Age-Related Differences in the Elasticity of the Human Cornea

Abstract

Purpose.: The goal of this study was to determine age-related variation in the elasticity of the human cornea using nondestructive means.

Methods.: Organ cultured human corneoscleral buttons were studied. Changes in strain were measured with a radial shearing speckle pattern interferometer after an increase in intraocular pressure from 15.0 to 15.5 mm Hg. Changes in central corneal displacement were calculated by integration, and a bulk corneal Young's modulus was derived by mathematical analysis.

Results.: Fifty corneas, including 17 pairs, were studied. Donors were aged between 24 and 102 years (mean, 73.1); 29 (58%) specimens were from male donors and 21 from female donors. Young's modulus of the cornea increased with age, with the line of best fit indicating an approximate doubling from 0.27 MPa at age 20 years (95% confidence interval, 0.22–0.31) to 0.52 (0.50–0.54) MPa at age 100 years (R ² = 0.70).

Conclusions.: The stiffness of the human cornea increases by a factor of approximately two between the ages of 20 and 100 years. This variation is relevant to the algorithms used to predict the response to incisional and ablative refractive surgery and will also affect the formulas used to calculate intraocular pressure by applanation.

Ocular biomechanics is a field of increasing importance to ophthalmologists. Overt corneal biomechanical problems have long been seen in conditions such as keratoconus and more recently have been seen as ectasia after corneal refractive surgery. ¹ In the former, the properties of the corneal collagen are changed such that the system loses rigidity over time and becomes deformed, whereas in the latter, the loss of tissue during ablation weakens the structural constraints, ² increasing fatigue and sometimes resulting in progressive deformation. In refractive surgical practice patients with preexisting ectasia are usually identified and excluded from treatment. However, individual variations in biomechanical integrity and postoperative wound healing mean that not all potentially vulnerable patients can be identified before surgery. 

There is considerable, but mostly indirect, evidence to suggest that the biomechanical properties of the cornea vary with age. For example, youth is a risk factor for both iatrogenic ectasia ³ and keratoconus progression, ^4,5 and the incidence of keratoconus decreases with age. ⁶ Quantifying the biomechanical properties of the cornea is difficult, even in the laboratory, but the available evidence supports the concept that the cornea stiffens with age because of increases in Young's modulus, ⁷ the ocular rigidity coefficient, ^8,9 and cohesive tensile strength. ¹⁰ The exception to these data was a decrease in corneal hysteresis ^{11 –13} obtained with a system that measures corneal biomechanics (Ocular Response Analyzer (ORA; Reichert Inc., Depew, NY). 

Optical interferometric techniques are well suited to measuring corneal biomechanical properties because they are noncontact, highly sensitive, and capable of simultaneously recording information from across the whole test surface. ^14,15 Holographic interferometry (HI) has been used to qualitatively assess keratoplasty wound integrity in vivo ¹⁶ and to quantitatively investigate the effect of radial keratotomy incisions in the laboratory. ¹⁷ Our group has described how electronic speckle pattern interferometry (ESPI) can be used to quantify the effect of microkeratome flap creation on the displacement response of the sheep cornea. ² Although these techniques were able to detect very small changes in displacement, the major limitation of both HI and ESPI is extreme sensitivity to environmental disturbances such as heat and vibration. This sensitivity requires separate image and reference laser beams to form interferograms that necessarily have a relatively long path separation during which phase decorrelation can occur. 

Shearing interferometers are much more resistant to physical disturbance than either HI or ESPI instruments, because they do not use a reference beam. Instead, interferograms are produced by interference of the image beam with a second, transformed copy of itself. ^{18 –20} In radial-shearing, speckle-pattern interferometry (RSSPI) the compound interferograms created comprise two concentric, differentially magnified images of the test surface (Fig. 1). The two images contain information on the topography of the surface location that changes as the applied pressure is altered. The differential magnification between the two images allows a mathematical analysis that detects changes in radial strain. ¹⁵  

Figure 1.

 

The optical arrangement of the RSSP interferometer used in this study.

The purpose of this study was to develop a RSSP interferometer for corneal measurement and to use the device to determine the biomechanical properties of the human cornea as a function of age. 

