1. Introduction

Retinal and choroidal blood flow are known to be reliable indicators of ocular diseases such as glaucoma, myopia and retinitis pigmentosa as these diseases are often associated with reduced blood flow [1–3]. There are several methods of quantifying blood flow and these include fluorescein and indo-cyanine (ICG) angiography [4,5], optical coherence tomography angiography (OCT-A) [6], laser doppler [7], and laser speckle contrast imaging (LSCI) [8]. Compared to other blood flow measurement techniques, LSCI is low-cost, non-invasive, and capable of producing full-field flow maps [9]. When a diffuse object is illuminated with laser light, a random interference effect known as a speckle pattern is produced. If there is movement in the object, the speckles fluctuate in intensity. These fluctuations can be used to provide information about the movement, such as retinal blood flow. Originally developed before modern camera technology [10], LSCI can now be performed near real-time [11], and has been used to measure blood flow in various biological tissues [12].

Significant advances in this technology have been achieved in recent years; Fercher and Briers [13] were the first to apply single-exposure LSCI to analyze retinal perfusion in the 1980s yet, only recent devices such as Nidek’s LSFG, Softcare’s LSFG-NAVI and the XyCam RI have demonstrated intra-day repeatable blood flow measurements [14–18]. Although clinically promising, Nidek’s and Softcare’s laser speckle flowgraphy devices are based on the computation of a Mean Blur Rate Metric that is not a quantitative estimation of blood flow [19]. Furthermore, the XyCam RI is based on single-exposure LSCI, which due to the influence of nonergodic light, static scattering, and experimental noise effects, cannot give linear estimates of decorrelation time with increasing flow [20,21]. Single exposure LSCI is also not linear; the blood flow values measured change less than the actual blood flow, especially at higher blood flow [20,21]. To overcome these problems, multiple exposure speckle imaging (MESI) has been proposed. By capturing images at different exposure times, a speckle model can be fit to experimentally determine the unknown parameters of nonergodic light, static scattering, and noise effects. These parameters now have a constant variance, giving decorrelation time estimates that are corrected for noise, and extending its linearity with increasing flow. However, repeatability using MESI has not yet been extensively studied in literature.

To estimate the repeatability of MESI, it is essential to first correct motion by post-processing the raw speckle images captured using image registration. Liu et al. and Miao et al. have previously used image registration to correct heart rate and respiration motion in the laser speckle images of anesthetized rat brains [22] and abdominal cavities [23]. Liu et al.’s LK-TPS non-rigid registration algorithm allowed for a more accurate estimation of contrast values and blood flow velocities, while Miao et al.’s rigid registration enabled improved spatial resolution to view smaller blood vessels. Other motion correction research included fixing opaque labels next to the region of interest on human forearm skin to approximate motion [25] as well as using a handheld gimbal stabilizer to image a mouse’s dorsal window chamber [26].

Similarly, in the human eye, imaging a motionless retina is difficult with respiration, heartbeats, and bulk human movements. In this manuscript, following the conversion of low signal-to-noise raw speckle retinal images into contrast maps, these contrast maps are subsequently registered using a custom registration pipeline. Registration is essential for producing more repeatable flow maps when compared to unregistered LSCI data on the same day (intra-day). We chose not to demonstrate comparisons of repeatability between unregistered and registered blood flow maps as it has been shown that registration improves flow repeatability [22, 23]. In this manuscript, we first studied the repeatability of flow measurements in the retina with the application of registration using data generated by a custom LSCI device on the same day (intra-day). Subsequently, the manuscript reports, for the first time, measures of repeatability of retinal blood flow estimations on two different days (inter-day).

2. Methods

2.1 Experimental laser speckle system

The retinal LSCI device consists of a modified-hardware system and a custom data acquisition software suite. The acquisition system consisted of a modified Kowa VX-10α fundus camera (Fig. 1(A)), with a coherent laser source of 40 mW and wavelength of 808 nm (Fig. 1(B)). This optical setup provided a small diffuse 2 mW annulus output which illuminated the retina with minimal corneal reflection. The raw speckle fundus images were acquired by an Andor Neo sCMOS camera attached to the Kowa Fundus camera. The Andor sCMOS chip was cooled to -20°C to keep the dark current low. Custom C++ software using OpenCV and the Andor SDK was developed to acquire raw 16-bit frames.

