Investigating neurovascular responses of the peripapillary retinal artery to focal flicker stimulation of temporal retinal neurons in the living human eye using AO-OCT

Abstract

We have developed an AO-OCT-based method to characterize microscopic vasodilatory responses of peripapillary major retinal artery (ppRA) to the focal luminous flicker stimulation of peripheral retinal neurons (>15^° temporal to the fovea) with various mean illuminance levels, frequencies, and spatial patterns in the living human eye. The results have demonstrated that our proposed method can effectively measure transient, microscopic vasodilatory responses of the ppRA to the focal flicker stimulation, which increased monotonically with mean illuminance levels (1, 5 and 11lx), and exhibited frequency band-pass-like behavior (2, 5, 10, 15, 20 and 30 Hz) consistent with expected increases in the activities of retinal ganglion cells (RGCs) and their associated axons. We also found that the proposed method can be used to measure the spatial interdependency of their neurovascular responses: superior arcuate ppRA response to the superior-temporal flicker was 58% greater than that to the inferior-temporal flicker, and the inferior arcuate ppRA response to the inferior-temporal flicker was 86% greater than that to the superior-temporal flicker. Collectively, these results indicate that, using the proposed method, we can now test the hypothesis that major retinal arteries respond in an orchestrated manner to increased firing activities of RGCs and their associated axons, by accounting for the spatial coordinates between the stimulated neurons and the ppRA arcs in the living human eye.

1. Introduction

Retinal vessel autoregulates retinal blood flow by dilating its diameter following the increased firing activity of retinal ganglion cells (RGC) and their axons, which is known as neurovascular coupling (NVC) [1–5]. Increasing evidence suggests that neurovascular dysfunction could play a critical role in the development and progression of glaucoma [6–10], a leading cause of blindness [11,12]. Although the exact pathophysiological mechanism underlying this process remains to be determined, neurovascular dysfunction within the retina and optic nerve head (ONH) has been extensively studied in human and animal models [1,2,7,13]. The field has grown rapidly with advances in in vivo imaging technologies which enable us to noninvasively assess vasodilatory response to flicker light stimulation [14], such as laser Doppler velocimetry (LDV) [15], laser Doppler flowmetry (LDF) [16], retinal vessel analyzer (RVA) [17], adaptive optics (AO) flood-illumination ophthalmoscope [18], AO scanning laser ophthalmoscope (AO-SLO) [19], laser speckle flowgraphy (LSFG) [20], Doppler optical coherence tomography (OCT) [21,22] and OCT angiography (OCTA) [23,24].

Many have already studied neurovascular dysfunction in the living human retina and ONH using various instrumentations, which aimed to detect subtle differences in the flicker-induced responses between glaucoma patients and healthy controls [25–31]. However, the results are convoluted by the facts that glaucomatous damage manifests in a complex, diverse, and dynamic manner and varies greatly across patients and even within the same eye, and that clinically detectable damage could be focal, widespread, or both [32] but their underlying cellular damage could be more diverse and, ultimately, vary across RGCs. Under such circumstances, it is extremely challenging to de-couple two dependent factors: neurovascular dysfunction and neurodegeneration. Indeed, we know much less about how damaged RGCs could interact with their neighbor feeding and drainage retinal vessels and how that may alter their neurovascular response to the visual stimulation in glaucoma patients. Conversely, it is unclear how impaired neurovascular unit could influence RGCs and their function, and ultimately, lead to their dysfunction and degeneration. Even in healthy human eyes, there have been only a few reports investigating the spatial properties of neurovascular response to the focal flicker stimulation of retinal neurons [18,19,33]. Thus far, we have limited knowledge about how much of neurovascular responses are selective and dependent on spatial distribution of downstream RGC bodies, their associated axons and other retinal neurons. Although early studies by Riva et al. and others indicate that ONH blood flow increases as neuronal activities increase within the ONH [2,3,16,34–38], it is unclear how much degree of the axon-vascular response can selectively react to the focal loss and damage of RGCs and their axons.

In this pilot study, we have carried out a series of focal flicker experiments in which we have used AO-OCT to measure the microscopic vasodilatory response of the peripapillary major retinal artery (ppRA) to the selective stimulation of temporal retinal neurons in the living human eye. The selected ppRAs are measured at approximately 8.5 mm from the stimulated retinal neurons, which extend their supplies toward both the macula and the peripheral retina and belong to the most studied neurovascular system in the eye. In doing so, we have characterized the impacts of firing activities within RGCs and their associated axons on the upstream ppRA diameter. Specifically, we have characterized the ability of AO-OCT to measure diameter changes of ppRA in response to various types of luminous focal flicker stimulation that are delivered at different mean illuminance levels, frequencies, and spatial patterns. Utilizing a statistical analysis tool developed for clinical studies, we first have studied whether the AO-OCT-based method can be used to measure known effects of flicker mean illuminance and frequency on ppRA vasodilatory responses even if the stimulated retinal neurons are farther apart from the feeding ppRA. We then have investigated whether the same method can be used to measure the selective responses of ppRA arcuate (superior or inferior) to the changes in neuronal activities of downstream RGCs, induced by external focal flicker stimulation of either superior-temporal or inferior-temporal retinal neurons. Collectively, our results demonstrate that our AO-OCT-based method can reliably measure subtle differences of diverse neurovascular responses, including their spatial property, to relatively low-light level focal flicker stimulation in the living human eye.

2. Methods

2.1. AO-OCT imaging and focal flicker stimulation protocols

Either superior or inferior temporal ppRA was measured before, during and after a luminous focal flicker stimulation of temporal retinal neurons using the high-resolution AO-OCT imaging system (see Section 2.3) [39]. The focal flicker was applied to selectively target the temporal patch of the eye (>15° temporal to the fovea), where a subset of RGCs was expected to increase flicker-induced firing rates (Fig. 1(A)) [40,41]. No major retinal vessels or their neighbor photoreceptors in the peripapillary regions were directly exposed to the flicker light stimulation, though the projected RGC axons are propagating action potential since their corresponding RGC somas were exposed to the stimulation.

Fig. 1.

