Analysis of the Intraocular Jet Flows and Pressure Gradients Induced by Air and Fluid Infusion: Mechanism of Focal Chorioretinal Damage

Abstract

Purpose.: To comprehend the mechanism of focal chorioretinal damage by analysis of the pressure distribution and dynamic pressure induced by infused air during fluid-air exchange.

Methods.: A precise simulation featuring a model eye and a fluid circuit was designed to analyze fluid-air exchange. The pressure distribution, flow velocity, and dynamic pressure induced by infusion of air into an air-filled eye were analyzed using an approach based on fluid dynamics. The size of the port and the infusion pressure were varied during simulated iterations. We simulated infusion of an air-filled eye with balanced salt solution (BSS) to better understand the mechanism of chorioretinal damage induced by infused air.

Results.: Infused air was projected straight toward a point on the retina contralateral to the infusion port (the “vulnerable point”). The highest pressure was evident at the vulnerable point, and the lowest pressure was recorded on most retinal areas. Simulations using greater infusion pressure and a port of larger size were associated with elevations in dynamic pressure and the pressure gradient. The pressure gradients were 2.8 and 5.1 mm Hg, respectively, when infusion pressures of 30 and 50 mm Hg were delivered through a 20-gauge port. The pressure gradient associated with BSS infusion was greater than that created by air, but lasted for only a moment.

Conclusions.: Our simulation explains the mechanism of focal chorioretinal damage in numerical terms. Infused air induces a prolonged increase in focal pressure on the vulnerable point, and this may be responsible for visual field defects arising after fluid-air exchange.

Introduction

In the time since it was initially reported that visual field defects (VFDs) arose after macular hole surgery, many investigators have observed the same phenomenon during fluid-air exchange, and have sought to define the mechanism of retinal injury. ¹ Suggestions include mechanical damage to the optic nerve caused by instruments, tractional damage to the peripapillary nerve fiber layer during posterior hyaloid removal, impaired blood circulation, and increased intraocular pressure. ^2–6 Several clinical studies on patients developing VFDs after macular hole surgery featuring fluid-air exchange have provided strong evidence that infusion of pressurized air is damaging. ^7–9 A relationship between the location of a VFD and that of the infusion cannula has been confirmed in multiple studies. ^9,10  

Several animal studies have shown that a pressurized air flow damages the inner retinal layer, creating irregularities in the internal limiting membrane (ILM), detachment of the ILM, and exposure of the Müller cells and nerve fiber bundles. ^11,12 Such surface changes in the retina provide direct evidence of mechanical damage caused by a pressurized air flow. Other studies have described damage to the retinal ganglion cell layer (GCL), the inner nuclear layer (INL), and the RPE. ^11,13,14 Some investigators have also used indocyanine green angiography (ICGA) to reveal damage to the choroid. ^4,7,14 Yonemura et al. ¹³ described long-term alterations to the rabbit retina, including a delay in filling of the choroidal circulation, a slightly rough ILM surface, disarrangement of retinal layers, disappearance of the outer segment of photoreceptor cells, a multilayered RPE, and the absence of the underlying choriocapillaris. These findings suggested that other mechanisms of injury, in addition to direct mechanical force applied to the retinal surface, were in play. Although Hirata et al. ¹⁰ reported a positive correlation between infusion pressure and the incidence of VFD, the underlying mechanism of injury remains unclear. 

If we are to understand the mechanism by which infused air causes retinal damage, it is necessary to analyze the air flow and pressure distribution on the retina during fluid-air exchange. However, neither the path nor the velocity of the air has been analyzed, and the air pressure distribution across the retina has not been measured. The primary aim of the present study was to analyze the flow of infused air, and the pressure distribution across the retina, using an approach based on fluid dynamics. 

