Summary
We present an automated method for characterizing the effective elastic modulus of an ocular lens using a compression test.
Abstract
The biomechanical properties of the ocular lens are essential to its function as a variable power optical element. These properties change dramatically with age in the human lens, resulting in a loss of near vision called presbyopia. However, the mechanisms of these changes remain unknown. Lens compression offers a relatively simple method for assessing the lens' biomechanical stiffness in a qualitative sense and, when coupled with appropriate analytical techniques, can help quantify biomechanical properties. A variety of lens compression tests have been performed to date, including both manual and automated, but these methods inconsistently apply key aspects of biomechanical testing such as preconditioning, loading rates, and time between measurements. This paper describes a fully automated lens compression test wherein a motorized stage is synchronized with a camera to capture the force, displacement, and shape of the lens throughout a preprogrammed loading protocol. A characteristic elastic modulus may then be calculated from these data. While demonstrated here using porcine lenses, the approach is appropriate for the compression of lenses of any species.
Introduction
The lens is the transparent and flexible organ found in the eye that allows it to focus on different distances by changing its refractive power. This ability is known as accommodation. The refractive power is altered due to the contraction and relaxation of the ciliary muscle. When the ciliary muscle contracts, the lens thickens and moves forward, increasing its refractive power1,2. The increase in refractive power allows the lens to focus on nearby objects. As humans age, the lens becomes stiffer and this ability to accommodate is gradually lost; this condition is known as presbyopia. The mechanism of stiffening remains unknown, at least in part due to the difficulties associated with the biomechanical characterization of the lens.
A variety of methods have been employed to estimate lens stiffness and biomechanical properties. These include lens spinning3,4,5, acoustic methods6,7,8, optical methods such as Brillouin microscopy9, indentation10,11, and compression12,13. Compression is the most accessible experimental technique as it can be performed with simple instrumentation (e.g., glass coverslips14,15) or a single motorized stage. We have previously shown how the biomechanical properties of the lens may be rigorously estimated from a compression test16. This process is technically challenging and requires specialized software not readily accessible to lens researchers interested in relative stiffness measurements. Therefore, in the present study, we focus on accessible methods for estimating the elastic modulus of the lens while accounting for lens size. The elastic modulus is an intrinsic material property related to its deformability: a high elastic modulus corresponds to a stiffer material.
The test itself is a parallel plate compression test and can therefore be performed on suitable commercial mechanical testing systems. Here, a custom instrument was constructed comprised of a motor, linear stage, motion controller, load cell, and amplifier. These were controlled using custom software which also recorded time, position, and load at regular intervals. Pig lenses do not accommodate but are easily accessible and inexpensive17. The following method was developed to incrementally compress the eye lens and quantify its elastic modulus. This method can be easily replicated and will be useful in the study of lens stiffness.
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Protocol
Pig eyes were obtained from a local abattoir. No ethical committee approvals were required.
1. Lens dissection (Figure 1)
- Remove all the surrounding tissue from the pig eyes and excess flesh from the sclera, until only the optic nerve remains. Use curved forceps and small dissection scissors to complete this process. Use the nerve as an anchor to hold the eye during dissection.
- Using a scalpel, make a short circumferential cut at the limbus, then another at the equator.
NOTE: This step is performed in this order to avoid damaging the lens and capsule. - Insert microscissors into the cut at the limbus and remove the cornea by lifting the cornea with fine blunt-tipped forceps while cutting around the circumference of the cornea.
- Remove the iris by lifting using blunt-tipped forceps and cut away with micro-scissors.
- Insert dissection scissors into the equatorial cut, then cut circumferentially around the entire equator until the sclera is bisected.
- Once the cut is completed, remove the posterior portion of the sclera. Remove the vitreous gently with forceps, leaving minimal remnants to avoid damaging the lens. If required, cut the vitreous humor coronally to allow the posterior to pull away from the lens and anterior segment.
- Make a meridional cut through the sclera from anterior to posterior using microscissors.
- Beginning at the new meridional cut through the sclera, use microscissors to cut the zonules away from the lens. Using the weight of the lens or edge of the dissection dish, gently stretch the zonules when pulling the lens and sclera apart slightly, allowing the microscissors to cut between the lens and ciliary body, through the zonules, and around the circumference of the lens. This will isolate the lens without damaging the lens capsule if done correctly.
- If desired, remove the capsule using forceps to puncture the capsule at its equator, then peel away the capsule using two forceps.