Experimental setup for simultaneous AO-OCT imaging and focal flicker stimulation. (A) A schematic representation of geometric relation between the imaging beam, flicker stimulation, and subject’s eye (OD). During the experiments, the subject was instructed to maintain their fixation at the target position (denoted by the green star), while the imaging beam (denoted by the red dashed line) continuously scans the selected ppRA. The focal flicker stimulation was introduced by the external LED panel, left from a subject view, which illuminates a temporal retinal patch (> 15° temporal to the fovea) as denoted by the shaded area. The stimulated area was rectangle with an approximated maximum field size of 40°×70° (H × V) for Experiments A-C and 40°×24° (H × V) for Experiment D . The modulation depth was set at maximum, the duty cycle was 50%, and the color was achromatic (see Supplement 1 ^{(1.3MB, pdf)} section A). The scale bar in the bottom left denotes 1 inch. (B) The imaging patch (denoted by the red box) and stimulated area (denoted by the shaded box) on the retinal fundus.

We used both Kowa retinal fundus image and Spectralis OCT/SLO images to pre-determine the targeted vessels located approximately at 1.8 mm superior temporal or inferior temporal to the ONH disc center. Using a calibrated map that projected a grid pattern of the LED array on the fundus image, we determined the LED pixel coordinates used for a fixational target and a subset of LED pixel coordinates used for a flicker stimulus (as denoted as the green star and the white stars in Fig. 1, respectively). Upon the participant’s arrival (see Section 2.2), we instilled 0.5% or 1.0% tropicamide and, if needed, added 2.5% phenylephrine for pupil dilation. The participant was then asked to wait for ∼20-minutes for full pupil dilation, during which their eyes were exposed to a room with ambient lighting (∼100-200lx), as measured with a commercial photometer (LX1330B, Dr. Meter, CA). After that, the room light was turned off (<0.1lx), and the participant was asked to sit, put their head on the chin-forehead-rest to minimize head movement, and look steadily at the fixation target. The examiner adjusted the participant’s head position by utilizing a motorized stage while observing the pupil position with the Shack-Hartmann wavefront sensor and the retinal depth with the OCT scan, displayed in real time on their respective AO-OCT graphical user interfaces. Although all the participants were already familiar with the imaging experiments and understood the importance of maintaining stable fixation during the testing sessions, we ensured compliance by having them one or two practice sessions before initiating AO-OCT data collection. We also carefully adjusted the fixation target position to image the exact target patch, all of which usually took us additional 20 minutes after the room light was turned off. Artificial tears were offered as needed, but only during breaks between testing sessions.

After the alignment, we initiated the AO-OCT data collection, which was typically divided into three testing conditions: Baseline, Flicker, and Recovery, during which we repeatedly acquired multiples of 4-second AO-OCT volume videos. Baseline was the condition without any visible stimulation to the temporal retina or prior to the flicker light stimulation. Flicker was the condition under which the temporal retinal neurons were continuously exposed to the focal flicker light. Recovery was the condition after the flicker light was turned off. We measured the vasodilation and vasoconstriction by comparing the vessel diameters during each of Baseline, Flicker, and Recovery conditions, while accounting for measurement variabilities including random measurement noises, biological and physiological variabilities, and variations in the light-tissue interactions (see Section 2.4).

Four experiments ( Experiments A-D ) were performed to characterize the ability of the AO-OCT-based method to measure the following neurovascular reactivities: (1) baseline behavior without any visible stimulation to the temporal retina except the fixation target and imaging beam, (2) focal flicker mean illuminance response, (3) focal flicker frequency response and (4) interdependency between focal flicker area and ppRA arcuate. Two subjects (H1 and H2) participated in almost all the experiments ( Experiments A-D ), while four additional subjects (H3-H6) were recruited specifically for Experiment D (see Section 2.2, Table 1).

Table 1. Subjects’ Information.

Subject ID	Sex	Age	Eye	SE (D)	AL (mm)	Experiment	Total number of sessions	Total number of visits
H1	M	38	OD	-7.50	26.48	A, B, C & D	19	6
			OS	-6.00	26.25	D	4
H2 a	F	34	OD	-0.75	26.18	A, C & D	11	4
			OS	-0.75	26.47	D	4
H3	F	29	OD	+1.00	23.03	D	4	1
			OS	+1.00	23.02	D	4
H4	F	36	OS	-6.50	25.01	D	4	1
H5	F	27	OD	+0.50	22.91	D	4	1
H6	F	34	OD	-0.25	23.02	D	4	1

^a Post-refractive surgery; preoperative SE = -5.25 D

Experiment A.

To characterize the baseline behavior of the ppRA measured by the AO-OCT in the two subjects (H1 and H2), we performed 10-minute control experiment. A 15-minute testing session that included a focal flicker stimulation with a mean illuminance level of 5lx and frequency of 10 Hz was added to determine whether the observed effects were specifically attributable to the flicker or influenced by other underlying factors. Approximately ten AO-OCT volume videos were acquired for each testing condition for five minutes.

Experiment B.

To characterize the mean illuminance response of the ppRA to the focal flicker stimulation measured by the AO-OCT in the one of the two subjects (H1), we conducted a series of 15-minute testing sessions with the focal flicker stimulation at the mean illuminance levels of 1, 5 or 11lx and the flicker frequencies of 2, 5, 10 or 15 Hz. Multiple breaks of at least five minutes were incorporated between 15-minute testing sessions in a dark room (a washout period) to minimize the impact of pre-stimulus condition and fatigue on subsequent measurements. To ensure the participant’s comfort and data quality, each visit included up to four 15-minute testing sessions, with the full experiment completed across multiple visits.

Experiment C.

To characterize the focal flicker frequency response of the ppRA measured by the AO-OCT in the two subjects (H1 and H2), we conducted additional testing sessions in which the flicker frequency was systematically varied across 2, 5, 15, 20 or 30 Hz, while maintaining the constant mean illuminance of 5lx.

Experiment D.

To assess whether our AO-OCT-based method can measure the selective responses of superior and inferior ppRA arcs (SA and IA) to increased neuronal activities in their corresponding hemifields in the six subjects (H1-H6), we conducted a total of four testing sessions following the general protocol used previously. However, the duration of each testing session was shortened to six minutes, as opposed to the 15 minutes in Experiments A-C. We used the halved focal flicker to stimulate either superior temporal retinal neurons (ST) or inferior temporal retinal neurons (IT) (>3° superior or inferior and >15° temporal to the fovea). The flicker mean illuminance and frequency were fixed at ∼8lx and 10 Hz, respectively. We measured the vessel diameter of either SA extending to the ST retina or the IA extending to the IT retina. Each vessel was imaged twice in two separate testing sessions, during which either the ST or IT retina was selectively stimulated. In doing so, we studied whether the proposed method can measure the selective neurovascular responses of the ppRA arcuate to the corresponding changes in neuronal activities.