Methods

The tenets of the Declaration of Helsinki were respected. Ethical approval was obtained from St Thomas's Hospital Research Ethics Committee. The experimental specimens comprised 34 paired and 16 unpaired human corneoscleral buttons. These were obtained from UK Corneal Transplant Service (Bristol), immersed in Eagle's minimal essential medium containing 5% dextran, 2% fetal bovine serum, penicillin 100 U/mL, streptomycin 0.1 mg/mL, and amphotericin B 0.25 μg/mL. 

On arrival in the laboratory the specimens were placed in minimal essential medium supplemented with dextran 5% (molecular weight, 500,000) and an antibiotic mixture of penicillin (100 U/mL), streptomycin (0.1 mg/mL), and amphotericin B (0.25 mg/mL) (all Sigma-Aldrich, Poole, UK) before being placed in a humidified incubator with 5% carbon dioxide at 37°C. 

After 24 hours the corneoscleral buttons were rinsed in culture medium without dextran and central corneal thickness (CCT) was measured ultrasonically (DGH-550 Pachette 2, DGH Technology, Exton, PA) before specimens were mounted in Barron artificial anterior chambers (AAC; Katena Products, Denville, NJ). To provide the corneal endothelium with its physiological environment, we filled the internal reservoir of the AAC with culture medium and maintained it at hydrostatic pressure of 15.0 mm Hg (2000 Pa) with a digital manometer with a resolution better than 1 Pa. ² A Petri dish with a hole in its base was glued to the locking ring of the AAC and filled with culture medium to the level of the limbus thus exposing the epithelial surface to moist air. 

Defining the mechanical properties of a material involves determining its response to change in physical load. Applied load is ordinarily characterized as stress (σ) which, assuming that the load is uniformly distributed and the material homogenous, is defined as  

 

The physical consequence of stress is conventionally expressed in terms of proportional change in dimension or strain (ε), where  

 

Perhaps the single best descriptor of a material's biomechanical properties at low strain is its Young's modulus (E), which is defined as the ratio of stress to strain or  

 

and so is dependent on both the material's physical properties and dimensions. It is important to note that, in most biological tissues, including the cornea, the relationship between stress and strain is nonlinear, and stiffening occurs as strain is increased.^21–23  

The optical pathways of the RSSPI instrument constructed are shown in Figure 1. The device was placed on a vibration-isolating optical table. A polarizing beam splitter was used to render the viewing and illumination systems coaxial, while minimizing unwanted internal reflections. Corneas were illuminated normal to their apex by a 532 μm 50-mW frequency-doubled, diode-pumped YAG laser (GLC-050-S; CrystaLaser LC, Reno, NV) with its beam expanded by a 40× microscope objective. The laser tube was rotated to maximize transmission through the polarizing beam splitter toward the cornea. 

From Figure 1, it can be seen that light reflected from the surface of the cornea was split via a second beam splitter, such that 50% passed through a biconcave lens (focal length [f] 150 mm) before falling on a concave mirror (f = −250 mm) and being reflected into the camera while the other 50% was directed onto a plane mirror before being reflected back into the camera. This arrangement provided radial shear, with the relative size of the images, or the shear ratio (μ), being 0.83. 

Interferograms were captured on a digital camera with 960 × 960 active pixels and 12-bit resolution (model MDC 1004; Imperx, Boca Raton, FL). To permit phase shifting and enable negative and positive strain changes to be distinguished, we mounted the plane mirror on a calibrated piezoelectric transducer (Piezosystems, Jena, Germany). The process of interferogram acquisition, including phase shifting and interferogram unwrapping, was managed by a commercial system and software (StrainMapper ver. 24b software; Laser Optical Engineering, Ltd., Loughborough, UK, running on a PXI-1002 computer; National Instruments, Newbury, UK). Interferograms were saved in TIFF format, and unwrapped phase-change data matrices were stored as tab-separated text files. 

Ideally, speckle-pattern interferometry requires that the tested surfaces reflect light and be optically rough. By contrast, the cornea is highly transparent with little reflection or scatter. To obtain measurements from specimens with properties similar to those of the cornea, industrial surfaces are coated with white aerosol sprays so as to both roughen them and render their surfaces opaque. Although such sprays can be applied to the cornea in the laboratory, ² they could not be used in vivo, because the solvents they contain would damage the epithelial surface. A variety of alternative surface coatings were trialed during the present study, including powders, paints, and membranes. It was determined that covering the corneal surface with a stretched layer of polytetrafluoroethylene tape (Dupont Chemicals, Wilmington, DE) gave results identical with those when the aerosol spray (Ardrox; Brent, UK) used in a previous ESPI study of the cornea ² was used. 

