Specimens were mounted in a BioTester biaxial test system (CellScale Biomaterials Testing, Waterloo, Canada) operated in uniaxial mode (no attachments were made to the specimens in the width-wise direction). A schematic of the system is shown in Fig. 3. Hydrogels, like rubber bands and most biological materials, narrow as they stretch (an effect often described by Poisson's ratio). So as not to impede this tendency and unnecessarily complicate interpretation of the test results, load was applied to the specimens using BioRakes (BT-305-10), having five tines spaced 1 mm apart (Figs. 1 and 3). The electrochemically sharpened tips of the rake tines easily pierced the lenses, and tines with a 30 mm free length (the distance between the bent attachment points and the base to which they were mounted), unlike clamps, allow the specimen to narrow freely. If clamps had been used, they would have impeded these natural lateral narrowing motions, and they would have induced high shear stresses near the edge of the clamps. The attachment points were symmetrical with respect to the ends of the specimens and were set 11 mm apart, a position that ensured that they did not tear out of any of the various lenses. During testing, specimens were submerged in a temperature-controlled bath of Unisol 4 saline solution (Alcon, Fort Worth, TX). A small preload was applied to the specimens to ensure that a well-defined and appropriate starting configuration was used, and when multiple cycles of loading were applied, as during some of the temperature tests, this preload ensured that any specimen elongation caused by viscoelastic effects, creep, or swelling did not adversely affect the stiffness measurements. All specimens were strained at a nominal rate of 1% per second (based on initial specimen length), a rate consistent with Young et al.,25 until a nominal strain of 20 to 25% was achieved. This nominal strain, the percentage increase in the distance between the attachment points, ensured that all regions of the specimen achieved a minimum regional strain of 10%. That is to say, even the thickest (and thus stiffest) regions of the lenses stretched by at least 10%, a minimum value sought for accurate modulus calculations. Since images and stress and strain data were collected at 1 Hz, 20 to 25 sets of such data were collected from each test.
Two approaches were used to quantify the sensitivity of lens modulus to temperature. In the first set of tests, specimens of all five lens materials at −3.25 diopters (D) were tested in saline solution at 23°C and at 37°C. These tests suggested that the mechanical properties of the hydrogels might be temperature dependent, but the effect was small, and the data were obscured by specimen variability. To remove this variability, a second set of tests was performed on all five lens materials, and a 0.5N load cell was used. In this set, the lenses were tested cyclically, one stretch cycle per minute, while the temperature of the fluid bath was increased steadily from 22 to 37°C over 30 min, and then reduced back to 22°C over the next 30 min. Because of the relatively high number of cycles involved and the possibility of specimen fatigue or tearing, the magnitude of the nominal strain was reduced from 20 to 25 to 8%. In these tests only, points were not tracked and the actual moduli were not measured, but instead the slope of the force-displacement curve was documented, thus providing a relative measure of the change in stiffness with temperature.
When the more typical tests were completed, a virtual grid consisting of 11 × 10 points was superimposed on the initial image of the specimen (Fig. 4B), and the motions of all points were tracked from one captured image to the next using the BioTester digital image-correlation software (Fig. 4C). In essence, the software identifies a template that is 27 pixels square (or of similar size) and centered on the grid point to be tracked. That window shows the distinctive pattern of graphite particles in the vicinity of the imaginary grid point. The tracking software identifies a best nearby location in each subsequent image where the same pattern of light and dark occurs and takes these locations to be the sequence of new positions that the grid point occupies over time. Cumulative tracking errors were eliminated by a tracking algorithm feature that continuously references the initial image (as suggested by the aforementioned description) rather than correlating pairs of adjacent images, as is common in image-tracking algorithms. Although the algorithms used can achieve tracking precisions of ⅛ of a pixel,26 the tests reported here are considered to have typical tracking accuracies of the order of ½ of a pixel.