2.2. Subjects

Six healthy volunteers were enrolled in this study (H1-H6; 1 male, 5 females; ages 27-38 yrs). Prior to the AO imaging session, all subjects underwent a comprehensive eye examination at Devers Eye Institute for screening purposes, including Humphrey 24-2 visual field testing (VF; Carl Zeiss Meditec, Inc., Dublin, CA), OCT scans using Spectralis HRA + OCT (Heidelberg Engineering, GmbH, Heidelberg, Germany), and color fundus photography (Nonmyd WX-3D, Kowa, Japan). The OCT scans and fundus photos were used to navigate AO-OCT imaging locations. To improve the fundus image clarity for distinguishing arteries from veins, the fundus photos were acquired after full pupil dilation with 1.0% tropicamide. They had the best corrected visual acuity of 20/20 or better. Spherical equivalent refraction (SE) ranged from +1.00 to -7.50 diopters, and their axial lengths (AL) were between 22.91 mm and 26.48 mm as measured by Lenstar LS900 (HAAG-STREIT AG, Switzerland), which were used to calibrate retinal image size [42]. The imaging protocol was selected for one or both eyes for each subject based on their ability to maintain fixation throughout the entire imaging session (Table 1). All procedures followed the research protocol approved by the Legacy Health Institutional Review Board and complied with the requirements of the Declaration of Helsinki. Written informed consent was obtained from the participants following a detailed explanation of the study’s nature and risks.

2.3. AO-OCT imaging system

We deployed a research-grade AO-OCT imaging system built at Discoveries in Sight Research Laboratories, a research arm of Devers Eye Institute (DIS/DEI) for measuring a small percentage change of retinal vessel diameter in response to the focal flicker stimulation. Briefly, the system combined a point-scanning spectral-domain OCT with a hardware-based AO to achieve the exquisite volumetric resolution of 2.4 × 2.4 × 4.6 µm in retinal tissue [39], which is an order of magnitude greater than clinical standard instruments. The AO-OCT depth scans (A-line scans) were acquired at the speed of 250 kHz. Each volume was composed of 256 × 256 A-line scans with the field of view 1°×1°. Our typical 4-second video contains 16 volume images. The AO-OCT imaging beam wavelength was 790 nm ± 22 nm, which optical power incident on the cornea was set below 430 μW by following the American National Standards Institute guidelines for laser safety [43].

2.4. Image analysis

We conducted an extensive analysis of ppRA to quantify its response to the focal flicker stimulation as described above (see Section 2.1). For each testing session, hundreds of AO-OCT volume images were reconstructed, registered, and averaged to enhance the image contrast and to precisely measure the retinal vessel diameter over three testing conditions—Baseline, Flicker and Recovery. To quantify vasodilation/constriction, we took the following approach based on a detailed discussion about how much we could accurately measure the absolute vessel diameter (see Supplement 1 ^{(1.3MB, pdf)} section B).

First, we found the principal axis of peripapillary retinal nerve fiber bundles (ppRNFBs) in the averaged AO-OCT volume image, as denoted by the cyan line in Fig. 2(A). Second, to mitigate spatial sampling bias, we selected up to five, evenly-spaced (35 slices apart), cross-sectional slices perpendicular to the principal axis of the ppRNFBs based on the extent of the registered and averaged volume image, as denoted by the white dashed lines in Fig. 2(A). We chose these sampling locations and spacing by ensuring coverage across the artery and overlap between individual registered images enough to track the same portion of the retinal vessel. Third, we extracted and averaged 25 cross-sectional slices at each sampled location and at each time point from which we measured the vessel depth diameter. Here, we defined the vessel depth diameter as the path length difference between two bright peak reflections on the top and bottom of the vessel, derived with an assumption of the tissue refractive index of 1.38. To measure the diameter, we manually identified spatial coordinates of the highest-intensity pixels on the arterial wall in the average cross-sectional image of the ppRA, as denoted by the orange arrowheads in Fig. 2(C). Then, a few A-scans centered at the midpoint between the two peaks were extracted and averaged to include both the peaks (Fig. 2(D)). The exact peak depth positions were determined at the sub-pixel accuracy by up-sampling the peak amplitude reflectance depth profile. We repeated this process for all the sampled locations and the time points.

Fig. 2.

Vessel depth diameter measurement in the AO-OCT volume image. (A) AO-OCT en face image of the peripapillary region (Fig. 1(B), the red box), where five separate cross-sectional images were extracted at their respective sampled locations denoted by the white dashed lines, perpendicular to the principal axis of RNFBs (the cyan line). (B) En face image at the depth centered on the vessel’s section, as indicated by the green double-headed arrow in C. (C) Cross-sectional image of the peripapillary region extracted at the yellow-dashed line in B. The blue line encompassed the A-line scans that were used for vessel depth diameter measurements. An hourglass pattern is visible within the vessel lumen in the averaged cross-sectional image [45,46], indicating shear flow of blood cells. (D) A plot of the averaged A-line depth profile with the peaks (the orange dashed lines) used for measuring the depth diameter. The white bar (100 µm) applies to all images.

It is noteworthy to mention that we chose to measure the depth diameter using the top and bottom surface reflections (the orange arrowheads) of the vessel, not the width, owing to their greater signal-to-noise ratio and robustness against residual en-face image blur and distortion even with AO correction and fine image registration. We also confirmed a lumen circularity of 0.95 ± 0.03 (mean ± SD across six subjects) and thus the vessel orientation had a minimal impact on %change measurements (see Supplement 1 ^{(1.3MB, pdf)} section B and Fig. S2).

