Optical coherence tomography is a technique that uses infrared light that is reflected to a detector from different depths in a tissue to create an image. By applying an acoustic force and measuring the change in displacement of the tissue, it is possible to measure the tissue stiffness [8, 9]. The weighted displacement of a tissue is obtained after correction for the displacement of the speaker and out of phase vibrations (viscoelasticity) as a function of frequency. The human mechanovibrational spectra of corneas from 20 normal control subjects were previously reported [10]. They were used in this study for comparison with the measurements made on fresh whole pig eyes. The pig eyes were studied intact as well as after the cornea, lens and iris were dissected away from the remaining components of the eyes. 15 fresh pig eyes were obtained from Spear products (Coopersburg, PA, USA) and kept on ice during transport for testing. The pigs weighed 220 to 280 lbs and were 6 to 12 months old. Pig eyes were studied using vibrational optical coherence tomography (VOCT) within 4 hours of harvesting at Ben Franklin Tech Ventures (Bethlehem, PA, USA). It was noted the cornea thickness increased within several hours of harvesting the eyes even when the eyes were kept on ice.

OCT image collection was accomplished using a Lumedica Spectral Domain OQ 2.0 Labscope (Lumedica Inc., Durham, NC, USA) operating in the scanning mode at a wavelength of 840 nm. The device generates a 512 $\times$ 512 pixel image with a transverse resolution of 15 micrometers and an A-scan rate of 13,000/sec. All gray scale OCT images were color coded to enhance the image details. The images were used to locate exactly where the VOCT measurements were made.

The OQ Labscope was modified by adding a speaker 2 inches in diameter (A106 Pro, JYM Electronics Co., Ltd, Shajing Town, China) to vibrate the tissue at 55 dB sound pressure density in the VOCT studies [9, 10, 11, 12]. The Labscope was also modified to collect and store single unprocessed raw OCT image data that was used to calculate sample displacements (amplitude information) from amplitude line data. The data was processed using MATLAB software R2020a version 9.8 (Mathworks, Natick, MA, USA) as discussed previously [12, 13]. The displacement of the tissue is detected by measuring the frequency dependence of the deformation based on the reflected infrared light and filtered to collect only vibrations that were in phase (elastic component) with the sound input. The vibrations for each frequency were collected and stored on the cloud for further analysis as a mechanovibrational spectrum. The mechanovibrational spectral peaks were normalized by dividing by the largest peak in each spectrum to correct for speaker orientation and varying sound levels that occur during data collection on different samples.

The resonant frequency of a tissue component is defined as the frequency at which the maximum in-phase displacement is observed in the amplitude data. The measured resonant frequencies are converted into elastic modulus values using a calibration equation (Eqn. 1) developed based on in vitro uniaxial mechanical tensile testing and VOCT measurements made on the same tissue at the same time as reported previously [8, 9, 10, 11, 12, 13]. The resonant frequency of each sample is determined by measuring the displacement of the tissue resulting from transversely applied sinusoidal audible sound driving frequencies ranging from 30 Hz to 300 Hz, in steps of 10 Hz. Since the measurements were made at 10 Hz steps the resonant frequencies were observed to occur at intervals of +/- 10 Hz. For this reason, the location of the peaks on some of the samples differ by as much as 20 Hz. The peak frequency (the resonant frequency), f${}_n$, is defined as the frequency at which the displacement is maximized after the vibrations due to the speaker are removed.

(1)$$E\times d=0.0651\times \left(f{n}^2\right)+233.16$$

Since soft tissues have a density very close to 1.0, Eqn. 1 is valid for most tissues found in the body; where the thickness d is in m and is determined from OCT images, $f{n}^2$ is the square of the resonant frequency, and E is the tensile elastic modulus in MPa as discussed previously [8, 9, 10, 11, 12, 13]. Eqn. 1 was used to calculate the modulus values and is an empirical equation based on calibration studies using decellularized human skin (dermal collagen) tested in uniaxial tension and simultaneously by VOCT [8, 9, 10, 11, 12, 13]. The elastic modulus measured using VOCT is a materials property at low strains since the viscous component of the behavior is only 2% to 3% of the total modulus at the resonant frequency [14] and the modulus is unchanged at strains less than about 7% for collagenous materials [14].