Materials and Methods

A computational model of the human eye was designed using three-dimensional modeling software (FLUENT version 6.3; ANSYS, Inc., Canonsburg, PA, USA). This software contains the many physical modeling features needed to analyze fluidics. Using the principles of fluid dynamics, we constructed a valid fluid circuit to analyze air flow in the vitreous cavity, and pressure distribution across the retina, upon air infusion. We also virtually infused pressurized balanced salt solution (BSS) to better understand how air infusion caused retinal damage. We supposed that vitreous cavity was filled with air, based on a procedure described previously to induce retinal damage. ^11,12  

Design of the Eye Model and Fluid Circuit

The schematic design of the eye model is shown in Figure 1. The eye was simplified to a sphere of axial length 24.0 mm and a white-to-white corneal diameter of 12.0 mm. As in the eye model suggested by Shunmugam et al., ¹⁵ the anterior 2.5 mm portion of the sphere was removed to best reflect the vitreous cavity of a pseudophakic eye. We used the experimental data of Hubschman et al. ¹⁶ to determine the sizes of infusion and exhaust ports (internal diameters of 475, 355, and 227 μm, respectively, for 20-, 23-, and 25-gauge). We regarded the infused air as an ideal gas and set the air temperature at 25°C. The physical properties of BSS and air are shown in Table 1. The fluid circuit of each simulation consisted of an infusion port through which pressurized air/BSS was infused, a vitreous cavity, and an exhaust port connected to the atmosphere (thus at a pressure of 0 mm Hg). The flow path and velocity of infused air/BSS, and the pressure distributions (that of total pressure, and that of the sum of dynamic and static pressure) were recorded throughout each simulation. Dynamic pressure, induced by the kinetic energy of infused air, was also recorded. The pressure gradient, defined as the difference between the maximal and minimal pressure on each area of the retina, was also calculated. The following parameters were altered in individual runs: 

Figure 1

 

Design of the model eye.

Table 1

 

Physical Parameters of Air and the Balanced Salt Solution Used in Simulations

Variables	Values
Density of air, kg/m3	1.225
Viscosity of air, kg/m·s	1.79 × 10−5
Density of BSS*, kg/m3	998.2
Viscosity of BSS*, kg/m·s	1.02 × 10−3

*  Values at 1 atmosphere and 25°C are shown.

1.  
   The gauge of the infusion and exhaust ports (20-, 23-, or 25-gauge)
2.  
   Infused air/BSS pressure (10, 20, 30, 40, 50, or 60 mm Hg)

Numerical Algorithm

Air flow in the vitreous cavity was simulated using conventional mesh-based techniques, in which particles represent a fluid. In this mathematical environment, pressure distribution, flow path, and flow velocity may be obtained by solving two governing equations: the continuity and momentum equation (Fig. 2). 

Figure 2

 

The two governing equations used to analyze fluid dynamics in our simulations: the continuity and momentum equation.

The continuity equation is a stronger and local application of the conservative law that can be used to analyze fluid transport. The momentum equation is a variation of Newton's second law of motion, and can be used to analyze fluid flow. To estimate pressure distribution and flow velocity, we used a comprehensive pressure-based coupling algorithm. 

To simulate BSS infusion, a finite fixed-grid element, derived from the volume-of-fluid model, was used to estimate pressure distributions in the retina and vitreous cavity when it was sought to define differences between the behavior of a fluid (BSS) and a gas (air). A precise and very detailed meshwork was built to best reflect the actual situation. The pressure-based coupled algorithm was also modified to allow full pressure-velocity coupling. 

Results

Simulation of Air Infusion

Prior to air infusion, the pressure of air in the vitreous cavity was equilibrated with that of the atmosphere, through the exhaust port (0 mm Hg), and the pressure gradient was 0 mm Hg. Infused air was projected directly into the vitreous cavity, in a narrow jet, at high velocity. The air velocity was highest at the orifice of the infusion port, and gradually decreased as air resistance came into play. The flow velocity varied depending on the diameter of the port and the infusion pressure. Greater flow velocities were observed in simulations featuring higher infusion pressures and larger-gauge ports. The average flow velocity was more than 10 m/s even when a 25-gauge port and an infusion pressure of 10 mm Hg were used. Infused air moved straight toward the retina and collided with a point on the retina contralateral to the infusion port (the “vulnerable point”). The kinetic energy of air particles generated dynamic pressure on the retina. In each simulation, pressure distribution on the retina and the air flow velocity attained steady-state conditions within 0.01 seconds of initial infusion, and did not subsequently change during infusion. 

