Ocular elasticity. Is engineering stiffness a more useful characterization parameter than ocular rigidity?

Optical coherence elastography for assessing the influence of intraocular pressure on elastic wave dispersion in the cornea

The cornea is a highly specialized organ that relies on its mechanical stiffness to maintain its aspheric geometry and refractive power, and corneal diseases such as keratoconus have been linked to abnormal tissue stiffness and biomechanics. Dynamic optical coherence elastography (OCE) is a clinically promising non-contact and non-destructive imaging technique that can provide measurements of corneal tissue stiffness directly in vivo. The method relies on the concepts of elastography where shear waves are generated and imaged within a tissue to obtain mechanical properties such as tissue stiffness. The accuracy of OCE-based measurements is ultimately dependent on the mathematical theories used to model wave behavior in the tissue of interest. In the cornea, elastic waves propagate as guided wave modes which are highly dispersive and can be mathematically complex to model. While recent groups have developed detailed theories for estimating corneal tissue properties from guided wave behavior, the effects of intraocular pressure (IOP)-induced prestress have not yet been considered. It is known that prestress alone can strongly influence wave behavior, in addition to the associated non-linear changes in tissue properties. This present study shows that failure to account for the effects of prestress may result in overestimations of the corneal shear moduli, particularly at high IOPs. We first examined the potential effects of IOP and IOP-induced prestress using a combination of approximate mathematical theories describing wave behavior in thin plates with observations made from data published in the OCE literature. Through wave dispersion analysis, we deduce that IOP introduces a tensile hoop stress and may also influence an elastic foundational effect that were observable in the low-frequency components of the dispersion curves. These effects were incorporated into recently developed models of wave behavior in nearly incompressible, transversely isotropic (NITI) materials. Fitting of the modified NITI model with ex vivo porcine corneal data demonstrated that incorporation of the effects of IOP resulted in reduced estimates of corneal shear moduli. We believe this demonstrates that overestimation of corneal stiffness occurs if IOP is not taken into consideration. Our work may be helpful in separating inherent corneal stiffness properties that are independent of IOP; changes in these properties and in IOP are distinct, clinically relevant issues that affect the cornea health.

Ultrasound Elastography in Ocular and Periocular Tissues: A Review

Ultrasound elastography has become available in everyday practice, allowing direct measurement of tissue elasticity with important and expanding clinical applications. Several studies that have evaluated pathological and non-pathological tissues have demonstrated that ultrasound elastography can actually improve the diagnostic accuracy of the underlying disease process by detecting differences in their elasticity. Ocular and periocular tissues can also be characterized by their elastic properties. In this context, a comprehensive review of literature on ultrasound elastography as well as its current applications in Ophthalmology is presented.

Smarce1 and Tensin 4 Are Putative Modulators of Corneoscleral Stiffness

The biomechanical properties of the cornea and sclera are important in the onset and progression of multiple ocular pathologies and vary substantially between individuals, yet the source of this variation remains unknown. Here we identify genes putatively regulating corneoscleral biomechanical tissue properties by conducting high-fidelity ocular compliance measurements across the BXD recombinant inbred mouse set and performing quantitative trait analysis. We find seven cis-eQTLs and non-synonymous SNPs associating with ocular compliance, and show by RT-qPCR and immunolabeling that only two of the candidate genes, Smarce1 and Tns4, showed significant expression in corneal and scleral tissues. Both have mechanistic potential to influence the development and/or regulation of tissue material properties. This work motivates further study of Smarce1 and Tns4 for their role(s) in ocular pathology involving the corneoscleral envelope as well as the development of novel mouse models of ocular pathophysiology, such as myopia and glaucoma.

