Mechanical testing of isolated senile human eye lens nuclei

Viscoelastic properties of porcine lenses using optical coherence elastography and inverse finite element analysis

The mechanical properties of the crystalline lens are crucial in determining the changes in lens shape that occur during the accommodation process and are also a major factor in the development of the two most prevalent age-related diseases of the lens, presbyopia and cataracts. However, a comprehensive understanding of these properties is currently lacking. Previous methods for characterizing the mechanical properties of the lens have been limited by the amount of data that could be collected during each test and the lack of complex material modeling. These limitations were mainly caused by the lack of imaging techniques that can provide data for the entire crystalline lens and the need for more complex models to describe the non-linear behavior of the lens. To address these issues, we characterized the mechanical properties of 13 porcine lenses during an ex vivo micro-controlled-displacement compression experiment using optical coherence elastography (OCE) and inverse finite element analysis (iFEA). OCE allowed us to quantify the internal strain distribution of the lens and differentiate between the different parts of the lens, while iFEA enabled us to implement an advanced material model to characterize the viscoelasticity of the lens nucleus and the relative stiffness gradient in the lens. Our findings revealed a pronounced and rapid viscoelastic behavior in the lens nucleus (g₁ = 0.39 ± 0.13, τ₁ = 5.01 ± 2.31 s) and identified the lens nucleus as the stiffest region, with a stiffness 4.42 ± 1.20 times greater than the anterior cortex and 3.47 ± 0.82 times greater than the posterior cortex. However, due to the complex nature of lens properties, it may be necessary to employ multiple tests simultaneously for a more comprehensive understanding of the crystalline lens.

Mechanical Evaluation of Retinal Damage Associated With Blunt Craniomaxillofacial Trauma: A Simulation Analysis

PURPOSE

To evaluate retinal damage as the result of craniomaxillofacial trauma and explain its pathogenic mechanism using finite element (FE) simulation.

METHODS

Computed tomography (CT) images of an adult man were obtained to construct a FE skull model. A FE skin model was built to cover the outer surface of the skull model. A previously validated FE right eye model was symmetrically copied to create a FE left eye model, and both eye models were assembled to the skull model. An orbital fat model was developed to fill the space between the eye models and the skull model. Simulations of a ball-shaped object striking the frontal bone, temporal bone, brow, and cheekbones were performed, and the resulting absorption of the impact energy, intraocular pressure (IOP), and strains on the macula and ora serrata were analyzed to evaluate retinal injuries.

RESULTS

Strain was concentrated in the macular regions (0.18 in average) of both eyes when the frontal bone was struck. The peak strain on the macula of the struck-side eye was higher than that of the other eye (>100%) when the temporal bone was struck, whereas there was little difference (<10%) between the two eyes when the brow and cheekbones were struck. Correlation analysis showed that the retinal strain time histories were highly correlated with the IOP time histories (r > 0.8 and P = 0.000 in all simulation cases).

CONCLUSIONS

The risk of retinal damage is variable in craniomaxillofacial trauma depending on the struck region, and the damage is highly related to IOP variation caused by indirect blunt eye trauma.

TRANSLATIONAL RELEVANCE

This finite element eye model allows us to evaluate and understand the indirect ocular injury mechanisms in craniomaxillofacial trauma for better clinical diagnosis and treatment.

Materials characterization and mechanobiology of the eye

The eye responds to a great deal of internal and external stimuli throughout its normal function. Due to this, a mechanical or chemical analysis alone is insufficient. A systematic materials characterization is needed. A mechanobiological approach is required for a full understanding of the unique properties and function of the eye. This review compiles the mechanical properties of select eye components, summarizes mechanical and chemical testing platforms, and overviews modeling approaches. Analysis is done across studies, experimental methods, and between species in order to summarize what is known about the mechanobiology of the eye. Several opportunities for future research are identified.

