**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/cm^{2} 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.

^{ 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 }

^{ 10 }

^{ 11–13 }A two-dimensional AC with a depth of 2.8 mm and its parameters are shown in Figure 1A. A three-dimensional AC with a depth of 2.8 mm was constructed by rotating the two-dimensional shape around the ocular axis. A cubic diagram of a divided three-dimensional AC model with a depth of 2.8 mm (adverse side and flip side) is shown in Figure 1B. In a similar manner, three-dimensional ACs were constructed for AC depths of 1.8, 1.5, and 1.0 mm (Fig. 1C). The 2.8-mm AC depth corresponded to that of a normal eye, 1.8 mm to an eye with a narrow angle, 1.5 mm to an eye with angle-closure glaucoma requiring preventive LI, and 1.0 mm to an eye with an extremely shallow AC during an episode of acute glaucoma requiring LI.

*v*

_{max}of the forward aqueous streaming through the LI window in eyes with the diameter of the LI window at 0.56 mm was 9.39 mm/s, determined by the particle-tracking velocimetry technique.

^{ 14 }The attenuation of the speed of aqueous streaming was approximated by a cosine function. Thus, calculations of the speed of aqueous streaming were executed every 0.033 second with the following equation: where

*V*is the speed of aqueous streaming (in millimeters per second) and

*T*is time (seconds).

^{ 15 }Cultured HCECs were maintained in a humidified incubator at 37°C and 10% CO

_{2}.

^{ 16 }Primary cultures of HCECs and all subsequent passages were performed by using our published method.

^{ 17 }We used cultured HCECs at the fifth passage for the experiments.

_{2}.

*P*< 0.05 was considered to be statistically significant.

^{2}for models with AC depths of 2.8, 1.8, 1.5, and 1.0 mm, respectively. For comparison, the shear stress caused by the descending thermal current in a normal eye with an AC depth of 2.8 mm and no LI window, was 0.0062 dyn/cm

^{2}at the center of the corneal endothelial surface.

^{2}· s, whereas in the eyes with LI windows, the total shear stresses were 0.06, 0.13, 0.2, and 0.29 dyn/cm

^{2}· s for eyes with AC depths of 2.8, 1.8, 1.5, and 1.0 mm, respectively. These values were 14.7, 31.9, 49.2, and 70.7 times greater than that of the control normal physiological aqueous flow without an LI window (Fig. 6).

^{2}shear stress for 4 hours (control); 7b, 0 dyn/cm

^{2}for 16 hours (control); 7c, 0.12 dyn/cm

^{2}continuous shear stress for 4 hours; 7d, 0.12 dyn/cm

^{2}continuous shear stress for 16 hours; 7e, 0.16 dyn/cm

^{2}continuous shear stress for 4 hours; 7f, 0.16 dyn/cm

^{2}continuous shear stress for 16 hours; 7g, 0.58 dyn/cm

^{2}continuous shear stress for 4 hours; 7h, 0.58 dyn/cm

^{2}continuous shear stress for 16 hours; 7i, 0.12 dyn/cm

^{2}intermittent shear stress for 4 hours; and 7j, 0.58 dyn/cm

^{2}intermittent shear stress for 4 hours. All images were taken at the same magnification.

^{2}of shear stress (Figs. 7e, 7g) appeared longer and narrower than the control cells (Fig. 7a). At a shear stress level of 0.58 dyn/cm

^{2}(Fig. 7g), some of the cells were detached from the slide. When the duration of the shear stress was 16 hours (Figs. 7d, 7f, 7h), elongation and detachment of the cells were observed at more sites and in larger areas. As the magnitude of shear stress or the duration of the shear stress increased, the stress had a greater influence on the cells.

^{2}for 4 hours, there were large patches of detached cells (Fig. 7i). At a magnitude of 0.58 dyn/cm

^{2}, the number of cells attached to the slide glass decreased considerably after 4 hours, and the size of the cells that remained attached to the slide had markedly decreased (Fig. 7j).

^{2};

*P*< 0.05; control > continuous shear stress 0.16 dyn/ cm

^{2};

*P*< 0.001; control > continuous shear stress 0.58 dyn/ cm

^{2};

*P*< 0.0001; control > intermittent shear stress 0.12 dyn/ cm

^{2};

*P*< 0.0001; control > intermittent shear stress 0.58 dyn/ cm

^{2};

*P*< 0.0001). When the cells were subjected to continuous shear stress, as the magnitude of shear stress increased, the number of cells became fewer.

^{2}> intermittent shear stress 0.12 dyn/cm

^{2};

*P*< 0.05; continuous shear stress 0.58 dyn/cm

^{2}> intermittent shear stress 0.58 dyn/ cm

^{2};

*P*< 0.001).

^{ 18–22 }

^{ 10 }and thermal current speeds from mathematical models in earlier reports.

^{ 22 }

^{ 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).

^{ 24,25 }such eyes may be at high risk of having considerable 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.

^{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 }

^{ 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.

*S*

_{m}is the mass source term.

*I*is the unit tensor.

*k*

_{eff}is the effective conductivity and

*J*is the diffusion flux of species

_{j}*j*. The first three terms on the right side of equation 4 represent energy transfer due to conduction, species diffusion, and viscous dissipation, respectively.

*S*

_{h}represents a volumetric heat source term. In equation 4,

*E*is given by: where the sensible enthalpy

*h*is defined for incompressible flows as

*Y*is the mass fraction of species

_{j}*j*and

*h*is expressed as where

_{j}*T*

_{ref}is 298.15 K.

_{0}is the (constant) density of the flow,

*T*

_{0}is the operating temperature, and β is the thermal expansion coefficient. Equation 5 is obtained by using the Boussinesq approximation ρ = ρ

_{0}(1 − βΔT) to eliminate ρ from the buoyancy term. This approximation is accurate as long as changes in the actual density are small.

^{ 18–22 }to be: density, 994 kg/m

^{3}; specific heat, 4178 J/kg · K; thermal conductivity, 0.6241 W/m · K; dynamic viscosity, 0.000746 kg/m · s; and volume expansion coefficient, 0.000335 1/K.