Effectiveness of the Goldmann Applanation Tonometer, the Dynamic Contour Tonometer, the Ocular Response Analyzer and the Corvis ST in Measuring Intraocular Pressure following FS-LASIK

Purpose: To test the performance of the four tonometers in providing IOP measurements that were free of the effects of corneal biomechanics changes caused by refractive surgery.Methods: Four tonometers were employed to provide IOP measurements for 65 participants who accepted Femtosecond laser-assisted LASIK (FS-LASIK). The measurements included GAT-IOP by the Goldmann Applanation Tonometer, DCT-IOP by the Dynamic Contour Tonometer, Goldmann-correlated IOP (ORA-IOPg) and corneal-compensated IOP (ORA-IOPcc) by the Ocular Response Analyzer, and uncorrected IOP (CVS-IOP) and biomechanically corrected IOP (CVS-bIOP) by the Corvis ST. Statistical analyses were performed to assess the association of the differences in IOP caused by FS-LASIK with central corneal thickness (CCT), mean corneal curvature (Km), age, refractive error correction (REC), optical zone diameter (OZD), ablation zone diameter (AZD), residual stromal bed thickness (RSB) and RSB ratio (RSB/CCT). Multiple linear regression models were constructed to explore factors influencing IOP changes.Results: All four tonometers exhibited significant differences between IOP measurements taken pre and post-surgery except for CVS-bIOP in the low to moderate myopia group (t = 1.602, p = .12). CVS-bIOP, followed by DCT-IOP, provided the best agreement between pre and post-FS-LASIK measurements with the lowest differences in IOP and the narrowest limits of agreement. The pre-post IOP differences were also significantly associated with the reduction in CCT in only GAT-IOP, ORA-IOPg, and CVS-IOP. CVS-bIOP and ORA-IOPcc were the only measurements that were not correlated with CCT, Km or age both before and after FS-LASIK.Conclusions: The biomechanically corrected bIOP from the Corvis ST provided post-FS-LASIK measurements that were in closest agreement with those obtained before surgery. In comparison, GAT-IOP, ORA-IOPg, ORA-IOPcc, and CVS-IOP appeared to be more influenced by the changes in corneal biomechanics caused by FS-LASIK.

Measurement of Ocular Compliance Using iPerfusion

The pressure-volume relationship of the eye is determined by the biomechanical properties of the corneoscleral shell and is classically characterised by Friedenwald's coefficient of ocular rigidity or, alternatively, by the ocular compliance (OC), defined as dV/dP. OC is important in any situation where the volume (V) or pressure (P) of the eye is perturbed, as occurs during several physiological and pathological processes. However, accurately measuring OC is challenging, particularly in rodents. We measured OC in 24 untreated enucleated eyes from 12 C57BL/6 mice using the iPerfusion system to apply controlled pressure steps, whilst measuring the time-varying flow rate into the eye. Pressure and flow data were analysed by a “Discrete Volume” (integrating the flow trace) and “Step Response” method (fitting an analytical solution to the pressure trace). OC evaluated at 13 mmHg was similar between the two methods (Step Response, 41 [37, 46] vs. Discrete Volume, 42 [37, 48] nl/mmHg; mean [95% CI]), although the Step Response Method yielded tighter confidence bounds on individual eyes. OC was tightly correlated between contralateral eyes (R² = 0.75, p = 0.0003). Following treatment with the cross-linking agent genipin, OC decreased by 40 [33, 47]% (p = 0.0001; N = 6, Step Response Method). Measuring OC provides a powerful tool to assess corneoscleral biomechanics in mice and other species.

Clinical Evaluation of Methods to Correct Intraocular Pressure Measurements by the Goldmann Applanation Tonometer, Ocular Response Analyzer, and Corvis ST Tonometer for the Effects of Corneal Stiffness Parameters

PURPOSE

To evaluate the effectiveness of methods to correct intraocular pressure (IOP) measurements obtained using the Goldmann applanation tonometer (GAT), the ocular response analyzer (ORA), and the Corvis ST tonometer (CVS) for the effects of corneal stiffness parameters: central corneal thickness (CCT), corneal curvature (R), and age in a Chinese population.

PATIENTS AND METHODS

Data were collected for 99 eyes of 99 participants. Whereas cornea-corrected IOP was obtained directly from ORA (ORA-IOPcc), cornea correction in GAT and CVS was implemented using multiparameter equations developed earlier. The study also included IOP measurements by the dynamic contour tonometer, which is thought to be less affected by corneal stiffness parameters than other tonometers. Statistical analyses were performed to determine the association of both uncorrected and corrected IOP with the main stiffness parameters: CCT, R, and age.

