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Published in final edited form as: J Biomech. 2020 Nov 10;115:110127. doi: 10.1016/j.jbiomech.2020.110127

Altered stress field of the human lens capsule after cataract surgery

Caleb C Berggren 1, Kurt A Ameku 1, Ryan M Pedrigi 1
PMCID: PMC7856179  NIHMSID: NIHMS1648435  PMID: 33223144

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: lens capsule, intraocular lens, biomechanics, computational modeling, hyperelasticity

1. Introduction

The lens capsule of the eye has two roles throughout a typical person’s lifespan. In youth, it encapsulates and molds the underlying lens fibers to allow precise focusing of light onto the retina, a process called accommodation. With age, accommodative function declines in the development of presbyopia due to lens stiffening (Heys et al., 2004) and an anteriorly/inward shift of the ciliary muscle (Strenk et al., 1999). Most people completely lose the ability to accommodate by 55 years of age. Concurrently, cataracts start to become prevalent with an incidence rate that continuously increases to over 70% by 75 years of age (Klein et al., 1998). This natural breakdown of the lens fibers with age often leads to their replacement with a prosthetic intraocular lens (IOL), which is implanted into the remnant lens capsule during cataract surgery. Thus, the second role of the lens capsule in life is to house an IOL. Biomechanics is important in both roles. While numerous studies have modeled the normal lens capsule and underlying fibers to investigate accommodation (Burd et al., 2002; David et al., 2017; Ljubimova et al., 2008) and presbyopia (Hermans et al., 2008), little modeling work has assessed the mechanics of the lens capsule after cataract surgery. This is surprising as cataract surgery is arguably the most medically relevant application of lens capsule mechanics and is the most common ophthalmic surgical procedure (Reyes Lua et al., 2016) with over 3 million performed annually in the United States alone (Wang et al., 2016).

Cataract surgery places a permanent hole in the anterior lens capsule through which the quasi-spherical native lens fibers are (typically) replaced with a flat IOL. Modeling can aid in optimizing the mechanical design of IOLs to mitigate complications such as IOL dislocation. More importantly, modeling can also aid in the advancement of IOLs with an accommodative feature (AIOLs) that functions through tractions exerted by the remnant accommodative apparatus. The goal of AIOLs is to restore youthful accommodative power, but these lenses are hindered by the fibrotic response of the remnant lens epithelial cells to surgery that can cause visual disturbances to the patient (e.g., posterior capsule opacification). Although the rates of capsule fibrosis are particularly high in AIOLs (Ong et al., 2014), even 10% of patients with monofocal IOLs, which are considered highly successful at preventing fibrosis, experience visual disturbances within 7 years after surgery (Chang et al., 2013). These errant cellular behaviors can last indefinitely and may be driven by the permanent disruption to the mechanical environment of the lens capsule during surgery (Pedrigi and Humphrey, 2011). Hence, rigorous characterization of this altered mechanical environment may lead to improved prosthetic lens designs.

To our knowledge, only three modeling studies have assessed any aspect of lens capsule mechanics after cataract surgery. One study modeled small segments of the anterior portion of the post-surgical lens capsule to examine the rim stability of the permanent hole created during surgery using a continuous circular capsulorhexis (CCC) versus femtosecond laser, demonstrating better stability of the CCC (Reyes Lua et al., 2016). The other two studies came from our group. The first quantified the altered stress field of the anterior capsule with placement of a CCC, while maintaining the pressure due to the underlying lens fibers (Pedrigi et al., 2007). The other examined the evolution of the stress field of an axisymmetric (1-D) model of the anterior lens capsule (without an implant) over time after cataract surgery using a growth and remodeling framework (Pedrigi and Humphrey, 2011). This latter work showed that the nearly stress-free state of the lens capsule after surgery is only partially resolved over time (Pedrigi and Humphrey, 2011). While these studies are important, the models do not consider the entire lens capsule or the interaction with an implant. Therefore, this study introduces a fully 3-D finite element model of the entire post-surgical human lens capsule that employed regionally-varying anisotropic hyperelastic mechanical properties. We report changes from normalcy in the capsule stress field after cataract surgery with implantation of a tension ring and, separately, an IOL.

