Altered stress field of the human lens capsule after cataract surgery

Abstract

The lens capsule of the eye is important in focusing light onto the retina during the process of accommodation and, in later life, housing a prosthetic lens implanted during cataract surgery. Though considerable modeling work has characterized the mechanics of accommodation, little has been done to understand the mechanics of the lens capsule after cataract surgery. As such, we present the first 3-D finite element model of the post-surgical human lens capsule with an implanted tension ring and, separately, an intraocular lens to characterize the altered stress field compared to that in a model of the native lens capsule. All finite element models employed a Holzapfel hyperelastic constitutive model with regional variations in anisotropy. The post-surgical lens capsule demonstrated a dramatic perturbation to the stress field with mostly large reductions in stresses (except at the equator where the implant contacts the capsule) compared to native, wherein maximal changes in Cauchy stress were -100% and -145% for the tension ring and intraocular lens, respectively. However, implantation of the tension ring produced a more uniform stress field compared to the IOL. The magnitudes and distribution of the perturbed stress field may be an important driver of the fibrotic response of inhabiting lens epithelial cells and associated lens capsule remodeling after cataract surgery. Thus, the mechanical effects of an implant on the lens capsule could be an essential consideration in the design of intraocular lenses, particularly those with an accommodative feature.

Keywords: Biomechanics; Computational modeling; Hyperelasticity; Intraocular lens; Lens capsule.

Fig. 1.

Finite element model of the native lens capsule. (A) The unloaded configuration of the model. (B) The thickness profile from the anterior pole to the posterior pole. (C) The loaded configuration of the model, where a hydrostatic pressure of 2 mmHg is applied to represent the load exerted by the underlying lens fibers in situ and a traction of 0.816 kPa is applied to an equatorial region to represent the load imposed by the zonules in the disaccommodated state.

Fig. 2.

Finite element model of the post-surgical lens capsule with implanted (A) tension ring and (B) IOL. The images show the model after simulated placement of the implants (i.e., in the deformed configuration).

Fig. 3.

Comparison of the mechanical behavior from simulated inflation testing of the anterior lens capsule to previously reported empirical data (Pedrigi et al., 2007). (A) The model at the maximum inflation pressure of 35 mmHg. Pressure versus Green strain behavior at the (B) pole and (C) mid-periphery of the lens capsule (corresponding to marker sets D and F from our previous inflation testing). Plots demonstrate the close fit of the model to the empirical inflation data in both the circumferential (C) and meridional (M) directions at both locations on the lens capsule.

Fig. 4.

Comparison of the mechanical behavior from simulated uniaxial tensile testing of an anterior lens capsule specimen (oriented in the circumferential direction) to previously reported empirical data (Krag et al., 1997). (A) The model at a maximum stretch of 1.25 (Green strain of 28.1%). (B) Cauchy stress versus Green strain behavior demonstrating the close fit of the model to the empirical data.

Fig. 5.

Cauchy stress along a meridian of the native lens capsule (highlighted in red). (A) The native lens capsule under a pressure of 2 mmHg that simulates loading by the underlying lens fibers and a traction of 0.816 kPa that simulates the load imposed by the zonules in the disaccommodated state. Cauchy stress in the circumferential (C) and meridional (M) directions as a function of meridional position (from the pole) in the (B) anterior and (C) posterior portions of the lens capsule.

Fig. 6.

Cauchy stress in the circumferential (C; S11) and meridional (M; S22) directions along the (A and B) anterior portion of the post-surgical lens capsule with implanted tension ring. (C and D) Cauchy stress as a function of meridional position showing a significant reduction in the stress field of the anterior portion of the post-surgical lens capsule (red symbols) along two meridians (M1 and M2), compared to the native stress field (black symbols). Meridional position is relative to the anterior pole for the native capsule and edge of the CCC for the post-surgical capsule.

Fig. 7.

Cauchy stress in the circumferential (C; S11) and meridional (M; S22) directions along the (A and B) posterior portion of the post-surgical lens capsule with implanted tension ring. (C and D) Cauchy stress as a function of meridional position showing a significant reduction in the stress field of the posterior portion of the post-surgical lens capsule (red symbols) along two meridians (M1 and M2), compared to the native stress field (black symbols). Meridional position is relative to the posterior pole.

Fig. 8.

Cauchy stress in the circumferential (C; S11) and meridional (M; S22) directions along the (A and B) anterior portion of the post-surgical lens capsule with implanted IOL. (C and D) Cauchy stress as a function of meridional position showing a significant reduction in the stress field of the anterior portion of the post-surgical lens capsule (red symbols) along two meridians (M1 and M2), compared to the native stress field (black symbols), except M1 at the equator where contact between the capsule and IOL causes an increase compared to native. Meridional position is relative to the anterior pole for the native capsule and edge of the CCC for the post-surgical capsule.

Fig. 9.

Cauchy stress in the circumferential (C; S11) and meridional (M; S22) directions along the (A and B) posterior portion of the post-surgical lens capsule with implanted IOL. (C and D) Cauchy stress as a function of meridional position showing a significant reduction in the stress field of the posterior portion of the post-surgical lens capsule (red symbols) along two meridians (M1 and M2), compared to the native stress field (black symbols), except M1 at the equator where contact between the capsule and IOL causes an increase compared to native. Meridional position is relative to the posterior pole.