RESULTS

After correction, a significantly decreased association between the GAT (from r=0.15 to r=-0.02), ORA (from r=0.24 to r=-0.19), and CVS (from r=0.47 to r=0.004) IOP measurements and the CCT was found, to levels below that with the dynamic contour tonometer-IOP (r=0.11). The IOP measurements made by the 4 tonometers, both uncorrected and corrected, did not correlate with age. The same was true for R except with ORA-IOPcc (r=0.23).

CONCLUSIONS

CCT accounted for the majority of variance in IOP, whereas age and R had a much smaller effect. The IOP correction processes studied were successful in reducing reliance of IOP measurements, especially those by GAT and CVS, on CCT in a healthy Chinese population.

Measuring Intraocular Pressure in Patients With Keratoconus With and Without Intrastromal Corneal Ring Segments

PURPOSE

To compare intraocular pressure (IOP) measurements made using 5 tonometers in keratoconic eyes with and without intrastromal corneal ring segments.

METHODS AND PATIENTS

This was an observational case series study. A total of 147 eyes of 147 patients with keratoconus, 74 of which had undergone corneal ring segment placement, were prospectively evaluated. IOP was measured using the tonometers Tonopen XL, Pascal dynamic contour tonometer, iCare Pro, ocular response analyzer (ORA), and Goldmann applanation (GAT) in random order. The Bland-Altman method was used to examine interinstrument agreement. Effects on readings of central corneal thickness, corneal curvature, and corneal astigmatism were assessed by multivariate regression analysis.

RESULTS

Smallest mean IOP differences with GAT measurements in eyes without and with ring segments, respectively, were detected for iCare Pro [0.2 (2.9) mm Hg and 0.4 (3.0) mm Hg, P=0.914] and greatest differences for ORA Goldmann-correlated IOP [5.8 (3.3) mm Hg and 6.0 (3.1) mm Hg, P=0.363]. Best agreement with GAT was shown by iCare Pro (ICC=0.829; 95% CI, 0.721-0.896) and worse agreement by ORA corneal-compensated IOP (ICC=-0.145; 95% CI, -0.826 to 0.283). All but the dynamic contour tonometer readings were influenced by central corneal thickness, yet these measurements were affected by the presence of ring segments (P=0.017) and corneal astigmatism (P=0.030). Corneal curvature only affected ORA Goldmann-correlated IOP (P=0.029).

CONCLUSIONS

All 5 tonometers provided reliable IOP readings in the keratoconic eyes regardless of the presence of corneal ring segments. iCare Pro readings were most consistent with GAT, whereas ORA readings were least consistent with this reference standard.

Indentation versus tensile measurements of Young's modulus for soft biological tissues

In this review, we compare the reported values of Young's modulus (YM) obtained from indentation and tensile deformations of soft biological tissues. When the method of deformation is ignored, YM values for any given tissue typically span several orders of magnitude. If the method of deformation is considered, then a consistent and less ambiguous result emerges. On average, YM values for soft tissues are consistently lower when obtained by indentation deformations. We discuss the implications and potential impact of this finding.

Material properties of the cornea and sclera: a modelling approach to test experimental analysis

Material properties of cornea and sclera are important for maintaining the shape of the eye and the requisite surface curvatures for optics. They also need to withstand the forces of external and internal musculature and fluctuations in intraocular pressure (IOP). These properties are difficult to measure and variable results have been reported. A previously published experimental procedure, from which the material properties of the eyeball coats were obtained, has been modelled in this paper using Finite Element Analysis, in order to test the accuracy of the experiment. Material parameters were calculated from the model and the resulting relationships between stress and strain for the cornea and sclera compared to their experimentally obtained counterparts. The comparison between model and experiment was close for the sclera but more varied for the cornea. The pressure vessel model can be applied for measuring the material properties of the sclera but is less accurate for the cornea.

MR elastography of the ex vivo bovine globe

PURPOSE

To evaluate the feasibility of using MR elastography (MRE) to assess the mechanical properties of the eye.