Before measurement, the corneoscleral buttons were mounted in the AAC and maintained at a pressure of 15.0 mm Hg for at least 5 minutes, to equilibrate. ¹⁷ During the measurement process, the corneas were stressed by an increase in anterior chamber hydrostatic pressure from 15.0 to 15.5 mm Hg over approximately 2 to 3 seconds, a magnitude and rate similar to that occurring in vivo with the cardiac pulse. ²⁴ Interferograms were captured immediately, and the measurement process was repeated five times for each cornea. 

In an RSSP interferometer, phase change at each point in the compound speckle pattern reflects the rate of change in displacement or strain between its superimposed constituent points. If the x–y plane is defined as viewing the cornea en face and the z-axis as perpendicular to that plane (i.e., viewing into the corneal depth), then, when both the viewing and illumination axes are parallel to the z-axis  

 

where r is the radial distance from the shear center, μ is the shear ratio (0.83), λ is the wavelength of the illuminating laser (532 μm), and φ is the measured phase change. ¹⁵ Change in central cornea displacement (z-axis) can then calculated by integration. 

If the cornea is assumed to be part of a thin-walled, isotropic sphere, then its Young's modulus (E) can be obtained by mathematical analysis based on thin-shell theory. ²⁵ Specifically,  

 

where the assumed constant v (Poisson's ratio) is 0.49, ²⁶ R (anterior corneal radius of curvature) is 7.5 mm, R _i (transverse radius of the AAC) is 6 mm and η is sin⁻¹(R _i /R), and the measured variables d is apical rise, p is pressure change, t is corneal thickness, and β is t is corneal thickness and β is

$\sqrt{R/t}.\sqrt[4]{1-{\upsilon }^2}$

. 

The five data matrices containing phase-change information for each cornea were imported into a commercial program (MatLab r2007a; The MathWorks Inc., Natick, MA) and averaged to produce a single data file. This compound result was converted into a strain map using equation 1 and then integrated to determine change in central corneal displacement, thus permitting Young's modulus to be calculated with equation 2. Individual CCT measurements were used in all calculations. 

Results

All donors were free from known ophthalmic disease and were aged between 24 and 102 years (mean, 73.1). Twenty-nine of the donors (58%) were male. Postmortem times ranged between 5 and 27 days but did not significantly affect the results of subsequent experiments. Measurements were obtained from all corneas and took approximately 3 minutes. No consistent differences were apparent between the first and last interferograms recorded from each cornea. Mean (SD) CCT was 531 (25) μm. A representative strain map and displacement plot are shown in Figure 2. 

Figure 2.

 

Representative corneal strain map after an increase in intracameral hydrostatic pressure from 15.0 to 15.5 mm Hg (top) and displacement plot map obtained by integration (bottom).

Measured change in corneal apical displacement after the rise in chamber pressure from 15.0 to 15.5 mm Hg is plotted against donor age in Figure 3. Individual displacements ranged between 3.1 and 6.0 μm (typical SD, 0.7–0.8 μm) with displacements being higher in specimens from younger donors. There was a strong concordance and no statistically significant difference between measurements obtained from paired eyes. To avoid correlation bias, one measurement from each pair of eyes was excluded at random from subsequent correlation analyses. After the date were obtained, the line of best fit for the relationship between displacement and age was  

 

with a correlation coefficient (R ²) of 0.79. This formula predicts that the increase in human corneal apical displacement after an increase in hydrostatic pressure from 15.0 to 15.5 mm Hg is 6.05 μm (95% confidence interval, 5.69–6.42) at age 20 decreasing to 3.31 μm (3.11–3.51) at age 100. 

Figure 3.

