Characterization of ocular tissues using microindentation and hertzian viscoelastic models

Finite element model of ocular adduction with unconstrained globe translation

Details of the anatomy and behavior of the structures responsible for human eye movements have been extensively elaborated since the first modern biomechanical models were introduced. Based on these findings, a finite element model of human ocular adduction is developed based on connective anatomy and measured optic nerve (ON) properties, as well as active contractility of bilaminar extraocular muscles (EOMs), but incorporating the novel feature that globe translation is not otherwise constrained so that realistic kinematics can be simulated. Anatomy of the hemisymmetric model is defined by magnetic resonance imaging. The globe is modeled as suspended by anatomically realistic connective tissues, orbital fat, and contiguous ON. The model incorporates a material subroutine that implements active EOM contraction based on fiber twitch characteristics. Starting from the initial condition of 26° adduction, the medial rectus (MR) muscle was commanded to contract as the lateral rectus (LR) relaxed. We alternatively modeled absence or presence of orbital fat. During pursuit-like adduction from 26 to 32°, the globe translated 0.52 mm posteriorly and 0.1 mm medially with orbital fat present, but 1.2 mm posteriorly and 0.1 mm medially without fat. Maximum principal strains in the optic disk and peripapillary reached 0.05-0.06, and von-Mises stress 96 kPa. Tension in the MR orbital layer was ~ 24 g-force after 6° adduction, but only ~ 3 gm-f in the whole LR. This physiologically plausible simulation of EOM activation in an anatomically realistic globe suspensory system demonstrates that orbital connective tissues and fat are integral to the biomechanics of adduction, including loading by the ON.

Finite element method for estimation of applanation force and to study the influence of intraocular pressure of eye on tonometry

PURPOSE

Discover the associations of force of applanation on the eye with the plunging depth of the cornea and quantify them. The results will be utilized as the feedback parameter in the new prototype development of eye care instruments as additional force may damage the internal structure of the eye or may result in erroneous output.

METHOD

A finite element-based eye model is designed utilizing the actual dimensions of the human eye. A standardized tonometer is designed and the simulation is carried out at predetermined deformation of the cornea to find the force of applanation on the cornea during tonometry. Adding on, the influence of IOP during tonometry is analyzed for a range of plunging depths of the cornea.

RESULTS

The graphical results inferred the linear relation between the force of applanation with the deformation of the cornea and the results are quantified. The resulting deformation and stress plot of FEM based simulation approach is analyzed and observations regarding deformations and stress are made.

CONCLUSION

The human eye is successfully developed and also computed force on the cornea during tonometry is validated. The inference drawn from the deformation plot and stress plot is that the junction of cornea-sclera along with cornea-tonometer periphery undergo maximum deformation and experiences the highest stress compared to other areas of the eye while during tonometry.

2021 update on thyroid-associated ophthalmopathy

PURPOSE

Our understanding of thyroid-associated ophthalmopathy (TAO, A.K.A Graves' orbitopathy, thyroid eye disease) has advanced substantially, since one of us (TJS) wrote the 2010 update on TAO, appearing in this journal.

METHODS

PubMed was searched for relevant articles.

RESULTS

Recent insights have resulted from important studies conducted by many different laboratory groups around the World. A clearer understanding of autoimmune diseases in general and TAO specifically emerged from the use of improved research methodologies. Several key concepts have matured over the past decade. Among them, those arising from the refinement of mouse models of TAO, early stage investigation into restoring immune tolerance in Graves' disease, and a hard-won acknowledgement that the insulin-like growth factor-I receptor (IGF-IR) might play a critical role in the development of TAO, stand out as important. The therapeutic inhibition of IGF-IR has blossomed into an effective and safe medical treatment. Teprotumumab, a β-arrestin biased agonist monoclonal antibody inhibitor of IGF-IR has been studied in two multicenter, double-masked, placebo-controlled clinical trials demonstrated both effectiveness and a promising safety profile in moderate-to-severe, active TAO. Those studies led to the approval by the US FDA of teprotumumab, currently marketed as Tepezza for TAO. We have also learned far more about the putative role that CD34⁺ fibrocytes and their derivatives, CD34⁺ orbital fibroblasts, play in TAO.