2.5. Data analysis

We utilized a statistical analysis tool for characterizing the ability of the AO-OCT-based method to measure diameter change in response to the flicker stimulation within this specific group of human subjects—not for testing biological hypotheses. Thus it’s noteworthy that the statistical results in this study should never be overinterpreted as biological findings/effects (see Supplement 1 ^{(1.3MB, pdf)} section C for its rationales), even though they are closely associated. Therefore, statistical significance (or p-value) we reported in this manuscript was confined to the group of human subjects we tested for each Experiment , and not for population-level statistical testing that is much more common in clinical studies. With that in mind, the analyses were performed with a software package, R (R version 4.5.1) [44]. We used a linear mixed effects model to test fixed effects of flicker parameters on the selected ppRA neurovascular responses, such as testing conditions (Baseline, Flicker and Recovery) in Experiment A , mean illuminance (1, 5, and 11lx) in Experiment B , frequency (2, 5, 10, 15, 20, and 30 Hz) in Experiment C , and an interdependency between the flicker area (IT or ST) and the ppRA arcuate (SA or IA) in Experiment D. All the raw depth diameters, measurable during the experiments, were included in the analysis, but those were not measurable due to eye and head motions, blink, tear film breaks, etc. were excluded (see Section 3.2). Random effects, such as the sampled locations, subjects, and eyes (OD or OS) were included into the model to mitigate the impacts of correlated variables on the results. Also, we included the mean baseline diameter as a covariant into the model by which we mitigated the influence of the mean baseline diameter on the fixed effects. Then, a post-hoc data analysis was performed using estimated marginal means and residual errors predicted from the model. Their significances were evaluated by Tukey-adjusted p-values. Percent vasodilation and vasoconstriction were computed from the estimated marginal means for each testing condition predicted from the model, but the percentage changes were not used for multiple comparisons due to uncertainties in their non-linear transformations.

3. Results

3.1. ppRA diameter remained stable or decreased slightly without flicker stimulation

Figure 3(A) shows the depth diameters of superior ppRA measured at all the sampled locations along the vessel (see the white dashed lines in Fig. 2(A)) and all the time points for 10 minutes without any visible stimulation to the temporal retina in two subjects (H1 and H2; Experiment A). Linear regression analysis showed a negative slope in subject H1, suggesting an extremely slow vasoconstriction occurs during the 10-minute session (-0.005 µm/sec, p < 0.001), whereas subject H2 exhibited no significant change (-0.0002 µm/sec, p = 0.732). The coefficient of variation (CV) of the repeatedly measured depth diameter was calculated at each location for both subjects. Mean ± standard deviation (SD) of the CV across the sampled locations was 0.0254 ± 0.0046 for subject H1 and 0.0237 ± 0.0034 for subject H2. Also, unpaired two-sample t-test showed no statistically significant differences in the depth diameter between two consecutive 5-minute intervals without flicker stimulation (p = 0.057 in H1 and p = 0.233 in H2). These results suggest that the depth diameter we measured during the baseline condition changed only slightly and remained largely stable.

Fig. 3.

(A) Trend analysis on the ppRA diameter over a 10-minute without focal flicker stimulation. The black and red solid lines denote the best-fitted lines for subject H1 (r² = 0.03, p < 0.001) and subject H2 (r² = 0.0002, p = 0.732), respectively. (B) Rates of ppRA diameter change for each Baseline, Flicker and Recovery conditions were computed by pooling results from all 15-minute sessions in Experiments A-C . The error bars denote standard deviation. (C) With the 5lx-10 Hz focal flicker stimulation, the measured depth diameter of ppRA increased during Flicker condition and decreased during Recovery condition in both subjects H1 and H 2. (D) Estimated marginal means of ppRA diameter predicted for each condition (Baseline, Flicker and Recovery) for the subjects H1 and H2 are denoted by the black triangles and red squares, respectively. The error bars denote the 95% confidence intervals.

Similar baseline behavior was observed when we examined baseline condition across all Experiments A-C for both subjects. Subject H1 experienced a slight decreasing trend with a mean slope of -0.0065 ± 0.075 µm/s across 14 testing sessions. In contrast, subject H2 showed no significance change with a mean slope of 0.0014 ± 0.0031 µm/s across six testing sessions (see Fig. 3(B)). These consistent trends suggested intriguing reproducible vascular behavior during the baseline condition in both subjects. Nevertheless, we found these baseline behaviors were too small to contribute to the results discussed in the following sections.

3.2. ppRA dilates and constricts by stimulating only the temporal retinal neurons

The 15-minute testing sessions with the 5lx-10 Hz focal flicker stimulation in Experiment A revealed flicker-induced neurovascular responses in both subjects (H1 and H2). Flicker-induced vasodilation and vasoconstriction were visible in the averaged cross-sectional image of the peripapillary region (see Visualization 1 ^{(11.6MB, mp4)} ). The vessel area increased, and also its surrounding tissues appeared deformed accordingly with focal flicker stimulation. Figure 3(C) shows a representative quantitative result of focal flicker-induced vasodilation and vasoconstriction observed in subjects H1 and H2. The ppRA depth diameters measured at all five sampled locations are plotted against time. As expected from previous studies [35,47], the measured diameter transiently increased and quickly reached a steady state after the initiation of the focal flicker stimulation, and then decreased sharply right after the termination of the flicker. The regression lines show an overall decreasing trend (H1) or no change (H2) during Baseline condition, as expected from the prior experiment (see Section 3.1), becoming more plateau (H1) or sloped upward (H2) during the Flicker condition. These trends were similar throughout the Experiments A-C (see Fig. 3(B)), except the Recovery condition that shows increasing (H1) or decreasing (H2) trend. Nonetheless, the overall rates of the changes were small (Fig. 3(B)) and thus disregarded in the following analyses.

Next, we tested whether the 5lx-10 Hz focal flicker stimulation of the temporal retinal neurons changed the ppRA diameter. Figure 4 shows the changes in mean vessel depth diameters measured at the five sampled locations on the same ppRA, spaced only by ∼35 µm, in both subjects H1 and H2. Although the responses were consistent, the measurements were highly dependent on the baseline diameters and on how well each AO-OCT A-scans were successfully sampled at the same location (see also Supplementary section C). Thus, when we utilized a linear mixed effects model for the data analysis, we specified the sampled locations as random intercepts. In subject H1, we found statistically significant fixed effects of testing conditions (Flicker, p < 0.0001 and Recovery, p < 0.0001) on the ppRA depth diameter (see also Table S1). Post-hoc multiple comparisons of estimated marginal means indicated that the ppRA diameter increased from 100.4 µm (95%CI 98.7−102.2 µm) to 103.4 µm (95%CI 101.7−105.2 µm) during Flicker condition, yielding the percent vasodilation of 3.0% (Tukey-adjusted p < 0.0001). Then, we observed the reduced ppRA diameter of 102.4 µm (95%CI 100.9−104.4 µm) during Recovery condition, yielding 1.0% vasoconstriction (Tukey-adjusted p < 0.0001), as shown in Fig. 3(D). We found a similar fixed effect of testing condition (Flicker; p < 0.0001) in subject H2 (see also Table S2). Post-hoc comparisons showed a 2.1% vasodilation during Flicker condition (Tukey-adjusted p < 0.0001), followed by a 2.1% vasoconstriction during Recovery condition (Tukey-adjusted p < 0.0001). The vessel diameter changed from 90.1 µm (95%CI 85.8−94.5 µm) to 92.0 µm (95%CI 87.6−96.3 µm) during Flicker, then decreased to 90.1 µm (95%CI 85.8−94.5 µm), the same as baseline, during Recovery condition.

