Abstract
Purpose.:
The study hypothesis was that shear stress caused by abnormal aqueous flow is one of the causes of corneal endothelial cell loss after laser iridotomy (LI). The shear stress exerted on the corneal endothelial cells (CECs) in anterior chambers (ACs) of different depths was calculated by a computational fluid dynamics program. The effect of shear stress was also examined on human corneal endothelial cells (HCECs) grown on microscope slides.
Methods.:
Three-dimensional models of the AC were constructed, with and without an LI window, and AC depths of 2.8, 1.8, 1.5, and 1.0 mm. The speed of aqueous streaming through the LI window was obtained from animal studies and used to calculate the shear stress exerted on the CECs. Cultured HCECs attached to glass slides were subjected to different magnitudes of shear stress by exposing the cells to different flow rates of the culture solution. The number of cells remaining attached to the slide under each condition was determined.
Results.:
The shear stresses were 0.14, 0.31, 0.48, and 0.70 dyn/cm2 for models with AC depths of 2.8, 1.8, 1.5, and 1.0 mm, respectively. When cultured HCECs were subjected to shear stress within the range calculated by the three-dimensional models, the number of cells remaining attached to the glass slide decreased as the magnitude and duration of the shear stress increased.
Conclusions.:
Shear stress exerted on CECs after LI may reach a magnitude high enough to cause cell damage and loss in eyes, especially in those with shallow anterior chambers.
The first case of irreversible corneal edema after argon laser iridotomy (LI) was reported by Pollack
1 in 1984, and five cases of phakic bullous keratopathy after argon LI were reported soon afterward by Schwartz et al.
2 Since then, the incidence of LI-induced bullous keratopathy has increased yearly
1–9 and is now one of the most common reasons for penetrating keratoplasty in Japan.
7–9 Although a variety of hypotheses have been made on the cause of this unique form of bullous keratopathy (e.g., excessive laser irradiation,
2,3,5 an acute glaucoma episode,
2,4 and preexisting corneal endothelial abnormalities such as Fuchs' corneal dystrophy),
2,4,5 many cases cannot be fully explained by these factors. Among these, excessive laser irradiation with subsequent thermal damage of the endothelial cells has been considered to be one of the dominant causes. However, it is puzzling that the corneal endothelial cell density decreases progressively over many years without any significant corneal edema or inflammation immediately after LI.
2–8
We have demonstrated in animal studies that during miosis, the aqueous humor streams into the anterior chamber (AC) from the posterior chamber through an LI window and strikes the corneal endothelium. During mydriasis, the aqueous humor in the AC is drawn back into the posterior chamber through the LI window.
10
From these findings, we hypothesized that the shear stress caused by the abnormal aqueous flow striking the corneal endothelium may be one of the pathogenetic mechanisms for progressive corneal endothelial cell loss. To test this hypothesis, we first constructed three-dimensional AC models of different depths, with or without an LI window, and calculated the speed of aqueous flow as well as the shear stress exerted on the corneal endothelium by using a computational fluid dynamics program. We further examined the effect of shear stress on endothelial cells in in vitro experiments. To determine whether the shear stress calculated could have an influence on the corneal endothelium, we exposed human corneal endothelial cells (HCECs) cultured on glass slides to shear stress by exposing them to different flow rates of the culture solution, and examined changes in cell morphology and adhesion.
Computational fluid dynamics is one of the techniques of fluid mechanics that uses numerical methods and algorithms to analyze and solve problems that involve fluid flow. A computational fluid dynamics program (Fluent; Ansys Japan K.K., Tokyo, Japan) was used in the study. The finite-volume method was used to solve the Navier-Stokes continuity equations on an arbitrary target flow domain, and appropriate boundary conditions were assigned. The speed of the thermal current was calculated in the geometrical AC models at various AC depths, where the temperature of the posterior corneal surface was set at 36°C and the temperature of the iris surface was set at 37°C. Then, a virtual LI window was created at the 12 o'clock position of the peripheral iris and values obtained from animal experiments were introduced into the model, to calculate the speed of the aqueous streaming through the LI. Changes in the speed of aqueous flow and in the shear stress on the corneal endothelium were calculated in models of different AC depths and streaming from the LI window.
The aqueous humor plays an important role in maintaining the homeostasis of the corneal endothelial cells and other structures in the anterior segment of the eye. Any changes in the dynamics of the flow of the aqueous humor can have profound effects on the corneal endothelial cells and may be associated with a variety of ocular disorders. Unfortunately, it is very difficult to observe aqueous flow in humans unless an AC inflammatory reaction is present or a tracer is intentionally introduced into the AC. Thus, computational fluid dynamics may be a more useful method for analyzing changes in the dynamics of aqueous flow.
18–22
Computational fluid dynamics techniques have been widely used in biomedical research (e.g., measuring blood flow in vessels or air flow in the respiratory airways). The computational fluid dynamics techniques are valuable, because they make it possible to simulate abnormal conditions that are difficult to produce, even in animal experiments. In addition, computational fluid dynamics techniques allow researchers to modify individual experimental parameters and provide reasonably accurate results under different conditions and assumptions.
However, it is not possible to include all the in vivo physiological or pathologic conditions in the computational fluid dynamics technique. The computational fluid dynamics technique requires some degree of simplification if a condition is to be analyzed properly. Therefore, it is necessary to consider whether the results obtained from the computational fluid dynamics simulation are consistent with the physiological values to be applicable to the in vivo situation.
In our computational fluid dynamics model, we used shapes of the AC based on clinical data, and we used these shapes for the in vivo measurements of aqueous flow speed found in experiments on rabbits, to ensure the precision of our calculations.