When the grid point locations are known over time, they can be used to calculate and map the local deformations, that is, the regional strains. To provide reliable strain estimates, a least squares procedure was used to find the strain tensor based on the initial and current positions of the four corners of each rectangular grid area.26 Only the strain in the direction of elongation is reported here. Calculating this value by least squares is similar to, but more reliable than, the following less abstract procedure: calculate the amount that the rectangular grid has elongated by taking the average amount that the points at the right end of the grid have moved to the right and subtracting from it the average amount that the points at the left end have moved to the right. Then divide this net elongation by the original spacing between the left and right grid points to obtain the strain (ε). In all cases, the resulting strain value is dimensionless, and it has the important property that if the strain in a certain neighborhood is essentially uniform, it does not depend on the size or shape of the original grid used for the calculations. Strain values were calculated for each rectangular grid area and used to construct a detailed map of the strain field27,28 over the specimen (Fig. 4D). The lenses were deemed to be sufficiently thin compared with their in-plane dimensions, and the thickness changes gradual enough that all points through the thickness could be considered to move together, making 3D tracking and strain calculations unnecessary. For the sake of completeness, we note that additional axial strains were introduced into the specimens when they were flattened during mounting. These strains were neglected because calculations based on typical lens geometries (calculations not shown) indicated that they were <1%, which is not problematic in view of the strains of ≥10% introduced during stretching and the linear character of the materials tested. Also neglected were any width variations associated with specimen preparation.
The specimens used here were designed so that the stress (σ) acting across any given cross-section was essentially uniform but could vary from one cross-section to another along the length of the specimen. Thickness changes and other factors affecting the cross-sectional area were deemed to be gradual enough that stress concentration effects could be neglected. The value of (σ) at a particular cross-section can then be estimated simply as the ratio of the load (P) applied to the end of the specimen, to the area (A) of the specimen at that cross-section. All stress calculations were based on areas measured in the undeformed configuration, and the stresses so calculated are called engineering stresses.
Finding the average thickness at any given cross-section is not trivial because the thickness is not uniform across the specimen width. Instead, it varies because the lens thickness is a function of radial distance from the lens center, and points at different locations across the specimen width are at different distances from the lens center. Finding the average thickness at a particular location involves a large number of geometric calculations, and we carried them out using 3D geometric modeling software (Solidworks Corp, Concord, MA). Steps in this procedure included transforming the thickness measurements from angular positions to distance-from-the-lens-center positions using arc-length calculations based on a radius of 8.5 mm. They also included calculating the radial distance to points off the specimen centerline using the Pythagorean theorem and determining the specimen thickness there by interpolation from the thickness vs. distance-from-the-lens-center profile (Table 1). For the −3.25 D lens reported in Fig. 2A, the centerline thickness (dashed curve) and average thickness across the specimen width (solid curve) are quite similar, but for higher power lenses, such as −8.0 D, the differences can be significant. To maximize calculation accuracy and consistency, average thickness values were used exclusively. Thus, the cross-sectional area (A) of any particular cross-section was taken to be
where (w) was the initial specimen width (5.5 mm), and the thickness was the average initial thickness (t) at that cross-section, as shown with a solid curve in Fig. 4A, and the engineering stress (σ) at that cross-section was assumed to be
Thickness changes along the length of the lens specimens were sufficiently gradual that, for analysis purposes, the specimen could be considered to consist of length segments having constant thickness equal to the value of the thickness midway along the length of each rectangular grid (Fig. 4A). It can be shown that as long as thickness varies linearly and by no more than 30% along the length of such a segment, the error introduced by this approximation is <1% (data unpublished).
A variety of mathematical models are available to describe the relationship between uniaxial strain (ε) and stress (σ). These models range from simple linear models in which a material is described by Young's modulus, to non-linear hyperelastic representations such as Mooney–Rivlin models, to complex visco-elastic models.29 The stress–strain curves for the materials tested here were found to be essentially linear for strains up to 40% (Fig. 5). That is to say, if the applied stress is doubled, the deformation also doubles. Although some of the regional strains reported here are large (up to 25%) and more advanced techniques should be used to analyze them, only the data up to 10% strain were used for modulus calculations. Based on the observed stress-strain characteristics, we chose to characterize the lens materials using Young's modulus (E).
Fig. 4 shows the deformation that occurred in a typical specimen. The deformation grid shown in Fig. 4C and the strain map reported in Fig. 4D are useful for assessing test quality. The slight peaks found at the ends of a few of the grids in Fig. 4C are likely due to rake tine effects. There was no evidence of the rake tines tearing out of the specimens or otherwise moving relative to their edges. However, even if there had been, it would not have made a large difference because all strain values were calculated from specimen motions rather than rake motions. A slight strain field asymmetry exists along the length of the specimen shown in Fig. 4D, but the strain field is smooth and symmetrical across the specimen width. The asymmetry may be due to a slight prismatic component of geometry in the specimen. In future tests, it might be useful to measure the full bilateral thickness profile of each specimen after it is cut so that more accurate thickness measures can be used in the calculations.