 

Fig. 1. (A) Modified Kowa VX-10α fundus camera with Andor Neo sCMOS camera used to capture the laser speckle pattern projected onto the retina. (B) Laser module attached externally to the fundus camera coupled to an optical cage system.

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2.2 Clinical process

Clinical experimentation was performed at the School of Optometry and Vision Science at the University of Auckland, approved by the University of Auckland board. A total of eight participants were recruited, three of which were emmetropic and the remaining had varying levels of myopia. Pre recruitment eye health check was performed for all participants to ensure their ocular health by registered optometrists. The clinical application of the system and collection of data was approved by Auckland Health Research Ethics Committee (AH2959). Each participant visited the clinic twice, with the second visit and scan occurring approximately 24 hours after the first. This arrangement was proposed so that both intra-day and inter-day repeatability of our LCSI system could be evaluated. Participants were instructed to refrain from taking caffeine or undertaking strenuous exercise before the imaging sessions.

On each visit, the participant was dark-adapted by staying in a dark room for 10 minutes. The participants were then asked to rest their chin on a chin rest to reduce the amount of involuntary and voluntary motion. They were then scanned five times using the LSCI on the same eye (7 right eyes, 1 left eye). In each scan, the operator aligned the device with the patient’s pupil to achieve maximum retinal illumination. The participant was then instructed to have a ‘big blink’ and to subsequently fixate on an internal LED fixation target. The scan was then initiated by the operator. The average scan durations were: 4696.5 +/- 80.8 ms (n = 80). Participants were asked to then take their heads off the chin rest and then rest for 5 minutes in between scans. On each visit, the participant had a new operator scan their eye (two operators total) to reduce the possibility of operator error and bias. 104 frames were captured in a single scan, equally divided between exposure times of 0.5, 1, 2, 4, 8, 16, 32, and 64 ms, resulting in 13 raw speckle frames per exposure time.

2.3 Data processing and flow map estimation

An overview of the processing pipeline, beginning with the raw speckle images to the final flow map is presented in Fig. 2. Emphasis was placed on the registration process in this study as this was previously found to be essential for repeatability in LSCI in retinal scans [22,23]. Further details are provided in the following subsections. The complete source code of the processing pipeline is openly available [24].

 

Fig. 2. Complete process from the acquisition of raw speckle images to the formation of flow maps.

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2.3.1 Contrast map generation

The first step to generate contrast maps was to subtract the readout noise from the raw speckle images. A master bias frame was created by averaging 200 individual images taken with the lens cap on at the camera’s minimum exposure time. Each raw speckle image then had the master bias frame subtracted off (Fig. 3(A)).

 

Fig. 3. (A) Raw speckle image at 32 ms (uint16) upscaled by 10x for visualization. (B) Contrast map at 32 ms upscaled by 10x. (C) Preprocessed contrast map at 32 ms. (D) First fixed image: all 104 preprocessed contrast maps averaged. (E) Second fixed image: averaged image of all successfully registered preprocessed contrast maps after one iteration. (F) Averaged image of all successfully registered preprocessed contrast maps after two iterations. (G) Averaged image of all 32 ms contrast maps after registration upscaled by 10x. (H) Decorrelation time map after curve fitting. (I) Flow map after inverting decorrelation times.

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For each frame, spatial contrast maps were then generated. A speckle contrast was calculated for each pixel by using the standard deviation divided by the mean of all the pixel intensities in a neighboring kernel window using Eq. (1).

In previous literature [8], kernel sizes of 5 × 5 or 7 × 7 were employed depending on the size of the speckle vs the size of the pixel. A smaller kernel is more susceptible to noise, but a larger kernel has decreased resolution. Testing revealed that a 9 × 9 kernel was an optimal balance of resolution and noise for the speckle images generated in this study. A representative contrast map is shown in Fig. 3(B).

2.3.2 Registration and contrast map averaging

All contrast maps were pre-processed to improve the definition of vessels for better registration against a ‘fixed image’ (discussed later). Preprocessing included median filtering to reduce the map noise, contrast enhancement with MATLAB (R2019b, Mathworks, Natick, MA, USA) functions adapthisteq() and imadjust(), morphological closing to improve vessel intensity, and resizing contrast maps to 30% the original size for faster registration and also noise reduction. The transform of the registration was later resized to be applied on the large contrast maps (Fig. 3(C)).

