Estimations of Critical Clear Corneal Incisions Required for Lens Insertion in Cataract Surgery: A Mathematical Aspect

Abstract

In a routine cataract operation cornea tissue may be damaged when an intra-ocular lens (IOL) injector of diameter between 1.467 and 2.011 mm is inserted through an empirically designed 2.2 mm corneal incision. We aimed to model and estimate the minimal length of the incision required to avoid wound tear. It was assumed that the damage was caused by tissue fracture at the tips of the incision, and this fracture could be studied using damage and fracture mechanics. The criterion of the damage was caused by a tear governed by the critical energy release rate (ERR) G _c , which is tissue dependent. Analytical and numerical studies were both conducted indicating the possibility of a safe and effective incision in cataract surgery. Six commonly used IOL injection systems were examined. Our results suggested that the recommended 2.2 mm incision cannot be treated as a universal threshold. Quicker IOL insertion may reduce wound damage. It was also recommended to advance IOL injector via its minor axis, and to cut the tear preferably along the circumferential direction due to tissue orthotropy. This study provides useful information and a deeper insight into the potential for mechanical damage to the corneal wound in cataract surgery.

Keywords: energy release rate; finite element analysis; intra-ocular lens (IOL) injection system; linear fracture mechanics; tissue damage.

FIGURE 1

In a 2D infinitely large cornea tissue piece, a incision cut by a blade of length 2a was subjected to a injector, which expanded the tissue to an Mode I opening.

FIGURE 2

Sketch of a large 2D plate with a transverse tear of length 2a under a uniformly distributed stress σ ₀ at each edge. Note that only left half of the problem was conducted in the FE simulation. The insert shows the designed FE mesh generation, where the crack tip was surrounded by a sweeping contour area for ERR calculation.

FIGURE 3

Energy release rates for an isotropic large plate plotted against the incision length 2a at three incision speeds given CT (black lines) and U injection systems (blue lines). Results at fast speed are in solid lines, medium speed in dashed lines and slow speed in dotted lines. The corresponding critical energy release rates G _c (red lines) are also given for reference. The six junctions points between same type of lines represent the critical lengths 2a _c .

FIGURE 4

ERRs plotted against the incision length 2a in ±50% moduli at fast incision speed. Note that G _c is plotted as a reference.

FIGURE 5

Numerical result of (A) the maximal principal in-plane stress and (B) values of ERR under 10 contours near the crack tip. Note that the first three contour integrals were neglected.

FIGURE 6

The comparison between FE numerical solutions (black dots) and analytical solutions (black line).

FIGURE 7

Sketch of fibril orientation adopted from (Pandolfi, 2020). The cornea is composed of bundles of collagen fibrils oriented in orthotropic manner.