A comparative study on the viscoelastic properties of human and animal lenses

A new method of compression between two parallel plates is used to measure the viscoelastic properties of whole and decapsulated human lenses and compare them with other animal species. Compressive load relaxation was performed by deforming the lens by 10% and measuring the force relaxation response for 100 s to obtain thickness, stiffness and relaxation of the induced loading force and Maxwell parameters for human, monkey, porcine and leporine whole and decapsulated lenses. Thickness and percentage loading force relaxation increased linearly with lens age, whereas stiffness and induced loading force increased exponentially. Human and monkey lenses aged at different rates. Loading force relaxation in a generalized Maxwell model was described by three time constants ranging from 1 to 1000 s. Compressive load relaxation is a very versatile method to study the viscoelastic properties of whole and decapsulated lenses and potentially also artificial accommodating lenses. The data presented in the study will help researchers choose the most suitable animal lenses based on the desired properties and age to be mimicked from the human lenses.

Stiffness gradient in the crystalline lens

BACKGROUND

While the overall stiffness of the lens has been measured in a number of studies, the knowledge about the stiffness distribution within the lens is still limited. The purpose of this study was to determine the stiffness gradient in the human crystalline lens. A secondary purpose was to determine whether the stiffness gradient depends on age.

METHODS

The local dynamic stiffness was measured in 10 human crystalline lenses (age range: 19 to 78 years). The lenses were stored at -70 degrees C before being measured. The influence of freezing on the mechanical properties has been determined in a previous study. A small oscillating probe was used to measure the local dynamic shear modulus as a measure of lens stiffness. The measurements were taken in the cross-sectional plane through the lens equator.

RESULTS

The local dynamic shear modulus varied with location for all tested lenses. The central stiffness of the oldest lens (78 years) was 10(4) times higher than the youngest (19 years) lens. The equatorial stiffness of the oldest lens was 10(2) times higher than the youngest lens. For the older lenses, the centre was 5.8-210 times stiffer than the periphery, as opposed to earlier results described by Fisher (1971), who found that the periphery was up to 3 times softer than the centre for lenses younger than 70-years-old. For the three youngest lenses (19 to 49 years), the periphery was 2.2-16.6 times stiffer than the centre.

CONCLUSIONS

The dynamic stiffness of the crystalline lens varies with location within the lens. The stiffness gradient depends on the age of the lens. The results of the 10 lenses indicate that the stiffness of both centre and periphery increase with age, but at a different rate.

Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force

Bubble-based acoustic radiation force aims to measure highly localized tissue viscoelastic properties. In the current investigation, acoustic radiation force was applied to laser-induced bubbles to measure age-related changes in the spatial distribution of elastic properties within in vitro porcine lenses. A potential in vivo technique to map lens elasticity is crucial to understanding the onset of presbyopia and develop new treatment options. Bubble-based acoustic radiation force was investigated as a technique to measure the spatial elasticity distribution of the lens in its natural state without disrupting the lens capsule. Laser-induced optical breakdown (LIOB) generated microbubbles in a straight line across the equatorial plane of explanted porcine lenses with 1mm lateral spacing. Optical breakdown occurs when sufficiently high threshold fluence is attained at the focus of femtosecond pulsed lasers, inducing plasma formation and bubble generation. A two-element confocal ultrasonic transducer applied 6.5 ms acoustic radiation force-chirp bursts with the 1.5 MHz outer element while monitoring bubble position within the lens using pulse-echoes with the 7.44 MHz inner element. A cross-correlation method was used to measure bubble displacements and determine exponential time constants of the temporal responses. Maximum bubble displacements are inversely proportional to the local Young's modulus, while time constants are indicative of viscoelastic properties. The apparent spatial elasticity distributions in 41 porcine lenses, ranging from 4 months to 5 years in age, were measured using bubble-based acoustic radiation force. Bubble displacements decrease closer to the porcine lens center, suggesting that the nucleus is stiffer than the cortex. Bubble displacements decrease with increasing lens age, suggesting that porcine lenses become stiffer with age. Bubble-based acoustic radiation force may be well-suited as a potential in vivo technique to spatially map elastic properties of the lens and guide therapeutic procedures aimed at restoring accommodation.

Can reliable values of Young's modulus be deduced from Fisher's (1971) spinning lens measurements?