2. Methods

2.1. Mechanical properties

2.1.1. Lens capsule

We previously performed in situ inflation testing of the anterior portion of normal human lens capsules and observed a nonlinear elastic and regionally anisotropic mechanical behavior. The degree of anisotropy increased from the pole to the equator resulting in increasing circumferential and decreasing meridional stiffness (Pedrigi et al., 2007). These mechanical behavior data were used to compute biaxial mechanical properties for a membrane (2-D) hyperelastic constitutive model using the Fung strain energy function (Pedrigi et al., 2007). Herein, we employed a 3-D form of the strain energy function given by the Holzapfel model, wherein the strain energy function, W, can be written as (Gasser et al., 2006):

W=C10(I1−3)+k1k2{exp[k2(κI1+(1−3κ)I4−1)2]−1}, (1)

where C10 is the ground matrix stiffness, k1 is the stiffness of the fiber families, k2 is a dimensionless material parameter, κ signifies the in-plane distribution of the fibers, and I1 and I4 are the first and fourth invariants of the right Cauchy-Green tensor, respectively. The invariants are given by

I1=λ12+λ22+λ32,I4=λ12cos2γ+λ22sin2γ, (2)

where γ represents the angle of each fiber family about the circumferential direction (we assumed two fiber families to be embedded symmetrically, which renders γ the same and leads to the given form of the constitutive model). λ1, λ2, and λ3 are the principal stretches in the circumferential, meridional, and thickness directions, respectively (Heistand et al., 2005; Pedrigi et al., 2007). The material parameters were obtained through a fit to mechanical behavior data derived from our defined 2-D Fung model using a nonlinear regression in MATLAB. Since the lens capsule exhibits increasing anisotropy from the pole to the equator, this process was repeated at 500 meridional locations (~10 μm increments). Parameters were then manually calibrated to optimize the fit to previously reported inflation (Pedrigi et al., 2007) and uniaxial (Krag et al., 1997) mechanical behavior data (Appendix A). The posterior capsule was prescribed the same mechanical properties as the anterior region (Table 1) (Krag and Andreassen, 2003b). Finally, the lens capsule was assumed to have a density equivalent to type IV collagen, 1.05x10−3 g/mm3 (Pedrigi and Humphrey, 2011), and considered nearly incompressible since soft tissues are mostly water (the lens capsule is immersed in aqueous humor and contains hydrophilic proteoglycans).

Table 1.

Holzapfel constitutive model parameters for the lens capsule and thickness for the anterior (AThk) and posterior (PThk) portions as a function of meridional distance from the pole (Dist).

Dist (mm) AThk (μm) PThk (μm) c10 (kPa) k1 (kPa) k2 k γ(°)
0.00 13.85 3.90 75.00 6931.42 28.97 0.23 45.00
1.60 18.92 5.45 75.00 4754.87 29.73 0.23 41.97
2.63 21.95 10.80 75.00 3978.01 30.53 0.23 39.90
5.28 14.67 14.67 75.00 6524.23 29.63 0.23 35.20
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2.1.2. Tension ring and intraocular lens

The IOL model was based on a single-piece Alcon AcrySof monofocal IOL made of hydrophobic acrylic with an overall length of 13 mm, optic diameter of 6 mm, and thickness of 0.43 mm (Nejima et al., 2006; Werner et al., 2018). The tension ring model was based on a HumanOptics Koch capsule measuring ring (used to measure contraction of the capsular bag based on the observed distance between the appendixes) made of polymethyl methacrylate (PMMA) with a diameter of 12 mm and thickness of 0.2 mm (Tehrani et al., 2003). Since both implants undergo small strains (<1%), we used a linearly elastic constitutive model with elastic moduli of 12 MPa and 3.2 GPa for the acrylic (Akinay and Laredo, 2012) and PMMA, respectively. A Poisson’s ratio of 0.37 and a density of 1.188x10−3 g/mm3 were used for both implants.

2.2. Finite element modeling

Model creation, meshing, and finite element analysis (FEA) were performed in Abaqus (2019). The lens capsule was meshed with 4-node reduced integration shell elements (S4R), while the implanted tension ring and IOL were meshed with 8-node 3-D continuum elements (C3D8). The final mesh density for each simulation was identified using a convergence test when the mean stresses along a meridian of the capsule differed by <2% and the mean displacement of either the capsule pole or equator (for pressure or post-surgical simulations, respectively) differed by <1%. Regionally-varying mechanical properties were implemented by modifying each Abaqus input file with a custom MATLAB program. A brief description of each model is given below. Further details are provided in Appendix A.