Pig eye studies were conducted in vitro using a microscope stand on which the tissue to be examined was placed [12, 13]. Whole pig eyes were examined after the fat, orbital muscles and conjunctiva were removed by dissection. The cornea, sclera, limbus, and lens were studied in the intact eye; the eye was then dissected, and the cornea, lens, and iris were excised for VOCT measurements.

All resonant frequencies and moduli were compared using a paired two tailed Student’s t-test. All differences were considered statistically significant if the p value was at a 0.05 level or less.

Our previous published results [10] suggest that the mechanovibrational spectrum of human cornea in vivo has peaks at 80, 120, 150 and 250 Hz (Figs. 1,7) which is similar to those found in the central cornea of pig eyes in vitro (Fig. 2). The cornea is made up of cellular and acellular components. The cellular components include the epithelial cells, keratocytes, and endothelial cells [15] and appear to contribute to the 80 Hz peak. The acellular components of the cornea include collagen and glycosaminoglycans that make up the stroma and tangentially oriented collagen fibrils at the corneal-limbus interface of the human eye [16, 17]. There are 200 to 250 distinct lamellae in the stroma; each layer is arranged at right angles relative to fibers in adjacent lamellae. Anterior corneal stromal rigidity appears to be particularly important in maintaining the corneal curvature [18]. However, these lamellae must be connected or else they could easily be peeled away from each other under mechanical loading. Based on our VOCT results it is hypothesized that the 150 Hz peak may represent the anterior cornea collagen fibrils since it has been reported that the anterior layers have a lamellar density some 50% greater than those in the deep layers [19]. These layers may contribute to the diamond shaped pattern of the interface between the collagen fibrils of the limbus and stroma proposed [18, 19, 20]. It is postulated that the 120 Hz peak represents the collagen fibrils of the posterior lamellae; these must be connected to the fibrils in the anterior lamellae to form a continuous mechanical network or separation of the layers would occur under mechanical loading. The 250 Hz peak may represent vibrations from the corneal-scleral junction (limbus) where the collagen fibrils from the limbus are believed to fuse with the corneal lamellae (see Fig. 8 for a model). Since the sclera and cornea fuse at the limbus, the stiffness of these components must be similar to prevent modulus mismatches that could lead to mechanical failure at the interfaces between the cornea and limbus and the limbus and sclera.

Fig. 7.

Bar graph comparing normalized weighted displacement versus frequency for pig cornea. A comparison of pig cornea (excised cornea), reversed excised pig cornea (posterior side up) and excised posterior cornea (posterior cornea only) is shown. Note the changes in peak heights after the different corneal treatments. The resonant frequencies depicted at 80 Hz actual represent values determined from 80 to 95 Hz, while the ones depicted at 250 were collected from 240–250 Hz.

Fig. 8.

Diagrammatic representation of the forces acting on the eye. This diagram illustrates the connections between collagen fibrils in the cornea and limbus that stabilize the corneal-limbus-scleral junction. The forces acting on the eye include the force of gravity, atmospheric pressure (A), tension in the sclera (B), lid pressure (not shown), the forces due to the orbital muscles (not shown), ciliary muscle (in the non-accommodation mode not shown), atmospheric pressure, and intraocular pressure. Hypothetical model of arrangement of collagen fibrils in the cornea (C), and limbus (D). The collagen molecule with its rigid and flexible regions is shown in E, the microfibril in (F) and crosslink connections between collagen fibrils of the limbus and cornea (G) that are part of the cornea-limbus-sclera mechanical unit that stabilizes the cornea from changes in size and shape during aging and mechanical loading. The collagen molecule in E is depicted as a series of light and dark bands that represent the flexible (light) and rigid (black) amino acid sequences in type I collagen that line up in register to form quarter-staggered microfibrils shown in F containing 5 molecules in cross-section and a longitudinal hole region. G shows an enlarged model showing that the connections between collagen fibrils in the limbus and cornea are stabilized by end-overlap crosslinks that form a continuous mechanical network.

