Mechanical Properties of the Human Posterior Lens Capsule

Abstract

purpose. To investigate mechanical properties of the human posterior lens capsule.

methods. Twenty-five human donor eyes were obtained from an eye bank. The age of the donors ranged from 1 to 94 years. Test specimens were prepared as tissue rings from posterior lens capsules by means of excimer laser. Capsular thickness was measured microscopically as the difference in focus between microspherules placed on the outer and inner surfaces of the capsule. The capsular rings were slipped over two pins connected to a motorized micropositioner and a force transducer and stretched at a constant rate with continuous recording of load and deformation. Data for the posterior lens capsule were compared with previously published data for the anterior lens capsule.

results. The thickness of the posterior lens capsule ranged from 4 to 9 μm and showed no significant changes with age. Ultimate mechanical strength of the posterior lens capsule decreased significantly with age. Ultimate strain ranged from 101% to 34%, ultimate load ranged from 15.9 to 1.1 mN, ultimate stress ranged from 16.1 to 1.1 N/mm², ultimate elastic stiffness ranged from 52.1 to 5.7 mN, and ultimate elastic modulus ranged from 27.4 to 3.3 N/mm². The load-strain and the stress-strain relationships in the posterior lens capsule were nonlinear, and therefore elastic stiffness and elastic modulus varied as a function of strain. In the low-strain region (0%–10% strain), elastic stiffness and elastic modulus ranged between 0.3 to 2.4 mN and 0.3 to 2.3 N/mm², respectively, and seemed to increase during the first part of life until middle age.

conclusions. Mechanical strength of the posterior lens capsule was found to decrease markedly with age. The age-related loss of mechanical strength seemed to begin earlier in the posterior lens capsule than in the anterior lens capsule. In accommodative function range (low strains), the mechanical quality of the posterior lens capsule was similar to the anterior lens capsule, which indicates that the mechanical effectiveness of the lens capsule in situ varies proportionally with capsular thickness.

Knowledge of the mechanical properties of the human lens capsule is essential for the understanding of its physiological function in relation to the accommodative function, its functional reserve in the elderly population, and its potential in relation to cataract surgery. 

Mechanical properties of the anterior human lens capsule have been investigated, ^{1 2} whereas mechanical properties of the posterior lens capsule have not yet been described quantitatively. The anterior and posterior lens capsule differ in several aspects. The posterior lens capsule is substantially thinner than the anterior capsule. ^{3 4 5} It loses its epithelial cells in fetal life ⁶ and has not been shown to increase essentially in thickness with age, in contrast to the anterior capsule. ^{3 4 5} Furthermore, the lamellar structure of the lens capsule disappears earlier with age in the posterior lens capsule than in the anterior capsule, ⁵ and differences have been described in the relative proportion of macromolecular components such as heparan sulfate proteoglycan and fibronectin. ^{7 8} This could indicate that the mechanical qualities of the anterior and posterior lens capsules are different. The present study was undertaken to investigate the mechanical properties of the human posterior lens capsule in relation to age and to compare the results with previously published data for the anterior capsule. ^{2 9}  

Materials and Methods

Twenty-five human posterior lens capsules were obtained from an eye bank. Donor age ranged from 1 to 94 years. Mean postmortem time was 44 ± 18 hours. Excluded from the study were donors with diabetes mellitus and eyes with cortical and subcapsular lenticular opacities or severe nuclear sclerosis. The posterior capsule was dissected from the lens and stored at −80°C until mechanical testing. The investigation was approved by the institutional ethics committee and adhered the tenets of the Declaration of Helsinki. 

Test specimens were prepared as tissue rings from the central part of the posterior lens capsule by an excimer laser technique. ^{2 10} A metal ring was placed on the central part of the posterior lens capsule to shape the laser output. The outer diameter of the metal ring was 3.2 mm and the width was 100 μm. Capsular thickness was measured optically as the difference in focus between latex spherules placed on the upper and the lower surfaces of the capsular rings (precision: 0.3 μm). Thickness measurements were repeated twice at eight points of the capsular rings, and the mean values were used as the average thickness of the capsular rings. The width of the capsular rings was measured with a micrometer eyepiece (precision: 1.3 μm). 