2.2.1. Model of the native lens capsule in situ

The stress-free configuration of the native lens capsule was modeled as a flattened circular membrane with a small gap between the anterior and posterior portions of 0.52 mm (Fig. 1A). The equatorial diameter was 10.56 mm (Dick et al., 2014; Tehrani et al., 2003) and a regionally varying thickness profile was obtained from a fit using MATLAB to previously reported measurements of a representative 55-year-old human lens capsule (Fisher and Pettet, 1972) (Fig. 1B). The in situ configuration of the lens capsule was obtained by imposing a hydrostatic pressure of 2 mmHg (Fig. 1C), which is based on previous observations of the pressure required to initiate separation of the lens capsule from the underlying lens fibers during inflation testing (Pedrigi and Humphrey, 2011). The traction exerted by the zonules in the disaccommodated state was approximated as 0.816 kPa and directed radially outwards (Stachs et al., 2006) from a continuous region 1 mm above and below the equator (the associated force was 60 mN (Hermans et al., 2006)). Finally, in addition to examining the stress field in the in situ configuration (at 2 mmHg), this model was also used to simulate our previously reported inflation testing of human anterior lens capsules (mean age of 67 years) from 5 to 35 mmHg (Pedrigi et al., 2007). Simulations were iteratively performed and results compared to the raw empirical data to calibrate the Holzapfel model parameters.

Fig. 1.

Fig. 1.

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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.

2.2.2. Model of a lens capsule specimen under uniaxial tension

An additional calibration of the Holzapfel parameter, κ, was performed by iterating a finite element simulation of a 1x10 mm lens capsule strip (oriented circumferentially) under uniaxial tension to a maximum stretch of 1.25. This lens capsule strip was endowed with the mechanical properties obtained at a meridional position of 1.6 mm from the pole (Table 1) to allow comparison to previously reported uniaxial testing data of an anterior capsule specimen obtained from a 65-year-old donor (Krag et al., 1997).

2.2.3. Model of the post-surgical lens capsule with implants

The reference configuration of the post-surgical models were also prescribed as flattened circular membranes with a small gap between the anterior and posterior portions of 0.4 mm and 0.63 mm for the tension ring (thickness of 0.2 mm) and IOL (thickness of 0.43 mm), respectively. This allowed the post-surgical lens capsule to be in apposition to the implant, thus representing the state of the capsule 1-2 weeks after surgery (Hayashi et al., 2002). The equatorial diameter, thickness profile, and mechanical properties of the post-surgical model were the same as used for the native model. The post-surgical model also featured a 5.2 mm diameter CCC in the anterior portion and, prior to placement of the implant, was assumed to be stress-free (Pedrigi and Humphrey, 2011). Although the zonules were not explicitly modeled, the assumed circular stress-free configuration is consistent with the stabilizing effect of the zonules after cataract surgery (Davis et al., 2009). The tension ring (Fig. 2A) was placed into the capsule by applying a traction to the appendixes to reduce its overall diameter, which was then released to allow the tension ring to unfurl and contact the capsule equator. For the IOL simulation (Fig. 2B), the haptics were compressed with an applied traction and then released to allow contact with the capsule equator.

Fig. 2.

Fig. 2.

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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).

2.2.4. Model Outputs

For all analyses, the primary readouts were the Cauchy stress tensor and the deformation gradient tensor, F. Green strain, E, was then computed via

E=12(FT⋅F−I). (3)

Both Cauchy stress and Green strain were determined with respect to the circumferential and meridional (principal) directions of the lens capsule in all simulations.

3. Results

3.1. The calibrated Holzapfel model accurately fits empirical data from inflation and uniaxial mechanical testing

To identify the optimal material parameters of the Holzapfel constitutive model used herein, we calibrated them to simulations of two previously reported mechanical behavior tests. First, we simulated hydrostatic pressure loading of the entire lens capsule (Fig. 3A) from 5 to 35 mmHg and compared to our previously reported pressure-strain data obtained in situ for the human anterior lens capsule over the same pressure range (Pedrigi et al., 2007). The calibrated model was able to capture both the isotropic response at the pole (Fig. 3B) and anisotropic response at the mid-periphery (Fig. 3C) with excellent agreement in both principal directions, circumferential and meridional. Second, we simulated a uniaxial tensile test of a rectangular lens capsule specimen oriented in the circumferential direction (Fig. 4A). Simulation results were compared to previously reported empirical data for an annular specimen excised from the mid-periphery of a human anterior lens capsule. The finite element model exhibited a very close mechanical behavior to the experimental data (Fig. 4B). Finally, to check the predictive capability of our model independent of the data used for calibration, we developed a finite element model of previously reported inflation testing of an isolated human anterior lens capsule specimen (Fisher, 1969) and found good agreement with the reported pressure-volume data (Appendix A).