Fig. 4.

Mean vessel depth diameter changes during a testing session at the five sampled locations of the ppRA. The ppRAs exhibited consistent dilation and constriction pattern across the five locations in response to a 5-minute focal flicker stimulation (5lx-10 Hz) in subject H1 (A) and H2 (B).

3.3. Arterial vasodilation in response to the focal flicker stimulation demonstrated an illuminance dependency

In Experiment B, we investigated the effect of mean illuminance on the ppRA response using a linear mixed effects model, followed by multiple comparisons of estimated marginal means. First, for simplicity, we tested a three-level illuminance-dependent response at a fixed frequency of 10 Hz. Then, we tested the same three-level illuminance-dependent response but with four flicker frequencies (see Fig. 5(A)-(D)). The results consistently show the effect of mean illuminance across the frequencies we examined.

Fig. 5.

Effect of mean illuminance on the ppRA vasodilation. (A-D) The estimated marginal means of ppRA depth diameters across all conditions (Baseline, Flicker and Recovery), predicted from the measurement data collected with three different mean illuminance levels (1, 5, and 11lx) and at flicker frequencies of 2, 5, 10 and 15 Hz, respectively. The error bars denote 95% confidence intervals.

First, we used the results obtained with the flicker whose mean illuminance level was set at either 1, 5, or 11lx whereas the flicker frequency was fixed at 10 Hz. We found that, in addition to a statistically significant fixed effect of testing condition (Recovery, p < 0.0001), there were statistically significant interactions between mean illuminance and testing conditions (Flicker, p < 0.0001 and Recovery, p < 0.0001; see also Table S3). The interaction analysis showed large variations in the ppRA vasodilatory response during the Flicker condition, due to the strong interaction with the mean illuminance, which was a reason why its fixed effect was not statistically significant (Flicker, p = 0.125). The post-hoc trend analysis revealed that the measured vasodilation increased with the mean illuminance of the flicker light stimulation (0.58 µm/lx; p = 0.0007) during Flicker condition whereas no significant increase was observed during Baseline condition (0.056 µm/lx; p = 0.6350), suggesting the neurovascular responses were indeed dependent on the mean illuminance. After the cessation of flicker stimulation, the ppRA reduced its diameter during Recovery condition; however, the effect of vasodilation sustained, which resulted in the remained dependency on the mean illuminance (0.46 µm/lx; p = 0.0028).

Next, we characterized a three-level illuminance-dependent response with the mean illuminances of 1, 5, and 11lx by including additional data collected with various flicker frequencies of 2, 5, and 15 Hz in subject H1 (see Fig. 5(A)-(D)). To account for frequency dependency, we added frequency as a fixed effect in our mixed effects model, which indeed significantly improved the fitting performance compared to the model without frequency (Type III ANOVA, p < 0.0001). In addition to a statistically significant fixed effect of the testing condition during Recovery (p < 0.0001), significant interactions were found between mean illuminance and testing condition (Flicker, p < 0.0001) as well as between frequency and testing conditions (Flicker, p < 0.0003 and Recovery, p < 0.0026). See also Table S4. No significant interaction was observed between mean illuminance and frequency (p = 0.3486). The post-hoc multiple comparisons and linear trend analysis revealed that vasodilation during the Flicker condition increased with the mean illuminance of the flicker light stimulation (0.23 µm/lx at the flicker frequency of 8.3 Hz; p < 0.0001), also with the flicker frequency (0.23 µm/Hz at the flicker mean illuminance of 7.6lx; p < 0.0001). These results suggest that the mean illuminance-dependent response remained significant while we accounted for the frequency dependency. No interaction between mean illuminance and frequency indicates that the mean illuminance response can be determined independently at any fixed frequency of interest within the range we examined (1-11lx and 2-15 Hz).

3.4. Arterial vasodilation in response to the focal flicker stimulation demonstrated a band-pass-like frequency response

In Experiment C, we investigated the effect of flicker frequency on the ppRA response using a mixed effects model followed by multiple comparisons of estimated marginal means. We used data collected from two subjects (H1 and H2) with the various flicker frequencies of 2, 5, 10, 15, 20 and 30 Hz and at the fixed mean illuminance of 5lx. We found, in addition to the fixed effects of testing conditions (Flicker, p < 0.0001 and Recovery, p = 0.0253; see Table S5), there were significant interactions between frequency and testing conditions (Flicker, p = 0.0366 and Recovery, p < 0.0001), suggesting there were significant frequency dependent components in the flicker-induced vascular responses. Also, the model was improved by treating frequency as a categorical variable (Type III ANOVA, p < 0.001), indicating that frequency response was better characterized in a nonlinear fashion. Indeed, the interaction plot in Fig. 6(A) shows a band-pass-like vasodilatory frequency response during Flicker condition and apparent nonlinear frequency response during Recovery condition.

Fig. 6.

Effect of focal flicker stimulation frequency on the ppRA vasodilation. (A) the ppRA depth diameter, measured with various focal flicker stimulation frequencies with a fixed mean illuminance of 5lx for both subjects (H1 and H2), was plotted against the flicker frequency, revealing a band-pass-like response. The error bars denote 95% confidence intervals. (B) Visually comparing the 5lx-flicker frequency response with previously published data from Polak et al. [47] and Falsini et al. [35] We converted the %dilation to %change in retinal blood flow using Poiseuille’s law. Following the report from Falsini et al., all the datasets normalized to their 10 Hz response.

To enable a qualitative comparison with prior studies, the %vasodilation was computed from the estimated marginal means and translated into a corresponding percent change in retinal blood flow using Poiseuille’s law with an assumption of circular cylindrical vessel structure (see Supplement 1 ^{(1.3MB, pdf)} section B for the detailed discussion). Table 2 summarizes the corresponding %change in blood flow estimated for each flicker frequency and subject. To visually compare the results against previous reports, we further normalized the frequency responses by its own response at 10 Hz, following the method described by Falsini et al. We found our results aligned with those reported by Polak et al. and Falsini et al. (Figure 6(B)) [35,47].