The limbus is thought to stabilize the cornea with a diamond shaped pattern of collagen fibrils that run in a circumferential direction [17, 18, 19]. In the model presented in this figure it is proposed that covalent connections exist between collagen fibrils in the cornea, and collagen fibrils and fibers in the limbus. This linkage is required to prevent delamination of these structures during mechanical loading. The model is an extension of the models described by Silver et al. [30] and was created using Biorender.com.

The sclera protects the intraocular structures from mechanical damage as well as prevents light scattering in the eye due its opacity from distorting the retinal image [21]. It is composed of several layers including tenon’s capsule, episcleral, stroma and a perilimbal layer where it interfaces with the limbus [17]. At its anterior boundary the sclera merges with the corneal perimeter at the limbus and extends backward to approximately form a sphere. At the back of the eye, the scleral connective tissue fuses with the dural sheath of the optic nerve [17].

Episclera is a dense layer of collagen found in bundles that run circumferentially around the eye and merge with the underlying stroma [17]. They prevent radial enlargement of the sclera due to increases in internal pressure in the eye by limiting “hoop strain” preventing “blow out” failure of the globe [21, 22, 23]. It merges with the superficial layer of the limbus and therefore should have a similar modulus to that layer. The episcleral and stroma merge together to form a continuous interface.

Stroma contains bundles of parallel-aligned individual collagen fibrils with diameters 25–230 nm, interspersed in places with elastic microfibrils and fibers. They form lamellae 0.5–6 $\mu$m thick that lie roughly in the plane of the eyeball surface [17]. Scleral lamellae overall demonstrate far more branching and interweaving than those of the corneal stroma, and the extent of this varies with both tissue depth and anatomical location [24]. Superficially, the scleral collagen fibril bundles merge with tenon fibers at the extraocular muscle insertion sites, while in the deepest stromal layers adjacent to the uvea they taper and branch to intermingle with the underlying choroid [17]. Since the stroma of the sclera intersects the limbus, this may explain the peaks at 120 and 150 Hz seen in both tissues.

While the organization of sclera is clearly different from that of the cornea, it exhibits similar resonant frequencies due to cells (80 Hz) and collagen fibrils that merge with the limbus and tenon fibers (120 and 150 Hz). The 150 Hz peak may represent the superficial collagen fibers that merge with the extraocular muscle tendon fibers while the 120 Hz peak may represent the behavior of the deeper collagen lamellae. The 250 Hz peak may also represent the interface with the limbus which is characterized by a similar large peak at that frequency. The increased stiffness of the limbus stabilizes the scleral-limbus-corneal junction and limits changes in shape, curvature and refractive power of the cornea during aging, space flight and accommodation.

The limbus forms the border separating the cornea, conjunctiva, sclera, and uvea [24]. It contains the pathways for aqueous humor outflow and supports epithelial progenitor movement to maintain corneal epithelial integrity [24, 25, 26]. Central to the anterior limbal cribriform layer, radial strands of collagen are found to connect the peripheral cornea to the limbus. These presumed anchoring fibers have both collagen and elastin and are found more extensively in the superficial layers than deep layers [24, 25, 26, 27]. The excess of circumferential fibrils in the limbus, based on the change in curvature in the surface of the eye at the limbus, appear to take the form of a well-defined annulus [20]. The 250 Hz peak for pig limbus is significantly higher compared to cornea and sclera suggesting that this peak represents the annulus shaped ring of stiff collagen fibers that occurs at the interface between the sclera and cornea. This ring of collagen fibers not only stabilizes the interface between cornea and sclera, but it also limits transfer of stresses and the resulting deformation of the limbus from the forces generated by the extraorbital muscles during eye movement. The presence of cells (80 Hz) and collagen fibrils that connect to the surface of the cornea (150 Hz peak) and deeper layers of cornea (120 Hz) provide for mechanical continuity between the cornea and sclera. The 250 Hz peak probably reflects the fusion of annular collagen fibrils and the collagen lamellae at the limbus as modeled in Fig. 8. Thinning associated with highly myopic eyes occurs in the sclera and not at the limbus or cornea. This suggests that mechanical loading and increases in the axial length of the globe do not lead to mechanical failure at the interface with the limbus but lead to mechanical “creep” of scleral tissue.