MATERIALS AND METHODS

The elastic properties of the corneoscleral shell of an intact, enucleated bovine globe specimen were estimated using MRE and finite element modeling (FEM), assuming linear, isotropic behavior. The two-dimensional (2D), axisymetric model geometry was derived from a segmented 2D MR image, and estimations of the Young's modulus in both the cornea and sclera were made at various intraocular pressures using an iterative flexural wave speed matching algorithm.

RESULTS

Estimated values of the Young's moduli of the cornea and sclera varied from 40 to 185 kPa and 1 to 7 MPa, respectively, over an intraocular pressure range of 0.85 to 9.05 mmHg (1.2 to 12.3 cmH(2)O). They also varied exponentially as functions of both wave speed and intraocular dP/dV, an empirical measure of "ocular rigidity."

CONCLUSION

These results show that it is possible to estimate the intrinsic elastic properties of the corneoscleral shell in an ex vivo bovine globe, suggesting that MRE may provide a useful means to assess the mechanical properties of the eye and its anatomy. Further development of the technique and modeling process will enhance its potential, and further investigations are needed to determine its clinical potential.

Optical coherence tomography measurements of the fresh porcine eye and response of the outer coats of the eye to volume increase

Corneal and scleral thickness and anterior chamber dimensions are required for understanding developmental and pathological processes. Parameters of the eyeball are also required to calculate optical and material properties. As the eyeball resembles a pressure vessel, it has been suggested that elasticity of the cornea and sclera could be calculated from the measurements of thickness. Baseline corneal and scleral thicknesses and anterior chamber dimensions and how these change with incremental increases of intraocular fluid are measured in fresh porcine eyes using the Visante OCT (optical coherence tomography). At baseline, corneal thickness is almost constant. Anterior scleral thickness is variable, decreasing from 0.91+/-0.07 mm near the limbus to a minimum of 0.58+/-0.13. Posterior scleral thickness is more constant with an average of 0.78+/-0.09 mm. Near the optic nerve the thickness increases to 1.00+/-0.09 mm. Average baseline anterior chamber angle, diameter, and depth were found to be 33.15+/-4.91 deg, 13.60+/-0.38 mm, and 2.13+/-0.22 mm, respectively. After fluid injections, maximum changes in corneal and scleral thicknesses were 9 to 10 and 1 to 3%, respectively. Anterior chamber angle and depth decreased slightly but significantly. Changes in the eyeball coats with fluid injections, indicate that the pressure vessel model can be applied to the eye to calculate corneal and scleral elasticities.

The effect of changing intraocular pressure on the corneal and scleral curvatures in the fresh porcine eye

AIM

To measure corneal and scleral radii of curvature in response to intraocular pressure (IOP).

METHODS

Using digital photographic profile images of 16 fresh porcine eyes, the curvatures of the cornea and sclera were determined in response to five consecutive incremental 100 mul saline intravitreal injections. IOP was measured and ocular rigidity calculated. Elastic moduli of the cornea and sclera were estimated.

RESULTS

Intraocular pressure and the radius of curvature of the sclera increased linearly with increasing volume. There was no statistical change in corneal curvature. The elasticity of the cornea and sclera was constant during the 15-50 mm Hg increase in IOP. The estimated range of the elastic moduli of the cornea and sclera were, respectively 0.07-0.29 MPa and 0.2 MPa to 0.5 MPa. The scleral rigidity ranged from 0.0017 to 0.0022.

CONCLUSIONS

The elastic moduli of the cornea and sclera are independent of IOP. The modulus of elasticity of the sclera is higher than that of the cornea. Elevation of IOP changes the curvature of the sclera but not that of the cornea. Porcine scleral rigidity is similar to human scleral rigidity. Scleral curvature could be a novel method for measuring IOP.

The use of the Reichert ocular response analyser to establish the relationship between ocular hysteresis, corneal resistance factor and central corneal thickness in normal eyes

PURPOSE

The aim of this study was to measure ocular hysteresis and corneal resistance factor (CRF), novel methods of analysing ocular rigidity/elasticity and to determine the relationship between central corneal thickness (CCT), hysteresis and CRF in normal subjects.