The temperature difference between the surface of the iris and the corneal endothelium is the most important factor that must be set to ensure a consistency of the data obtained by the model and the eye in situ. However, there are currently no published data on the in vivo temperature of the corneal endothelial surface. In our model, the iris surface temperature was assumed to be the same as internal body (rectal) temperature of 37°C, and the corneal endothelial surface temperature was set at 36°C, based on preliminary calculations of thermal current speed made using our 2.8 mm AC depth model (
Fig. 9), experimental thermal current speeds found in particle tracking velocimetry experiments on rabbit eyes,
10 and thermal current speeds from mathematical models in earlier reports.
22
There may be some concern that the flow of the aqueous caused by the thermal currents is affected by the flow through the pupil and drainage of aqueous from the trabecular meshwork. In the literature, the speed of aqueous flow from the pupil was reported to be 0.0017 mm/s by Maurice
23 and 0.002 mm/s by Kumer et al.
21 Fitt and Gonzalez
22 reported that the maximum speed of aqueous flow from the pupil was 0.0075 mm/s and that the thermal convection caused by the temperature difference between the iris surface and corneal endothelial surface is greater than that produced by any other physical mechanism (e.g., lens phakodonesis or rapid eye movements).
In addition, the aqueous flow due to thermal convection caused by 1°C difference between the iris surface and corneal endothelial surface was 0.16 to 0.21 mm/s (
Fig. 9), and the aqueous streaming from the LI window was 9.89 mm/s which is >100 to 1000 times faster than that of aqueous flow through the pupil. For our results, the flow of aqueous through the pupil was omitted to simplify the computational fluid dynamics model.
We found that the shear stress exerted on the corneal endothelium by aqueous streaming from the LI window was greater in the eyes with shallower AC depth. The total shear stress (the area under the shear stress versus time curve in
Fig. 5) exerted on the corneal endothelial surface by aqueous streaming during a single miosis cycle was greater as the AC depth decreased (
Fig. 6). In the extreme case in which the AC depth was 1.0 mm, the total shear stress in eyes with an LI was 70 times greater than that produced by physiological thermal currents. Therefore, in clinical cases in which the peripheral AC depth does not become sufficiently large after LI,
24,25 such eyes may be at high risk of having considerable shear stress.
Miosis commonly occurs in daily life in response to changes in light levels. Because increases in aqueous streaming occur repeatedly after each episode of miosis in eyes with an LI, the corneal endothelial cells can be expected to be more strongly influenced by shear stress because the stress results from intermittent rather than continuous flow.
Shear stress can be either advantageous or disadvantageous for maintaining the homeostasis of different types of cells, depending on the magnitude and properties of the shear stress.
26–28 At physiological levels, shear stress has a protective effect on vascular endothelial cells, because it inhibits apoptosis.
29–31 On the other hand, vascular smooth muscle cells exposed to nonphysiological shear stress levels show reduced proliferation and increased apoptosis.
32,33 Therefore, shear stress not only leads to the physical detachment of cells, but may also cause apoptosis and wound-healing disorders and may be a factor in the disruption of the homeostasis of corneal endothelial cells.
According to the estimates from our model, the maximum shear stress exerted by aqueous streaming through the LI window was 0.70 dyn/cm
2. This shear stress is far greater than that which caused morphologic changes and cell detachments in our flow experimental model. Moreover, in the cultured cells, intermittent flow had a greater effect than continuous flow. The reason for this is unclear, but it has been shown that when vascular endothelial cells are subjected to identical magnitudes of shear stress, cells that are subjected to changes in flow were more likely to show morphologic changes or responses on a cellular or molecular level than are the cells that are exposed to constant flow.
34–36
Some discrepancies may arise when in vitro data are applied to in vivo situations, because the attachment of cells to a culture slide or to Descemet's membrane should not be the same. However, it should still be remembered that prolonged periods of stress on the corneal endothelium caused by aqueous streaming can lead to corneal endothelial cell decompensation.
Irreversible corneal edema developed in the upper region of the cornea where the LI was performed, but in some cases it developed in the lower region of the cornea far from the site of the LI.
1–6,9 We did not study the relationship between the area of LI and initial corneal edema, because in most of the cases of bullous keratopathy caused by LI, the patients had diffuse edema at the initial visit to our clinic.
In our model, the flow of the aqueous back through the LI window into the posterior chamber during mydriasis, aqueous flowing through the pupil, and drainage of aqueous through the trabecular meshwork were not simulated. Therefore, we did not examine how these combined factors affected the aqueous streaming in and out through the LI window in eyes with shallow ACs and slow thermal currents. To construct a computational fluid dynamics model that will allow investigation of these factors, clinical data regarding changes in the volume of the anterior and posterior chambers during miosis and mydriasis are needed. In addition, changes in the relative positions of the iris and lens are necessary. However, many of these parameters have not been determined for the eye in vivo, and obtaining these clinical data is critical for further development of the computational fluid dynamics model.
Aqueous humor dynamics appear to play a role not only in post-LI disorders, but also in many other disorders, such those occurring after cataract surgery and in glaucomatous eyes. The continuing development of applications of computational fluid dynamics has the potential to contribute to the understanding of the pathogenesis of a variety of anterior segment disorders.
Supported by Grant-in-aid for Innovation 206003 from the Science and Technology Agency of Japan.
Disclosure:
Y. Yamamoto, None;
T. Uno, None;
T. Joko, None;
A. Shiraishi, None;
Y. Ohashi, None
Continuity and Momentum Equations.
Mass Conservation Equation.
Momentum Conservation Equation.
Energy Conservation Equation.
Boussinesq Model.