**Purpose**:
To mathematically model the temporal dynamic responses of retinal vessel diameter (D), oxygen saturation (SO_{2}), and inner retinal oxygen extraction fraction (OEF) to light flicker and to describe their responses to its cessation in humans.

**Methods**:
In 16 healthy subjects (age: 60 ± 12 years), retinal oximetry was performed before, during, and after light flicker stimulation. At each time point, five metrics were measured: retinal arterial and venous D (D_{A}, D_{V}) and SO_{2} (SO_{2A}, SO_{2V}), and OEF. Intra- and intersubject variability of metrics was assessed by coefficient of variation of measurements before flicker within and among subjects, respectively. Metrics during flicker were modeled by exponential functions to determine the flicker-induced steady state metric values and the time constants of changes. Metrics after the cessation of flicker were compared to those before flicker.

**Results**:
Intra- and intersubject variability for all metrics were less than 6% and 16%, respectively. At the flicker-induced steady state, D_{A} and D_{V} increased by 5%, SO_{2V} increased by 7%, and OEF decreased by 13%. The time constants of D_{A} and D_{V} (14, 15 seconds) were twofold smaller than those of SO_{2V} and OEF (39, 34 seconds). Within 26 seconds after the cessation of flicker, all metrics were not significantly different from before flicker values (*P* ≥ 0.07).

**Conclusions**:
Mathematical modeling revealed considerable differences in the time courses of changes among metrics during flicker, indicating flicker duration should be considered separately for each metric. Future application of this method may be useful to elucidate alterations in temporal dynamic responses to light flicker due to retinal diseases.

^{1,2}One method to investigate the retinal vascular and metabolic functions is by presenting a physiological challenge such as light flicker stimulation. Light flicker has been shown to increase neural activity,

^{3,4}which leads to augmentation of retinal vessel diameter (D),

^{5}increased blood flow (BF),

^{6}and alteration of oxygen saturation of hemoglobin (SO

_{2}) in retinal veins.

^{7,8}As a result of these changes, inner retinal oxygen delivery (DO

_{2}) and oxygen metabolism (MO

_{2}) increase in humans,

^{9}whereas the inner retinal oxygen extraction fraction (OEF) decreases.

^{8}

_{2}, or OEF by either measuring these values before and during a light flicker-induced steady state,

^{8,10,11}or by averaging their temporal dynamic responses to light flicker.

^{6,12–14}Some studies have reported the nonlinear temporal dynamic responses of D and BF to light flicker

^{4,5,15–17}or its cessation,

^{5,6,13,15–17}and one study qualitatively reported the nonlinear responses of SO

_{2}to light flicker.

^{7}These temporal dynamic responses to light flicker and its cessation indicate how the retina accommodates physiological challenges during both the transient nonsteady state and the induced steady state, as opposed to the static effect of light flicker, which only provides information on the flicker-induced steady state. However, to the best of our knowledge, previous studies have only reported the mathematical modeling of temporal dynamic responses of D and BF to light flicker,

^{3,17,18}while the temporal dynamic responses of SO

_{2}and OEF to light flicker and their mathematical modeling have not been described. Therefore, the purpose of the current study was to simultaneously assess the temporal dynamic responses of retinal D, SO

_{2}, and OEF to light flicker and its cessation, and to propose a mathematical model for the behavior of these temporal dynamics during light flicker.

*N*= 2), reduced visual acuity (

*N*= 1), or choroidal nevus (

*N*= 1) in the right eye. Subjects were excluded if the coefficient of variation of three repeated measures of D, SO

_{2}, or OEF before light flicker was greater than 0.1.

_{2}, and OEF)

^{8}was modified to assess the temporal dynamic responses of these metrics to light flicker and its cessation. Briefly, a slit lamp biomicroscope was fitted with a rapid-switching filter wheel containing bandpass filters to illuminate the retina at multiple wavelengths. The optical imaging system provided light flicker stimulation at 10 Hz using light at 530 nm. In the current study, retinal reflectance images at 606 and 570 nm wavelengths were acquired periodically every 13 seconds over a time course consisting of 29 seconds before flicker (three time points), 78 seconds during flicker (six time points), and 39 seconds after the cessation of flicker (three time points). The schematic diagram of the image acquisition protocol is shown in Figure 1. The 13-second interval was chosen to allow 3 seconds for image acquisition followed by a 10-second period for the subject to blink comfortably, regain fixation, and allow the operator to optimize alignment before the next image acquisition.

_{2}from each major vessel within the ROI were obtained and averaged to yield a mean retinal arterial and venous D (D

_{A}, D

_{V}) and SO

_{2}(SO

_{2A}, SO

_{2V}), as previously described.

