In this study, measurements of the pressure characteristics of the AGVs were performed in vitro, and five flow pressure characteristics of the AGV were assessed. The results indicated that the pressure of the repriming air (+) was twice that of the pressure of the repriming air (−), but constant pressures were equivalent between both conditions.
The initial priming pressure was the amount of pressure required to open the AGV valve when it was first used. According to the manufacturer's instructions, the initial priming should be performed by injecting 1 mL of physiologic saline.
1,6,9 In addition to opening and reducing the valve resistance in the AGV before its implantation, another purpose is to remove air in the device and ensure that there are no manufacturing defects.
8 Cheng et al.
9 measured this priming pressure and reported an average of 3000 mm Hg; even with priming 3 times, the pressure greater than priming did not damage the function of the silicone-plate valve of the AGV.
9 In our experiments, the initial priming pressure exceeded the measurement scale in some devices; thus, the observation reproduced the previous report that showed an extremely high initial priming pressure.
The function of the AGV valve is to maintain the pressure to prevent postoperative hypotony.
4 When the flow of physiologic saline was stopped or decreased drastically, the valve closes to prevent the liquid from continuing to flow out, so that the pressure at the inlet tube is maintained at a certain pressure. Based on previous research, the closing pressure on the AGV was around 10 mm Hg.
4 In the current study, when physiologic saline was reflowed at the same volume rate, the pressure transducer showed that the pressure continued to increase to the peak to reopen the valve that was previously closed. We referred to this peak pressure as the pressure of repriming air (−) (see
Fig. 3④). The increased pressure in this state was caused by the closing of the valve and the increased volume of fluid as the rate of physiologic saline continuing to flow until the valve reopened. This pressure increase can be explained by the water hammer equation approach on the pipeline. The following is a description of
Equation 110:
\begin{eqnarray}c = \frac{{1425}}{{\sqrt {1 + \frac{{2,1{\rm{\;}} \times {{10}^4}d}}{{E\partial }}} }}\end{eqnarray}
where с is the pressure wave propagation (increased and decreased pressure) in a pipeline (m/s); where ∂ (pipeline wall thickness) = 1.65 × 10
−4 m,
d (inner diameter) = 3.05 × 10
−4 m,
E (module of elasticity) = 1 × 10
6 N/
cm2, Δ
v (velocity diffrence) = 4.56 × 10
−4 m/
s, and ρ (density of water) = 1000
Kg/
m3.
\begin{eqnarray}\Delta P = \rho \left( {\frac{c}{g}} \right)\Delta v\end{eqnarray}
where Δ
P is the pressure difference between
P1 and
P2 (
P1 −
P2)
\begin{eqnarray}{P_1} - {P_2} = \frac{{1425{\rm{\;}}\rho \Delta v}}{{g\sqrt {1 + \frac{{2.1{\rm{\;}} \times {{10}^4}d}}{{E\partial }}} {\rm{\;}}}}\end{eqnarray}
\begin{eqnarray}{P_1} - {P_2} = 64.98{\rm{\;}}Pa = 0.487{\rm{\;}}mm\;Hg\end{eqnarray}
Equations 2 and
3 served as approximations to explain the increasing pressure on repriming. By entering the approximate value of each variable, the value of the pressure difference was calculated to be 0.487 mm Hg, as in (
Equation 4). This value is even smaller than the measured pressure difference between the repriming pressure and the constant pressure after repriming in the air (−) condition (i.e. 12.1–10.4 =1.7 mm Hg), and may indicate the presence of other factors that affect the magnitude of the increase in the repriming pressure (e.g. resistance derived from valve stiffness).
The above equations describe the air (−) condition, and the measurement results indicated that the pressure of the repriming air (+) condition was about two times higher than that of the repriming air (−) condition; thus, the trapped air in the tube became an additional factor that increased the valve resistance. The pressure of the repriming air (+) was measured as in
Figure 5, in which the measured pressure was
P1. The increase in pressure
P1 can be explained by complex fluid dynamics because the role of the air in the tube was affected by various factors, including the tube diameter and material. Given that the inner tube diameter was in micrometers, the flow was associated with the capillary phenomenon and surface tension. This capillarity phenomenon also was affected by the cohesion force (attraction between similar particles) and the adhesion force (attraction between different types of particles). In addition, AGV FP7 is made of medical grade silicone, which is water-repellent.
11,12 This water-repellent characteristic made the cohesion force exceed the adhesion force.
12,13 That scenario makes the surface of the liquid a convex meniscus so that the fluid in the tube forms a larger angle contact (θ > 90°).