For mechanical testing, the capsular rings were slipped over two pins connected to a motorized micropositioner and a force transducer and stretched at a constant rate, with continuous recording of load (resolution: 0.01 mN) and elongation (resolution: 0.1 μm). ^{2 10} Strain values were calculated as the elongation expressed in percent of the initial length of the test specimen. 

Load-strain data showed the mechanical response of the capsular rings and reflected the mechanical effectiveness of the lens capsule in situ. The following parameters were calculated from the load-strain curves: ultimate strain (strain at failure), ultimate load (load at failure), elastic stiffness (0%–10% strain) determined as the slope of the load-strain curves from 0–10% strain, and ultimate elastic stiffness determined as the slope of the linear steepest part of the load-strain curves up to the point of failure. 

Stress values were calculated by normalizing the load values to the cross-sectional area of the capsular rings. Stress-strain data reflect the mechanical quality of the capsule tissue. The following parameters were calculated from the stress-strain curves: ultimate stress (stress at failure), elastic modulus (0%–10% strain) determined as the slope of the stress-strain curves from 0–10% strain, and ultimate elastic modulus determined as the slope of the linear steepest part of the stress-strain curves up to the point of failure. 

Data for the posterior lens capsule were compared with previously published data for the anterior capsule using the same mechanical testing procedure (67 anterior capsules obtained from eye bank eyes). ^{2 9} In eight cases, the anterior and posterior lens capsules were obtained from the same donor. In the remaining cases the donors were different. 

Data Analysis

Linear regression analyses were used to describe quantitatively the relationship between mechanical data and age for the age group 16 to 94 years. The single data point at age 1 year is discussed separately. To compare mechanical data for the posterior lens capsule with data for the anterior capsule, regression analyses were performed sequentially, testing the interaction between age, slope, and position of the regression lines, respectively. Data that showed no association with age were compared using an unpaired t-test. Data are reported as mean ± SEM. P < 0.05 was considered statistically significant. 

Results

Thickness of the posterior lens capsule ranged from 4 to 9 μm (Fig. 1) . The association between thickness and age was not significant (slope = 0.02 ± 0.01 μm per year, P = 0.06). The thickness of the posterior lens capsule was three to five times less than the thickness of the anterior capsule. 

Load-strain and stress-strain curves for anterior and posterior lens capsules from a 1-year-old child and a 74-year-old adult are shown in Figure 2 . Individual data points for the different mechanical parameters are shown in Figures 4 5 6 . 

Ultimate strain of the posterior lens capsule decreased significantly with age (range: 101%–34%; Fig. 3 , Table 1 ). The range was similar to ultimate strain of the anterior capsule (range: 108%–40%). 

Ultimate load of the posterior lens capsule decreased significantly with age (range: 15.9–1.1 mN; Fig. 4A , Table 1 ) and was three to seven times lower than ultimate load of the anterior capsule (range: 52.4–5.6 mN). Ultimate stress of the posterior lens capsule decreased significantly with age (range: 16.9–1.1 N/mm²; Fig. 4B , Table 1 ). The range was similar to ultimate stress of the anterior capsule (range: 17.5–1.5 N/mm²). 

Ultimate elastic stiffness of the posterior lens capsule decreased significantly with age (range: 52.1–5.7 mN; Fig. 5A , Table 1 ) and was two to six times lower compared with ultimate stiffness of the anterior capsule (range: 131.9–21.8 mN). Ultimate elastic modulus of the posterior lens capsule decreased significantly with age (range: 55.7–5.4 N/mm²; Fig. 5B , Table 1 ). The range was similar to ultimate elastic stiffness of the anterior capsule (range: 44.8–4.4 N/mm²). 

In contrast to the anterior lens capsule, mechanical strength of the posterior lens capsule (ultimate strain, ultimate load, ultimate elastic stiffness, ultimate stress, and ultimate elastic modulus) seemed to decrease most markedly during the first decades of life (Figs. 3 4 5 6 ; Table 1 ). The single data point at age 1 showed that ultimate strain, ultimate stress, and ultimate elastic modulus of the posterior lens capsule were similar to those parameters in the anterior capsule in a 1-year-old child. Statistical evaluation of data points for the age group 16 to 94 years showed that ultimate strain, ultimate stress, and ultimate elastic modulus at age 16 were significantly lower for the posterior lens capsule than the anterior capsule. No significant differences were detected at age 85 (Table 1) . 