CONCLUSION

The past decade has been filled with substantial scientific advances that should provide the necessary springboard for continually accelerating discovery over the next 10 years and beyond.

Prostaglandin F2α and EP2 agonists, and a ROCK inhibitor modulate the formation of 3D organoids of Grave's orbitopathy related human orbital fibroblasts

3D organoid cultures were used to elucidate the periocular effects of several anti-glaucoma drugs including a prostaglandin F2α analogue (bimatoprost acid; BIM-A), EP2 agonist (omidenepag; OMD) or a Rho-associated coiled-coil containing protein kinase (ROCK) inhibitor (ripasudil; Rip) on Grave's orbitopathy (GO) related orbital fatty tissue. 3D organoids were prepared from GO related human orbital fibroblasts (GHOFs) obtained from patients with GO. The effects of either 100 nM BIM-A, 100 nM OMD or 10 μM Rip on the 3D GHOFs organoids were examined with respect to organoid size, physical properties by a micro-squeezer, and the mRNA expression of extracellular matrix (ECM) proteins including collagen (COL) 1, COL 4, COL 6, and fibronectin (FN), ECM regulatory genes including lysyl oxidase (LOX), Connective Tissue Growth Factor (CTGF) and inflammatory cytokines including interleukin-1β (IL1β) and interleukin-6 (IL6). The size of the 3D GHOFs organoids decreased substantially in the presence of BIM-A, but also increased substantially in the presence of the others (OMD or Rip). The physical stiffness of the 3D GHOFs organoids was significantly decreased by Rip. BIM-A caused significantly the down-regulation of three ECM genes, Col 1, Col 6 and Fn, and two ECM regulatory genes and the up-regulation of IL6. In the presence of OMD, two ECM genes, Col 1 and Fn, and LOX were significantly down-regulated but IL1β and IL6 were significantly up-regulated. In the case of Rip, Col 1, FN and CTGF were significant down-regulated. Our present findings indicate that anti-glaucoma drugs modulate the structures and physical properties 3D GHOFs organoids in different manners by modifying the gene expressions of ECM, ECM regulatory factors and inflammatory cytokines. The results indicate that the benefits and demerits of anti-glaucoma medications need to be scrutinized carefully, in cases of patients with GO.

Gaze-evoked deformations of the optic nerve head in thyroid eye disease

PURPOSE

To assess gaze evoked deformations of the optic nerve head (ONH) in thyroid eye disease (TED), using computational modelling and optical coherence tomography (OCT).

METHODS

Multiple finite element models were constructed: one model of a healthy eye, and two models mimicking effects of TED; one with proptosis and another with extraocular tissue stiffening. Two additional hypothetical models had extraocular tissue softening or no extraocular tissue at all. Horizontal eye movements were simulated in these models. OCT images of the ONH of 10 healthy volunteers and 1 patient with TED were taken in primary gaze. Additional images were recorded in the same subjects performing eye movements in adduction and abduction. The resulting ONH deformation in the models and human subjects was measured by recording the 'tilt angle' (relative antero-posterior deformation of the Bruch's membrane opening).

RESULTS

In our computational models the eyes with proptosis and stiffer extraocular tissue had greater gaze-evoked deformations than the healthy eye model, while the models with softer or no extraocular tissue had lesser deformations, in both adduction and abduction. In healthy subjects, the mean tilt angle was 1.46°±0.25 in adduction and -0.42°±0.12 in abduction. The tilt angle measured in the subject with TED was 5.37° in adduction and -2.21° in abduction.

CONCLUSION

Computational modelling and experimental observation suggest that TED can cause increased gaze-evoked deformations of the ONH.

Bilaminar Mechanics of the Human Optic Nerve Sheath

PURPOSE/AIM

The adult human optic nerve (ON) sheath has recently been recognized to be bilaminar, consisting of inner layer (IL) and outer layer (OL). Since the ON and sheath exert tension on the globe in large angle adduction as these structures transmit reaction force of the medial rectus muscle to the globe, this study investigated the laminar biomechanics of the human ON sheath.

