Measurement of Outflow Facility Using iPerfusion

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.


S2-1 Analysing Uncertainty
Every measurement has associated with it some error, which results in the measurement deviating from the true value. Given this limitation, it is only possible to state the true value using the measured value M sens with some degree of uncertainty M true = M sens ± s sens (S1-1) In order to characterise the uncertainty in the sensor, s sens , one must devise an experiment wherein the true value can be defined, and then analyse the deviation between the sensor measurement and the true value.
In the iPerfusion system, the height of the pressure reservoir is controlled using a linear actuator that has a stepper-motor with a microstep size of 1.25µm. A single microstep would therefore correspond to a pressure change of 0.00009 mmHg. In practice, although imperfect alignment of the spindle would likely add some variability, it seems reasonable to expect that the error between the specified and actual height would deviate by less than 10 microsteps. We therefore assume that the applied pressure can be controlled with an accuracy exceeding 0.001 mmHg.
The applied pressure from the reservoir for a given pressure step j, P a,j , is thus considered to be the true pressure, and P a is used to determine the uncertainty in both the pressure and the flow sensors, as described below.

S2-2 Pressure Sensor Uncertainty
For the custom Omegadyne PX409 used in the iPerfusion system, the accuracy is reported to be 0.08% of the full scale range of 0 − 50 mmHg, corresponding to 0.04 mmHg. Here, we characterise the uncertainty in the pressure sensor within the context of the iPerfusion system.
The pressure sensors are calibrated for each day of use and these data can be used for analysis of sensor uncertainty. The following process is used for calibrating the pressure sensors.
Firstly, the pressure on both sides of the sensor is set to be exactly equal, corresponding to zero 1 Supporting Information 1: Analysis of Sensors pressure difference, by opening both sides to the same reservoir and recording the voltage output from the pressure sensor. One side of the pressure sensor is then opened to the actuated pressure reservoir, and the control software programmatically locates the height that gives the voltage recorded in the first step, which by definition corresponds to zero pressure. An 8-step automated calibration is then carried out, increasing P a in increments of 60 mm, and averag-ing the voltage over 5 seconds at 1000 Hz for each step (in order to minimise the influence of electrical noise). A linear fit is then applied to the voltage-pressure relationship This straight line fit yields parameters V p and V 0 , which can be used to calculate the measured In order to estimate s P sens , we analyse the residuals between the measured and applied pressure. To perform this analysis, we consider 50 calibrations selected randomly and taken over a period of more than a year. Figures S1-1a where N is the number of pressure steps, and N − 2 is the number of degrees of freedom in the linear regression. Over the 100 calibrations using both sensors, the median value of s P sens was 0.007 mmHg, with a maximum value of 0.012 mmHg. The maximum s P sens value is used as a conservative estimate of the standard deviation in pressure attributable to sensor uncertainty, and is indicated by the dotted lines in Figures S1-1c and d.

S2-3 Flow Sensor Uncertainty
The flow sensor used in this study was the Sensirion SLG64-0075. This sensor has a range of ±5000 nl/min, and an accuracy reported by the manufacturer of 10% of the measured value for flow rates greater than 250 nl/min and ±25 nl/min for lower flow rates. Here, we characterise the uncertainty in the flow sensor within the range appropriate for mouse eye perfusion (< 500 nl/min).
In order to evaluate the uncertainty in the flow sensors, we developed the following protocol. Firstly, using a bypass tube of large diameter, the pressure on the upstream and downstream ends of the flow sensor were set to be exactly equal, and the output from the sensor 3 Supporting Information 1: Analysis of Sensors was recorded over 20 seconds. The mean and variance over this period are defined as Q zero and s 2 zero , respectively. The bypass tubing was then closed, and the upstream end of the flow sensor was opened to the actuated reservoir, whilst the downstream end was opened to an outlet reservoir at a fixed height. In the range of flow rates examined, there is negligible change in reservoir heights. The applied pressure, P a , was then incremented by 0.1 mmHg with 20 seconds at each step j. The central 10 seconds of each step are used to calculate the mean, Q j , and variance, s 2 Qave,j , of the flow rate. The applied pressure is increased in this manner until the flow rate exceeds 500 nl/min, at which point the pressure is decremented until the flow rate is lower than zero.
A straight line fit with zero intercept was calculated for Q sens = Q j − Q zero against P a using weighted linear regression, with the weights defined according to s 2 Qave,j + s 2 zero −1 . The slope of this line is the hydrodynamic conductance of the flow sensor, C q . As the true flow rate is unknown, it is estimated based on the applied pressure according to Q true = P a C q , as C q is theoretically constant. Figure S1-2 shows the results of these tests, with the colours indicating three tests on separate days. Figures S1-2a and b show the flow rate output from the sensor against P a C q , using a logarithmic abscissa to demonstrate the sensor accuracy at low flow rates. Figures S1-2c and d show the difference between the sensor output and the true flow rate, plotted against P a C q . The uncertainty in the flow sensor was calculated according to where N is the number of steps and N − 1 is the number of degrees of freedom in the linear regression of Q sens versus P a C q .
The average value of s Qsens from the three experiments on both sensors was 1.7 nl/min, whilst the maximum value was 2.0 nl/min. This maximum value is used as a conservative estimate of the standard deviation in flow rate attributable to uncertainty in the flow sensor and is indicated by the dotted lines in Figures S1-2c and d.

S2-4 Relative Uncertainty Pressure Measurement Uncertainty
Despite the highly regulated environment, the measured pressure signal still retains a degree of uncertainty, predominantly due to electrical noise and minute movements of the tubing within the system. In order to define a steady state pressure, the pressure signal is averaged over a period of time, and the standard deviation of the pressure signal over this period gives a measure of uncertainty associated with the averaging. The data set of 66 individual eyes was analysed to calculate the values of s P ave arising from the averaging process. From the 490 pressure steps analysed, the median of s P ave was 0.009 mmHg and the 95 th percentile (used as a robust estimate of the upper limit) was 0.022 mmHg.
The total uncertainty in measured pressure for a given pressure step, j, can be estimated according to s 2 P,j = s 2 P ave + s 2 P sens (S1-6) Using the maximum sensor uncertainty and the 95 th percentile on the uncertainty associated with averaging yields a conservative upper limit of s P,j = 0.025 mmHg. As the pressures recorded in the perfusion protocol range from approximately 4 − 20 mmHg, the maximum relative uncertainty in the pressure measurement is 0.6%.

Flow Measurement Uncertainty
An additional uncertainty arises due to averaging of the flow rate over the measurement period. Analysis of the 490 pressure steps from the 66 individual eyes yields a median s Qave of 1.1 nl/min with a 95 th percentile of 2.3 nl/min.
The total uncertainty in the measured flow for a given pressure step j can be estimated as s 2 Q,j = s 2 Qave + s 2

Qsens
(S1-7) Based on the maximum sensor uncertainty and the 95 th percentile averaging uncertainty, we get an upper limit of s Q,j = 3.1 nl/min. The flow rates measured in the mouse eye perfusions are dependent on the facility of a given eye, but considering a representative facility of 6nl/min/mmHg at the lowest perfusion pressure of 4mmHg, the flow rate would be 24nl/min.
For this value, the uncertainty in the flow rate would be approximately 15% of the measured value.
We thereby conclude that the measurement uncertainty in the pressure is sufficiently small such that it can be neglected, whereas the uncertainty in the flow rate should be considered in the analysis.