As with most biological materials, the load-strain curves for the posterior lens capsule showed a high degree of nonlinearity (Fig. 2) , and therefore elastic stiffness and elastic modulus of the posterior lens capsule (slope of the curves) varied with strain. In the low-strain region (0%–10% strain) elastic stiffness of the posterior lens capsule ranged from 0.3 mN to 2.4 mN (Fig. 6A) and elastic modulus ranged from 0.3 to 2.3 N/mm² (Fig. 6B) . Data for the anterior lens capsule have been described by a two-straight-line model, which showed that elastic stiffness (0%–10% strain) and elastic modulus (0%–10% strain) of the anterior lens capsule increases until age 35, after which stiffness remains stable. ⁹ For a comparison between the anterior and posterior lens capsules, data for the posterior lens capsule also were analyzed separately for age groups aged less than 35 years or 35 years or more. The five data points for the posterior lens capsule aged less than 35 years indicated an increase in elastic stiffness (0%–10% strain) and elastic modulus (0%–10% strain) of the posterior lens capsule during the first part of life, similar to the anterior capsule (slope_{elastic stiffness} = 0.03 ± 0.008 mN per year, P = 0.04 and slope_{elastic modulus} = 0.02 ± 0.003 N/mm² per year, P = 0.02). In the age group 35 years and older, elastic stiffness (0%–10% strain) and elastic modulus (0%–10% strain) of the posterior lens capsule showed no significant changes with age. Elastic stiffness (0%–10% strain) of the posterior lens capsule was significantly lower than in the anterior capsule (mean difference: 5.7 ± 0.3 mN, P < 0.001), whereas the elastic modulus (0%–10% strain) of the posterior lens capsule was not significantly different from the anterior capsule (mean difference: 0.25 ± 0.1 N/mm², P = 0.07). 

Discussion

The mechanical strength of the human posterior lens capsule was found to decrease markedly with age. Extensibility (ultimate strain) of the posterior lens capsule decreased by a factor of two during the life span, and the forces required to break the posterior lens capsule were found to decrease by a factor of five. 

Load data obtained in the present study are of particular interest from a functional point of view, because they reflect the mechanical effectiveness of the lens capsule in situ, which is influenced by its thickness. On the whole, load data depend on the cross-sectional area of the test specimens. In the present study, the test specimens were cut very uniformly and the variation in cross-sectional area therefore mainly was caused by the variation in thickness of the lens capsule. ¹⁰ The load data (Figs. 4A 5A 6A) showed that the mechanical effectiveness of the posterior lens capsule was less than that of the anterior capsule, in accordance with the fact that the posterior lens capsule was thinner than the anterior capsule (Fig. 1) . 

Stress data express the mechanical quality of the capsule tissue. The stress data obtained from the 1-year-old child may indicate that the mechanical qualities of the anterior and posterior lens capsules are similar at birth. Statistical analysis of stress data in the group aged 16 to 94 years showed that the mechanical quality of the posterior lens capsule at age 16 was significantly less that that of the anterior capsule, whereas no significant difference was found in the oldest age group (Table 1) . On the assumption that the data obtained from the 1-year-old child are representative for this age group, aging of the lens capsule seems to initiate earlier in the posterior lens capsule than in the anterior capsule. 