To register the contrast maps, MATLAB’s imregtform function [27] was used for iterative intensity-based automatic image registration. A multimodal configuration was selected to register contrast maps of different exposure times against a constant ‘fixed image’ [28,29]. The registration optimizer’s ‘initial radius’ parameter was adjusted from the default to a smaller radius value of 3.90625e-4 to prevent the registration algorithm from diverging [30]. The transform type was also set to be ‘rigid’, which considers only rotations and translations during the registration process as there was negligible scaling of the eye within scans.

To create a ‘fixed image’, an approach similar to Santos et al. [31] was employed, where multiple iterations of registration were performed. The ‘fixed image’ at each iteration was the average of all frames registered and it was determined that two iterations of registration were sufficient. The ‘fixed image’ for the first registration iteration was an averaged image of all contrast maps before registration (Fig. 3(D)). All preprocessed contrast maps (representative map shown in Fig. 3(C)) were registered against this ‘fixed image’ (Fig. 3(D)). All registered images were then averaged to produce a sharp registered image (Fig. 3(E)) after just one iteration of registration. In the second iteration of registration, Fig. 3(E) becomes the new ‘fixed image’ and then all preprocessed contrast maps were again registered to obtain Fig. 3(F).

Registration success was determined by considering the horizontal translation taken from matrix index (3,1) of the transformation array output from MATLAB’s imregtform function. Failure of registration resulted in large vertical and horizontal translations. After experimentation, a horizontal translation value greater than 70 pixels indicated a failure in the registration process and subsequently, the frame was discarded. The second indicator of registration success was performed in case poorly registered frames passed the first assessment. This was achieved by examining the output of MATLAB’s correlation coefficient function corr2 between a registered image and the averaged image of all registered images at the same exposure time. If the correlation coefficient was too low (a correlation coefficient of 1 between two images indicates perfect alignment), this implied dissimilarity between two contrast maps, possibly caused by a blink or uncorrected motion [32]. In this study, frames with correlation values lower than three standard deviations from the mean of correlation values at that exposure time were removed.

The MATLAB output of all registration transforms from the second iteration were stored and applied to the original contrast maps without preprocessing using MATLAB’s imwarp function with the default parameters.

2.3.3 Curve fitting to contrast maps and generation of retinal flow maps

Following registration, all 13 registered contrast maps from each independent exposure time were averaged to reduce the noise and pulsatile variations in the individual contrast maps (Fig. 3(G)). Initially, the 0.5 ms and 1 ms exposure times were measured because it was believed that the low exposure times were influential in constraining the exponential model fitted to the contrast vs decorrelation time curve. However, the raw intensity values of the registered and averaged contrast maps generated from 0.5 ms and 1 ms exposure times were too small and therefore could not contribute to the decorrelation curve fit. As such, only exposure times of at least 2 ms were included to extract the speckle fluctuations [9]. Ultimately, six independent exposure times (2, 4, 8, 16, 32, and 64 ms) each with 13 frames were used, resulting in a total of 78 frames for one scan. The 78 frames generate six registered and averaged contrast maps that corresponded to exposure times of 2, 4, 8, 16, 32, and 64 ms. After resizing each contrast map by 0.1 to reduce the problem size (90% reduction in the width and height of each contrast map), a model relating the speckle contrast and decorrelation time was fit through every pixel intensity value at the same spatial position in all six averaged contrast maps (Fig. 3(H)). However, the choice of the model to fit was not immediately apparent. Many different models describing the relationship between speckle contrast and decorrelation time have previously been reported [8,11,13,20,23,33]. The use of an additional term to account for camera noise, which causes an offset in the speckle contrast, has also been discussed [20,34,35]. However, there is no current consensus on which models and parameters are most appropriate for quantifying human retinal blood flow. Ultimately, after fitting several different models the Duncan and Kirkpatrick (Eq. (2)) [33] and Liu model [11] proved to produce the best repeatability. Fitting both these models was performed using MATLAB’s fit() function. A comparison of the two models revealed that the primary difference is the term, $\rho $, to account for static scattering in the Liu model. The addition of this term considers the nonergodicity caused by light scattering from static particles. When $\rho $ was estimated according to $K \approx \sqrt \beta ({1 - \rho } )$ [11], fitting either model resulted in similar flow maps. Where $\beta $ is an instrument-dependent constant, $\rho $ is the proportion of light that is dynamically scattered, and K is the contrast at the longest exposure time (64 ms). This concluded that accounting for static scattering did not lead to more repeatable flow maps. As such, due to simplicity, the Duncan and Kirkpatrick model was employed to estimate the decorrelation time. The decorrelation time had an initial optimization value of 0.2 with a lower boundary of 0 and an upper boundary of 50.

