A structural model for the in vivo human cornea including collagen-swelling interaction

Corneal biomechanics and diagnostics: a review

PURPOSE

Corneal biomechanics is an emerging field and the interest into physical and biological interrelations in the anterior part of the eye has significantly increased during the past years. There are many factors that determine corneal biomechanics such as hormonal fluctuations, hydration and environmental factors. Other factors that can affect the corneas are the age, the intraocular pressure and the central corneal thickness. The purpose of this review is to evaluate the factors affecting corneal biomechanics and the recent advancements in non-destructive, in vivo measurement techniques for early detection and improved management of corneal diseases.

METHODS

Until recently, corneal biomechanics could not be directly assessed in humans and were instead inferred from geometrical cornea analysis and ex vivo biomechanical testing. The current research has made strides in studying and creating non-destructive and contactless techniques to measure the biomechanical properties of the cornea in vivo.

RESULTS

Research has indicated that altered corneal biomechanics contribute to diseases such as keratoconus and glaucoma. The identification of pathological corneas through the new measurement techniques is imperative for preventing postoperative complications.

CONCLUSIONS

Identification of pathological corneas is crucial for the prevention of postoperative complications. Therefore, a better understanding of corneal biomechanics will lead to earlier diagnosis of ectatic disorders, improve current refractive surgeries and allow for a better postoperative treatment.

Glycosaminoglycans and collagen fibril distribution at various depths of the corneal stroma of normal and CXL treated rats

Corneal collagen cross-linking (CXL) is widely used to treat keratoconus and ecstatic corneal disorders. The present studies were carried out to investigate the distribution of glycosaminoglycans (GAGs) and collagen fibril (CF) at different depths of the normal and CXL treated corneal stroma of four week old rats 7 days after standard CXL application. Ten Wistar rats' corneas were used for the study. The epithelium of the cornea from the left eye of each rat was removed and treated with standard CXL application using riboflavin and Ultraviolet-A (UVA) (3 mW/cm2 for 30 min). The cornea from the right eye was used as the control cornea. The cornea was removed from the eye and processed for transmission electron microscopy. A bottom mounted Quemesa camera was used to capture digital images and these images were analysed using iTEM software. In the control cornea, the GAGs area size was not significantly different in the anterior, middle, and posterior stroma. In the CXL treated rats the GAGs area size gradually increased from the anterior to the posterior stroma whereas the spacing between the GAGs gradually decreased. There were very large GAGs present in the posterior stroma of the CXL treated rats. When comparing the control and CXL cornea, the GAGs area in the CXL cornea was significantly higher and inter-GAGs-spacing was smaller than in the control cornea. In the control cornea, the collagen fibrils diameter was higher in the anterior stroma and lowest in the posterior stroma. In the CXL treated cornea, the CF diameter and the interfibrillar spacing gradually decreased from the anterior to the posterior stroma. On comparison between the control and the CXL treated cornea, the interfibrillar spacing was significantly smaller in the CXL treated cornea than the control cornea in the anterior, middle, and posterior stroma but there was no difference in the diameter. The CXL treatment significantly increased the GAGs area and decreased the inter-GAGs-spacing, and inter-CF-spacing. This could be due to the gradual decline in the availability of riboflavin, UVA, and oxygen in the middle and posterior stroma. Further studies are required to investigate the role of keratan sulphate and chondroitin sulphate by using monoclonal antibodies with immunogold technique.

Direct measurements of collagen fiber recruitment in the posterior pole of the eye

Collagen is the main load-bearing component of the peripapillary sclera (PPS) and lamina cribrosa (LC) in the eye. Whilst it has been shown that uncrimping and recruitment of the PPS and LC collagen fibers underlies the macro-scale nonlinear stiffening of both tissues with increased intraocular pressure (IOP), the uncrimping and recruitment as a function of local stretch have not been directly measured. This knowledge is crucial to understanding their functions in bearing loads and maintaining tissue integrity. In this project we measured local stretch-induced collagen fiber bundle uncrimping and recruitment curves of the PPS and LC. Thin coronal samples of PPS and LC of sheep eyes were mounted and stretched biaxially quasi-statically using a custom system. At each step, we imaged the PPS and LC with instant polarized light microscopy and quantified pixel-level (1.5 μm/pixel) collagen fiber orientations. We used digital image correlation to measure the local stretch and quantified collagen crimp by the circular standard deviation of fiber orientations, or waviness. Local stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers than the LC at the low levels of stretch. At 10% stretch the curves crossed with 75% bundles recruited. The PPS had higher uncrimping rate and waviness remaining after recruitment than the LC: 0.9º vs. 0.6º and 3.1º vs. 2.7º. Altogether our findings support describing fiber recruitment of both PPS and LC with sigmoid curves, with the PPS recruiting faster and at lower stretch than the LC, consistent with a stiffer tissue. STATEMENT OF SIGNIFICANCE: Peripapillary sclera (PPS) and lamina cribrosa (LC) collagen recruitment behaviors are central to the nonlinear mechanical behavior of the posterior pole of the eye. How PPS and LC collagen fibers recruit under stretch is crucial to develop constitutive models of the tissues but remains unclear. We used image-based stretch testing to characterize PPS and LC collagen fiber bundle recruitment under local stretch. We found that fiber-level stretch-recruitment curves of PPS and LC approximated sigmoid functions. PPS recruited more fibers at a low stretch, but at 10% bundle stretch the two curves crossed with 75% bundles recruited. We also found that PPS and LC fibers had different uncrimping rates and non-zero waviness's when recruited.