The highest pressure was always observed on the vulnerable point, independent of port diameter or infusion pressure. The retinal area surrounding the vulnerable point was also under relatively high pressure, but most retinal areas were under lower pressure. The maximal and minimal pressures on each area of the retina varied depending on the diameter of the port and the infusion pressure. A higher maximal pressure and a greater pressure gradient were noted in simulations using higher infusion pressures and larger-gauge ports. Pressure on the optic nerve head was slightly higher (<0.5 mm Hg) than the minimal pressure in each simulations. The pressures on the vulnerable point were at least 2.3 and 4.6 mm Hg higher than those on the optic disc at infusion pressures of 30 and 50 mm Hg, respectively, when air was delivered through a 20-gauge system. The maximal and minimal pressure values during air infusion are shown in Table 2. Flow paths, air velocities, pressure distributions, and dynamic pressures induced by infused air, are shown schematically in Figure 3. 

Figure 3

 

Schematic drawing of the total pressure distribution, flow velocity of air, and dynamic pressure induced by infused air, using a 20-gauge system. The highest pressure (total pressure, thus the sum of static and dynamic pressure) is always observed on the part of the retina contralateral to the infusion port (the vulnerable point). The highest dynamic pressure is observed on the retinal area surrounding the vulnerable point.

Table 2

 

Pressures at the Vulnerable Point of the Retina Upon Air Infusion Into an Air-Filled Eye

Infusion Pressure, mm Hg	Total Pressure, mm Hg			Dynamic Pressure, mmHg
	Max	Min	Gradient
20-gauge infusion and exhaust port
10	6.6	5.6	1.0	0.4
20	13.7	11.8	1.9	0.8
30	21.2	18.4	2.8	1.2
40	29.0	25.0	4.0	1.6
50	36.6	31.5	5.1	2.0
60	43.8	38.1	5.7	2.4
23-gauge infusion and exhaust port
10	5.5	5.1	0.4	0.2
20	11.7	10.7	1.0	0.4
30	18.0	16.6	1.4	0.6
40	24.4	22.5	1.9	0.8
50	30.9	28.7	2.2	1.0
60	37.5	34.7	2.8	1.3
25-gauge infusion and exhaust port
10	5.1	4.8	0.3	0.1
20	10.7	10.2	0.5	0.2
30	16.6	15.8	0.8	0.3
40	22.7	21.6	1.1	0.5
50	28.7	27.3	1.4	0.6
60	34.9	33.0	1.9	0.8

 Total pressure = static pressure + dynamic pressure.

Simulation of BSS Infusion

Prior to BSS infusion, the pressure of air in the vitreous cavity was equilibrated with that of the atmosphere, through the exhaust port (0 mm Hg). Therefore, the initial pressure gradient was 0 mm Hg. BSS flowed straight into the vitreous cavity through the infusion port. The time to the initial impact of the BSS stream on the vulnerable point depended on the infusion pressure and port gauge. In most cases, the impact occurred within 0.03 seconds. As BSS flowed toward the retina, the pressures on most areas of the retina remained at 0 mm Hg. The highest pressure was observed on the vulnerable point. The retinal area surrounding the vulnerable point was also under relatively high pressure during BSS infusion. These phenomena were consistently observed in simulations using various parameters (Fig. 4). 

Figure 4

 

Representative data on fluid flow velocity, and pressure distribution across the retina, induced by infusion of BSS into an air-filled eye under 60 mm Hg of infusion pressure using a 20-gauge system. Note that high pressure develops on the part of the retina contralateral to the infusion port.