This allowed the estimation of the decorrelation time (${\tau _c}$) at each pixel. The decorrelation time parameter can be subsequently used to quantitatively determine blood flow velocity (Eq. (3)) or a blood flow index by simply using 1/${\tau _c}$ (Fig. 3(I)) [36].

2.4 Quantitative estimate of registration quality

MESI required the contrast-decorrelation function to be fitted at the same spatial location over the different exposure contrast maps, so it was important to evaluate registration quality after the exclusion of outlier frames in the contrast maps and before the generation of flow maps. The structural similarity (SSIM) index metric was used [37] to quantitatively evaluate similarity and therefore registration quality between contrast maps of different scans of the same subject on the same day. MATLAB’s ssim() function with a dynamic range between 0 and 1, and an 11 × 11 isotropic circular Gaussian weighting function, were used to compute the SSIM index.

The steps used to compare each set of five scans on the same day are described in Fig. 4. Each scan had six averaged contrast maps for the 2 ms, 4 ms, 8 ms, 16 ms, 32 ms, and 64 ms exposure times. For the five scans of the same ID on each day, there were 30 (five scans ${\times} $ six averaged exposures) averaged contrast maps in total (Fig. 4(A)). The contrast maps of the same exposure time were then registered from the different scans (Fig. 4(B)), and subsequently, all possible pairs were then compared by computation of an SSIM map (Fig. 4(C) & (D)). The overall SSIM, described by a single value, was obtained by application of a mask to remove the outer boundaries and then averaging all the SSIM values within the mask for each exposure (Fig. 4(E)). After repeating this procedure for all exposure times, the single value average SSIM values for each exposure time were then averaged again to provide a final estimation of registration quality (Fig. 4(F)).

 

Fig. 4. Process of computing a structural similarity value for estimation of registration quality. (A) Each scan has six averaged contrast maps for the 2ms, 4ms, 8ms, 16ms, 32ms, and 64ms exposure times. For the five scans of the same ID on each day, there are 30 averaged contrast maps in total. (B) Registration between scans is necessary as SSIM comparisons require the images to be at the same location. (C) SSIM computes the difference between two images, so each pair of the five scans must be compared, leading to 10 SSIM comparisons in total for each exposure time. Comparisons are only made within the same exposure time due to similar contrast values between images. (D) For each pair, 2-dimensional SSIM maps are created using MATLAB’s ssim() function. (E) Averaging all values within each of the 10 masked SSIM maps leads to 10 SSIM values for each exposure time. (F) A total of 60 SSIM values for all six exposure times are averaged to give a single average SSIM for each ID on each day.

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2.5 Quantifying repeatability

Post-registration of contrast maps and generation of retinal flow maps, the goal of the study was to evaluate the repeatability of the LSCI hardware system and analysis pipelines developed. Repeatability was quantified two-fold; intra-day, which is deemed the repeatability within the same imaging session and the same day, and inter-day, which is the repeatability compared between two different sessions on different days.

2.5.1 Intra-day repeatability

To validate the inter-day repeatability of our laser speckle analysis, the intra-day repeatability of flow maps must first be demonstrated. For intra-day repeatability, all five flow maps of the same eye were registered across day 1 and day 2 independently. Registration enabled a direct comparison of the same spatial pixels across multiple flow maps. Without registration, such direct comparisons would not be possible because comparing one region of a flow map to another would likely result in different regions being compared.

Two methods of quantifying intra-day repeatability were used. Firstly, as demonstrated in previous studies [15–18] rectangular ROIs covering the veins and arteries in the flow maps were manually selected (Fig. 5(A)). For each of the five scans on each day, the flow value of each pixel was averaged within the ROI to obtain five averaged arterial flow values and five averaged venous flow values. The coefficient of variation (CV) [3,38,39] of the averaged flow values over a set of five scans was calculated as a ratio of the standard deviation to the mean. However, this only indicated flow variation in small regions of the total flow map.