- Place the lens in phosphate-buffered saline (PBS). Visually inspect the lens for any damage prior to mechanical testing.
2. Lens compression-with/without lens capsule (Figure 2)
NOTE: All steps here with the exception of steps 2.1 and 2.4 are computer-controlled.
- Obtain or construct a parallel plate compression apparatus having a 50 gram-force capacity load cell with the ability to measure displacement on the order of 1 µm.
- Program the motorized stage and load the cell to perform the loading regimen described below (e.g., Supplemental File 1).
- Nearly fill a square box of 1 5/8 inches x 1 5/8 inches with PBS and place it on the compression platform.
- Lower the upper plate into contact with the lower plate to determine the lower limit of motion and absolute gap height.
- Raise the upper plate by ~15 mm.
- Center the lens in the box, taking care that the equatorial plane is horizontal.
- Lower the upper plate close to, but not in contact with, the upper surface of the lens.
- Initiate motion to move the upper plate into contact with the lens, using force feedback with a contact threshold of 3 mN.
- Commence data recording upon determination of contact, recording time, position of the upper plate relative to the lower plate, and force at 500 Hz.
- Apply a preconditioning loading where the lens is compressed by 2.5% of its initial height three times, then 5% three times, then 7.5% three times at a rate of 1%/s.
- Hold the position of the upper plate constant for 1 min after preconditioning.
- Apply a 15% compression at a rate of 1%/s, followed by unloading at the same rate.
- Continue the unloading motion until the upper plate has traveled an additional 2% of the unloaded lens thickness away from the bottom plate to ensure the lens is de-adhered from the upper plate.
3. Estimation of lens modulus
- Estimate the thickness of the lens based on the instrument's gap at the point of contact. Alternatively, use image analysis to measure the thickness from a photograph taken before testing.
- Compute the elastic modulus E using the Hertz model for compression of a sphere between parallel plates (equation [1]; Supplemental File 2).
(1)
Where R is the radius of curvature at the point of contact (assumed equal to half the lens thickness); F is the compression force reported by the load cell;
is the Poisson's ratio (assumed equal to 0.5 corresponding to an incompressible material); and u is the downward approach of the upper stage from the point of contact. Note that the elastic modulus and Poisson's ratio are material properties indicating respectively the intrinsic stiffness of the lens and the lens' relative compressibility.
NOTE: This method neglects any role of the lens capsule but does approximately account for the size of the lens, allowing comparison between species.
(1)
is the Poisson's ratio (assumed equal to 0.5 corresponding to an incompressible material); and u is the downward approach of the upper stage from the point of contact. Note that the elastic modulus and Poisson's ratio are material properties indicating respectively the intrinsic stiffness of the lens and the lens' relative compressibility.Subscription Required. Please recommend JoVE to your librarian.
Representative Results
Six porcine lenses were compressed, first with the capsule intact, then after careful removal of the capsule. Thickness values were 7.65 ± 0.43 mm for encapsulated lenses and 6.69 ± 0.29 mm for decapsulated lenses (mean ± standard deviation). A typical loading history is shown in Figure 3. The resulting force-displacement curves were well-fitted by the Hertz model (i.e., they had a force proportional to the displacement raised to the power of 1.5; Figure 4). This was true for both the encapsulated and decapsulated lenses.
Lenses were first compressed by 15% of their unloaded thickness with an intact capsule, then after removal of the capsule. Axial compression by 15% of the initial thickness has previously been shown not to cause damage to the lens sutures18. Decapsulation resulted in a significant decrease in effective elastic modulus (n = 6; p = 0.0138; Figure 5).
Figure 1: Dissection technique. (A) The extraocular tissues are removed. (B) A circumferential cut is made at the limbus. (C) A circumferential cut is made at the equator. (D) The cornea is removed. (E) The iris is removed. (F) The eye is bisected at the equator, then (G) the vitreous is removed, leaving (H) an annular ring containing the lens, ciliary body, and zonules still attached to the sclera. (I) A meridional cut is made through the sclera to (J) give access to the zonules, (K) which are cut away leaving (L) the encapsulated lens. Please click here to view a larger version of this figure.
Figure 2: Compression testing apparatus. (A) Schematic and (B) photograph of the lens compression apparatus. Please click here to view a larger version of this figure.
Figure 3: Applied loading history for an encapsulated porcine lens. Top: Displacement history. Bottom: Force history. Please click here to view a larger version of this figure.