 

Increase in corneal apical displacement against donor age after an increase in intraocular pressure from 15.0 to 15.5 mm Hg. (●) Measurements from unpaired corneas and one randomly selected measurement from paired specimens. (○) Measurements obtained from fellow eyes. The line of best fit for first eyes (solid line) has the equation: apical displacement (in micrometers) = 6.84 – 0.0035(age in years); R ² = 0.84. Dashed lines: 95% confidence limits; dotted lines: measurement prediction boundaries.

Calculated values of corneal Young's modulus are plotted against donor age in Figure 4. Again there was an association between this parameter and age. Young's moduli ranged between 0.299 and 0.579 MPa, with higher values found in specimens from older donors. When one corneoscleral button of each pair was excluded in the same manner as before, the line of best fit for the relationship between Young's modulus and age was  

 

with R ² = 0.70. This formula predicts that human corneal Young's modulus is 0.27 (95% confidence interval, 0.22–0.31) MPa at age 20 and almost doubles to 0.52 (0.50–0.54) MPa by age 100. 

Figure 4.

 

Relationship between corneal Young's modulus (E) and age. (●) Measurements from unpaired corneas and one randomly selected measurement from paired specimens. (○) Measurements obtained from fellow eyes. The line of best fit for first eyes (solid line) has the equation Young's modulus = 0.0031(age in years) + 0.21; R ² = 0.74. Dashed lines: 95% confidence limits; dotted lines: measurement prediction boundaries.

Discussion

Clinically it has long been appreciated that corneal biomechanical properties change with age, but attempts to quantify this variation have been complicated by almost all previous studies having analyzed either isolated strips of tissue or having used supraphysiological forces to distort intact globes. This is the first report to characterize the biomechanical responses of intact corneas to a physiological range of pressure transients using RSSPI. 

It was found that apical corneal displacement after an intraocular pressure change equivalent to that occurring in vivo due to the cardiac cycle decreased in a linear manner with age from approximately 0.25 MPa at age 20 to 0.5 MPa at age 100. These values are toward the lower end of previously published values of human corneal Young's modulus, which have varied from 0.15 to 57 MPa, ^{7,22,23,27 –34} a range that is greater than is physiologically plausible. Studies that have used strip extensometry or ultrasonography have given rise to higher values ^{27,28,30 –35} while studies inflating intact globes to greater than physiological pressures determined values more closely related to those of the present study. ^7,22,23,29 Higher values from extensometry studies may reflect the greater load necessarily supplied to the tissue in this type of experiment, resulting in measurements being obtained at greater strain and so derived from the upper limits of the nonlinear stress strain relationship. ^21,22 By contrast the convergence of measurements in this study with others obtained from intact globes may reflect the importance of integrating measurements over the whole intact cornea. 

The only other published study to have investigated the change in human corneal Young's modulus occurring with age was that of Elsheikh et al. ⁷ It is difficult to compare directly that study and the current investigation, because the previously published data included only data from subjects aged between 50 and 95 years and used rates of pressure change that were nonphysiological. If the increase in Young's modulus was between 11% to 16% per decade as claimed, then the change between 20 and 100 years would be between 2.1- and 3.3-fold, comparable to the doubling determined in the present study. However, when only the physiological measurements are considered, Young's modulus more than doubles every 30 years, a very much greater rate of increase. By contrast, Randleman et al. ¹⁰ found that the interlamellar cohesive tensile strength of the cornea increases in a linear manner by 38% between the ages of 20 and 78 years, a rate of increase about half that calculated here. 

Using different approaches Ytteborg ⁸ and Pallikaris et al. ⁹ both calculated what they termed the ocular rigidity coefficient of living human eyes. ^8,9 Each found there to be a positive linear correlation with age, but this reached statistical significance only in the latter study in which ocular rigidity doubled between the ages of 20 and 100 years, ⁹ identical with the present study. Although this variation in ocular rigidity coefficient almost exactly mirrors the change in corneal Young's modulus determined in this study, it is important to note that there is not a direct relationship between the two parameters because ocular rigidity is affected by noncorneal factors, such the mechanical properties of the sclera. 