At initial impact, the pressure on the vulnerable point was momentarily high. Thereafter, the pressure dropped rapidly (Fig. 5). The pressure depended on both infusion pressure and port diameter. When a 20-gauge port was used, the pressure on the vulnerable point at initial impact was approximately 2- to 3-fold greater than the infusion pressure. Pressure on the vulnerable point after initial impact was similar to the infusion pressure. Initially, the pressures on the vulnerable point increased to 62.6, 130.2, and 184.2 mm Hg at infusion pressures of 20, 40, and 60 mm Hg, respectively. In the 23-gauge system, the pressure on the vulnerable point at initial collision was ∼1.5-fold higher than the infusion pressure. The pressure after initial collision was slightly lower than the infusion pressure. In the 25-gauge system, the pressure on the vulnerable point was relatively lower than when 20- or 23-gauge systems were used, but was also higher than the infusion pressure at initial impact. The pressure difference between the vulnerable point and the optic disc head was equal to the pressure on the vulnerable point until the infused BSS covered the optic disc head. However, the initial pressure gradient induced by BSS infusion abruptly decreased within 2 seconds, because the BSS level rose quickly in the vitreous cavity. Details of the pressures on the vulnerable point during BSS infusion are shown in Table 3. 

Figure 5

 

Time-dependent analysis of the highest pressure levels induced by infusion of BSS into an air-filled eye using a 20-gauge system. Note that a very high peak pressure was observed momentarily on the part of the retina contralateral to the infusion port, at the time of initial impact of the BSS stream on the retina.

Table 3

 

Pressures at the Vulnerable Point of the Retina Upon BSS Infusion Into an Air-Filled Eye

Infusion Pressure, mm Hg	Time to IC, s	Pressure at IC, mm Hg	Pressure After IC, mm Hg
20-gauge infusion and exhaust port
10	0.026	23.5	8.0
20	0.019	62.6	18.1
30	0.015	73.7	28.4
40	0.013	130.2	38.6
50	0.012	166.5	48.2
60	0.011	184.2	59.0
23-gauge infusion and exhaust port
10	0.027	13.3	4.4
20	0.019	35.4	12.4
30	0.015	44.7	21.1
40	0.013	64.7	29.8
50	0.012	68.3	39.5
60	0.011	89.9	48.9
25-gauge infusion and exhaust port
10	0.031	10.0	4.0
20	0.023	22.0	10.0
30	0.018	37.5	17.0
40	0.015	45.0	24.0
50	0.013	53.0	33.0
60	0.012	72.0	40.0

 IC, initial collision.

Discussion

Computer simulations using mathematical models are powerful tools in studies of fluid dynamics. High reproducibility and precise control of variables are major advantages of such techniques. In the present study, we estimated pressure distributions, flow paths, and velocities of air infused into the vitreous cavity; these parameters are extremely difficult to measure during real surgery. Although it would be difficult to verify our results in actual experiments, the validity of fluidic computer simulations is well-recognized in many fields of science and industry, and also in ophthalmology. ^15,17 The fluid circuit formed upon continuous infusion of air after completion of fluid-air exchange can be simulated without too much difficulty. Furthermore, the air flow velocities used in the present study were comparable with those noted in previous animal studies and employed in computer simulations, supporting the notion that our results are valid and reliable. ^11,15  

We found that infused air tended to move straight toward the retina to impact the vulnerable point at a high flow velocity. After impact, air particles moved along the surface of the retina, with markedly decreased velocity. As pressurized air particles were of high energy when they hit the focal area of the retina, the pressure on the vulnerable point was higher than that on other areas. Obviously, a higher basal intraocular pressure and a steeper pressure gradient were observed when the infused air pressure was increased. Our results provide detailed information on pressure distributions and air flows during air infusion into an air-filled eye. Using the angiographic and histological findings of previous studies, and the results of our present study, we can define the mechanisms by which VFDs and chorioretinal damage are caused by infusion of pressurized air. 