Agreement of intraocular pressure measurement with Corvis ST, non-contact tonometer, and Goldmann applanation tonometer in children with ocular hypertension and related factors

AIM

To access the agreement of intraocular pressure (IOP) values obtained from biomechanically corrected tonometer [Corvis ST (CST)], non-contact tonometer (NCT), and Goldmann applanation tonometer (GAT) in children with NCT measured-IOP (NCT-IOP) values of 22 mm Hg or more, and related factors.

METHODS

A total of 51 eyes with NCT-IOP≥22 mm Hg in children aged 7 to 14y were examined and IOP was measured by CST, NCT, and GAT. Based on GAT measured IOP (GAT-IOP), ocular hypertension (OHT) group (≥22 mm Hg, 24 eyes) and the non-OHT group (<22 mm Hg, 27 eyes) were defined. We compared the agreement of the three measurements, i.e., CST measured IOP (CST-IOP), GAT-IOP, and NCT-IOP, and further analyzed the correlation between the differences in tonometry readings, central corneal thickness (CCT), axial length (AL), optic disc rim volume, and age.

RESULTS

Compared with the OHT group, thicker CCT, larger rim volume, and higher differences between NCT-IOP and GAT-IOP, were found in the non-OHT group. The differences between CST-IOP and GAT-IOP were lower than the differences between NCT-IOP and GAT-IOP in both groups. The mean differences in CST-IOP and GAT-IOP were 1.26 mm Hg (95% limit of agreement ranged from 0.1 to 2.41 mm Hg, OHT group) and 1.20 mm Hg (95% limit of agreement ranged from -0.5 to 3.00 mm Hg, non-OHT group), and the mean differences in NCT and GAT were 3.90 mm Hg (95% limit of agreement ranged from -0.19 to 9.70 mm Hg, OHT group) and 6.00 mm Hg (95% limit of agreement ranged from 1.50 to 10.50 mm Hg, non-OHT group). The differences between CST-IOP and GAT-IOP were not related to CCT, age, and AL in both groups; while the differences between NCT-IOP and GAT-IOP were related to CCT in the OHT group (r=0.93, P<0.001) and to CCT and AL in the non-OHT group (r=0.66, P<0.001, r=-0.81, P<0.001).

CONCLUSION

The accuracy of NCT in the diagnosis of pediatric OHT is low. The agreement of CST-IOP and GAT-IOP was significantly higher in children with and without OHT than in those with NCT-IOP and GAT-IOP. Therefore, CST can be used as a good alternative for IOP measurement in children. The impacts of CCT and AL on NCT measurement need to be fully considered when managing childhood IOP.

Biomechanics of keratoconus: Two numerical studies

BACKGROUND

The steep cornea in keratoconus can greatly impair eyesight. The etiology of keratoconus remains unclear but early injury that weakens the corneal stromal architecture has been implicated. To explore keratoconus mechanics, we conducted two numerical simulation studies.

METHODS

A finite-element model describing the five corneal layers and the heterogeneous mechanical behaviors of the ground substance and lamellar collagen-fiber architecture in the anterior and posterior stroma was developed using the Holzapfel-Gasser-Ogden constitutive model. The geometry was from a healthy subject. Its stroma was divided into anterior, middle, and posterior layers to assess the effect of changing regional mechanical parameters on corneal displacement and maximum principal stress under intraocular pressure. Specifically, the effect of softening an inferocentral corneal button, the collagen-based tissues throughout the whole cornea, or specific stromal layers in the button was examined. The effect of simply disorganizing the orthogonally-oriented posterior stromal fibers in the button was also assessed. The healthy cornea was also subjected to eye rubbing-like loading to identify the corneal layer(s) that experienced the most tensional stress.

