cells are dark and vice versa. If we assume that plasma “packets” in the same capillary have the same sign of curvature and axial depth as the red cells, contrast inversion must result from a sign inversion of the refractive index difference, i.e., the index of red cells and of plasma must lie on either side of that for the surrounding retinal tissue. Published data supports this: refractive index is $\sim 1.40$ for red cells (at 633 nm [15]), $\sim 1.34–1.35$ for plasma (at 633 nm [16]), and $\sim 1.36$ for retinal tissue (measured at 589 nm [17]). These figures suggest that red cell contrast should exceed that of plasma; however, our attempts at automatic identification of red cells based on this idea did not match subjective impressions of corpuscle flow. The refractive index of retinal tissue may therefore be located more symmetrically between that for red cells and for plasma than the published data would indicate.

Automatic identification of red cells from image intensity is difficult due to the dominance of phase contrast noted above. This is not an issue for identity-agnostic measures, such as velocity, flow, or linear cell density, but it is important for red cell specific measures such as hematocrit or red cell volume. The latter measures are more directly analogous to those measured by standard clinical blood panels, which would make their automated measurement in AO images a useful tool for blood research. In general, assignment errors are quite destructive for such metrics because they cause a bias as opposed to “averaging out” (e.g., for hematocrit, the bias is toward a value of 50%). Thus until an appropriate automatic method can be developed (perhaps based on packet shape instead of intensity) to distinguish red cells from plasma, manual identification will remain necessary.

The dominance of phase contrast renders quantification of capillary oxygen content in AO retinal images currently impractical. These considerations explain the previous work we presented [18] in which the temporal variability in optical density of the capillary network declined by a factor $\le 2$ as the imaging wavelength was varied from 570 to 650 nm, despite a decrease in the absorptance of hemoglobin by more than an order of magnitude.

Relative to fluorescent approaches, our data shows focus dependence that reduces the correlation of intensity between separate positions on the same vessel. We also expect physiological changes in velocity, flow, and hematocrit through time and as a function of position along a vessel. Therefore, to determine the precision of our measurements, it is necessary to establish the extent over which intensity remains correlated in space and time.

The “spatiotemporal plot” is commonly used for the quantification of blood-flow statistics such as velocity and linear cell density, both in fluorescent labeling studies [19,20] and in AO imaging of larger vessels [2,3,21]. Figure 2(a) shows a spatiotemporal plot for one capillary segment of our data; image gray scale values indicate how intensity changed along the vessel (horizontally) and across time (vertically). The slope of the plot (blue line) is a measure of velocity, while the periodicity in the time direction is a measure of flow (cells per unit time); these measures can be combined to give linear cell density [19].

 

Fig. 2. Spatiotemporal analysis in one vessel: (a) spatiotemporal plot and (b) 2D spatial correlogram. Arrows indicate longest distance over which peak of correlation with central point remained above threshold. (c) 2D temporal correlogram. (d) Radon transform of (a). (e) Variance of the radon transform for the spatiotemporal plot (blue), 2D spatial correlogram (red), and 2D temporal correlogram (black).

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To find the slope, we use the radon transform of the spatiotemporal plot [depicted in Fig. 2(d)]. The greatest local peak in the variance of the radon transform, shown in Fig. 2(e), is a robust means of determining the angular projection that best matches the data. To quantify flow, at each spatial location we calculate the 1D Fourier transform, average these, and then find the peak.

The spatiotemporal plot should be robust when there is high correlation of vessel appearance between positions in space and between points in time. Such coherence in space and time would arise as long as cells look reasonably identical, if their appearance is maintained while traversing the capillary network, and if flow parameters are relatively constant in space and time.

To explore spatiotemporal coherence, we imaged several retinal locations in our subjects. Fixation was directed in 0.5° steps from 2.5° nasal to 2.5° temporal from fixation, in two horizontal strips (one slightly superior and one slightly inferior to the foveal avascular zone). Motion contrast images and skeletonized traces were generated as above. Regions immediately surrounding each branch or crossing point were removed, defining a series of 171 capillary segments that were pooled for further analysis.

For each labeled capillary segment, we used the spatiotemporal plot to calculate the cross correlation of the intensity sequence of the central pixel with that for each other vessel pixel. The result, which we term a “2D spatial correlogram,” is shown in Fig. 2(b). Similarly, we calculated the cross correlation of the instantaneous vessel intensity of the central frame in the sequence with that for each other frame in the sequence. We term this a “2D temporal correlogram” [shown in Fig. 2(c)].

Figure 3 plots the extent in space (left) and in time (right) over which peak correlation was greater than some threshold (drawn from the 2D spatial and 2D temporal correlogram, respectively). Many vessels lost correlation in local areas of the correlogram, which hampers flow measurement in those areas; we therefore required peak correlation to remain contiguously above threshold. Regions of correlograms, where peak correlation dropped as low as $\sim 0.25$, did not contain sufficient contrast for subjective determination of velocity by flow angle; at this threshold, Fig. 3 therefore shows that, typically, velocity is amenable to subjective assessment over a distance of $\sim 22\pm 15\mathrm{\mu m}$ and over a period of $\sim 154\pm 49\mathrm{ms}$. For the spatial measure, this is $\sim 1$ cycle of an alternating blood cell and plasma gap, while it is $\sim 8$ cycles for the temporal measure (based on average measurements of linear cell density and of flow, given below). Thus signal correlation decreased less rapidly with time (due to dynamics in flow during the imaging sequence) than it did across space (due to dynamics in flow as well as due to phase-related changes in appearance along the vessel as described above). Nonetheless, the spatial measure is comparable to the extent employed in typical fluorescence imaging modalities, where the limitation instead results from the requirement for the vessel segment to be sufficiently well aligned with the scan axis [19].