DESIGN

Prospective, cross-sectional, clinical trial.

PARTICIPANTS

The study included 207 normal eyes.

METHODS

Hysteresis and CRF were measured by the ocular response analyser. The CCT was measured using a hand held ultrasonic pachymeter.

MAIN OUTCOME MEASURES

Ocular hysteresis and CRF in normal patients and their relationship with CCT.

RESULTS

The mean hysteresis was 10.7+/-2.0 mmHg standard deviation (S.D.) (range 6.1-17.6 mmHg); the mean CRF was 10.3+/-2.0 (range 5.7-17.1 mmHg). The mean CCT was 545.0+/-36.4 microm (471-650 microm). The relationship between hysteresis and CCT; CRF and CCT; CRF and hysteresis were significant (p<0.0001).

CONCLUSION

This study demonstrated that corneal hysteresis increased with increasing CCT, however, the correlation was moderate. It would appear that CCT, hysteresis and CRF may measure different biomechanical aspects of ocular rigidity and are likely to be useful additional measurement to CCT in the assessment of ocular rigidity when measuring intraocular pressure (IOP). This may be of particular importance when trying to correct IOP measurements for increased or decreased ocular rigidity.

The preoperative intraocular pressure level predicts the amount of underestimated intraocular pressure after LASIK for myopia

AIMS

To evaluate the statistical significance of the parameters that affect underestimation of intraocular pressure (IOP) after laser in situ keratomileusis (LASIK) for myopia.

METHODS

In this prospective case series study, patient age, axial length, preoperative corneal curvature, preoperative central corneal thickness (CCT), preoperative IOP, and ablation depth were studied to determine whether they affect the underestimation of IOP in the right eyes of 100 consecutive patients who underwent LASIK.

RESULTS

The preoperative IOP was the most important parameter for an amount of underestimated Goldmann applanation tonometric IOP (GAT) and non-contact tonometric IOP (ncIOP) at 1 month (r = 0.654, p<0.0001, R(2) = 0.427, and r = 0.694, p<0.0001, R(2) = 0.481, respectively) and 3 months (r = 0.637, p<0.0001, R(2) = 0.406, and r = 0.726, p<0.0001, R(2) = 0.527, respectively). Patient age was statistically significant for underestimating the GAT at 1 month, and both the ablation depth and CCT were statistically significant parameters for underestimating the ncIOP at 1 month and at 3 months by stepwise multiple regression analysis (F>4.000). However, these parameters had small bivariate correlation coefficients, and were considered as minor parameters.

CONCLUSION

Preoperative IOP is the most important parameter that affects an underestimation of IOP after LASIK for myopia. Eyes with a higher true IOP have a larger underestimation of the IOP after LASIK for myopia. From these results, the importance of the modulus of elasticity on IOP measurements was discussed.

Progressive post-LASIK keratectasia: biomechanical instability or chronic disease process?

Progressive post-LASIK keratectasia (PPLK) is a progressive deformation of corneal anatomy that occurs rarely but may have severe consequences. Using the scientific literature and new hypotheses, we attempted to determine whether PPLK is a biomechanical result of laser in situ keratomileusis (LASIK), a chronic disease process affecting individuals predisposed to the condition, or a combination of processes. We look at whether the combination of fatigue, specifically a form of dynamic fatigue, and proteolysis provides an environment conducive to the occurrence and progression of PPLK. This review may raise more questions than it answers and in so doing may move us toward a better understanding of this occasionally serious consequence of LASIK.

Modeling passive mechanical interaction between aqueous humor and iris

Certain forms of glaucoma are associated with displacement of the iris from its normal contour. We present here a mathematical model of the coupled aqueous humor-iris system that accountsfor the contribution of aqueous humor flow and passive iris deformability to the iris contour. The aqueous humor is modeled as a Newtonian fluid, and the iris is modeled as a linear elastic solid. The resulting coupled equation set is solved by the finite element method with mesh motion in response to iris displacement accomplished by tracking a pseudo-solid overlying the aqueous humor. The model is used to predict the iris contour in healthy and diseased eyes. The results compare favorably with clinical observations, supporting the hypothesis that passive iris deformation can produce the iris contours observed using ultrasound biomicroscopy.