The lens and iris are compositionally different than the sclera, cornea, and limbus. The lens is composed of a high concentration of proteins termed crystallines and is surrounded by a collagenous capsule composed of type IV collagen, laminin, and other macromolecules [28]. The iris is composed of the anterior and posterior leafs with the anterior leaf consisting of loose connective tissue, blood vessels, melanocytes and fibroblasts. The posterior leaf contains the dilator and sphincter muscles and posterior epithelium [29].

It is curious that both tissues exhibited resonant frequency peaks at about 80, 120, 150 and 250 Hz similar to the cornea, sclera and limbus suggesting that all the tissues in the anterior part of the eye appear to be mechanically similar. Modulus matching of the layers in the different components of the eye may provide a manner that energy can be stored and transmitted efficiently without stiffness mismatches or excessive dissipation in any one structure. Modulus mismatches in tissues with implants leads to intimal hyperplasia in arteries and hernia implant failures in humans [11]. The stiffness for both iris and lens at 250 Hz were significantly higher at a 0.95 confidence level than in the cornea and sclera and may reflect the stiff crystalline proteins in the lens and the muscular tissue in the iris.

The cornea, sclera and limbus have been considered individual anatomic structures based on histology and microscopic anatomy. The observation that blunt mechanical trauma, globe elongation, scleral thinning in myopia, and corneal ballooning and rupture in keratoconus do not result in delamination of any of these components suggests that the cornea, limbus and sclera are one biomechanical unit. The fact that these structures are composed of layers of tissue that are integrated together suggests that forces applied, and energy stored in any of these anatomic structures is eventually transmitted to the back of the sclera and the posterior chamber. Forces applied to the eye including gravity, eye lid pressure, surface tension, orbital muscle tension, intraocular pressure, and ciliary muscle tension all affect the corneal-limbal-scleral biomechanical unit. The cornea-limbus-sclera biomechanical unit may involve self-assembly and crosslinking of collagen molecules at the limbus into a reinforcing network similar to that seen in tendon [30] as diagrammed in Fig. 8. Each of these tissues has components with resonance frequencies of about 80, 120, 150 and 250 Hz that are involved in cellular events during mechanotransduction (peak at 80 Hz), transmission of mechanical loading information through the collagen network (peaks at 120 and 150 Hz) and prevention of premature mechanical failure (peak at 250 Hz). The importance of the coordination of these structures in maintaining corneal curvature is essential to maintaining normal vision. Any change in corneal shape or curvature induced by mechanical loading would alter the ability to see. Scleral thinning and globe elongation while altering the focal point of light on the retina do not alter the ability to correct for these changes. The ability of the cornea-limbus-scleral mechanical unit to store energy through elastic deformation and transfer it back through the sclera to the posterior chamber provides a means to maintain correction and maintain normal vision. It is only when the energy transmitted back to the posterior chamber through the sclera causes permanent alteration of the tissues in the posterior chamber that normal vision is threatened. It is important in future studies to consider if changes in the corneal-limbal-scleral biomechanical unit may be involved in the development of myopia and glaucoma especially if the sclera thins excessively with age.

The limitations of the study include the inability of being able to separate by dissection the anterior and posterior parts of the sclera. Future measurements on isolated layers of the sclera, limbus and cornea are needed to understand how each of the layers contribute to the mechanical properties of the whole tissues.