 

Fig. 3. Coherence of flow data over space (left) and over time (right). Data averaged over 171 vessel segments. Error bars show ± one standard deviation from the mean.

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Following the above, all velocity and flow estimates presented here were obtained by limiting the extent of the spatiotemporal plot to the central 22 μm and 154 ms of data. This significantly improved the number of vessels for which valid data was obtained.

It is worth noting that apparent temporal dynamics in flow could be induced by sources, such as eye movements, tear film variations, or residual accommodation of the lens (which was mostly paralyzed by 0.5% tropicamide administered 20 min prior to imaging). We do not believe these were factors here since acquisition lasted only 80 ms, our subjects are experienced at maintaining fixation, and there were no apparent intrasequence variations in image quality (depth of focus is $\sim 0.05\mathrm{D}$ for our system). An additional source of variability that we did not control here may be the phase of the cardiac cycle at the time of imaging, i.e., perhaps the variability in capillary flow is reduced at certain epochs relative to the heartbeat.

The 2D correlograms shown in Fig. 2 give the impression of higher contrast compared with the raw spatiotemporal plot, while matching its angle of inclination and periodicity [e.g., in Fig. 2(e) compare the radon variance plots for the 2D correlograms, shown in red and black, with that for the spatiotemporal plot shown in blue]. To determine whether this does in fact produce a clearer signal for analysis of flow parameters, we calculated velocity for each vessel segment based on the 2D spatial and temporal correlograms, comparing them to the velocity obtained from the spatiotemporal plot.

Results for two representative vessels are shown in Fig. 4, with the estimate based on the raw spatiotemporal plot in blue, that of the 2D spatial correlogram in red, and that of the 2D temporal correlogram in black. Both spatiotemporal plots (Fig. 4, left) suffer from areas of poor data. In the lower dataset, the variance in the radon transform based on the 2D temporal correlogram (black) gave a single, well-defined peak that matched the subjective orientation of the data, while the other two methods did not. Conversely, in the upper dataset, the 2D spatial correlogram (red) gave the most well-defined peak. To automatically select the best approach for each vessel, we chose the one with the highest ratio between the maximum and median of the radon transform variance data. This combined approach matched subjective assessment in every case for which a subjective assessment was able to be made, whereas the spatiotemporal plot alone often failed as shown in Fig. 4.

 

Fig. 4. Spatiotemporal plot (left) and the variance in its radon transform (right) for two different vessel segments (top and bottom). Straight lines indicate slope determined from three complementary approaches: the spatiotemporal plot (blue), the 2D spatial correlogram (red), or the 2D temporal correlogram (black). For vessels in which subjective confirmation of slope was deemed reliable, strong agreement was always obtained by accepting the alternative with greatest “peakedness” (ratio of peak/median for the variance of the Radon transform). This corresponded to one of the 2D correlograms in 87% of vessel segments analyzed.

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Since flow velocity in each vessel can only be verified subjectively, it is difficult to know how accuracy is compromised by loss of contrast (e.g., vessels too far from focus). However, for “phantom” data comprised of simple sinusoidal gratings overlaid with noise, our approach recovers the correct velocity for noise levels significantly beyond the subjective limit and notably also beyond the limit encountered by the recently explored particle image velocimetry (PIV) approach [8]. Thus while there are vessels that should not be analyzed due to low signal-to-noise, the algorithm itself should not require supervision.

An additional advantage of the present approach is that computation time ($\sim 0.25\sec /\mathrm{vessel}$) was significantly less than for the PIV approach [8] ($\sim 6.0\sec /\mathrm{vessel}$).

The 2D correlogram should also be useful for assessment of flow in fluorescent modalities, which will see variability due to physiological changes in flow and due to misalignment between the scan axis and the vessel path. There is little drawback, since the analysis can be applied on the spatiotemporal plot post hoc.

In line with our previous report that used PIV [8], there was marked variability in flow parameters across the capillary network. Median velocity (± median absolute deviation) across our 171 vessel segments was $1.49\pm 0.61\mathrm{mm}/\mathrm{s}$, while flow was $58.8\pm 24.1\mathrm{cells}/\mathrm{s}$ (aggregates of multiple cells are encountered in the slightly larger vessels, the influence of which is partially ameliorated by use of the median). Measurements of velocity (mm/s) and flow (cells/s) were combined to give a figure for linear cell density of $46.1\pm 19.3\mathrm{cells}/\mathrm{mm}$ that agrees well with previously published data (e.g., $51\pm 12\mathrm{cells}/\mathrm{mm}$ reported in rodent neural tissue [19]).