Fig 1.
Lumped-parameter viscoelastic model of an eye perfusion system.
FS, fluid infusion rate (pump-driven system); P, reservoir pressure (gravity-driven system); RS and CS, system resistance and compliance; PS, system pressure; RC, cannula resistance; PE, intraocular pressure; FA, aqueous production rate; FU, uveoscleral outflow rate; RT, trabecular outflow resistance; PV, episcleral venous pressure; RW and CW, resistance and compliance of globe wall, where 1/CW = 1/CW1 + 1/CW2.
Table 1.
Parameter values of model simulations of eye perfusion techniques.
Fig 2.
Intrinsic dynamics of simulated eye perfusion techniques.
(A) Pressure (left) and flow (right) responses of the CF model (top) to a step change in FS, the CPg model (middle) to a step change in P (CPg1: red, CPg2: black), and the CPp model (bottom) to a step change in PT. Solid lines give PS and FS, dashed lines give PE and FE. (B) Time for pressure and flow to reach 99% of plateau level versus model feedback gain. Symbols indicate the gain and setting time of the CP models in A.
Fig 3.
Analysis and simulation of enucleated eye noise.
(A) Left, IOP data published by [18] for an ex vivo mouse eye [P15CL-01]. Right, histogram of IOP fluctuations. Thick line is a Gaussian fit of the probability distribution. (B) Average power spectrum of published IOP data from 12 ex vivo mouse eyes [18]. PSD: power spectral density. (C) Response of the CPg2 model to a noisy pressure step having statistics matched to ex vivo eyes. Red box indicates the window criterion for steady state, which is the 5-min running window wherein PS must vary <0.5 mmHg. Blue line indicates the ratio criterion for steady state, which is the last 5-min running interval wherein the slope of FS/PS must remain <0.1 nl·min-2·mmHg-1. Filled and unfilled arrowheads indicate the model settling time for the noise record in A for the window and ratio criterion, respectively.
Fig 4.
Simulation of facility experiments on enucleated eyes.
(A) Pressure (top) and flow (bottom) responses of CF and CP models with ex vivo noise to a series of 0.1 μl/min steps in flow or 5-mmHg steps in pressure, respectively. Successive steps were initiated using the ratio criterion. Arrowheads indicate total duration of the simulated experiment. Note that the high gain of the CPp model necessitated a change in flow axis. (B) Summary of facility experiment durations across 12 ex vivo noise simulations using the window and ratio criteria (filled and unfilled symbols). (C) Steady-state PE and FE for the step response series in A. Dashed line is a linear regression fit (R>0.99 and slope = 23 nl·min-1·mmHg-1 for all models). (D) Summary of outflow facility estimates across noise simulations for the various models using the window and ratio criteria (filled and unfilled symbols). Diamond indicates the actual facility of the simulated rat eye. Error bars give standard deviation. Box and whiskers give 10, 25, 50, 75, and 90 percentiles. Asterisks indicate statistical differences between denoted groups.
Table 2.
Statistics of outflow facility simulations with ex-vivo noise.
Fig 5.
Analysis and simulation of anesthetized animal noise.
(A) Left, IOP data of an anesthetized rat collected previously by the lab [17]. Right, histogram of IOP fluctuations. Thick line is a Gaussian fit of the probability distribution. (B) Raw (black) and filtered (red) step response of the CPg2 model for the noise record in A. Filtered responses are a 3-min moving average of model PS and FS data. Filled and unfilled arrowheads indicate the settling time using window and ratio criteria on filtered responses, respectively. (C) Effect of filter width on settling time of different CP models for the noise record in A using window and ratio criteria (filled and unfilled black circles). Mean and standard deviation of model settling times across 12 anesthetized noise records are indicated by lines (thick: window, thin: ratio) and shaded areas (dark: window, light: ratio), respectively. Diamonds mark the filter width with the fastest settling time and least variability (CPg1: 2 s, CPg2: 3 min, CPp: 3.25 min).
Fig 6.
Tradeoff of feedback gain and noise filtering on flow regulation.
(A) Effect of smoothing the feedback signal with a 15-s moving average filter on the pressure (top) and flow (bottom) responses of the CPp model to a step change in PT for a feedback gain of 7 (gray), 1 (red), 0.3 (blue), and 0.1 (green). (B) Effect of smoothing the feedback signal with a 5-s (green), 15-s (red), and 60-s (blue) moving average filter on pressure and flow responses of the CPp model with a feedback gain of 0.3. Black traces give step responses of the CPp model without feedback filtering.