MATERIALS AND METHODS

Biomechanical characterization was performed in ON sheath specimens from 12 pairs of fresh, post-mortem adult eyes. Some ON sheath specimens were tested completely, while others were separated into IL and OL. Uniaxial tensile loading under physiological temperature and humidity was used to characterize a linear approximation as Young's modulus, and hyperelastic non-linear behavior using the formulation of Ogden. Micro-indentation was performed by imposing small compressive deformations with small, hard spheres. Specimens of the same sheaths were paraffin embedded, sectioned at 10 micron thickness, and stained with van Gieson's stain for anatomical correlation.

RESULTS

Mean (± standard error of the mean, SEM) tensile Young's modulus of the inner sheath at 19.8 ± 1.6 MPa significantly exceeded that for OL at 9.7 ± 1.2 MPa; the whole sheath showed intermediate modulus of 15.4 ± 1.1 MPa. Under compression, the inner sheath was stiffer (7.9 ± 0.5 vs 5.2 ± 0.5 kPa) and more viscous (150.8 ± 10.6 vs 75.6 ± 6 kPa s) than outer sheath. The inner sheath had denser elastin fibers than outer sheath, correlating with greater stiffness.

CONCLUSIONS

We conclude that maximum tensile stiffness occurs in the elastin-rich ON sheath IL that inserts near the lamina cribrosa where tension in the sheath exerted during adduction tethering may be concentrated adjacent the ON head.

HIF2A-LOX Pathway Promotes Fibrotic Tissue Remodeling in Thyroid-Associated Orbitopathy

Thyroid-associated orbitopathy (TAO) is a disfiguring periocular connective tissue disease associated with autoimmune thyroid disorders. It is a potentially blinding condition, for which no effective pharmacological treatment has been established. Despite a suggested role played by autoimmune thyrotropin receptor activation in the pathogenesis of TAO, the cellular and molecular events contributing to the fibrotic and inflammatory disease process of TAO are not fully defined. By developing a three-dimensional organoid culture of human orbital fibroblasts (OFs), we sought to determine the molecular mechanism underlying the fibrotic disease process of TAO. In this ex vivo model, we have demonstrated that hypoxia-inducible factor (HIF) 2α (HIF2A), but not its paralog HIF1A, accelerates extracellular matrix (ECM) deposition by inducing a collagen-cross-linking enzyme, lysyl oxidase (LOX). Inhibiting HIF2A and LOX with short hairpin RNA or small molecular antagonists effectively ameliorated fibrotic disease process within TAO organoids. Conversely, the overexpression of a constitutively active HIF2A in mouse OFs was sufficient to initiate LOX-dependent fibrotic tissue remodeling in OF organoids. Consistent with these findings, HIF2A and LOX were highly expressed in human TAO tissues paralleling excess ECM deposition. We propose that the HIF2A-LOX pathway can be a potential therapeutic target for the prevention and treatment of TAO.

Finite Element Biomechanics of Optic Nerve Sheath Traction in Adduction

Historical emphasis on increased intraocular pressure (IOP) in the pathogenesis of glaucoma has been challenged by the recognition that many patients lack abnormally elevated IOP. We employed finite element analysis (FEA) to infer contribution to optic neuropathy from tractional deformation of the optic nerve head (ONH) and lamina cribrosa (LC) by extraocular muscle (EOM) counterforce exerted when optic nerve (ON) redundancy becomes exhausted in adduction. We characterized assumed isotropic Young's modulus of fresh adult bovine ON, ON sheath, and peripapillary and peripheral sclera by tensile elongation in arbitrary orientations of five specimens of each tissue to failure under physiological temperature and humidity. Physical dimensions of the FEA were scaled to human histological and magnetic resonance imaging (MRI) data and used to predict stress and strain during adduction 6 deg beyond ON straightening at multiple levels of IOP. Young's modulus of ON sheath of 44.6 ± 5.6 MPa (standard error of mean) greatly exceeded that of ON at 5.2 ± 0.4 MPa, peripapillary sclera at 5.5 ± 0.8 MPa, and peripheral sclera at 14.0 ± 2.3 MPa. FEA indicated that adduction induced maximum stress and strain in the temporal ONH. In the temporal LC, the maximum stress was 180 kPa, and the maximum strain was ninefold larger than produced by IOP elevation to 45 mm Hg. The simulation suggests that ON sheath traction by adduction concentrates far greater mechanical stress and strain in the ONH region than does elevated IOP, supporting the novel concept that glaucomatous optic neuropathy may result at least partly from external traction on the ON, rather than exclusively on pressure on the ON exerted from within the eye.