Figure 4: Typical force-displacement data fitted with the Hertz model. Left: Data for an encapsulated porcine lens. Right: Compression data for the same lens after decapsulation. Please click here to view a larger version of this figure.
Figure 5: Box and whisker plot of encapsulated and decapsulated porcine lens effective elastic moduli. The effective modulus of the encapsulated lenses was significantly higher than those of the decapsulated lenses (p = 0.013), indicating that the presence of the capsule can substantially alter the effective stiffness of the lens. Data are for six lenses. Please click here to view a larger version of this figure.
Supplemental File 1: MATLAB application to control the lens compression apparatus. Please click here to download this File.
Supplemental File 2: MATLAB function to estimate the elastic modulus from force-compression data. Please click here to download this File.
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Discussion
Lens compression is a versatile method for estimating lens stiffness. The procedures described above allow comparison between lenses of different species and different sizes. All deformations are normalized against lens size, and the calculation of the elastic modulus approximately accounts for lens size. The effective modulus is considerably higher than the modulus reported previously for the porcine lens4,7,11,19, at least in part due to the use of thickness rather than the radius of curvature: the porcine lens' polar radii of curvature are significantly larger than half the thickness20.
The simple analysis (i.e., use of the Hertz model) presented here has several key limitations. First, it does not account for the presence of the lens capsule. It has been shown that the presence of the capsule may significantly alter the biomechanical properties of the lens16,21. Therefore, this method is best applied to decapsulated lenses. This is particularly important when comparing species in cases where the capsule may have significantly different thicknesses or biomechanical properties. This method also assumes that the lens is mechanically homogeneous; we and others have previously shown that this is generally not the case for porcine or human lenses4,5,6,10,11,22. Thus, it is best to consider the elastic modulus value calculated as an effective modulus, which is presumably related to the volumetric average of the spatially varying modulus within the lens. The Hertz model assumes that the lens is linearly elastic, whereas it is known to be viscoelastic; thus, the simple analysis proposed here is incapable of providing information regarding lens viscoelasticity. Previous work has also shown that the method and duration of lens storage prior to testing can alter lens properties4; all porcine lenses were therefore tested immediately following dissection upon arrival in the lab.
The difference in the force-displacement measurements is due to noise from the load cell amplifier: removal of the capsule makes the force measurements considerably lower, and therefore the signal-to-noise ratio is lower. The assumptions used in deriving the Hertz model importantly include that the sphere is a homogeneous material; therefore, the effective elastic modulus is somehow averaging the deformability of the lens and its capsule when the capsule is present. This makes inter-species and inter-age comparisons particularly difficult because a porcine lens has a capsule ~60 µm thick, whereas a mouse or human lens has a capsule in the 5-15 µm thick range. The elastic modulus of the capsule may also vary with species and age, though these dependencies are unknown. Thus, while it is possible to get a less noisy fit with the capsule, the comparison is inherently confounded by the presence of the capsule-this is the reason we recommend performing the test without the capsule.
Finally, the effective modulus was computed assuming that the radius of curvature was half the thickness of the lens. This is true only for a spherical lens; the porcine lens is significantly aspherical and so the effective modulus values are considerably higher than they would be if the radius of curvature was used instead. This last assumption can be overcome by measuring the radii of curvature, though this can be complicated for the lower surface which is always flat due to contact with the lower plate. It is also less important for more spherical lenses such as murine lenses. Better still is the use of inverse finite element analysis to ascertain the mechanical properties of the lens16.
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Disclosures
The authors have no conflicts of interest to declare.
Acknowledgments
Supported by National Institutes of Health grant R01 EY035278 (MR).
Materials
| Name | Company | Catalog Number | Comments |
| Curved Medium Point General Purpose Forceps | Fisherbrand | 16-100-110 | |
| Galil COM Libraries | Galil Motion Control | ||
| High Precision Scalpel Handle | Fisherbrand | 12-000-164 | |
| Linear Stage | McMaster-Carr | 6734K4 0.125" | |
| Load Cell | FUTEK | LSB200-FSH03869 | |
| Load Cell Amplifier | FUTEK | IAA300-FSH03931 | |
| MATLAB | The Mathworks, Inc. | ||
| Microprobe | Surgical Design | 22-079-740 | |
| Miniature Self Opening Precision Scissors | Excelta | 63042-004 | |
| Motion Controller | Galil Motion Control | DMC-31012 | |
| Motor | Galil Motion Control | BLM-N23-50-1000-B | |
| Straight Hemastats | Fine Science | NC9247203 | stainless steel, 14cm |
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