Accuracy of clinical estimates of intraocular pressure in Chinese eyes

PURPOSE

To investigate the validity of clinical estimates of intraocular pressure (IOP) in Chinese people.

DESIGN

Prospective, cross-sectional, hospital-based in vivo study.

PARTICIPANTS

Twenty-three ethnic Chinese adults (aged 35-82 years) undergoing routine phacoemulsification surgery were examined.

TESTING

"True" IOP was measured with a solid-state hemodynamic monitor through a cannula in the anterior chamber. IOP was set successively to 10, 20, and 30 mmHg in each subject, using a reservoir of balanced salt solution. Intraocular pressure was simultaneously estimated by use of a hand-held applanation tonometer (Perkin's) and a Tono-Pen. The association between ocular biometric variables and measurement error was examined.

MAIN OUTCOME MEASURES

The median of three readings at each IOP level was taken as the IOP estimate of each instrument. Measurement error was calculated as the mean difference (tonometer minus direct measurement).

RESULTS

The error for the hand-held applanation tonometer was -1.6, -4.3 and -5.7 at 10, 20, and 30 mmHg, respectively. For the Tono-Pen the measurement error was +0.4, -2.0, and -4.1 at 10, 20, and 30 mmHg, respectively. We could identify no association between measurement error and corneal thickness or curvature, anterior chamber depth, or axial length.

CONCLUSIONS

The applanation tonometer and Tono-Pen underestimate the true IOP in Chinese eyes. Error increases as true IOP increases. These tonometers do not give an accurate estimate of IOP in East Asians.

Age related compliance of the lamina cribrosa in human eyes

AIMS

To investigate changes in the mechanical compliance of ex vivo human lamina cribrosa with age.

METHODS

A laser scanning confocal microscope was used to image the surface of the fluorescently labelled lamina cribrosa in cadaver eyes. A method was developed to determine changes in the volume and strain of the lamina cribrosa created by increases in pressure. The ability of the lamina cribrosa to reverse its deformation on removal of pressure was also measured.

RESULTS

Volume and strain measurements both demonstrated that the lamina cribrosa increased in stiffness with age and the level of pressure applied. The ability of the lamina cribrosa to regain its original shape and size on removal of pressure appeared to decrease with age, demonstrating an age related decrease in resilience of the lamina cribrosa.

CONCLUSIONS

The mechanical compliance of the human lamina cribrosa decreased with age. Misalignment of compliant cribriform plates in a young eye may exert a lesser stress on nerve axons, than that exerted by the rigid plates of an elderly lamina cribrosa. The resilience of the lamina cribrosa also decreased with age, suggesting an increased susceptibility to plastic flow and permanent deformation. Such changes may be of importance in the explanation of age related optic neuropathy in primary open angle glaucoma.

The supramolecular organisation of fibrillin-rich microfibrils determines the mechanical properties of bovine zonular filaments

The zonular filaments from the eyes of cows are rich in microfibrils containing fibrillin. Tensile tests, stress-relaxation tests and X-ray diffraction studies were used to study the relationship between the mechanical behaviour of zonular filaments and the molecular packing and structure of the fibrillin-rich microfibrils. Zonular filaments show a non-linear (J-shaped) stress-strain curve and appreciable stress-relaxation. It is proposed that the non-linear properties are due to local variations in waviness in the microfibrils or assemblies of microfibrils, which straighten out and become more regularly aligned with strain. Previous and current X-ray diffraction results consistently show a partial ordering of microfibrils in zonular filaments into staggered aggregates which become more ordered and laterally aligned on stretching. Although the removal and re-addition of Ca(2+) is known to change the molecular structure of fibrillin, no effect was observed on the tensile properties of the zonular filaments. It is hypothesised that strain-induced deformation in the supramolecular aggregate packing may not be Ca(2+)-sensitive but could dominate the mechanical behaviour of microfibrillar arrays in zonular filaments.