Tangential Traction by Air Particles

Infused air tends to move straight toward the vulnerable point. When an air particle hits the retina, the kinetic energy of the particle generates dynamic pressure on that point. The tangential element of dynamic pressure at the vulnerable point can mechanically damage the retinal surface via application of shear stress. Previous studies have reported focal changes in the retinal surface, including irregularities in the ILM, detachment of the ILM, and exposure of underlying Müller cells and nerve fiber bundles, after air infusion. ^11,12 These findings are in line with direct mechanical damage of the retina caused by tangential traction applied by infused air. However, this mechanism may not be adequate to explain histological changes in the outer retina or VFDs developing after fluid-air exchange. In the present study, the estimated dynamic pressure on the vulnerable point did not exceed 2.4 mm Hg. Given the small area of the vulnerable point, the tangential element of force induced by pressurized air would be too small to damage the outer retina and choroid. The BSS simulation data also support the notion that shear stress is not the main cause of VFDs. The pressure on the vulnerable point induced by BSS infusion was much higher than that caused by air infusion. However, to our knowledge, retinal damage upon BSS infusion into an air-filled eye has not been reported. Furthermore, a recent report claimed that even when macular ILM peeling was evident, shear stress did not affect postoperative visual recovery, rather causing transient swelling of the retinal nerve fiber layer. ¹⁸  

Collapse of Retinal Capillaries Under the Vulnerable Point

Retinal perfusion pressure is defined as the difference between the pressure of the central retinal artery (P_a ) and the central retinal vein (P_v ). ^19,20 Previous studies using mathematical models reported that P_a was approximately 40 mm Hg under normal conditions. ^21,22 It is easy to observe venous pulsation of the optic disc. This implies that P_v just before the exit of blood from the eye must equal, or slightly exceed, the operative pressure at the optic nerve head (P_o ). ¹⁹ Takahashi et al. ²² calculated P_a , P_o , and the retinal capillary pressure, using mathematical models. The retinal capillary pressure was 3.1 mm Hg higher than P_o when P_o was 17.9 mm Hg. If P_o became elevated, both the retinal perfusion pressure and retinal capillary pressure fell. ¹⁹  

We found that the minimal pressure was 31.5 mm Hg when the infused air pressure was 50 mm Hg, and the pressure on the vulnerable point was 4.6 mm Hg higher than P_o . Such a pressure difference is enough to completely compress retinal capillaries under the vulnerable point. Prolonged focal collapse of such capillaries can induce ischemic changes in associated retinal structures. An earlier light microscopic study showed that the immediate retinal damage caused by pressurized air infusion featured injury to the retinal ganglion cell layer, swelling of the IPL, distension of the INL, and triggering of an irregular rearrangement of the INL. ¹¹ These damaged layers are the locations of both superficial and deep retinal capillary plexuses. Long-term alterations at the vulnerable point, including disarrangement of retinal layers and atrophic changes of the IPL and INL, would trigger ischemic damage. ¹³ Observation of retinal whitening contralateral to the air infusion port during air infusion also constitutes strong evidence of focal retinal ischemia. ⁷  

Pressure-Induced Choroidal Vessel Thrombosis

Ivert et al. ²³ showed that choroidal blood flow could be affected by local pressure. A glass rod was used to exert brief pressure (below 1 mm Hg) on the RPE and choroid. Such pressure produced no hemorrhage or discoloration, but choroidal abnormalities became apparent upon ICGA. A nonperfused area was evident where the pressure had been applied. Histology revealed evidence of thrombotic-like material in the choroidal vessels of areas lacking perfusion. Similar angiographic findings were observed in the air-infused rabbit retina. ^13,14 ICGA of the air-infused area revealed hypofluorescent regions, suggesting filling delays in the choroidal circulation. If the pressure on the vulnerable point sufficiently exceeds the retinal capillary pressure, the pressure on the RPE and choroid may be adequate to disturb choroidal blood flow during air infusion. We believe that this phenomenon is responsible for the observed damage to photoreceptors and the multilayered RPE, and the subretinal fibrosis noted, after air infusion into an air-filled eye. ^11,13,14  