Fig. 3.

Fig. 3.

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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.

Fig. 4.

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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.

3.2. The post-surgical lens capsule models predict a significantly altered stress field from native

The stress field of the disaccommodated native lens capsule was assessed by simulating the loads imposed by the lens fibers and zonules using a pressure of 2 mmHg and traction of 0.816 kPa, respectively (Fig. 5A). The anterior portion of the capsule showed an axisymmetric and nearly uniform equibiaxial stress of 67 kPa from the pole to the equator (Fig. 5B). The posterior capsule also showed a nearly equibiaxial stress field, but it was non-uniform with stresses that ranged from 307 kPa at the pole to 7 kPa at the equator with a mean of 167 kPa (Fig. 5C).

Fig. 5.

Fig. 5.

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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.

The stress field of the post-surgical lens capsule was evaluated with two implants, a tension ring and an IOL. In both cases, the circumferential and meridional stresses were substantially reduced compared to native, except at the equator. Placement of the tension ring demonstrated anterior and posterior stresses that were nearly axisymmetric, equibiaxial, and constant across the post-surgical capsule (Figs. 6 and 7). Circumferential and meridional stresses in the anterior capsule at the edge of the CCC were 16 and 0.2 kPa (−76% and −100% compared to the mean stress in the native anterior capsule), respectively, which did not change significantly until the point of contact between the tension ring and equator of the capsule. Here, stresses increased to 28 and 14 kPa (−58% and −79% compared to native), respectively (Fig. 6A-D). Similarly, posterior stresses in the circumferential and meridional directions were uniform and nearly equibiaxial over this portion of the capsule with circumferential and meridional stresses of 30 and 24 kPa (−82% and −86% compared to the mean stress in the native posterior capsule), respectively (Fig. 7A-D).

Fig. 6.

Fig. 6.

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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.

Fig. 7.

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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.

In contrast to the tension ring, placement of the IOL yielded less uniformity and, in some regions, a highly non-equibiaxial stress field (Figs. 8 and 9). The stress field was evaluated along two meridians, the first oriented to the point of contact between one of the IOL haptics and the capsule equator (M1) and the second at 90 degrees from this orientation (M2). At M1, the circumferential and meridional stresses in the anterior portion of the capsule at the edge of the CCC were −30 and −0.8 kPa (−145% and −101% compared to the mean stress in the native anterior capsule), respectively, which steadily increased to the equator. Here, the stresses were 99 and 61 kPa (+48% and −9% compared to native), respectively (Fig. 8C). The posterior capsule showed a similar trend with a mostly steady increase in circumferential and meridional stresses from the pole to equator, wherein the maximum was 105 and 87 kPa (−37% and −48% compared to the mean stress in the native posterior capsule), respectively (Fig. 9C). Away from the IOL haptic at M2, the stresses were more uniform. Here, the circumferential and meridional stresses in the anterior portion of the capsule at the edge of the CCC were 48 and 0.8 kPa (−28% and −99% compared to the mean stress in the native anterior capsule), respectively. From the CCC towards the equator, the circumferential stress steadily decreased to −5 kPa, whereas the meridional stress was nearly zero over the entire meridian (Fig. 8D). Similarly, the posterior capsule exhibited maximum stresses near the pole of 81 and 53 kPa (−51% and −68% compared to the mean stress in the native posterior), respectively, that decreased to zero at approximately 4 mm from the pole and remained constant to the equator (Fig. 9D).

Fig. 8.

Fig. 8.

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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.

Fig. 9.

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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.

4. Discussion

Modeling the mechanical interaction between the post-surgical lens capsule and implanted IOL can aid in determining IOL efficacy. This is particularly important for AIOLs, most of which leverage the mechanical mechanism of the remnant accommodative apparatus. To date, AIOLs only restore a maximum of ~2.5 diopters of power or ~20% of youthful accommodative ability (Koopmans et al., 2006; Nishi et al., 2014). One reason may be the lack of suitable modeling approaches to elucidate the associated biomechanics. Previous models of the human lens capsule have focused on the mechanics of accommodation. Most of these models have used a 2-D approach and characterized the mechanics of the lens capsule assuming a linear elastic, homogeneous, and isotropic material behavior (Burd et al., 2002; Hermans et al., 2008; Ljubimova et al., 2008). Herein, we developed fully 3-D models of the native and post-surgical lens capsule that employed the Holzapfel hyperelastic constitutive model with regional (element-to-element along the meridional direction) variations in anisotropy.