Table 2. Estimated %changes in retinal arterial blood flow in Experiment C.

Frequency (Hz)	H1; 5lx	H2; 5lx
2	3.28	4.37
5	7.03	13.95
10	12.59	8.37
15	10.90	6.97
20	2.43	6.26
30	2.42	7.29

3.5. ppRAs exhibited selective vasodilation during a modified focal flicker stimulation

In Experiment D , we investigated the effects of the modified focal flicker stimulation on superior and inferior arcs ppRA (SA and IA) responses using a mixed effects model. The illumination pattern of the LED array was modified so that we can stimulate either superior temporal (ST) or inferior temporal (IT) retinal neurons at the fixed mean illuminance of 8lx and the fixed flicker frequency of 10 Hz. We used all the data collected from eight eyes of six subjects to test the combined fixed effects of ppRA arcuate (SA vs IA) and focal flicker area (ST vs IT) on the ppRA neurovascular responses. We used a linear mixed effects model in which we treated subjects, eyes, and sampled locations of the ppRA as random intercepts. We found statistically significant fixed effects of testing condition (Flicker, p < 0.0001; see Table S6) and the ppRA arcuate (SA, p < 0.0001). In addition, there were significant interactions between the ppRA arcuate and testing condition (SA and Recovery, p < 0.0001) and between the focal flicker area and testing conditions (ST and Flicker, p < 0.0001; ST and Recovery, p = 0.0007). Most importantly, we found a significant interaction among the ppRA arcuate, focal flicker area and testing condition (SA, ST, and Flicker p < 0.0001; SA, ST and Recovery, p < 0.0001), suggesting that ppRA response varies with ppRA arcuate (SA or IA) and focal flicker area (ST or IT), those of which were interdependent on each other.

Figure 7(A)-(B) shows interaction plots of estimated marginal mean vessel diameters for the ppRA arcs, focal flicker areas, and testing conditions. First, the overall response of SA was greater than IA (the significant fixed effect of SA; p < 0.0001). Second, we found the significant interaction between the ppRA arcs and the focal flicker areas during the Flicker condition (a significant interaction among SA, ST, and Flicker p < 0.0001) and Recovery condition (a significant interaction among SA, ST, and Recovery p < 0.0001). In other words, the superior ppRA arcuate (SA) vasodilatory response to the ST stimulation was 58% greater than that to the IT stimulation during Flicker condition. Similarly, the inferior ppRA arcuate (IA) vasodilatory response to the IT stimulation was 86% greater than that to the ST stimulation during the Flicker condition. And these responses retain during the Recovery condition. Figure 7(C) qualitatively compares estimated %changes in blood flow among four separate tests. These findings support the hypothesis that ppRA has a selective autoregulatory ability to adjust its blood flow precisely by sensing the increased activities of its feeding RGCs and their associated axons.

Fig. 7.

Changes in ppRA depth diameter in response to either ST or IT focal flicker stimulation. (A) Superior ppRA and (B) Inferior ppRA, measured at a mean illuminance of ∼8lx and a frequency of 10 Hz. (C) Estimated %change in retinal blood flow in superior and inferior ppRAs with two distinct flicker areas (superior temporal vs inferior temporal), computed from the changes in the estimated marginal means shown in (A) and (B) using Poiseuille’s law. ‘*’ denotes statistically significant differences found during the post-hoc multiple comparisons of estimated marginal means (Tukey-adjusted p < 0.0001), not from those of the estimated %changes in the blood flow.

4. Discussion

We have developed a high-resolution in vivo imaging method to investigate microscopic neurovascular responses of ppRA to various types of flicker light stimulation in the human eye using AO-OCT. Our results showed that the proposed method was capable of measuring, flicker-induced microscopic vasodilatory responses of the ppRA, which were transient, increased monotonically with the mean illuminance of the flicker light, exhibited a band-pass-like frequency response, and were dependent on the combinations of the ppRA arcuate (superior or inferior) and the focal flicker area (superior temporal or inferior temporal).

Our overall goal of this study was to characterize the signal and noise properties of the AO-OCT-based vessel depth diameter measurements at the sub-resolution level, i.e., how well we could characterize microscopic neurovascular responses to the flicker stimulation in the living human eye using the proposed AO-OCT-based method. The results were compelling. The neurovascular system appeared to respond extremely well to the focal flicker stimulation; however, we realized that the diameter measurements were generally noisy at the stimulus power we used and thus required the descent image registration algorithm [48], the greater image resolution with AO [39,49], and many repeated measurements to capture these subtle and important differences. Further improvements to the proposed method would enable us to characterize important microscopic neurovascular responses in the living human eye, as discussed below.

Following Riva et al. [13,36], in vivo evidence has suggested that increased firing activities of RGCs and their associated axons can induce an increase in ONH blood flow, which can be characterized by following factors: (1) rapidity of ONH blood flow response, (2) ONH blood flow increases are expected solely for RGC activities, (3) frequency response of ONH blood flow increase mimics that of RGC activities, (4) dark adaptation curve of ONH blood flow resembles that of RGCs. Moreover, experimental studies have shown evidence supporting the working hypothesis that neurovascular units are tightly coupled within the retina and ONH [2,3,34,37,50]. Here, we have demonstrated that ppRA vasodilatory responses to the flicker light stimulation of temporal retinal neurons shared the similar characteristics as ONH blood flow responses, which are (1) transient (see Section 3.1, Fig. 3), (2) expected solely from RGC activities (ppRA was located farther apart from the stimulated RGC bodies and other retinal neurons) (see Section 3.2, Fig. 3), (3) frequency dependency, resembling a band-pass-like frequency response of RGCs (see Section 3.4, Fig. 6). Collectively, these results indicate that increased activities within RGC axons, in addition to their cell bodies, has contributed to the vasodilatory responses of the ppRA. Indeed, the subsequent experiments have demonstrated both selective and diffusive responses of ppRA to the modified focal flicker stimulation (see Section 3.5). Overall, these results indicate that the peripapillary retinal vasculature in humans has a remarkable ability to control retinal blood flow by precisely adjusting its diameter in response to increased activities of the RGCs and their associated axons.