In the present study, the pressure gradient induced by BSS infusion was much greater than that induced by air infusion, under the same infusion pressure. A peak of high pressure restricted to the vulnerable point, occurring at the time of fluid impact, was momentarily observed during BSS infusion into an air-filled eye. The pressure gradient was greater upon BSS infusion than upon air infusion. However, the initial pressure gradient was maintained only briefly because the vitreous cavity became filled with BSS within a few seconds. In contrast, the initial pressure gradient caused by infused air was steadily maintained until infusion ended. In another simulation (data not shown), the pressure difference between the vulnerable point and the optic disc was lower upon simulation of BSS infusion into a BSS-filled eye than upon air infusion into an air-filled eye. This suggests strongly that the pressure on the vulnerable point was not much higher than the pressure on the optic disc after BSS covered both the vulnerable point and the disc. Oshitari et al. ¹² showed that the intensity of damage was correlated with the duration of infusion. This may explain why no retinal damage caused by BSS infusion has been noted, despite the initial pressure gradient being greater. 

When the viscosity and density of BSS are considered, it is obvious that the pressure gradient induced by BSS infusion would be higher than that induced by air infusion into a BSS-filled eye. Therefore, we did not simulate air infusion in a BSS-filled eye. The method used earlier to induce retinal damage supports the validity of our simulation method, thus air infusion into an air-filled eye. In previous studies, one side port was held open for 30 seconds or more to allow free air introduction into the vitreous cavity after completion of fluid-air exchange. ^11,12  

We did not consider gravity in our simulations. In real surgery, each infused air particle is accelerated by gravity until it collides with the retina. The velocity of infused air was highest at the orifice of the infusion port, and gradually decreased as air resistance was encountered. If the average flow velocity is taken to be 10.0 m/s, each particle collides with the retina within 0.003 seconds after infusion. The increase in velocity caused by gravity is 0.03 m/s when it is considered that the acceleration caused by gravity is 9.8 m/s². Therefore, the maximal displacement caused by gravity is 0.045 mm at an infusion pressure of more than 10 mm Hg. Given the eye axial length of 24.0 mm, ignoring the gravity effect does not weaken the results of our simulations. 

The main disadvantage of computer simulation is that it is impossible, in real life, to measure the many variables employed. However, computer simulations help us to understand the fluidics of certain circuits. As the fluid circuit of the present study is not complicated, we believe that our results are reliable. Our work explains why the incidence of VFDs is markedly decreased when the infused air pressure is held at 30 mm Hg or less during fluid-air exchange. ¹⁰ In addition, our study suggests how possible surgical complications of vitrectomy may be minimized. 

The simulations showed that 25-gauge air infusion reduced P_o by ∼15%, and the pressure gradient by 70%, compared with 20-gauge air infusion at the same infusion pressure. Therefore, use of a small-gauge instrument might allow chorioretinal perfusion under the vulnerable point to be maintained during air infusion into an air-filled eye. This may be helpful in surgical cases, when manipulation of the retina and changes in the instruments used are frequent in air-filled eyes under air infusion (e.g., during retinal detachment surgery). In addition, valved cannulae would be safer than open cannulae in such surgical circumstances, in that valved cannulae prevent unnecessary air flow when instruments are exchanged, thereby decreasing the duration of air infusion. 

In conclusion, our simulation affords a better understanding of how VFDs arise after fluid-air exchange; we conducted numerical analysis of pressure distributions to this end. Our work will help physicians achieve favorable visual outcomes when performing vitreoretinal surgery. 

Acknowledgments

Supported by the Soonchunhyang University Research Fund. 

The authors alone are responsible for the content and writing of the paper. 

Disclosure: Y.J. Kim, None; S. Jo, None; D. Moon, None; Y. Joo, None; K.S. Choi, None