We chose the Holzapfel model because it was developed for a collagenous soft tissue (artery) and incorporates parameters with physically meaningful interpretations that can be calibrated to improve fits to both uniaxial and biaxial mechanical data (Gasser et al., 2006). Indeed, our finite element models of the native lens capsule demonstrated excellent agreement to empirical data for both inflation and uniaxial testing. This is important as it can be difficult for a constitutive model with a single set of parameters to capture behavior from multiple mechanical tests (Appendix A). Only one other study has demonstrated the ability to fit both inflation and uniaxial testing data for the lens capsule, wherein they employed a custom hyperelastic constitutive model (Burd and Regueiro, 2015). Although this model was isotropic and material parameters were held constant over the capsule (except for the use of different strain energy functions to capture a range of lower versus higher stretches), it also provided an excellent fit to isolated inflation and uniaxial data, as well as prediction of other previously reported mechanical data, including a reasonable prediction of our in situ inflation data. This study, and our observation that the Holzapfel model predicted less anisotropy of the lens capsule compared to our originally defined Fung model (Appendix A), suggests that an isotropic hyperelastic constitutive model (with homogeneous properties) may be sufficient to capture the mechanical behavior of the lens capsule. Although this may depend on the specific constitutive model chosen.

Several studies report a variety of mechanical testing approaches for the lens capsule, in general, including uniaxial (Krag and Andreassen, 2003a), isolated inflation (Fisher, 1969), and osmotic swelling (Powell et al., 2010). Yet, the overall amount of mechanical behavior data for the human lens capsule is still limited. Our previous report of in situ inflation testing of the human anterior lens capsule is the only study to evaluate anisotropy and regional heterogeneities. Thus, we calibrated our constitutive model using these inflation data and previously reported uniaxial data (Krag and Andreassen, 2003a). There is a need for more biaxial mechanical behavior data, as well as better quantification of changes in zonular insertion geometry and tractions, particularly as a function of biological variables such as sex and age.

The finite element models presented herein address the need for accurate characterization of altered mechanics of the post-surgical lens capsule with different implants relative to native. We found that both the tension ring and IOL dramatically altered the stress field of the lens capsule. However, the tension ring produced a nearly uniform stress field with circumferential and meridional stresses markedly lower than homeostatic, whereas the IOL produced a highly non-uniform stress field with mostly lower stresses compared to homeostatic, except at the point of contact between the IOL haptic and capsule equator where stress concentrations exceeded homeostatic values. Interestingly, it has been shown that implantation of a tension ring during cataract surgery reduces lens epithelial cell-mediated fibrosis (Halili et al., 2014; Menapace et al., 2000), which may result from maintaining a nearly uniform stress field, even if lower in magnitude. We have previously proposed that the long-term cellular response after cataract surgery is driven by the altered stress field (Pedrigi et al., 2007; Pedrigi et al., 2009; Pedrigi and Humphrey, 2011) and a recent study has directly demonstrated the mechanosensitive nature of porcine lens epithelial cells (Kumar et al., 2019). If the epithelial cells of the remnant lens capsule after surgery are reacting to an altered mechanical environment, implants that can induce a uniform stress field with magnitudes closer to homeostatic, particularly in the anterior portion of the lens capsule, may attenuate fibrotic cellular behaviors and the associated capsule remodeling.

In conclusion, we have created the first 3-D finite element model of the post-surgical lens capsule with an implant, providing an in silico tool to assess the performance of implanted IOLs. Our results demonstrate a dramatic perturbation to the stress field of the post-surgical lens capsule compared to native, which may be an important driver of the long-term fibrotic response of the inhabiting lens epithelial cells and associated capsule remodeling. Overall, this provides an important additional consideration in the design of IOLs, particularly those with an accommodative feature.

Supplementary Material

Appendix A. Supplementary Material

Acknowledgements

We gratefully acknowledge support for this work from the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health under grant R03EB026837. We would also like to thank Dr. Mehrdad Negahban and Dr. Jay Humphrey for helpful discussions.

Footnotes

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Conflict of Interest

None of the authors have any professional or financial conflicts of interest.

Appendix A. Supplementary material

Supplementary methods associated with this article can be found in the online version.

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Supplementary Materials

Appendix A. Supplementary Material
NIHMS1648435-supplement-Appendix_A__Supplementary_Material.pdf (3.7MB, pdf)

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