The effect of mean illuminance on the flicker-induced ONH blood flow response has been well characterized in vivo with respect to RGC activities [34,35,38]. Vascular response increases as mean illuminance increases along with its peak frequency shift toward higher frequencies, resembling the phasic cell (primarily parasol cell) response to luminous flicker stimulation in magnocellular pathway, though evidence suggests other pathways contribute, too. Given the ONH blood flow measured by LDF primarily reflects the blood flow of major retinal vasculature, it is reasonable to hypothesize that ppRA reacts to the flicker light in a similar way. However, ppRA resides within the retina. Therefore, full-field diffuse flicker, such as the one used in RVA, could stimulate other retinal neurons near the ppRA of interest, resulting in unwanted neurovascular responses that may not be specific to the RGC activities. We, instead, have placed the focal flicker to stimulate only the temporal retinal neurons 8.5 mm farther away from the ppRA, which could have made RGC axons as a primary contributor to the ppRA diameter response [13,34,51,52]. Though, RGC somas and other retinal neurons could still be a major source triggering a retrograde propagation of vasodilatory electrical signals via endothelium to dilate upstream arterioles, like those reported in cerebral vascular system [5,53]. Regardless of exact underlying mechanisms, our results have confirmed that, under such an enforced environment, the ppRA diameter response increases as the mean illuminance of the focal flicker increases from 1 to 11lx in the living human eye (see Section 3.3, Fig. 5), similar to the ONH blood flow increases reported by Falsini et al. [35].

Compared to the diameter measurements with RVA reported by Polak et al. [47], the flicker light levels in our experiments were orders of magnitudes dimmer but more consistent with the light level reported by Falsini et al. [35]. This difference could be explained by RVA setup that requires bright illumination level for both imaging and stimulation. Therefore, most diameter changes reported by RVA were likely from saturated neurovascular responses. Our results have shown that, with AO-OCT, we can now quantify mean illuminance response reliably below the room light level (∼100-200lx) and without superimposing flicker light stimulation with the imaging beam. Moreover, benefiting from the improved lateral resolution offered by AO, imaging becomes extremely sensitive to subtle motion artifacts that could not be appreciated otherwise with low resolution instruments. By correcting for such subtle motion-induced artifacts at the subcellular level [48], we can now track the same position of the vessel precisely for over 15 minutes, which later we found necessary to detect subtle differences in the vasodilatory responses to the different flicker light levels in the living human eye (see Visualization 1 ^{(11.6MB, mp4)} ). Although further studies will be needed to test a linearity of the mean illuminance response as well as its interaction with frequency in humans, like those reported by Falsini et al. with LDF [35], our preliminary results have shown evidence that AO-OCT is also capable of measuring such mean-illuminance-dependent vasodilatory responses. Of course, it is important to note that, measuring diameter is not equal to measuring blood velocity and flow [13,54,55], though they are strongly dependent on each other. Especially, when elevated or controlled intraocular pressure is involved, as in glaucoma, it is crucial to measure both retinal blood flow and vessel diameter simultaneously to better understand their respective mechanisms, roles and dysfunctions. Moreover, it is noteworthy that we did not study the flicker amplitude response by varying the modulation depth, which could allow more direct comparisons with psychophysical thresholds in healthy individuals and with visual field loss in patients. However, near the psychophysical thresholds, flicker-induced vasodilation became too small to be measured with AO-OCT. Indeed, the lowest flicker light level we used in this study was 1lx, whose flicker stimulation was easily perceptible but did not induce a statistically significant vasodilation. Nevertheless, further studies are needed to test any relation among NVC, psychophysical thresholds, and visual field loss.

The frequency response of the ONH blood flow and peripapillary retinal vasculature to the flicker have been also well characterized in vivo with respect to RGC activities [34,35,38,47]. Most notably, Falsini et al. has shown that the red luminance flicker (λ = 630 nm; mean illuminance = 1.3lx) induced changes in the ONH blood flow exhibit a band-pass frequency response, broadly peaking at approximately 12 to 20 Hz (N = 5 subjects) [35], which resembles temporal contrast sensitivity curve obtained from psychophysical thresholds and electrophysiological recordings of RGCs, indicating contributions both from magnocellular and parvocellular pathways [40,56–58]. Polak et al. also characterized the vasodilatory frequency response but using much brighter, mixed luminance and chromatic flicker. They measured either superior or inferior temporal retinal arteries and veins using RVA (N = 9) [47]. The frequency response has shown a relatively broader bandpass window (a plateau between 4 and 40 Hz). Our results (N = 2) show that the frequency response of ppRA to the focal flicker resides somewhere between the two curves (see Fig. 6(B)). The peak frequency appears between 5 and 15 Hz, which is slightly lower than the peak frequency reported by Falsini et al. in humans, but similar to the psychophysical sensitivity to the luminous flicker obtained from human [40,59,60]. This is intriguing. Since we stimulated only the temporal periphery where the proportion of parasol cells increases as well as midget cells that can behave like phasic cell may increase [61], we anticipate that neurovascular responses are coupled more with phasic cell-specific activities responding to the luminance flicker in the magnocellular pathway. However, our results have shown that vasodilatory responses appear to be coupled still with a mixture of both magnocellular and parvocellular subsystems (similar to unpublished data with focal flicker to fovea in Fig. 6(B) by Riva et al. [13]), though this could be convoluted by other factors such as light level, adaptation, subjects, etc., as we discussed later.