^{8}

_{2A}−O

_{2V}))/(BF*O

_{2A}), where O

_{2A}is the arterial oxygen content, O

_{2V}is the venous oxygen content, and BF is retinal blood flow. Since BF is a determinant of both the numerator and denominator, this term cancels. Further, since the dissolved oxygen content of blood is minimal,

^{19}oxygen content is closely approximated by SO

_{2}. Thus, OEF was calculated as (SO

_{2A}−SO

_{2V})/SO

_{2A}. According to the Fick principle, which applies to steady state conditions, OEF is also equal to the ratio of MO

_{2}to DO

_{2}.

^{8,20}MO

_{2}is the rate that the inner retinal tissue consumes oxygen provided by the retinal circulation, and DO

_{2}is the rate that oxygen enters the retinal circulation. Therefore, OEF calculation under steady state conditions can be used to provide information on the ratio of MO

_{2}to DO

_{2}, without calculating either directly. However, under nonsteady state conditions, such as those immediately after the initiation or cessation of light flicker, the ratio defined by MO

_{2}to DO

_{2}differs from OEF according to the accumulation or depletion of oxygen in the inner retina.

_{A}, D

_{V}, SO

_{2A}, SO

_{2V}, and OEF) from the three repeated measurements acquired during the 29 seconds before light flicker were determined per subject. Intrasubject variability was assessed by coefficient of variation (SD/mean) and averaged over all subjects. Based on data in all subjects, mean and SD of metrics before light flicker were determined and intersubject variability was calculated by the coefficient of variation.

_{A}(D

_{A}R) at the first time point during light flicker was calculated as D

_{A_first time-point}/D

_{A_mean before flicker}. Data analyses were performed on metric ratios rather than metric values to normalize data in each subject. Metric ratios (D

_{A}R, DVR, SO

_{2A}R, SO

_{2V}R, OEFR) were averaged among subjects at each time point to generate mean temporal dynamic responses during light flicker and after its cessation. All statistical analyses were performed using SPSS software (version 22; SPSS, Chicago, IL, USA).

^{21–24}General shape of this exponential change in metric ratios during light flicker was given by the following equation:

*t*represents time during light flicker, A represents the fitted metric ratio at

*t*= 0, B represents the difference in the fitted metric ratio from

*t*= 0 to

*t*→∞ (i.e., the maximal flicker-induced change in the metric ratio), and C represents the time constant; that is, the time for the fitted metric ratio to reach 1−e

^{−1}(∼63%) of the maximal change. Using this notation, the sum of A and B represents the metric ratio at the flicker-induced steady state.

*R*

^{2}for each fitted exponential function.

*t*-tests.

_{A}, D

_{V}, SO

_{2A}, SO

_{2V}, and OEF was 2%, 1%, 1%, 4%, and 5%, respectively. Mean D

_{A}, D

_{V}, SO

_{2A}, SO

_{2V}, and OEF before light flicker stimulation was 86 ± 7 μm, 105 ± 16 μm, 92% ± 4%, 60% ± 6%, and 0.35 ± 0.05, respectively (

*N*= 16). Intersubject variability of D

_{A}, D

_{V}, SO

_{2A}, SO

_{2V}, and OEF was 8%, 16%, 5%, 10%, and 16%, respectively. Metric ratios D

_{A}R, D

_{V}R, SO

_{2A}R, SO

_{2V}R, and OEFR during and after light flicker are provided in the Tables 1 and 2.

_{A}R and D

_{V}R

_{A}R and D

_{V}R. For both metrics, the exponential function was a good fit (

*R*

^{2}≥ 0.87). From the exponential functions, the flicker-induced steady state values of D

_{A}R and D

_{V}R were 1.046 and 1.053, respectively, indicating vasodilation of 5% during light flicker. Time constants of exponential fits for D

_{A}R and D

_{V}R were 14 and 15 seconds, respectively, indicating relatively rapid vasodilation in response to light flicker. Further, at the last time point during light flicker (i.e., 78 seconds after the initiation of light flicker), the changes in D

_{A}R and D

_{V}R had reached over 99% of their maximal flicker-induced changes, as indicated by their exponential fits.

_{2A}R, SO

_{2V}R, and OEFR

_{2A}R and SO

_{2V}R, while Figure 4 shows the temporal dynamic response of OEFR. The exponential functions were excellent fits for both SO

_{2V}R and OEFR (

*R*

^{2}≥ 0.93), whereas the fit for SO

_{2A}R had a lower

*R*

^{2}of 0.77. From the exponential functions, the flicker-induced steady state values of SO

_{2A}R, SO

_{2V}R, and OEFR were 0.991, 1.071, and 0.868, respectively. Time constants of exponential fits for SO

_{2A}R, SO

_{2V}R, and OEFR were 70, 39, and 34 seconds, respectively. At the last time point during light flicker (i.e., 78 seconds after the initiation of light flicker), changes in SO

_{2V}R and OEFR from the exponential fits had reached nearly 90% of their maximal flicker-induced changes, whereas the change of the SO

_{2A}R fit had only reached 70% of its maximal change.

