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Expect Resistance: A Field Manual

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The present work proposes that the distance over which this signal propagates following a certain time delay is a source of velocity information. If true this offers a way to redress the limited spatial resolution noted above for the other methods, as velocity can be determined for individual pairs of pixels. The temporal resolution would remain high if a time delay of a single frame is found to be sufficient. Such an approach would hold great promise for analysis of microvascular network flow properties e.

As will be shown below, a complete spatial map of velocity also offers a powerful tool by which to judge the physiological plausibility of returned velocity measurements. Further, the method need not require cellular material to be separated by plasma gaps as with the STK method and does not require noisy pairwise comparisons between frames as with the PIV method.

The time-shifted pixel that yields the greatest similarity to the reference pixel is found, and the distance of this match from the pixel in question gives the velocity when divided by the inter-frame period. The specifics of our data processing pipeline are given below, with some brief commentary regarding each step. Three young, healthy human subjects age 23—33 years were recruited from staff and students at the University of Melbourne. All subjects had clear optical media and were adept at maintaining steady fixation.

Subjects reported no systemic or ocular disease. Approval was granted by the Human Research Ethics Committee of the University of Melbourne, and subjects were provided with written informed consent prior to experiments.

The study conformed with the tenets of the Declaration of Helsinki. Details of our adaptive optics flood illuminated ophthalmoscope system design are as published previously [ 4 ]. Data presented here were retrospectively analysed from 3 subjects and were acquired using various imaging wavelengths, frame rates and positions in the retina:. Acquired image sequences were background-subtracted and flat-fielded before being registered via a standard cross-correlation approach as previously described [ 4 ].

We corrected only for translational differences and not rotational artifacts in the sequences shown. We believe that the proposed velocimetry method should be applicable to raster-based systems for which intra-frame eye motion-induced distortions become significant, although more complex registration may be required to account for eye movements during frame acquisition [ 24 ]. Each step is applied without any manual guidance. Data from two representative sequences obtained from the same subject at fps with nm light. Bottom shows lower quality data obtained 6.

Top left: Average of 80 frames. Top right: Motion contrast image standard deviation. Bottom left: White shows binary segmentation, red shows skeletonized vessel segments. Bottom right: Labelled vessel segments. Corresponding raw and filtered data sequences are shown in S1 Video high signal: noise and S2 Video low signal: noise.

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For the velocity calculation itself, the following steps are carried out for each pixel to be processed within a given temporal window for example, for each pixel within the image, or for each pixel within a binary segment mask such as shown in Fig 1. The reference pixel whose velocity is to be determined is shown in red. All available image pixels are assayed to determine the best match white boxes show example candidates ; b shows intensity over time for the reference pixel red , for the pixel producing the best match after shifting forwards by one frame blue , and for the other example pixels that were indicated in a black ; c shows the similarity image for the reference pixel red , which is populated by calculation of root-mean-square RMS error between the reference signal and all considered image pixels after shifting by one frame.

The calculation of velocity for this example is overlaid on the image. A MATLAB implementation of the core steps outlined above, together with sample data at fps during a ms epoch, are included in S1 Demonstration. The pre-processing steps described above have already been carried out.

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The present algorithm was compared to current state-of-the-art methods in retinal capillary velocimetry, i. Details of our implementation of these approaches have been given previously [ 4 , 18 ]. The STK method has been independently advocated by, and is currently in favour with, several laboratories [ 17 — 21 ]. To make comparisons between the 3 methods it was useful to attribute velocities to individual vessel segments.

As described above, we used a fully automated procedure to segment the vasculature, which will inevitably produce some errors. However, it does afford an objective means by which to compare measurements from different vessels. Post-processing steps used were identical to those described above. Pre-processing steps were identical other than the following: the temporal filtering step step 3 in pre-processing above was not applied to the other methods, as it was found to either make no difference or to produce slightly worse results in some cases; for the PIV approach, to minimize spurious correlations and save processing time we did not compute correlations for regions of interest that did not include the binary vascular mask this is analogous to step 5 in pre-processing above ; the STK approach, being one-dimensional, was conducted on the automatically generated skeleton e.

Parameters employed in image processing and velocimetry are compared in Table 1. In two vessel segments of high image quality, many individual erythrocytes were labelled and tracked throughout longer sequences of frames at fps 3. This corresponds to approximately 3 cardiac cycles in a healthy participant and hence provides a way to compare the ability for each algorithm to track cardiac induced pulsatility, a phenomenon recently reported in the retinal capillaries [ 15 , 19 ]. Individual cell velocities were grouped into temporal windows corresponding to those used by the automated approaches see Pre-processing Step 6 above.