Unlike the mean illuminance and frequency response to the flicker light stimulation, the spatially property of NVC within the human retina is not well understood. Zhong et al. has reported, using their AO-SLO, that the branched retinal vasculature responses to focal flicker stimulation in a selective and systematic manner, following a spatial relationship between stimulated retinal neurons and their feeding vasculature (N = 2) [19]. Our results (N = 6) in Experiment D is supporting this hypothesis. The retinal vasculature, ppRA, is indeed capable of regulating its blood flow by changing its diameter in response to the focal flicker stimulation, which follows the retinal nerve fiber arcuate arrangement of the superior and inferior hemifields. The meaningful difference and interaction observed in this study cohort further confirms that the retinal vessels are coupled spatially to downstream retinal neurons. That said, both selective and diffusive components coexist in their response, and more than half of the response came from diffusive components. We argue that this could be partly explained by several working hypotheses about NVC suggested in brain and retina. First, we observed the vasodilatory responses in both superior and inferior ppRA regardless of the stimulation patch (diffusive components), which may indicate that diffusive vasodilators, particularly nitric oxide (NO; a vasoactive byproduct of spiking activities in unmyelinated axons), quickly propagate around the retina and ONH, especially within the ONH where all the retinal vasculatures and nerve fibers get together [13,34,51,52,62]. Second, the selective components we observed are not as selective as expected from anatomical arrangement in superior and inferior hemifields. Vascular responses appear spatially more heterogenous compared to neuronal activities. This partial de-coupling has been also reported in the cerebral vascular system [63,64] and is still active research area to elucidate its underlying mechanism. However, such spatial property has not been well understood in the human retina, in particular with respect to disease. Third, concerning both the rapidity of the vasodilatory response we observed in the ppRA and the distance between the ppRA and the stimulated RGC bodies, glial communications are too slow to activate this rapid response [65] and thus unlikely to be a major contributor for the ppRA vasodilatory response. It would be interesting to further test this spatial dependency in the living primate visual system, aiming to probe the functional integrity of NVC between RGCs and retinal vasculature.

Finally, it is important to note that we have stimulated a selected peripheral retinal area which is known to be vulnerable to glaucoma (nasal, superior-nasal or inferior-nasal fields) for two purposes: (1) emulating hemifield loss of RGCs and (2) designing upcoming future studies in glaucoma. Since focal loss is common in glaucoma patients, we anticipate that the selective responses and their interactions we observed will be significantly altered by the disease. We anticipate that normative data like ours reported here would eventually help differentiate autoregulatory dysfunction from neurodegeneration.

Our study has following limitations: (1) the limited number of subjects (N = 6) and the required prolonged imaging session (the minimum of six minutes), (2) unknown contributions from RGCs’ spatial contrast sensitivity to the spatial pattern of the flickering LED array, incomplete photopic adaptation, and myogenic autoregulation, and (3) findings made by a research-grade AO-OCT system that is not widely available. First, our diameter measurements heavily rely on the imaging ability offered by AO-OCT which enables us to precisely track the same positions of the vessel over time. Owing to its greater sensitivity to any subtle motions, fixational eye movements, head positions, blink, and other biological and physiological perturbations to the diameter measurement were magnified and became so significant with AO-OCT. Thus, our experiments required repeated measurements of the same retinal vasculature over prolonged period of time (at least four minutes for measuring vasodilatory responses). We found these repeated measurements necessary to mitigate measurement variabilities including: (1) random noises such as shot noise, source intensity noise, and detector thermal noise, (2) biological and physiological variabilities, such as pulsatile motions, breathing, tissue deformation, tear film changes, etc., and (3) variations in light-tissue interaction such as speckles, directionality, multiple scattering, etc. Although the majority of measurement variabilities can be suppressed after precisely aligning AO-OCT volume images [48], it is inevitable to have many missing data points due to blink, saccadic eye movements, and low image quality. We, therefore, have decided to use a linear mixed effects model to account for unbalanced samples in our statistical analysis, which helps identify and detect the fixed effects of interest without deleting any precious data points.

Another limitation is unknown contributions from RGCs’ spatial contrast sensitivity to the flicker pattern. Since the flicker light was produced by the RGB LED array, its illumination spatial pattern was not diffused. And optics vary across the eyes and so they could have been exposed to different spatial information. In addition, although we intended to stimulate a large temporal patch >15° form fovea (up to 40°H × 70°V) to minimize variations in stimulus size and power across the eyes, the variations could have impacted on the vasodilatory responses across the eyes. That said, these variations would not influence most of the test results we showed in this study since each effect was tested within each individual eye. Indeed, the results in Experiment D could have been influenced by the partial obstruction of the inferior nasal visual field by the subject’s nose (see Fig. 1(A)); however, we found no significant effect of stimulation site (ST; p = 0.9061; see Table S6) and therefore considered negligible though their exact spatial property was of our interest. We also do not know the exact degree of light/dark adaptation state (or bleach level) of cones and rods precisely, as is also the case in other human subject studies. In this study, it is reasonable to assume that all the participants were in a similar mesopic condition that both cone and rod systems are active throughout the experiments, since we performed all the testing sessions in the dark room. Indeed, the subject’s eye was never fully dark or light adapted, because they were exposed to the fixation target and imaging beam during the head/eye alignment as well as testing sessions even when the subject stays in the dark room, Moreover, we started the first testing session of each visit began ∼20 minutes or more after the room light were turned off (a transition period during which most dramatic change in the visual sensitivity took place [36,66]). In fact, we found no evidence of consistent, systematic increase in the neurovascular response during each hour-long visit, due to a potential effect of mild dark adaptation. All that said, further studies will be needed to determine how the light/dark adaptation condition have interacted with the neurovascular responses. Especially given the remarkable accuracy of vascular control system that our results indicated in this study, careful calibration would be necessary to compare the results among studies. Moreover, myogenic autoregulation could have contributed to the overall response we measured. Unlike metabolic autoregulatory function, including a flicker-induced vasodilatory response, which are tightly controlled via negative feedback and feedforward mechanisms [1,51], myogenic autoregulation reacts to changes in flow (shear stress), circumferential wall stretch, and transmural pressure [1,67]. Importantly, both mechanisms coexist. Although Experiment A indicates small evidence of such autoregulatory function may exist (vasoconstriction during Baseline in subject H01), their contributions to our results were too small. However, the prolonged session might have resulted in unwanted autoregulation effects which mixed with neurovascular responses, especially during Recovery condition. Finally, our findings were obtained using the research-grade AO-OCT system that is not widely available; however, the knowledge gained in this study may help refine the detailed requirements for measuring microscopic vasodilatory responses in this living human eye.

5. Conclusion

We have demonstrated that, using the AO-OCT-based method, we can detect subtle diameter differences in ppRA’s microscopic vasodilatory responses to various types of focal flicker stimulation of temporal retinal neurons in the living human eye. Our results revealed mean-illuminance-, frequency- and spatial-dependencies in the vasodilatory responses of upstream ppRA by stimulating downstream retinal neurons. These findings further support a hypothesis that ppRA’s vasodilatory system is coupled with firing activities of RGC axons, in addition to somas, in an orchestrated manner, in the living human eye.

Funding

Legacy Good Samaritan Foundation.

Disclosures

The authors declare no conflicts of interest

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 ^{(1.3MB, pdf)} for supporting content.