Opto-mechanical characterization of sclera by polarization sensitive optical coherence tomography

Polarization sensitive optical coherence tomography (PSOCT) is an interferometric technique sensitive to birefringence. Since mechanical loading alters the orientation of birefringent collagen fibrils, we asked if PSOCT can be used to measure local mechanical properties of sclera. Infrared (1300 nm) PSOCT was performed during uniaxial tensile loading of fresh scleral specimens of rabbits, cows, and humans from limbal, equatorial, and peripapillary regions. Specimens from 8 human eyes were obtained. Specimens were stretched to failure at 0.01 mm/s constant rate under physiological conditions of temperature and humidity while birefringence was computed every 117 ms from cross-sectional PSOCT. Birefringence modulus (BM) was defined as the rate of birefringence change with strain, and tensile modulus (TM) as the rate of stress change between 0 and 9% strain. In cow and rabbit, BM and TM were positively correlated with slopes of 0.17 and 0.10 GPa, and with correlation coefficients 0.63 and 0.64 (P < 0.05), respectively, following stress-optic coefficients 4.69, and 4.20 GPa^-1. In human sclera, BM and TM were also positively correlated with slopes of 0.24 GPa for the limbal, 0.26 GPa for the equatorial, and 0.31 GPa for the peripapillary regions. Pearson correlation coefficients were significant at 0.51, 0.58, and 0.69 for each region, respectively (<0.001). Mean BM decreased proportionately to TM from the limbal to equatorial to peripapillary regions, as stress-optic coefficients were estimated as 2.19, 2.42, and 4.59 GPa^-1, respectively. Since birefringence and tensile elastic moduli correlate differently in cow, rabbit, and various regions of human sclera, it might be possible to mechanically characterize the sclera in vivo using PSOCT.

Quantitative characterization of viscoelastic behavior in tissue-mimicking phantoms and ex vivo animal tissues

Viscoelasticity of soft tissue is often related to pathology, and therefore, has become an important diagnostic indicator in the clinical assessment of suspect tissue. Surgeons, particularly within head and neck subsites, typically use palpation techniques for intra-operative tumor detection. This detection method, however, is highly subjective and often fails to detect small or deep abnormalities. Vibroacoustography (VA) and similar methods have previously been used to distinguish tissue with high-contrast, but a firm understanding of the main contrast mechanism has yet to be verified. The contributions of tissue mechanical properties in VA images have been difficult to verify given the limited literature on viscoelastic properties of various normal and diseased tissue. This paper aims to investigate viscoelasticity theory and present a detailed description of viscoelastic experimental results obtained in tissue-mimicking phantoms (TMPs) and ex vivo tissues to verify the main contrast mechanism in VA and similar imaging modalities. A spherical-tip micro-indentation technique was employed with the Hertzian model to acquire absolute, quantitative, point measurements of the elastic modulus (E), long term shear modulus (η), and time constant (τ) in homogeneous TMPs and ex vivo tissue in rat liver and porcine liver and gallbladder. Viscoelastic differences observed between porcine liver and gallbladder tissue suggest that imaging modalities which utilize the mechanical properties of tissue as a primary contrast mechanism can potentially be used to quantitatively differentiate between proximate organs in a clinical setting. These results may facilitate more accurate tissue modeling and add information not currently available to the field of systems characterization and biomedical research.

Depth-Dependent Out-of-Plane Young's Modulus of the Human Cornea

Purpose/Aim: Despite their importance in accurate mechanical modeling of the cornea, the depth-dependent material properties of the cornea have only been partially elucidated. In this work, we characterized the depth-dependent out-of-plane Young's modulus of the central and peripheral human cornea with high spatial resolution.