The current textbook view of the causes of presbyopia rests very largely on a series of experiments reported by R.F. Fisher some three decades ago, and in particular on the values of lens Young's modulus inferred from the deformation caused by spinning excised lenses about their optical axis (Fisher 1971) We studied the extent to which inferred values of Young's modulus are influenced by assumptions inherent in the mathematical procedures used by Fisher to interpret the test and we investigated several alternative interpretation methods. The results suggest that modelling assumptions inherent in Fisher's original method may have led to systematic errors in the determination of the Young's modulus of the cortex and nucleus. Fisher's conclusion that the cortex is stiffer than the nucleus, particularly in middle age, may be an artefact associated with these systematic errors. Moreover, none of the models we explored are able to account for Fisher's claim that the removal of the capsule has only a modest effect on the deformations induced in the spinning lens.

Dynamic mechanical properties of human lenses

The purpose of this study was to determine the shear compliance of human crystalline lenses as a function of age and frequency. Dynamic mechanical analysis was performed on 39 human lenses, ranging in age from 18 to 90 years, within the frequency range of 0.001-30 Hz. The lenses were stored at -70 degrees C before being measured. The influence of freezing on the mechanical properties was determined using pairs of porcine lenses, with one lens measured directly after enucleation and the other after freezing. The measurement method had a repeatability standard deviation of 4 and 6% for the storage and loss compliance, respectively. The reproducibility standard deviation was 31 and 33% for the storage and loss compliance respectively. On average, freezing increased the storage compliance by 8% and increased the loss compliance by 32%, both depending slightly on age and frequency. The human lenses exhibited a distinct viscoelastic behavior. The storage and loss compliance depended strongly on age and decreased a factor 1000 over a lifetime. Dynamic mechanical analysis has proven to be a successful technique for characterizing the mechanical properties of the human crystalline lens. The shear compliance decreases exponentially with age.

A nonlinear finite element model of the eye with experimental validation for the prediction of globe rupture

Over 2.4 million eye injuries occur each year in the US, with over 30,000 patients left blind as a result of the trauma. The majority of these injuries occur in automobile crashes, military operations and sporting activities. This paper presents a nonlinear finite element model of the eye and the results of 22 experiments using human eyes to validate for globe rupture injury prediction. The model of the human eye consists of the cornea, sclera, lens, ciliary body, zonules, aqueous humor and vitreous body. Lagrangian membrane elements are used for the cornea and sclera, Lagrangian bricks for the lens, ciliary, and zonules, and Eulerian brick elements comprise the aqueous and vitreous. Nonlinear, isotropic material properties of the sclera and cornea were gathered from uniaxial tensile strip tests performed up to rupture. Dynamic modeling was performed using LS-Dyna. Experimental validation tests consisted of 22 tests using three scenarios: impacts from foam particles, BB's, and baseballs onto fresh eyes used within 24 hours postmortem. The energies of the projectiles were chosen so as to provide both globe rupture and no rupture tests. Displacements of the eye were recorded using high speed color video at 7100 frames per second. The matched simulations predicted rupture of the eye when rupture was seen in the BB and baseball tests, and closely predicted displacements of the eye for the foam tests. Globe rupture has previously been shown to occur at peak stresses of 9.4 MPa using the material properties included in the model. Because of dynamic effects and improvements in boundary conditions resulting from a more realistic modeling of the fluid in the anterior and posterior chambers, the stresses can be much higher than those previously predicted, with the globe remaining intact. The model is empirically verified to predict globe rupture for stresses in the corneoscleral shell exceeding 23 MPa, and local dynamic pressures exceeding 2.1 MPa. The model can be used as a predictive aid to reduce the burden of eye injury, and can serve as a validated model to predict globe rupture.

The relationship between nuclear colour and opalescence on the LOCSIII scale and physical characteristics of cataract nuclei

PURPOSE

To evaluate the compression characteristics of the human lens nucleocortex in relation to its LOCSIII clinical grading.