Synthesis and growth of the posterior lens capsule are not understood. In contrast to the anterior lens capsule, which is synthesized by the lens epithelium ^{11 12} and continues to grow and increase in thickness throughout most of life, ^{1 2 3 4 5} the posterior capsule loses its epithelial cells in fetal life. ⁶ It has been suggested that the posterior lens capsule is synthesized and secreted by nucleated cortical lens fibers or by anterior epithelial cells and secreted into the posterior aspects of the lens during the first part of life, after which the production of posterior lens capsule substance is supposed to cease. ^{5 11 12 13} Audioradiographical studies of the postnatal growth of the rat lens capsule have shown that the posterior rat lens capsule grows and increases in thickness after birth. Growth of the posterior rat lens capsule, however; seems to cease earlier in life than growth of the anterior capsule. ^{11 12} Regarding the postnatal growth of the human posterior lens capsule, there is no consensus in the literature. Saltzmann ³ and Fisher and Pettet ⁴ did not find any change in thickness of the posterior lens capsule with age. Seland ⁵ reported a slight increase in thickness of the posterior lens capsule with age, and the present study showed a slight, nonsignificant increase in the thickness of the posterior lens capsule with age (0.3% increase per year corresponding to 1 to 2 μm at age 75, compared with 1.3% increase per year of the anterior lens capsule corresponding to approximately 15 μm at age 75 ² ). These studies together indicate that thickness of the human posterior lens capsule does not increase essentially after birth in contrast to thickness of the anterior capsule. ^{2 3 4 5} Growth of the human posterior capsule therefore seems to cease earlier in life than growth of the anterior capsule, in accordance with the fact that capsular lamination, which seems to be a genuine sign of relatively active capsular production, is lost in the human posterior capsule before the age of 6, whereas it starts disappearing later in the anterior capsule (in middle age). ⁵ Different growth patterns of the anterior and posterior lens capsules may influence their mechanical properties in different ways, as indicated in the present study. 

The mechanical quality of a material is usually characterized by the material constant, Young’s modulus of elasticity, which is a measure of stiffness in simple extension (stress increment per unit strain) and refers to the slope of the stress-strain curve. As a material constant, Young’s modulus of elasticity applies to linear stress-strain relationships in accordance with Hook’s law. ¹⁴ Similar to the anterior lens capsule, the posterior capsule, however, was found to exhibit a nonlinear stress-strain relationship (i.e., elastic stiffness varied as a function of strain). Therefore, to calculate Young’s modulus of elasticity, the stress-strain curves for the posterior lens capsule were divided into two regions, where the stress-strain relationship could be considered to be linear: a low-strain region (0%–10% strain), which has importance in relation to accommodation, and a high-strain region, corresponding to the linear part of the stress-strain curve up to the point of failure, which is of interest from a surgical point of view (Fig. 2) . In the accommodative function range (<10% strain) the elastic modulus of the posterior lens capsule was comparable with the elastic modulus of the anterior lens capsule. This indicates that the mechanical quality of the anterior and posterior lens capsules at low strains (accommodative function range) was similar and shows that the forces required to strain the anterior and posterior part of the lens capsule vary proportionally with capsular thickness. 

The relative roles of capsular versus internal lens substance elasticity in determining the lens shape during accommodation have been under debate since Helmholtz published his relaxation theory of accommodation in 1855. ^{15 16 17 18 19} In the accommodative process, it is the interaction between the lens capsule and the lens fibers that determines the shape of the lens, and in this respect the lens capsule fulfills an important role in transmitting the effect of changes in the ciliary ring diameter to modify the shape of the lens. The present study indicates that the forces that could be transmitted to the lens substance per unit thickness of the anterior and posterior lens capsules are equal. That the thickness of the posterior capsule is three to five times less than the thickness of the anterior capsule (Fig. 1) indicates that less force can be transmitted to the posterior part of the lens substance during accommodation, in accordance with the fact that the shape and position of the posterior part of the lens change less during accommodation. ^{20 21}  

The lens capsule has been proposed to play an important role during accommodation, in molding the lens substance into its accommodated form—that is, energy is applied to the lens capsule when stretched in the unaccommodated state and released during accommodation. ^{15 16 17} Fisher ¹ found that the elastic modulus (elastic stiffness) of the anterior lens capsule decreases with age, indicating that the lens capsule loses its capacity to transmit energy to the lens substance with age, and he concluded that a decrease in the elastic modulus (stiffness) with age in part could explain the loss in accommodative amplitude. Fisher’s data, however, presumably refer to a nonphysiological deformation level, because he ignored the first, flat part of the stress-strain curves and defined his starting point by extrapolation from the steep, linear part to zero stress. In contrast to Fisher’s study, our data for the anterior and posterior lens capsules ^{2 9} showed that the elastic modulus of the lens capsule—pertaining to the accommodative function range (first part of the stress-strain curve)—increases during the first part of life, in accordance with the calculations performed by van Alphen and Graebel. ²² This indicates that the lens capsule becomes increasingly effective with age in transmitting forces to the lens substance. 