Fig 7.
Simulation of facility experiments on anesthetized animals.
(A) Raw (black) and filtered (red) pressure (top) and flow (bottom) responses of CP models to a series of 5-mmHg steps in PT contaminated with IOP noise recorded from an anesthetized rat. Successive steps were initiated using the ratio criterion, and responses were filtered with a moving average window that provided best model performance for anesthetized noise according to Fig 5C. Arrowheads indicate the experiment duration for the noise record in Fig 5A. Note that the high gain of the CPp model necessitated a change in flow axis. (B) Summary of facility experiment durations across 12 anesthetized noise simulations using the window and ratio criteria (filled and unfilled symbols). (C) Steady-state PE and FE for the filtered step response series in A. Dashed line is a linear regression fit (R>0.99 and slope = 23 nl·min-1·mmHg-1 for all models). (D) Summary of outflow facility estimates across 12 anesthetized noise records for the various models using the window and ratio criteria (filled and unfilled symbols). Diamond indicates actual facility of the simulated rat eye. Error bars give standard deviation. Box and whiskers give 10, 25, 50, 75, and 90 percentiles. Asterisks indicate statistical differences between denoted groups.
Table 3.
Statistics of outflow facility simulations with in-vivo anesthetized noise.
Fig 8.
Analysis and simulation of conscious animal noise.
(A) Left, IOP data of an awake free-moving rat collected previously by the lab [40]. Right, histogram of IOP fluctuations. Thick line is a Gaussian fit of the probability distribution. (B) Unfiltered and 14-min lowpass filtered (thin and thick black lines) step responses of the CPg2 model for the noise record in A. Unfiltered step responses were processed by a recursive regression method based on the eye model in Fig 1 to yield fitted pressure and flow responses (red lines). Filled and unfilled arrowheads indicate settling time of the filtered (black) and fitted (red) responses for the window (19.0 and 7.0 min) and ratio (52.8 and 16.2 min) criteria, respectively. (C) Effect of filter width on average settling time of the various CP models across 12 conscious noise records for the window (thin black line) and ratio (thick black line) criteria. Thin and thick red lines indicate the mean settling time of recursively-fitted model responses for the window and ratio criteria, respectively. Shaded areas give the standard deviation of filtered and fitted response settling times using window (dark gray and dark pink) and ratio (light gray and light pink) criteria. Diamonds mark the filter width with the fastest settling time and least variability (CPg1: 10 min, CPg2: 14 min, CPp: 14 min, CPpx: 13 min).
Fig 9.
Simulation of facility experiments on conscious animals.
(A) Raw (black) and regression-fitted (red) pressure (top) and flow (bottom) responses of CP models to a series of 5-mmHg steps in PT contaminated with IOP noise recorded from a conscious rat. Successive steps were initiated using the ratio criterion, and responses were filtered with a moving average window that provided best model performance for conscious noise according to Fig 8C. Arrowheads indicate the experiment duration for the noise record in Fig 8A. Note that the high gain of the CPp model necessitated a change in flow axis. (B) Summary of facility experiment durations across 12 records of conscious noise using the window and ratio criteria on fitted (dark and light red symbols) and best-filtered (black and while symbols) responses and using the novel fitting criterion on fitted responses (blue symbols). (C) Steady-state PE and FE for the fitted step response series in A. Solid line is a linear regression fit (R>0.98 for all models, slope = 23 nl·min-1·mmHg-1 for CPg1, CPg2, and CPpx models and 21 nl·min-1·mmHg-1 for CPp model). (D) Summary of outflow facility estimates across 12 conscious noise records for the different models using the window and ratio criteria on fitted (dark and light red symbols) and best-filtered (black and while symbols) responses and the novel fitting criterion on fitted responses (blue symbols). Diamond indicates actual facility of the simulated rat eye. Error bars give standard deviation. Box and whiskers give 10, 25, 50, 75, and 90 percentiles.
Table 4.
Statistics of outflow facility simulations with in-vivo conscious noise.
Fig 10.
Optimizing facility experiment design.
(A) Summary of simulated experiment durations (top) and facility estimates (bottom) of the CPg1 model across conscious noise records using the window (left), ratio (middle), and fitting (right) criteria for pressure step series ranging in step size and number. Red boxes indicate the baseline series of 5 steps of 5 mmHg. (B) Dependence of facility data in A on the maximum IOP elevation of the step series. Error bars give standard deviation.