 

Fig. 5. (A) Manually selected vein and artery ROIs. The average coefficient of variation values were computed for both vessels across five independent scans. (B) CV map, lower values indicate regions of high repeatability and higher values indicate regions of lower repeatability. N.B. the mask at the center of the flow map and CV map is due to an optical reflection artifact and is excluded from analyses.

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Since reproducibility of the total flow map is also of interest, the second measure of repeatability was by calculation of the CV for each pixel across five registered flow maps of the same eye on the same day to generate a CV map (Fig. 5(B)). A circle mask was then applied to exclude the image periphery where illumination was poor. A whole map averaged CV was then computed by averaging all CV values within the masked map. Lower CV values indicated flow values that were more reproducible over the same day.

2.5.2 Inter-day repeatability

To estimate inter-day repeatability, all flow maps generated on day 1 and day 2 first had to be registered against each other (i.e. registration inter-day) to allow for a spatial pixel-to-pixel comparison. Two methods were used to quantify inter-day and inter-observer repeatability. The first method quantifies repeatability using the coefficient of reproducibility (CR) [40], whilst the second method utilizes the means of the averaged total flow maps to determine if there is a statistically significant difference between two days.

Region of interest inter-day repeatability: For the manually selected ROIs, the flow value within the ROIs was averaged (five values corresponding to five measurements per day), then the five average flow values for the region of interest selected for each day (day 1 and day 2) were further averaged to obtain a single flow value for each day. The two averaged flow values of each ROI on each day were then used to calculate a single value CR.

Statistical test of inter-day repeatability: In the statistical test of difference in flow on two independent days, five flow maps corresponding to the five scans on day 1 of a participant were averaged and similarly the five flow maps of the same participant on day 2 were averaged. The means of the total maps were then computed so that a single mean flow value for a participant on each of the two days was obtained. This was repeated for all eight participants, enabling a standard paired t-test to be performed. A paired t-test was carried out to reveal whether there was evidence against the null hypothesis that the mean difference is zero between flow maps on day 1 and flow maps on day 2 of all participants. If the p-value is >0.05, then there is no evidence against the null hypothesis that the difference in mean flow measurements between the two days is zero, providing a loose indication of flow repeatability.

3. Results

3.1 Registration quality

To begin the data analysis for inter-day and intra-day repeatability, the registration quality of the raw speckle images must be validated. To demonstrate this, MATLAB’s SSIM function was employed as an overall estimate of registration quality. This same technique is used by MathWorks Inc. in their Registration Estimator Application. Table 1 summarizes the results of the SSIM analysis, where a value of 1, indicates perfect registration between two images, and therefore the higher the SSIM value, the better the registration. The SSIM’s of all registered contrast maps were higher than their corresponding unregistered contrast maps. Comparison of the difference in means of registered and unregistered images using a paired t-test, we found a significant difference in the degree/quality of registration using the SSIM index metric (p < 0.001 for both day 1 and day 2), indicating a quantitative improvement in the alignment of the contrast maps. Objective assessment pre and post-registration also indicated an improvement in registration. SSIM values are unitless.

Table 1. Average of SSIM across all IDs (p < 0.001 for both day 1 and day 2).

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3.2 Intra-day repeatability

Post-registration, flow maps estimating the intra-day retinal blood flow of each of the eight participants were computed and are presented in Fig. 6. Across the five independent scans, it is visually evident that the flow maps are similar across scans. Although the absolute quantitative flow values were not able to be validated against another reference flowgraphy measurement, it shows that in the same session, on any day, the laser speckle system and the processing pipelines developed, demonstrate a degree of robustness.

 

Fig. 6. Day 1 flow maps generated from five independent repeated scans of all participants in the study. There is a clear indication of intra-day repeatability across independent scans. 1/τ has been used as an approximation of flow, so flow values have been given in instrument-dependent arbitrary units.

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An interesting observation is the higher flow observed in ID0 of this study. Looking at the isolated intra-day data, it was initially believed that this may have been an experimental or operator error, however, the inter-day data (shown in section 3.3.1), and the introduction of a different operator, produced almost identical flow maps, effectively dismissing this hypothesis.