Example velocity maps generated by the PIX algorithm are shown in Fig 3 left column , for sequences of high and low quality top and bottom panels respectively; sequences correspond to those underlying Figs 1 and 2 , and can be viewed in S1 Video and S2 Video. For each sequence, both raw data first row and filled data second row is shown, with the latter facilitating comparison between methods.

The right column shows spatial maps generated by the PIV method maps generated by STK are omitted because they provide limited spatial resolution, with each vessel being coloured uniformly. Comparison of the filled data between PIX and PIV shows strong qualitative agreement for the high quality sequence, but poor agreement for the lower quality sequence.

It is possible that alteration of algorithm parameters Table 1 , such as size of sub-regions of interest, could improve the PIV outcome, however, we anticipate little improvement having already made considerable efforts to optimize PIV parameters in previous work [ 4 ]. Raw maps are shown at top in each panel, and interpolated maps are shown in the second row.

Fig 4 plots data from another subject, for two segments for which a large number of cells have been manually tracked across multiple cardiac cycles at fps see S3 Video. The mean velocity, pulsatility index PI; amplitude normalised to mean , quality of correlation R 2 and residual error root-mean-square are shown for ease of comparison. Some discrepancy is expected between areal methods such as manual tracking, PIV and PIX, compared with the STK approach which determines velocity tangential to a presumed vessel centreline.

There was strong agreement between the new method, the other automated methods and the manual tracking data, demonstrating proof of principle of the algorithm. Sequence was acquired at fps and can be viewed in S3 Video. Two simultaneously imaged segments were tracked manually left and right panels. Black crosses show manually tracked data, blue shows the output of the proposed PIX method, red shows output for particle image velocimetry PIV , and green shows output for the spatiotemporal kymograph STK.

Fig 5 top presents data which highlights some advantages of the new method. The plot corresponds to another, faster segment from the same sequence as Fig 4. Relative to the phase of the presumed cardiac waveform that was seen in Fig 4 , we observe the following discrepancies:. Top: Velocity trace for one segment showing long-term and short-term fluctuations in velocity captured with the PIX algorithm.

Bottom: PIX velocity maps corresponding to the time points indicated by arrows. White boxes: the vessel segment plotted whose average velocity is plotted in top. Raw and mean-subtracted sequence can be viewed in S3 Video , and evolution of velocity maps in time can be viewed in S4 Video. White boxes indicate the vessel whose average velocity is plotted top. Inspection of S3 Video reveals subjective aliasing of flow at certain time points; for example, seeming reversal of flow at each of the sudden troughs reported above for the STK algorithm.

Aliasing likely explains the poor performance of the PIV algorithm as well, which similarly has no way to easily handle multiple particles appearing in the same ROI [ 4 ]. It might be concluded that the vessel is not able to be easily studied, however, PIX produced a convincing cardiac waveform albeit with the large trough noted above.

Further inspection reveals the trough to be a physiological event, not an error. At frames — in S3 Video a period of stasis and cell accumulation is evident, associated with the passage of a white blood cell. The temporal windows just before and during this event are contrasted in the PIX velocity map of Fig 5. This can be further appreciated in S4 Video which shows the evolution of the PIX spatial map in time played at one-quarter of real-time speed. The faithful rendering of transient changes such as this demonstrates the potential for PIX to offer superior short-term tracking of flow.

The faithful reproduction of the cardiac cycle in this segment whose phase, as expected, matches the easier-tracked segments from Fig 4 further suggests that the method is resilient to aliasing which affects not only the other two methods, but the subjective impression of flow when watching the movie S3 Video. To determine whether a velocity map is physiologically plausible, it is useful to consider what reasonable constraints should be applied.

We would propose that:. The data shown in Figs 3 , 4 and 5 and the evolution shown in S4 Video offer compelling evidence that the PIX algorithm does produce physiologically plausible output. Fig 6 builds on this by showing data from another subject at a presumed diastolic minimum left and systolic maximum right , as confirmed by the velocity waveform shown for one segment, top.

The PIV map is also included for comparison bottom row. The corresponding video sequence is shown in S5 Video. In the systolic portion fast flow , PIX produces a physiologically plausible output according to the criteria defined above, however the PIV map displays segments containing unexpected oscillations, many of which appear to have much lower than expected velocity comparable to their diastolic velocity. The maximum velocities reported for PIV are well below those of the PIX algorithm, presumably because the PIV signal has become aliased for many of these vessels at the faster rates of flow experienced during systole.

This echoes the observations made for Fig 5 regarding the comparative resilience of PIX to aliasing. Top: velocity trace used to infer phase of the cardiac cycle. Left column: presumed diastole.