In conclusion, the mechanical strength of the posterior lens capsule was found to decrease markedly with age. The age-related loss of mechanical strength seemed to begin earlier in the posterior lens capsule than in the anterior lens capsule. In accommodative function range (low strains), the mechanical quality of the posterior lens capsule was similar to the anterior lens capsule, which indicates that the mechanical effectiveness of the lens capsule in situ varies proportionally with capsular thickness. 

 Supported by grants from The Danish Association for Prevention of Blindness and the Family Foundation of Erna and Aage Jensen.

 Submitted for publication January 28, 2002; revised July 12, 2002; accepted July 23, 2002.

 Commercial relationships policy: N.

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

Thickness of the human posterior lens capsule in relation to age compared with thickness of the anterior capsule. ²

Figure 2.

 

Load-strain curves (A) and stress-strain curves (B) of the posterior and the anterior lens capsules obtained from a 1-year-old child and a 74-year-old adult. The load-strain curves (A-1, A-2) show the mechanical response of the capsular rings and reflect the mechanical effectiveness of the lens capsule in situ. The stress-strain curves (load data corrected for cross-sectional area; B-1, B-2) show the mechanical quality of the capsule tissue (material properties). The load-strain curves clearly show that the mechanical effectiveness of the posterior lens capsule is substantially less than in the anterior capsule, whereas the stress-strain curves indicate that the mechanical qualities of the anterior and posterior lens capsules are almost identical in these two samples.

Figure 3.

 

Ultimate strain of the human posterior lens capsule in relation to age compared with that of the anterior capsule. ²

Table 1.

 

Mechanical Strength of the Posterior Lens Capsule Compared to the Anterior Lens Capsule in Relation to Age

Variable	Regression Coefficient (± SEM)*					Difference between Posterior and Anterior Lens Capsule
		Posterior Capsule (n = 24)	Anterior Capsule (n = 69)	Difference	Age 1 Year, †	Age 20 Years, ‡ (Diff ± SEM)	Age 85 Years, ‡ (Diff ± SEM)
Ultimate strain (%)	−0.22 ± 0.08	−0.49 ± 0.04	0.28 ± 0.08	−1.9	−17.8 ± 3.7	0.2 ± 3.0
	(P = 0.008)	(P < 0.001)	(P = 0.002)		(P < 0.001)	(P = 0.96)
Ultimate load (mN)	−0.05 ± 0.01	−0.46 ± 0.03	0.42 ± 0.05	−33.1	−39.1 ± 2.4	−11.9 ± 1.9
	(P = 0.005)	(P < 0.001)	(P < 0.001)		(P < 0.001)	(P < 0.001)
Ultimate stress (N/mm2)	−0.05 ± 0.01	−0.13 ± 0.01	0.08 ± 0.01	−0.5	−5.4 ± 0.5	−0.01 ± 0.4
	(P < 0.001)	(P < 0.001)	(P < 0.001)		(P < 0.001)	(P = 0.90)
Ultimate stiffness (mN)	−0.11 ± 0.03	−0.87 ± 0.06	0.76 ± 0.11	−73.2	−85.6 ± 4.6	−35.9 ± 3.8
	(P = 0.009)	(P < 0.001)	(P < 0.001)		(P < 0.001)	(P < 0.001)
Ultimate elastic modulus (N/mm2)	−0.12 ± 0.02	−0.26 ± 0.01	0.14 ± 0.02	10.9	−9.0 ± 1.0	0.4 ± 0.8
	(P < 0.001)	(P < 0.001)	(P < 0.001)		(P < 0.001)	(P = 0.66)

Figure 4.

 

(A) Ultimate load and (B) ultimate stress of the human posterior lens capsule in relation to age compared with that of the anterior capsule. ²

Figure 5.

 

(A) Ultimate elastic stiffness and (B) ultimate elastic modulus of the human posterior lens capsule in relation to age compared that of the anterior capsule. ²

Figure 6.

 

(A) Elastic stiffness (0%–10% strain) and (B) elastic modulus (0%–10% strain) of the posterior lens capsule in relation to age compared with data obtained for the anterior lens capsule. ^{2 9}

The authors thank Medico-Legal Institute and the Eye Bank of Aarhus University Hospital for providing the donor eyes.