Table 2 summarizes the quantitative intra-day CV results. Except for one participant, all CVs across the veins and arteries for both days were below 20%. The mean CVs for ROIs of arteries and veins on day 1 were consistent with previously reported CV results for LSCI in the retina of 7.82% ± 2.38% in veins and 9.60% ± 2.41% in arteries (n = 11) [18]. The exclusion of an outlier (ID 7) on day 2 also resulted in mean and standard deviation values consistent with those reported in literature [18].

Table 2. Summary of Intra-day Reproducibility Across 8 Participants

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The mean intra-day CVs of the whole flow maps were 10.14% ± 3.33% on day 1 and 14.92% ± 8.33% on day 2. Two participants (ID 1 and 7) had CVs greater than 25% for the whole flow map on day 2. The high CVs of both these subjects appear to be caused by the clinical process as the averaged dissimilarity of the unregistered contrast maps for these two subjects was the highest amongst all subjects on day 2 (Table 1).

3.3 Inter-day repeatability

3.3.1 Region of interest inter-day repeatability

Across all eight participants with varying degrees of ametropia, the inter-day and inter-observer CR of veins and arteries were 12.01 ± 8.90% (standard error = 3.14%) and 10.73 ± 9.65% (standard error = 3.41%), respectively. The averaged flow maps for the individual days are shown in Fig. 7 for all the participants in this study. Visually, it can be observed that some variability of flow is present between the two days, particularly in the retinal background.

 

Fig. 7. Averaged Day 1 and Day 2 flow maps for all participants. ID 6 did not show up to the study. Only the left eye data was available for ID7.

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Furthermore, it appears that the inter-day variability of the CR values between different subjects seems to be large and biased heavily by a few subjects. Unfortunately given the low total number of subjects in this study, it is difficult to exclude such subjects statistically. Exclusion of subjects (n = 2, out of a total of n = 8) with CR values larger than 20% results in a CR value of 7.50 ${\pm} $ 2.81% for veins and 6.08 ${\pm} $ 4.58% for arteries which becomes better than the current inter-day measurements reported in literature (discussed in section 4).

3.3.2 Statistical and flow profile analysis of inter-day repeatability

Previous works by Liu et al. [23] and Miao et al. [22] demonstrated the use of plotting blood flow values or contrast values against pixel position as a way of analyzing their results. While Liu et al. used this method to convey which registration technique was superior, and Miao et al. looked at the differences between registered and unregistered contrast maps, here the method is used to compare the blood flow profiles between day 1 and day 2 of the same participants.

In the flow maps generated of approximately 187 × 227 pixels in dimension (Fig. 8(A)), the flow values in six rows spaced 30 pixels apart were plotted for a representative participant (ID 2), indicated by the horizontal lines in Fig. 8(A). Figure 8(B) plots the flow profile of a representative row (row 30) across all ten scans (five on day 1 and five on day 2), and demonstrates a good correlation between peaks and troughs in the flow profiles between days. Figure 8(C) shows the mean flow profiles of the five independent scans on day 1 compared to day 2 at different row positions in the flow map (rows 30, 60, 90, 120, 150, 180), and again demonstrates a good correlation in the peak and troughs. However, both Fig. 8(B) and Fig. 8(C) also indicate a clear flow offset between flow profiles on the two days. Figure 8(D) shows the mean flow values of all five independent scans of day 1 and day 2 for the representative ID. Similar trends were observed in all participants in the study.

 

Fig. 8. (A) Flow map (187 × 227) of ID 2 Scan 2 where flow values along all 6 rows (pixel position 1-227) are sampled and plotted. (B) Flow values plotted for Row 30 of all 10 scans of ID 2. (C) Average of all five scans of a particular day in panel B but also including the other six rows to give a visualization of flow difference in day 1 compared to day 2. (D) Flow values along all six rows for all scans of day 1 are plotted against that of day 2.

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Quantitatively, the mean blood flow of all the participants over the six rows across the five independent scans on day 1 and day 2 are presented in Table 3.

Table 3. Mean flow values of the six rows taken in Day 1 and Day 2 for all participants

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While there is a good correlation between peaks and troughs of all participants in the averaged day 1 and day 2 flow values across the six rows, a paired t-test was then performed to analyze whether there was a statistically significant difference in blood flow of scans taken on two independent days (subsection 2.5.2). This resulted in a p-value of 0.09 with the null hypothesis that the mean difference between paired observations is zero. The p-value found indicates no evidence against the null hypothesis, but does not directly suggest that the registration pipelines and post-processing developed are repeatable across different days. A higher p-value would provide more confidence and indication of flow repeatability. Therefore to supplement the statistical analysis, Table 4 shows the mean CR values which is another indicator of repeatability. Mean CR values describing the absolute difference in flow between the two days of all the participants in the study and also with the participants that had CR values greater than the mean CR excluded are shown.