The lens shown in Fig. 4 is thinnest at its center, and that is the portion of the lens that elongates the most. As a consequence of the larger stretching that occurs there, specimen narrowing is also largest there. This narrowing causes both the horizontal and vertical grid lines to be slightly curved. From a mechanics point of view, it is helpful that the grid intersections remain essentially normal to each other, as this indicates that little strain energy goes into in-plane shear deformations, and that the modulus calculations are not degraded by in-plane shear effects. For lenses that were thicker in the center, the ends of the specimens elongated and narrowed more than did the center.
Stress–strain information is obtained from the material corresponding to each column of the grid at each moment that an image was captured. For example, at the instant of time captured in Fig. 4C and D, the stress in the material represented by the left-most column of the grid can be calculated using the initial width (w) of the specimen (5.5 mm), the average thickness (t) of the lens across that portion of the specimen (0.125 mm, as shown in Fig. 4A), and the load p = 0.101 N associated with that moment in time. Substituting these values into Eqn (2) gives σ = 0.14 MPa. The strain is taken to be the average of the values shown in the two corresponding mirrored columns (21.2%). These data provide a single stress–strain point (σ = 0.14 MPa, ε = 21.2%). One such data point is obtained from each of the 20 to 25 images captured per test and produces a set of points like those shown for each symbol, such as the open boxes in Fig. 5 associated with the parts of the lens that were nominally 125 μm in thickness.
Similar plots are shown in Fig. 5 for the other four pairs of columns, corresponding to regions of the lens of different thicknesses. In essence, five independent stress–strain curves have been obtained using a single tensile test. Two features of the resulting plots are immediately evident: the materials in the five areas have very similar stress–strain plots, and the stress–strain relationship is almost linear. Some of the regions of the lens experienced strains as high as 36%, and it is remarkable that the material response is still linear, especially considering the significant changes in cross-sectional area that occur at such high strains. The slopes of the stress–strain plots associated with each symbol correspond to Young's modulus for that local area of the lens and, for consistency, all modulus values were based on a straight-line fit to the stress–strain data between 0 and 10% strain.
The five Young's modulus values associated with the five regions of this lens are shown in Fig. 6 with open diamonds, the symbol for senofilcon A lenses, at the abscissa values corresponding to their thicknesses. Data from multiple repetitions and lens powers of this type are also shown, as are results from the four other lens materials. If the material properties were the same on the surface of the lens as in their interior, it would be expected that the measured Young's modulus would be independent of lens thickness. If instead, for example, a constant-thickness portion of the lens surface was less stiff than its interior, the apparent stiffness of thinner parts of the lens would be lower than that of thicker parts. To extract quantitative information about such surface layers would require further analysis. For some of the products, such as the senofilcon A lenses, the indicated material moduli are nearly independent of thickness, whereas for others, there might be a small dependence on thickness. The margin of error in the tests is such that further testing would be required to confirm whether any trends suggested by the figure are real, and to determine whether the surface treatments used in the making of certain lens types affects the mechanical properties of the surface layer enough to be detected by in-plane stretching. Indentation tests30 might also be useful for identifying surface property changes.
To investigate whether material modulus might depend on temperature, average material modulus values were calculated from data like that shown in Fig. 6 and plotted against test temperature. Fig. 7 suggests that most materials increase in stiffness as temperature falls, but owing to statistical variability inherent in the tests, meaningful differences could be demonstrated in only a few cases. When the revised protocol, in which a single specimen is loaded at multiple temperatures, was used, a much clearer picture arose of how modulus depends on temperature (Fig. 8). Table 2 reports the percentage change in modulus per degree of temperature change from room temperature, and the precision of that linear relationship is characterized by the R2 value of a best-fit line.
Fig. 9 shows how material modulus at room temperature quoted by the manufacturer of each product (from French14), Young and co-workers (at 20°C)24 and our tests (at 23°C), correlates with quoted water content. The values are in generally good agreement with each other, even though they were obtained by different test apparatus and protocols.