MATERIALS AND METHODS

Central and peripheral corneal buttons from human donors were subjected to unconfined axial compression followed by stress relaxation for 30 min. Sequences of fluorescent micrographs of full-thickness corneal buttons were acquired throughout the experiment to enable tracking of fluorescently labeled stromal keratocyte nuclei and measurements of depth-dependent infinitesimal strains. The nominal (gross) out-of-plane Young's modulus and drained Poisson's ratio for each whole specimen was computed from the equilibrium stress and overall tissue deformation. The depth-dependent (local) out-of-plane Young's modulus was computed from the equilibrium stress and local tissue strain based on an anisotropic model (transverse isotropy).

RESULTS

The out-of-plane Young's modulus of the cornea exhibited a strong dependence on in-plane location (peripheral versus central cornea), but not depth. The depth-dependent out-of-plane Young's modulus of central and peripheral specimens ranged between 72.4-102.4 kPa and 38.3-58.9 kPa. The nominal out-of-plane Young's modulus was 87 ± 41.51 kPa and 39.9 ± 15.28 kPa in the central and peripheral cornea, while the drained Poisson's ratio was 0.05 ± 0.02 and 0.07 ± 0.04.

CONCLUSIONS

The out-of-plane Young's modulus of the cornea is mostly independent of depth, but not in-plane location (i.e. central vs. peripheral). These results may help inform more accurate finite element computer models of the cornea.

Viscoelastic characterization of extraocular Z-myotomy

PURPOSE

Z-myotomy is an extraocular muscle (EOM) weakening procedure in which two incisions are made from longitudinally-separated, opposite EOM margins for treatment of strabismus. We examined the in vitro biomechanics of Z-myotomy using tensile loading.

METHODS

Fresh bovine rectus EOMs were reduced to 20 × 10 × 2-mm dimensions, and clamped in a microtensile load cell under physiological conditions. Extraocular muscles were elongated until failure following scissors incisions made from opposite sides, spaced 8 mm apart and each encompassing 0%, 40%, 50%, 60%, or 80% EOM width. Initial strain to 30% elongation was imposed at 100 mm/s, after which elongation was maintained for greater than 100 seconds during force recording at maintained deformation. Stress relaxation tests with nonincised specimens having widths ranging from 1 to 9 mm were conducted for viscoelastic characterization of corresponding equivalence to 20% to 80% Z-myotomy. Data were modeled using the Wiechert viscoelastic formulation.

RESULTS

There was progressively reduced EOM failure force to an asymptotic minimum at 60% or greater Z-myotomy. Each Z-myotomy specimen could be matched for equivalent failure force to a non-Z-myotomy specimen with a different width. Both tensile and stress relaxation data could be modeled accurately using the Wiechert viscoelastic formulation.

CONCLUSIONS

The parallel fiber structure results in low shear force transfer across EOM width, explaining the biomechanics of Z-myotomy. Z-myotomy progressively reduces force transmission to an asymptotic minimum for less than 60% surgical dose, with no further reduction for greater amounts of surgery. Equivalence to EOM specimens having regular cross-sections permits viscoelastic biomechanical characterization of Z-myotomy specimens with irregular cross-sections.

Computational model of matrix remodeling and entrenchment in the free-floating fibroblast-populated collagen lattice

Tissue equivalents represent excellent model systems for elucidating principles of mechanobiology and for exploring methods to improve the functionality of tissue-engineered constructs. The simplest tissue equivalent is the free-floating fibroblast-populated collagen lattice. Although introduced over 30 years ago, the associated mechanics of the cell-mediated compaction of this lattice was only recently analyzed in detail. The goal of this paper was to build on this recent stress analysis by developing a computational model of the evolving geometry, regionally varying material properties and cell stresses, and overall residual stress fields during the first two days of compaction. Baseline results were found to agree well with most experimental observations, namely evolving changes in radius, thickness, and material symmetry, yet hypothesis testing revealed aspects of the mechanobiology that require more experimental attention. Given the generality of the proposed framework, we submit that modifications and refinements can be used to study many similar systems and thereby help guide future experiments.

An inverse method to determine the mechanical properties of the iris in vivo

BACKGROUND

Understanding the mechanical properties of the iris can help to have an insight into the eye diseases with abnormalities of the iris morphology. Material parameters of the iris were simply calculated relying on the ex vivo experiment. However, the mechanical response of the iris in vivo is different from that ex vivo, therefore, a method was put forward to determine the material parameters of the iris using the optimization method in combination with the finite element method based on the in vivo experiment.