13 Equation 5 for capillary pressure and its relationship to the surface tension in the pipe tube is as follows
14–16:
\begin{eqnarray}{P_{capillary}} = \frac{{2\gamma \cos \theta }}{r}\end{eqnarray}
In addition to capillary pressure, fluid viscosity also affects high pressures, with the drag force of fluid viscosity as follows in (
Equation 6)
14,15:
\begin{eqnarray}{F_v} = 8\pi l\eta v\end{eqnarray}
where
\begin{eqnarray}{P_v} = \frac{{{F_v}}}{A} = \frac{{8\pi l\eta v}}{{\pi {r^2}}}\end{eqnarray}
and
\begin{eqnarray}{P_v} = \frac{{8\eta lv}}{{{r^2}}}\end{eqnarray}
Pressure
Equation 7 was obtained by dividing the drag force
Equation 6 into the cross-sectional area (A = π
r2).
Equation 8 then was a simplification of
Equation 7, namely, the pressure equation by drag force. Based on Newton's second law, the equation of the motion of the meniscus liquid is as follows:
\begin{eqnarray}({P_1} - {P_2} - {P_{air}})\pi {r^2} = {\rm{\;}}8{\rm{\;}}\pi l\eta v - 2{\rm{\;}}\gamma \pi r\cos \theta \end{eqnarray}
\begin{eqnarray}{P_1} - {P_2} = {\rm{\;}}{P_{air}} + \frac{{8\eta lv}}{{{r^2}}} - \frac{{2\gamma \cos \theta }}{r}\end{eqnarray}
In
Equation 9, after dividing both sides by the cross-sectional area of the tube (π
r2), the pressure difference (
P1 −
P2) is expressed as in
Equation 10.
P1 is the pressure measured at the pressure transducer,
Pair, air pressure; η, fluid viscosity; γ, surface tension;
v, fluid velocity;
l, tube length;
r, inner radius of the tube; and θ, contact angle. In
Equation 10, the value of
P1 was determined by the air pressure plus the viscosity pressure and minus the capillary pressure. Because of the characteristics of the tube material (θ > 90°), the cos θ is negative. Mathematically, capillary pressure should reduce the value of
P1, but the minus sign (−) on the capillary pressure when multiplied by the minus (−) value of cos θ produces a positive value, which will make the value of
P1 increase. Accordingly, capillary pressure and drag force should explain in part the effect of the trapped air on the increase in the repriming pressure rise.
After priming, the AGV works as a drain where the fluid will flow through the AGV tube and then flow out through the valve. In this condition (
Fig. 6), the AGV works as a venturi with Bernoulli's principle as in the following
Equation 111:
\begin{eqnarray}{P_1} + \frac{1}{2}\rho v_1^2 + \rho g{h_1} = {P_2} + \frac{1}{2}\rho v_2^2 + \rho g{h_2}\end{eqnarray}
\begin{eqnarray}{P_1} = {P_2} + \frac{1}{2}\rho (v_2^2 - v_1^2) + \rho g(\Delta h)\end{eqnarray}
Equation 12 was obtained after simplifying
Equation 11, the heights of
h1 and
h2 were considered equal in our setting, so that Δ
h =
h2 −
h1 = 0 and then obtained
Equation 13:
\begin{eqnarray}{P_1} = {P_2} + \frac{1}{2}\rho (v_2^2 - v_1^2)\end{eqnarray}
In
Figure 6, the
P1, pressure was measured at the pressure transducer;
P2, pressure at the valve; ρ, density of the fluid;
v1, fluid velocity at the tube input; and
v2, fluid velocity coming out of the valve. From
Equation 13, the value of
P1 represented the value of the constant pressure measured after the repriming pressure. Given that the trapped air was exhausted at this stage, the constant pressure after repriming should be equal between the air (+) and air (−) conditions, and, in fact, our results agreed with the theory.
Intra-operatively, after the initial priming, air can be trapped in the AGV tube when the needle is pulled out of the tube (
Fig. 7). To avoid the unintended postoperative pressure rise (although the rise may be transient), the authors recommend that surgeons avoid leaving the air in the tube intra-operatively. Another translational relationship of our observation is that using the pars plana tube insertion combined with gas tamponade surgery, such as when treating neovascular glaucoma,
17,18 may result in higher IOPs than expected during the early postoperative days. Conversely, use of air/gas can be a good way to avoid postoperative hypotony when the AGV is implanted in eyes with a high risk of hypotony, such as in the presence of high myopia, aphakia, uveitis, and in elderly patients.
18,19
In addition to the results of this study at constant pressure after repriming air (-), we also compared the mean values of the new and old AGVs, which have almost the same mean pressure values. To avoid early postoperative hypotony, the manufacturer changed the inspection standards of the valve closing pressure in 2020. A concern may be that this change increases the final IOP level with new lots compared with old lots. However, because the constant pressures after repriming were equivalent between the old and new lots, we can expect that the final pressures postoperatively do not differ greatly between the current and older devices.
Considering that the current results were all derived from experimental settings, the clinical relevance remains to be proven. Therefore, translational use of the evidence requires particular attention for patients’ safety.
In conclusion, based on precise measurement of the flow characteristics, the presence of trapped air in the AGV tube increases the repriming pressure, whereas the air does not affect the constant pressure afterward.