_{A}R and D

_{V}R

_{A}R was not significantly different from the preflicker reference ratio (

*P*= 0.4), whereas D

_{V}R remained elevated by 3% (

*P*< 0.001) (Fig. 2). However, for all following time points after the cessation of light flicker, both D

_{A}R and D

_{V}R were not significantly different from the preflicker reference ratio (

*P*≥ 0.07).

_{2A}R, SO

_{2V}R, and OEFR

_{A}R, D

_{V}R, SO

_{2A}R, SO

_{2V}R, and OEFR during light flicker and after its cessation were reported in human subjects. To the best of our knowledge, this is the first study to mathematically model the temporal dynamic responses of SO

_{2A}R, SO

_{2V}R, and OEFR to light flicker stimulation.

_{A}R and D

_{V}R were 1.046 and 1.053, consistent with previous studies that found vasodilation of a similar magnitude during light flicker.

^{5,10,12,15–17}The flicker-induced steady state values of SO

_{2V}R and OEFR were 1.071 and 0.868, in agreement with previous studies that found an increase in SO

_{2V}

^{7,8}and a decrease in OEF

^{8}with light flicker. The flicker-induced steady state value in SO

_{2A}R was 0.991 and represents essentially no change in SO

_{2A}during light flicker, consistent with previous studies.

^{7,8}

_{A}R and D

_{V}R in response to light flicker were similar to those reported by previous studies,

^{3,17}which substantiates the exponential modeling of the temporal dynamic responses in the current study. The rapid rise time of these metrics is also in agreement with a previous study that reported a 10-second time constant for the response of BF at the optic disk to light flicker.

^{3,18}Taken together, the time constants of D

_{A}R, D

_{V}R, and BF indicate that DO

_{2}would likely have a similar time constant, indicating a rapid increase of DO

_{2}at the initiation of light flicker. Indeed, the ability of DO

_{2}to increase rapidly during light flicker has been previously described as a result of complex neurovascular coupling mechanisms.

^{1,25,26}In contrast, the time constants of changes in SO

_{2V}R and OEFR in response to light flicker were more than twofold larger than those of D

_{A}R, D

_{V}R, and BF. The apparent mismatch between the supposed time constant of DO

_{2}and that of OEFR may have important implications concerning the temporal dynamic response of MO

_{2}to light flicker. However, OEF is the ratio of MO

_{2}to DO

_{2}only under steady state conditions,

^{8,20}and thus we cannot infer relative changes in MO

_{2}to DO

_{2}from OEFR measured during light flicker prior to the establishment of a flicker-induced steady state. Ultimately, future studies that directly measure the temporal dynamic responses of MO

_{2}and DO

_{2}to light flicker are necessary to determine the relationship between OEFR and the ratio of MO

_{2}to DO

_{2}in the nonsteady state. Nevertheless, this study demonstrates, for the first time, that the time courses of changes in SO

_{2V}R and OEFR to light flicker are considerably different from those of D

_{A}R and D

_{V}R. Indeed, to achieve 95% of the maximal flicker-induced change in a metric, a flicker duration of thrice the time constant is necessary. From the current study, a flicker duration of 45 seconds would be necessary for changes in D

_{A}R and D

_{V}R to reach 95% of their maximal flicker-induced changes, whereas 117 seconds would be necessary for SO

_{2V}R. Thus, the duration of light flicker should be carefully considered when comparing the results of previous studies, particularly for metrics that have longer time constants.

_{A}R, SO

_{2V}R, and OEFR had returned to the preflicker reference ratio, whereas D

_{V}R remained elevated. These findings in D

_{A}R and D

_{V}R are consistent with previous studies that reported minimal arterial vasoconstriction and slight venous vasodilation within 10 seconds after the cessation of light flicker.

^{15–17}Although D

_{A}R returned to baseline within 13 seconds after the cessation of light flicker, the continued elevation of D

_{V}R may correspond to the phenomenon of delayed venous compliance.

^{27}Nevertheless, within 26 seconds after the cessation of light flicker, all metric ratios were not significantly different from the reference ratio, and the retina had essentially returned to its preflicker steady state.

^{28–31}and one study reported a correlation between maximal vessel constriction after the cessation of light flicker and age.

^{29}Since the current study reported findings only in older subjects, future studies in younger individuals are necessary to elucidate any potential effects of age on temporal dynamics responses, particularly those after the cessation of light flicker. Third, the acquisition of images every 13 seconds limited the temporal resolution of data obtained in the current study. Future studies with finer temporal resolutions may permit the modeling of temporal dynamic responses after the cessation of light flicker, as well as better modeling of those during light flicker. Last, we modeled the complex temporal dynamic responses of metrics to light flicker with a relatively simple exponential function. Future studies may reveal better models of the temporal dynamic responses to light flicker.

**A.E. Felder**, None;

**J. Wanek**, None;

**N.P. Blair**, None;

**M. Shahidi**, None

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