MATERIAL AND METHODS

Ocular hypertension was induced by rapid perfusion to the anterior chamber, during perfusion intraocular pressures in the anterior and posterior chamber were record by sensors, images of the anterior segment were captured by the ultrasonic system. The displacement of the characteristic points on the surface of the iris was calculated. A finite element model of the anterior chamber was developed using the ultrasonic image before perfusion, the multi-island genetic algorithm was employed to determine the material parameters of the iris by minimizing the difference between the finite element simulation and the experimental measurements.

RESULTS

Material parameters of the iris in vivo were identified as the iris was taken as a nearly incompressible second-order Ogden solid. Values of the parameters μ1, α1, μ2 and α2 were 0.0861 ± 0.0080 MPa, 54.2546 ± 12.7180, 0.0754 ± 0.0200 MPa, and 48.0716 ± 15.7796 respectively. The stability of the inverse finite element method was verified, the sensitivity of the model parameters was investigated.

CONCLUSION

Material properties of the iris in vivo could be determined using the multi-island genetic algorithm coupled with the finite element method based on the experiment.

Atomic force microscopy determination of Young׳s modulus of bovine extra-ocular tendon fiber bundles

Extra-ocular tendons (EOTs) transmit the oculorotary force of the muscles to the eyeball to generate dynamic eye movements and align the eyes, yet the mechanical properties of the EOTs remain undefined. The EOTs are known to be composed of parallel bundles of small fibers whose mechanical properties must be determined in order to characterize the overall behavior of EOTs. The current study aimed to investigate the transverse Young׳s modulus of EOT fiber bundles using atomic force microscopy (AFM). Fresh bovine EOT fiber bundle specimens were maintained under temperature and humidity control, and indented 100nm by the inverted pyramid tip of an AFM (Veeco Digital Instruments, NY). Ten indentations were conducted for each of 3 different locations of 10 different specimens from each of 6 EOTs, comprising a total of 1800 indentations. Young׳s modulus for each EOT was determined using a Hertzian contact model. Young׳s moduli for fiber bundles from all six EOTs were determined. Mean Young׳s moduli for fiber bundles were similar for the six anatomical EOTs: lateral rectus 60.12±2.69 (±SD)MPa, inferior rectus 59.69±5.34MPa, medial rectus 56.92±1.91MPa, superior rectus 59.66±2.64MPa, inferior oblique 57.7±1.36MPa, and superior oblique 59.15±2.03. Variation in Young׳s moduli among the six EOTs was not significant (P>0.25). The Young׳s modulus of bovine EOT fibers is highly uniform among the six extraocular muscles, suggesting that each EOT is assembled from fiber bundles representing the same biomechanical elements. This uniformity will simplify overall modeling.

Biomechanics of superior oblique Z-tenotomy

BACKGROUND

A recent report suggests that 70%-80% Z-tenotomy of the superior oblique tendon is necessary to effectively treat A-pattern strabismus associated with over depression in adduction. To clarify the clinical effect, we compared the biomechanics of Z-tenotomy on the superior oblique tendon, superior rectus tendon, and isotropic latex material.

METHODS

Fresh bovine superior oblique tendons were trimmed to 20 mm × 10 mm dimensions similar to human superior oblique tendon and clamped in a microtensile load cell under physiological conditions of temperature and humidity. Minimal preload was applied to avoid slackness. Tendons were elongated until failure following Z-tenotomies, made from opposite tendon margins, spaced 8 mm apart and each encompassing 0%, 20%, 40%, 50%, 60%, or 80% tendon width. Digitally sampled failure force was monitored using a precision strain gauge. Control experiments were performed in similar-sized specimens of bovine superior rectus tendon and isotropic latex.

RESULTS

Progressively increasing Z-tenotomy of latex caused a linearly graded reduction in force. In contrast, Z-tenotomy of up to 50% in superior oblique and superior rectus tendons caused nonlinear reduction in force transmission that reached a negligible value at 50% tenotomy and greater.

CONCLUSIONS

Z-tenotomy up to 50% progressively reduces extraocular tendon force transmission, but Z-tenotomy of ≥50% is biomechanically equivalent in vitro to complete tenotomy.