This study reports a novel method to determine the modulus of contact lens materials and its application to five commercial products at three optimal powers (−8, −3, and +4) and three temperatures (5, 23, and 37°C). The novel testing methodology enabled us to obtain regional property information in lenses of different optical powers, over a range of temperatures—including room and ocular surface temperature—and to examine the relationship between water content and modulus.
No conclusive evidence was found of meaningful material property variations within a single lens (Fig. 5), nor were differences found in properties from one optical power to another (Fig. 6). As shown in Fig. 8 and Table 2, material modulus was found to be relatively insensitive to temperature in the two polyhydroxyethylmethacrylate-based materials (etafilcon A and omafilcon A), but all three silicone hydrogel materials exhibited a reduction in modulus with increasing temperature, with senofilcon A and balafilcon A reducing by approximately 20%, when the testing temperature was changed from 23 to 37°C. This result is supportive of recent data investigating the effect of temperature on modulus using a differing method, in which small, but clinically significant, changes in modulus occurred with polyhydroxyethylmethacrylate-based hydrogels, but larger reductions were seen with silicone hydrogels.25 These data suggest that the modulus reported for silicone hydrogels at room temperature may be higher than that which exists in the eye, and this warrants further study.
The commonly accepted correlation between material modulus and water content,18–19,21 in which low water content materials have a higher modulus, was found to apply to four of the lens materials (Fig. 9), the exception being senofilcon A, in which the modulus was lower than that predicted from its water content. This material is the only one of those tested that includes an internal wetting agent to aid wettability,26 – 29 and it may transpire that this also reduces the modulus, but further work is required to confirm this.
The method reported in this article provided unique mechanical information on the lens materials examined. The deformation grids and strain maps (Fig. 4C, D) served a number of important roles. They made it possible to associate points in the deformed specimens with corresponding points in the undeformed configuration, so that correct thickness values could be determined and accurate modulus values calculated at multiple points along the specimen length. They also made it possible to accurately determine regional strains so that independent stress–strain plots could be obtained from multiple points along the specimen. These grids and maps were also useful for validating individual tests because if mistracked points, errors in specimen preparation or mounting, or irregularities in specimen geometry or properties had occurred, these tools had the potential to identify them.
In future tests, specimens as narrow as 3 mm might be considered. BioRakes are available for such specimens, and using narrow specimens would avoid the extra calculations needed to correct for variations in specimen thickness across its width. However, low-force load cells (0.5) would be required for such tests. That the specimens narrow considerably is evident from a comparison of Figs. 4B and 4C, confirming our initial concern that if clamps were used, significant aberrant shear stresses and strains would have been introduced at the ends of the specimens,30 and the data would have been more difficult to accurately interpret.
Future tests might focus on generalizing the techniques developed here, so that surface property changes could be identified. There is evidence that subtle mechanical property changes can occur during wear,24 and if the experimental techniques presented here were further refined and combined with a suitable mechanics analysis, perhaps supported by finite element analyses, it might be possible to identify subtle mechanical property changes in the material close to the lens surface. Indentation or microcompression testing might also be used as part of such a testing program.31
In conclusion, this article reports on a novel method to determine the mechanical properties of hydrogel materials. The results show that mechanical properties can be affected by subtle variations in composition and temperature and that modern lens materials need to be carefully designed to optimize their performance. Because the stiffness of a lens affects its mechanical interaction with the eye, testing of the kind reported here is important for assessing the efficacy of current and proposed contact lens designs and materials, especially if such designs should involve material property variations.
G. Wayne Brodland
Department of Civil and Environmental Engineering
University of Waterloo
Waterloo, Ontario N2L 3G1
The study was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). In-kind support for this study was provided by CellScale Biomaterials Testing. No funding was obtained for this research from any company involved in the manufacturing or distribution of contact lenses. We thank Sarah Guthrie for obtaining the thickness profiles of the lenses. G.W. Brodland has a financial interest in CellScale Biomaterials Testing. A portion of this work was previously presented as a poster at the British Contact Lens Association (BCLA) Conference, Manchester, England, May 2009.
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Keywords:© 2012 American Academy of Optometry
contact lenses; mechanical testing; material properties; property variations; stiffness; Young's Modulus