METHODS

Sixteen subjects undergoing planned extracapsular cataract surgery had pre-operative slit-lamp examination and assessment of cataract LOCSIII grade followed by postoperative in vitro evaluation of the nucleus with measurement of 'linear compressibility' by a purpose-designed caliper incorporating a strain gauge, enabling the derivation of a graph of nuclear compression (D (mm) against applied force (F (N)).

RESULTS

Nuclear colour correlates with the force required to compress a lens to 75% of its original depth (F75) (R = 0.625, P = 0.017). Nuclear opalescence correlates with the force required to compress a lens to 75% of its original depth (R = 0.651, P = 0.012) and inversely with linear compressibility (DeltaD/DeltaF, the slope of the graph of nuclear compression against applied force) (R = -0.610, P = 0.014). F75 is a direct and linear compressibility is an inverse related parameter of lens nucleus 'hardness'.

CONCLUSION

A new instrument is described which allows measurement of 'hardness'-related compression characteristics of the human cataract in vitro. There is a relationship between the LOCSIII clinical classification of nuclear cataracts and mechanical compression characteristics of the cataractous lens. LOCSIII classification may aid the preoperative planning of an appropriate surgical approach to an individual cataract.

Hydrogels as potential probes for investigating the mechanism of lenticular presbyopia

PURPOSE

To synthesize and characterize hydrogels with viscoelastic properties comparable to those of the natural lens.

METHODS

Hydrogels were synthesized in water by free-radical polymerization of the monomer poly(ethyleneglycol)-monomethacrylate. Three different molecular weights of poly(ethyleneglycol)-dimethacrylates were used as crosslinkers. For each crosslinker used, five different monomer-to-crosslinker weight ratios were utilized while the total mass of the reactants was kept constant. In another series, the concentration of the reactants was varied while the weight ratio of monomer to crosslinker was kept constant at 95 : 5. The percent optical transmission, equilibrium water content, moduli (elastic, shear, storage, and loss), and retardation time constant of the hydrogels were determined. In addition, endocapsular polymerization was performed in the capsular bag of porcine eyes.

RESULTS

The hydrogels examined exhibited the following ranges for viscoelastic properties: elastic modulus, 1.33-2.37 x 10(4) Pa; shear modulus, 3.35-6.72 x 10(3) Pa; storage modulus, 1.65-6.24 x 10(4) Pa. For any given hydrogel, raising its crosslinker's weight ratio increased its moduli and decreased its equilibrium water content and optical transmission. For any given monomer-to-crosslinker weight ratio, increasing the molecular weight of the crosslinker reversed these trends. Reactant concentrations increased the elastic modulus and decreased the equilibrium water content. The hydrogels formed ex vivo (in the evacuated capsular bag of porcine eyes) allowed for the clear and undistorted viewing of objects.

CONCLUSIONS

Hydrogels that exhibit physical and mechanical properties comparable to those of the natural lens were successfully identified, synthesized, and characterized, and the feasibility of endocapsular polymerization was demonstrated.

Age-related changes in the kinetics of water transport in normal human lenses

Magnetic resonance microscopy (MRM) has been used to study the kinetics of water transport in human eye lenses. Fresh lenses obtained from the Queensland Eye Bank were incubated at 34.5 degrees C in artificial aqueous humour (AAH) containing nutrients and metabolites similar to those that are present in vivo. MR images were acquired over approximately a 20 hr period following replacement of H(2)O based AAH with deuterium oxide (D(2)O) based AAH. NMR signal intensity from the lenses decreased with time corresponding to a decrease in concentration of H(2)O within the lenses. A statistically significant correlation (P<0.001) was found between the rate of NMR signal loss from the lens nuclei and increasing age of the lenses. The results show that as lenses age, there is a reduction in the rate at which water and presumably also water soluble low molecular weight metabolites, can enter the cells of the lens nucleus via the epithelium and cortex. A decrease in the rate of transport of water, nutrients and anti-oxidants (e.g. glutathione) would be expected to lead to progressive oxidative damage to lenses with age, and may ultimately contribute to presbyopia and senile nuclear cataract.