Studies of scleral biomechanical behavior related to susceptibility for retinal ganglion cell loss in experimental mouse glaucoma

PURPOSE

To study anatomical changes and mechanical behavior of the sclera in mice with experimental glaucoma by comparing CD1 to B6 mice.

METHODS

Chronic experimental glaucoma for 6 weeks was produced in 2- to 4-month-old CD1 (43 eyes) and B6 mice (42 eyes) using polystyrene bead injection into the anterior chamber with 126 control CD1 and 128 control B6 eyes. Intraocular pressure (IOP) measurements were made with the TonoLab at baseline and after bead injection. Axial length and scleral thickness were measured after sacrifice in the CD1 and B6 animals and compared to length data from 78 eyes of DBA/2J mice. Inflation testing of posterior sclera was conducted, and circumferential and meridional strain components were determined from the displacement response.

RESULTS

Experimental glaucoma led to increases in axial length and width by comparison to fellow eyes (6% in CD1 and 10% in B6; all P < 0.03). While the peripapillary sclera became thinner in both mouse types with glaucoma, the remainder of the sclera uniformly thinned in CD1, but thickened in B6. Peripapillary sclera in CD1 controls had significantly greater temporal meridional strain than B6 and had differences in the ratios of meridional to effective circumferential strain from B6 mice. In both CD1 and B6 mice, exposure to chronic IOP elevation resulted in stiffer pressure-strain responses for both the effective circumferential and meridional strains (multivariable regression model, P = 0.01-0.03).

CONCLUSIONS

Longer eyes, greater scleral strain in some directions at baseline, and generalized scleral thinning after glaucoma were characteristic of CD1 mice that have greater tendency to retinal ganglion cell damage than B6 mice. Increased scleral stiffness after glaucoma exposure in mice mimics findings in monkey and human glaucoma eyes.

Materials characterization and mechanobiology of the eye

The eye responds to a great deal of internal and external stimuli throughout its normal function. Due to this, a mechanical or chemical analysis alone is insufficient. A systematic materials characterization is needed. A mechanobiological approach is required for a full understanding of the unique properties and function of the eye. This review compiles the mechanical properties of select eye components, summarizes mechanical and chemical testing platforms, and overviews modeling approaches. Analysis is done across studies, experimental methods, and between species in order to summarize what is known about the mechanobiology of the eye. Several opportunities for future research are identified.

Determination of poisson ratio of bovine extraocular muscle by computed X-ray tomography

The Poisson ratio (PR) is a fundamental mechanical parameter that approximates the ratio of relative change in cross sectional area to tensile elongation. However, the PR of extraocular muscle (EOM) is almost never measured because of experimental constraints. The problem was overcome by determining changes in EOM dimensions using computed X-ray tomography (CT) at microscopic resolution during tensile elongation to determine transverse strain indicated by the change in cross-section. Fresh bovine EOM specimens were prepared. Specimens were clamped in a tensile fixture within a CT scanner (SkyScan, Belgium) with temperature and humidity control and stretched up to 35% of initial length. Sets of 500–800 contiguous CT images were obtained at 10-micron resolution before and after tensile loading. Digital 3D models were then built and discretized into 6–8-micron-thick elements. Changes in longitudinal thickness of each microscopic element were determined to calculate strain. Green's theorem was used to calculate areal strain in transverse directions orthogonal to the stretching direction. The mean PR from discretized 3D models for every microscopic element in 14 EOM specimens averaged 0.457 ± 0.004 (SD). The measured PR of bovine EOM is thus near the limit of incompressibility.

Empirical measurements of biomechanical anisotropy of the human vocal fold lamina propria