Right column: presumed systole. Sequence was acquired at fps and can be viewed in S5 Video. Top plot confirms the phase of the pulse wave. Second row: PIX raw. Third row: PIX filled. Bottom row: PIV filled. Physiological consistency across the network appears preserved in this sequence during systole with PIX, but not with PIV, which is unable to track the faster systolic flow. It is difficult to prove that the PIX output should be more physiologically plausible in general, as the true velocity is not known and is liable to vary from the cardiac output according to dynamics events as noted above.

Nonetheless, we may expect each vessel to be correlated to the cardiac output to varying degrees, and that any errors in velocimetry will on the whole be destructive rather than constructive to this correlation. Taking the average of a large number of segments in each field as indicative of the cardiac output at the capillary level, we calculated the Pearson correlation of each segment in a field to this model.

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This analysis was repeated over 7 non-overlapping fields in 2 subjects for which we had acquired data over multiple cardiac cycles at fps, for a total of unique vessel segments. The resulting R 2 of the fit for each segment is plotted in Fig 7 for each algorithm. Values have been sorted in ascending order for ease of visualization. This procedure was repeated over 7 non-overlapping fields acquired at fps in 2 subjects, yielding a total of unique vessel segments. The goodness of fit R 2 to the field average is plotted for each vessel.

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The higher R 2 values obtained for the PIX algorithm indicate that it generally returned more physiologically plausible outputs under the imaging parameters used here. We have presented a new velocimetry algorithm, demonstrated proof of principle and provided example cases which demonstrate its ability to. Fig 4 , the other examples given show clear departures for c through g. It is important to note that, although not presented here for brevity, we have reviewed a large number of samples acquired from several subjects at varying positions across the retina, and have not observed the opposite pattern in which PIX produced a non-plausible result where the other two did not.

Current understanding of the relationship between capillary flow and oxygen exchange suggests that both overall flow and distribution of flow are important for efficient oxygen delivery [ 22 ]. To demonstrate the ability of the proposed algorithm to capture network flow properties in a manner relevant to the modelling of oxygen exchange, we converted measured velocities to capillary transit time CTT , which is the more appropriate input to such models [ 22 ].

CTT is defined as the length of each capillary segment divided by its velocity. The output of this analysis is shown in Fig 8. More subjects will be needed to establish the normative range for this relationship in healthy human retina, however, the present results are of interest to demonstrate the capability of the proposed algorithm to capture these features of network flow, and to highlight the potential for wide variability between individuals, which could in turn influence susceptibility to development of vascular disease.

Sequences correspond to S3 Video and S5 Video. Capillary transit time for individual segments was calculated by dividing segment length by velocity. Network heterogeneity was quantified by the standard deviation CTTH and this was plotted against the mean CTT for each ms temporal window symbols. Systolic and diastolic extrema were identified from a representative velocity trace in each field circles. A strong linear relationship was evident in both subjects, though marked variability in slope exists. In addition to differences in flow distribution across the network, some capillaries in the images presented above e.

Fig 3 , top; Fig 5 , longest segment appeared to show marked gradients in velocity, with smooth and monotonic variation in flow along the length. To our knowledge this phenomenon has not been reported previously. It is possible for such changes to result at least in part from a change in vessel trajectory in the axial direction, however, the fact that they are rendered by the proposed algorithm speaks to its high spatial fidelity. In cases where the flow is subjectively ambiguous in a vessel e. The criterion that we have adopted is one of physiological plausibility, hence we have pointed above to the faithful replication of the expected cardiac cycle across time, contiguity of the spatial map within a segment, and demarcation of sudden changes between segments to infer the appropriateness of the PIX output.

These features are particularly compelling because there is no spatial or temporal smoothing applied to the raw data. Overall, these considerations lead us to believe that the PIX method may offer reduced sensitivity to noise and aliasing compared to other methods, especially in regards to the extraction of periodic variations in the data sudden discontinuities seen in the other methods are not evident with PIX.

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Such features are highly desirable for practical application to the study of large numbers of capillary segments and in clinical populations which may feature aberrant flow profiles, increased scatter, require the use of longer imaging wavelength or more peripheral imaging location with commensurately lower contrast , or yield fewer frames in a given area due to poorly controlled eye movements. The potential for PIX to avoid aliasing at lower frame rates allows imaging over an extended field with present adaptive optics imaging hardware.

In our system, the frame rate is limited by the number of pixel rows which must be read out in order to constitute a frame; hence a faster frame rate must be accompanied by a shorter field height. Raster based systems possess analogous limitations [ 15 , 19 ]. However, a shorter field height allows only a smaller portion of the vascular network to be imaged which greatly diminishes the efficiency of data collection and observation of natural flow patterns across the network.

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