Table 4. Mean CR for the absolute flow difference from the sample of six rows

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4. Discussion

The primary purpose of this study was to investigate both the intra and inter-day repeatability of multi-exposure LCSI and evaluate the potential for the technology to be applied in a clinical setting. For a technology to be clinically relevant, accurate and repeatable measurements are two fundamental requirements. In this study, repeatability of flow within veins and arteries assessed in terms of intra-day coefficient of variation (CV) and inter-day coefficient of reproducibility (CR) is approximately 7% and 11%. Both of these are consistent with results presented in literature and commercially available laser speckle devices that either do not use quantitative approaches to estimate flow or use only a single exposure time [15]. A comparison with the limited number of repeatability studies in the literature is presented in the following:

Intra-day Repeatability: In general, the intra-day repeatability observed in this study is better than those previously reported in the literature in the retinal veins and arteries (Table 2). When excluding one outlier, participant ID 7, with a CV greater than 20% in both ROIs, the mean CVs for ROIs on both day 1 and day 2 were lower when compared with Rege’s study [18]. However, this study appears to have a higher standard deviation in the CVs compared to Rege’s work. This may be explained by differences in the clinical procedures. Rege excluded all subjects with high blood pressure or pupils dilated to < 4 mm, whereas this study did not monitor these factors. This study also had a longer interval between scans of up to five minutes, in contrast with Rege’s one-to-two-minute interval. The CVs of ROIs are comparable with studies of commercially available laser speckle devices, although these devices use normalized blur values rather than the inverse of decorrelation time [15].

Inter-day Repeatability: To our knowledge, the only study that examined the inter-day (24-hour interval between measurements on healthy subjects) repeatability of laser speckle was performed by Tamaki et al. [41]. The authors reported CR of normalized blur values in the ONH rim tissue and choroid-retina to be 13.0${\pm} $ 3.0% and 9.7${\pm} $ 2.5% respectively (mean ${\pm} $ standard error of the mean; n = 12), but they did not examine vein or artery ROIs. Such CR values are comparable with the values measured in our work of 12.01 ± 3.14% and 10.73 ± 3.41%, respectively. However, such comparisons are not directly equivalent due to the different ROIs used and the different lengths in scan time. More importantly, the study by Tamaki et al. is based on normalized blur values which are only a qualitative estimate of blood velocity. Therefore, the CR values reported by Tamaki et al. are expected to be lower because of the decorrelation process, which can introduce errors that directly propagate to quantitative flow estimates. Averaging the flow values over a ROI larger than a single vein or artery could also reduce the impact of any measurement noise. Statistical analyses yielded a p-value of 0.09 indicating no evidence of a difference in blood flow inter-day, but does not directly suggest that the registration pipelines and post-processing developed are necessarily repeatable across different days. A higher p-value would provide more confidence in stating flow repeatability, and generally, a much higher critical p-value is adopted (>0.25).

In conclusion, multi-exposure LSCI appears to demonstrate a level of repeatability intra-day within the same session (guided by low CV values in Table 2) and statistically, there was no evidence to suggest a mean difference between inter-day scans, however, there appeared to be a fixed offset in the flow between two different days that may be due to a lack of full experimental and patient control and is difficult to isolate in the post-analysis of the data. For example, the experimental protocols did not measure the room luminance quantitatively nor control the ambient light reaching the retina. The patients were also not dilated and thereby non-uniform speckle illumination due to pupil size variations could not be corrected. More specifically, even if head motion could be corrected by post-registration processing using the central more uniformly illuminated part of the retina, the illumination variations caused by motion cannot be corrected. This may have resulted in the larger CV values towards to outer region of the circular mask in the intra-day repeatability analysis. The natural day-to-day flow variability or exogenous impacts such as caffeine and strenuous exercise were also not controlled for or measured. A follow-on study with patient dilation, a larger cohort of participants, and better experimental and patient control would improve the inter-day repeatability estimations of the technology.