Measurement of Outflow Facility Using iPerfusion

Abstract

Elevated intraocular pressure (IOP) is the predominant risk factor for glaucoma, and reducing IOP is the only successful strategy to prevent further glaucomatous vision loss. IOP is determined by the balance between the rates of aqueous humour secretion and outflow, and a pathological reduction in the hydraulic conductance of outflow, known as outflow facility, is responsible for IOP elevation in glaucoma. Mouse models are often used to investigate the mechanisms controlling outflow facility, but the diminutive size of the mouse eye makes measurement of outflow technically challenging. In this study, we present a new approach to measure and analyse outflow facility using iPerfusion™, which incorporates an actuated pressure reservoir, thermal flow sensor, differential pressure measurement and an automated computerised interface. In enucleated eyes from C57BL/6J mice, the flow-pressure relationship is highly non-linear and is well represented by an empirical power law model that describes the pressure dependence of outflow facility. At zero pressure, the measured flow is indistinguishable from zero, confirming the absence of any significant pressure independent flow in enucleated eyes. Comparison with the commonly used 2-parameter linear outflow model reveals that inappropriate application of a linear fit to a non-linear flow-pressure relationship introduces considerable errors in the estimation of outflow facility and leads to the false impression of pressure-independent outflow. Data from a population of enucleated eyes from C57BL/6J mice show that outflow facility is best described by a lognormal distribution, with 6-fold variability between individuals, but with relatively tight correlation of facility between fellow eyes. iPerfusion represents a platform technology to accurately and robustly characterise the flow-pressure relationship in enucleated mouse eyes for the purpose of glaucoma research and with minor modifications, may be applied in vivo to mice, as well as to eyes from other species or different biofluidic systems.

Fig 1. The iPerfusion system.

(a) Schematic of the experimental setup. Inset shows internal (green), external (red) and resultant (blue) pressures acting on the eye. Flow (b) and pressure (c) traces from a sample mouse eye perfusion. Red highlighted regions show steady-state periods, over which data were averaged.

Fig 2. In vitro validation of the system.

Data points show the ‘facility’ (hydraulic conductance) of various lengths of glass capillary with 95% confidence intervals. The fit in red is a linear relationship between hydraulic resistance and length, with 95% confidence bounds shown in grey. Deviations from the fit can be used to estimate the accuracy of facility measurement using iPerfusion.

Fig 3. Selecting an appropriate model for the flow-pressure relationship.

(a) A sample flow-pressure curve for the enucleated mouse eye perfusion shown in Fig 1b and 1c. Points show measured data with 95% confidence intervals. Blue: linear fit (Eq 3), C = 9.1 nl/min/mmHg, Q₀ = −27.8 nl/min. Red: power law (Eq 9), C_r = 5.4 nl/min/mmHg, β = 0.44. Shaded regions show 95% confidence bounds. (b) The facility as calculated by the linear and power law models. Black markers show Q/P, which is independent of the fit, and green markers show facility as calculated according to Eq 8, (Q − Q₀)/P, showing the large influence of the model on the calculated facility. (c) and (d) show equivalent plots for a more non-linear case. Linear fit, C = 14.2 nl/min/mmHg, Q₀ = −66.2 nl/min. Power law, C_r = 5.4 nl/min/mmHg, β = 0.85.

Fig 4. Comparing linear and power-law models.

Outer ellipses show 95% CI on each parameter. (a) Power law exponent, β, against the logarithm of reference facility for the power law model: no correlation is observed (p = 0.49). (b) Pressure independent flow, Q₀, against the logarithm of facility for the linear fit: a strong correlation is observed (p < 10⁻⁶), suggesting that the linear model is inappropriate. (c) Pressure-independent flow against power law exponent: a strong correlation is observed: p < 10⁻⁶, indicating that non-zero Q₀ values are a result of the non-linearity in the Q − P relationship. (d) Comparison between log facility predicted by linear and power law models. Red line shows average over-prediction of ≈103% by the linear model.

Fig 5. Population distributions of the regression parameters for the power law model.

(a) Reference facility C_r: histogram of 66 eyes with overlaid normal (blue) and lognormal (red) distributions. Shaded blue regions show predicted facilities below 2 nl/min/mmHg and below 0 nl/min/mmHg. (b) β: histogram from 66 eyes with overlaid normal distribution.

Fig 6. Comparison of facility for paired eyes using ‘Paired Facility plots’.

Each data point represents one individual, with the log-transformed facility of each eye defining the co-ordinates. Filled ellipses indicate 95% confidence intervals from the regression fitting of Eq 9 (1.96s_reg) and outer ellipses indicate additional uncertainty due to intra-individual variability (s_con). Inset: facility in nl/min/mmHg. Unity line is shown in blue. Red line shows average difference $\overline{Z}$, with its confidence intervals in grey. (a) Untreated contralateral pairs. No pairs exhibited a significant difference between contralateral eyes when accounting for uncertainty. (b) Effect of PDA205 treatment compared to control eyes. A significant increase in the facility following treatment is observed, although there is considerable variability ($s_{\text{tre}}^2$) introduced by the drug.

Fig 7. Comparison of facility for unpaired eyes using the ‘Cello plot’.

Unpaired analysis of facility for PDA205 treated and control eyes. Each data point shows the reference facility, C_r, with the error bars showing 95% confidence intervals from the regression fitting of Eq 10 (1.96s_reg). Shaded regions show best estimates of the sample distributions, with the geometric mean and two-sigma shown by the thick and thin horizontal lines respectively. Dark central bands show 95% CI on the mean values.