Computational modeling of fluid flow and intra-ocular pressure following glaucoma surgery

Abstract

Background: Glaucoma surgery is the most effective means for lowering intraocular pressure by providing a new route for fluid to exit the eye. This new pathway is through the sclera of the eye into sub-conjunctival tissue, where a fluid filled bleb typically forms under the conjunctiva. The long-term success of the procedure relies on the capacity of the sub-conjunctival tissue to absorb the excess fluid presented to it, without generating excessive scar tissue during tissue remodeling that will shut-down fluid flow. The role of inflammatory factors that promote scarring are well researched yet little is known regarding the impact of physical forces on the healing response.

Methodology: To help elucidate the interplay of physical factors controlling the distribution and absorption of aqueous humor in sub-conjunctival tissue, and tissue remodeling, we have developed a computational model of fluid production in the eye and removal via the trabecular/uveoscleral pathways and the surgical pathway. This surgical pathway is then linked to a porous media computational model of a fluid bleb positioned within the sub-conjunctival tissue. The computational analysis is centered on typical functioning bleb geometry found in a human eye following glaucoma surgery. A parametric study is conducted of changes in fluid absorption by the sub-conjunctival blood vessels, changes in hydraulic conductivity due to scarring, and changes in bleb size and shape, and eye outflow facility.

Conclusions: This study is motivated by the fact that some blebs are known to have 'successful' characteristics that are generally described by clinicians as being low, diffuse and large without the formation of a distinct sub-conjunctival encapsulation. The model predictions are shown to accord with clinical observations in a number of key ways, specifically the variation of intra-ocular pressure with bleb size and shape and the correspondence between sites of predicted maximum interstitial fluid pressure and key features observed in blebs, which gives validity to the model described here. This model should contribute to a more complete explanation of the physical processes behind successful bleb characteristics and provide a new basis for clinically grading blebs.

Figure 1. Anatomy of a bleb.

(A) Photograph of an eye with a fluid bleb (labeled). Note in this case the lack of observable capillaries above the bleb. (B) Cross-sectional schematic of the key anatomical structures in an eye containing a bleb as a result of a trabeculectomy. Aqueous humor is produce by the ciliary body into the anterior chamber. The aqueous humor passes in front of the, lens through the iris and out through the sclera into the bleb. Note flow through the trabecular meshwork or via the uveoscleral pathway has not been depicted.

Figure 2. Bleb geometry.

Cross-sectional Ocular Coherence Tomography image left eye of a simple bleb morphology, functioning bleb of IOP 10 (“Visante OCT” Zeiss HE 10/1/37 RVEEH – image date 8/4/08). Note this does not imply that this bleb size or shape is optimal. Dimensions shown are the approximate dimensions of the bleb to be used as a standard for model construction. Note it is unclear where the sclera barrier is from this image and so the line drawn is approximate. In the subsequent models (e.g. see Figure 3) we assume the bleb sits directly on the sclera and is axisymmetric. Further we assume the curvature of the sclera is unimportant to the mass transport problem.

Figure 3. Geometry and pressure predictions of the standard functioning bleb.

(A) Without scar tissue and (B) with a layer of scar tissue surrounding bleb. Color scale indicates interstitial fluid pressure. (C) IOP with degree of blockage ε of the fluid flow through the trabecular meshwork leading to a reduced outflow facility. Three cases are shown. The first (solid line) shows increase in IOP with reduction of outflow facility for an unoperated eye. The second case (solid line with squares in (C)) shows the relatively controlled IOP due to additional outflow pathway of 100µm radius into a typical bleb within normal sub-conjunctival tissue. The third case (solid line with triangles) shows the effect of a scar layer of uniform thickness (0.2mm) encapsulating the bleb.

Figure 4. Variation of IOP with tissue properties for the standard bleb shown in Figure 2 and 3A .

Tissue properties varied are tissue hydraulic conductivity K (bleb K kept constant) and L_pS_A/V (a measure of capacity of tissue to absorb fluid). A scar layer has not been included. Heavy solid line represents best estimate of absorption capacity over a range of K. Other solid lines represent variation in IOP with K for L_pS_A/V changes by ×100, ×10, ×0.1, ×0.01 from original L_pS_A/V. Short heavy vertical line indicates best estimate of K and L_pS_A/V. i.e. intersection of heavy solid and light dashed give best estimate of K and absorption capacity from Table 2.

Figure 5. The effect of bleb size on aqueous humor interstitial pressure and IOP.

(A) interstitial pressure distribution around three bleb sizes: a small bleb (top) 50% radius and height of functioning (standard) bleb (middle) and a large bleb (bottom) 200% radius and height of functioning bleb. Shown for each bleb size are the case of a scar layer and no scar layer. (B). The effect of bleb size on IOP for a range of outflow facility for the three blebs sizes shown in (A) without a scar layer.

Figure 6. The effect of bleb aspect ratio on aqueous humor interstitial pressure and IOP.

(A) Interstitial pressure distribution around three bleb shapes: a tall narrow bleb (top) with 50% radius and 200% height of standard bleb (middle) and a wide flat bleb (bottom) 200% radius and 50% height of standard bleb. Shown for each bleb shape are the case of a scar layer and no scar layer. (B). The effect of bleb aspect ratio on IOP for a range of outflow facility for the three blebs shapes shown in (A) without a scar layer.

Figure 7. The effect of scar layer properties on aqueous humor interstitial pressure and IOP.

(A) tissue pressure distribution around a bleb with a scar cap (partially formed scar layer) of radius 1.5 mm. Note pressure scale is same as that used in Figure 3A, (B) IOP for standard bleb without scar, the scar cap in Figure 7A and full scar layers of various thickness (1× refers to scar thickness used in previous figures i.e. 0.2mm; 0.5× refers to a scar layer of 0.1mm thickness and 1.5× refers to a scar layer of 0.3mm thickness). For each thickness of a full scar layer the effect of fluid absorption is also shown.