It has been claimed that the biomechanical properties of the entire cornea are almost entirely determined by the highly ordered ultrastructure of the stroma,³⁶ and so age-related stiffening almost certainly reflects the changes known to occur in this layer.³⁷ Within the stroma, the parallel collagen fibril bundles, each composed of many collagen molecules, are grouped into lamellae that are believed to run from limbus to limbus, parallel to the corneal surface.³⁸ As the cornea ages, the collagen fibrils increase in diameter, due to both collagen deposition and expansion of intermolecular Bragg spacing, and lengthen as a result of reduced molecular tilting.³⁷ These latter two changes reflect increased glycation-mediated collagen cross-linking, manifested as replacement of free thiol groups (SH) with disulfide bonds (SS), a process that occurs in all connective tissues.³⁹ It is important to note that the mechanism responsible for age-related cross-linking may differ from those currently being exploited clinically when cross-linkage is brought about using activated oxygen radicals derived from ultraviolet irradiation of riboflavin-saturated corneas.⁴⁰  

Although the use of RSSPI is well established in mechanical engineering, ^14,15 and other optical interferometric techniques have been used to study the cornea in both the clinic ¹⁶ and laboratory, ^2,17 this was the first investigation to use RSSPI for ophthalmic purposes. The greatest advantage that RSSPI has over other measurement techniques is that it is capable of simultaneously detecting small mechanical changes over the whole area of the cornea while at the same time being much more resistant to environmental disturbances than no-shear optical interferometric techniques. 

The optical arrangement of RSSPI results in these instruments' being impervious to nonradial mechanical changes and causes their sensitivity to strain to increase linearly from the center toward the periphery (equation 1). However, the topography of the cornea is such that purely radial mechanical changes cannot occur and the central cornea is the region that experiences the least out-of-plane strain change, meaning that it is believed that neither of these factors have a significant effect on the results obtained. Both of these limitations could be overcome if a double lateral shearing method was used and interferograms simultaneously recorded along different axes before being recombined by vector analysis. ⁴¹  

More general limitations of this study relate both to the experimental approach used and to the method of data analysis. Although the corneas studied were ex vivo, the organ culture system used has been shown to permit physiological wound healing. ⁴² The effect of severing the corneoscleral sample from the structural integrity of the posterior globe may have weakened the system but clamping specimens to the AAC chamber posterior to the limbus may have to some extent mitigated such problems. Although the delay between mounting the corneas in the AAC and obtaining measurements was sufficiently long to eliminate any significant creep response, ¹⁷ it would have permitted the test corneas to cool toward room temperature. Providing that hydration is maintained, this effect is generally assumed to be nonsignificant in the eye, but there is evidence that such cooling can increase stiffness by up to 10% in ligaments. ⁴³  

In common with all studies that have used thin-shell theory to analyze the mechanical response of the cornea, it was necessary to regard it as a purely elastic, mechanically isotropic, rotationally symmetric part sphere of uniform thickness that is fixed at the limbus. ^7,44 Although attempts have been made to model the cornea in a more complex way during finite element analysis, the uncertainty surrounding the true values of corneal characteristics such Young's modulus ^{7,22,23,27 –35} and Poisson ratio ^45,46 means that this process also requires assumptions to be made that can greatly affect the results obtained. For these reasons the thin shell model is generally accepted to be a reasonable approximation, especially when surgical incisions are not considered. ^7,44  

Given that radial-shearing wavefront interferometry measurements can be performed in vivo, ^{47 –49} it is expected that RSSPI technology can also be translated into clinical practice and provide valuable diagnostic information. In parallel with work toward this goal, it would be of interest to perform further laboratory experiments on a larger number of specimens, to permit multivariate analysis of the effect of factors such as gender, CCT and tissue storage time on corneal stiffness and to develop a means of quantifying regional strain changes so as to compare objectively different surgical techniques. At present the major constraint on the introduction of a clinical device is the development of procedures to enhance the reflections from the corneal surface and allow actual measurements in the living eye. 

In summary, this study is the first to have used the optical interferometric technique RSSPI to quantify age-related human corneal biomechanical change. The results showed that human corneal stiffness approximately doubled between the ages of 20 and 100. This information will allow the development of more accurate algorithms for refractive surgery in relation to the age of patients and affect interpretation of applanation intraocular pressure measurements. 

Footnotes

 Supported by research grants from the Royal College of Surgeons and TFC Frost Charitable Trust.

Footnotes

 Disclosure: N.E. Knox Cartwright, None; J.R. Tyrer, None; J. Marshall, None

The authors thank Val Smith (Bristol Eye Bank).