The vocal folds are known to be mechanically anisotropic due to the microstructural arrangement of fibrous proteins such as collagen and elastin in the lamina propria. Even though this has been known for many years, the biomechanical anisotropic properties have rarely been experimentally studied. We propose that an indentation procedure can be used with uniaxial tension in order to obtain an estimate of the biomechanical anisotropy within a single specimen. Experiments were performed on the lamina propria of three male and three female human vocal folds dissected from excised larynges. Two experiments were conducted: each specimen was subjected to cyclic uniaxial tensile loading in the longitudinal (i.e., anterior-posterior) direction, and then to cyclic indentation loading in the transverse (i.e., medial-lateral) direction. The indentation experiment was modeled as contact on a transversely isotropic half-space using the Barnett-Lothe tensors. The longitudinal elastic modulus E(L) was computed from the tensile test, and the transverse elastic modulus E(T) and longitudinal shear modulus G(L) were obtained by inverse analysis of the indentation force-displacement response. It was discovered that the average of E(L) /E(T) was 14 for the vocal ligament and 39 for the vocal fold cover specimens. Also, the average of E(L)/G(L), a parameter important for models of phonation, was 28 for the vocal ligament and 54 for the vocal fold cover specimens. These measurements of anisotropy could contribute to more accurate models of fundamental frequency regulation and provide potentially better insights into the mechanics of vocal fold vibration.

Increased iris-lens contact following spontaneous blinking: mathematical modeling

The purpose of this work was to study in silico how iris root rotation due to spontaneous blinking alters the iris contour. An axisymmetric finite-element model of the anterior segment was developed that included changes in the iris contour and the aqueous humor flow. The model geometry was based on average values of ocular dimensions. Blinking was modeled by rotating the iris root posteriorly and returning it back to the anterior. Simulations with maximum rotations of 2°, 4°, 6°, and 8° were performed. The iris-lens contact distance and the pressure difference between the posterior and anterior chambers were calculated. When the peak iris root rotation was 2°, the maximum iris-lens contact increased gradually from 0.28 to 0.34mm within eight blinks. When the iris root was rotated by 6° and 8°, the pressure difference between the posterior and anterior chambers dropped from a positive value (1.23Pa) to negative values (-0.86 and -1.93Pa) indicating the presence of reverse pupillary block. Apparent iris-lens contact increased with steady blinking, and the increase became more pronounced as posterior rotation increased. We conclude that repeated iris root rotation caused by blinking could maintain the iris in a posterior position under normal circumstances, which would then lead to the clinically observed anterior drift of the iris when blinking is prevented.

The nonlinearity of passive extraocular muscles

Passive extraocular muscles (EOMs), like most biological tissues, are hyperelastic, that is, their stiffness increases as they are stretched. It has always been assumed, and in a few occasions argued, that this is their only nonlinearity and that it can be ignored in central gaze. However, using novel measurement techniques in anesthetized paralyzed monkeys, we have recently demonstrated that EOMs are characterized by another prominent nonlinearity: the forces induced by sequences of stretches do not sum. Thus, superposition, a central tenet of linear and quasi-linear models, does not hold in passive EOMs. Here, we outline the implications of this finding, especially in light of the common assumption that it is easier for the brain to control a linear than a nonlinear plant. We argue against this common belief: the specific nonlinearity of passive EOMs may actually make it easier for the brain to control the plant than if muscles were linear.

Mechanical interferometry imaging for creep modeling of the cornea

PURPOSE

A novel nanoindentation technique was used to biomechanically characterize each of three main layers of the cornea by using Hertzian viscoelastic formulation of creep, the deformation resulting from sustained-force application.

METHODS

The nanoindentation method known as mechanical interferometry imaging (MII) with <1-nm displacement precision was used to observe indentation of bovine corneal epithelium, endothelium, and stroma by a spherical ferrous probe in a calibrated magnetic field. For each specimen, creep testing was performed using two different forces for 200 seconds. Measurements for single force were used to build a quantitative Hertzian model that was then used to predict creep behavior for another imposed force.

RESULTS

For all three layers, displacement measurements were highly repeatable and were well predicted by Hertzian models. Although short- and long-term stiffnesses of the endothelium were highest of the three layers at 339.2 and 20.2 kPa, respectively, both stromal stiffnesses were lowest at 100.4 and 3.6 kPa, respectively. Stiffnesses for the epithelium were intermediate at 264.6 and 12.2 kPa, respectively.

CONCLUSIONS

Precise, repeatable measurements of corneal creep behavior can be conveniently obtained using MII at mechanical scale as small as one cell thickness. When interpreted in analytical context of Hertzian viscoelasticity, MII technique proved to be a powerful tool for biomechanical characterization of time-dependent biomechanics of corneal regions.