RESULTS

Conical deformation and corneal thinning emerged when the corneal button or the mid-posterior stroma of the button underwent gradual softening or when the collagen fibers in the mid-posterior stroma of the button were dispersed. Softening the anterior layers of the button or the whole cornea did not evoke conical deformation. Button softening greatly increased and disrupted the stress on Bowman's membrane while mid-posterior stromal softening increased stress in the anterior layers. Eye rubbing profoundly stressed the deep posterior stroma while other layers were negligibly affected.

DISCUSSION

These observations suggest that keratoconus could be initiated, at least partly, by mechanical instability/damage in the mid-posterior stroma that then imposes stress on the anterior layers. This may explain why subclinical keratoconus is marked by posterior but not anterior elevation on videokeratoscopy.

Assessing Corneal Endothelial Damage Using Terahertz Time-Domain Spectroscopy and Support Vector Machines

The endothelial layer of the cornea plays a critical role in regulating its hydration by actively controlling fluid intake in the tissue via transporting the excess fluid out to the aqueous humor. A damaged corneal endothelial layer leads to perturbations in tissue hydration and edema, which can impact corneal transparency and visual acuity. We utilized a non-contact terahertz (THz) scanner designed for imaging spherical targets to discriminate between ex vivo corneal samples with intact and damaged endothelial layers. To create varying grades of corneal edema, the intraocular pressures of the whole porcine eye globe samples (n = 19) were increased to either 25, 35 or 45 mmHg for 4 h before returning to normal pressure levels at 15 mmHg for the remaining 4 h. Changes in tissue hydration were assessed by differences in spectral slopes between 0.4 and 0.8 THz. Our results indicate that the THz response of the corneal samples can vary according to the differences in the endothelial cell density, as determined by SEM imaging. We show that this spectroscopic difference is statistically significant and can be used to assess the intactness of the endothelial layer. These results demonstrate that THz can noninvasively assess the corneal endothelium and provide valuable complimentary information for the study and diagnosis of corneal diseases that perturb the tissue hydration.

Effect of Ultraviolet-A and Riboflavin treatment on the architecture of the center and periphery of normal rat cornea: 7 days post treatment

Corneal collagen cross-linking (CXL) is a treatment that is widely applied to halt the progression of ectatic diseases such as keratoconus by creating biomechanical strength in the cornea. Most of the studies assessed the effect of the CXL on the cornea without any differentiation of its effect between periphery and the center of the untreated control cornea especially after the 7 days of CXL application. We investigate the ultrastructural changes in the architecture of the center and periphery of rat corneas, 7 days after standard CXL application. Five Wistar rats (10 corneas) were used in the present study. The left eye corneas (5 mm area) were de-epithelialized and irradiated with standard CXL application using riboflavin and Ultraviolet-A (UVA) (3 mW/cm² for 30 min). The right eye corneas were used as a control. The sclera-cornea button was removed and processed for electron microscopy. Digital images were captured with a bottom mounted Quemesa camera and analyzed using the iTEM software. The ultrastructure of epithelium, hemi-desmosomes, Bowman's layer and stroma were organized in both untreated control and CXL rat cornea in both untreated control and CXL rat cornea. Within the same CXL cornea, both the collagen fibril (CF) diameter and interfibrillar spacing at the center were significantly smaller compared to the peripheral diameter and spacing of the cornea. When comparing the untreated control and CXL cornea, the central interfibrillar spacing of the CXL cornea was significantly smaller than the central spacing the untreated control cornea. In the CXL cornea the peripheral spacing was significantly higher compared to the peripheral interfibrillar spacing of the untreated control cornea. Within the CXL cornea, the proteoglycans (PGs) area and density of the periphery was significantly higher compared to the area and density of the center of the cornea. It suggests that CXL was more effective at the periphery of the cornea. This could be due to the higher amount of leucine rich PG lumican and higher diffusion of oxygen and riboflavin at the periphery cornea.

Non-contact terahertz spectroscopic measurement of the intraocular pressure through corneal hydration mapping

Elevated intraocular pressure (IOP) results in endothelial layer damage that can induce corneal hydration perturbations. We investigated the potential of terahertz spectroscopy in measuring the IOP levels through mapping corneal water content. We controlled the IOP levels in ex vivo rabbit and porcine eye samples while monitoring the change in corneal hydration using a terahertz time-domain spectroscopy (THz-TDS) scanner. Our results showed a statistically significant increase in the THz reflectivity between 0.4 and 0.6 THz corresponding to the increase in the IOP. Endothelial layer damage was confirmed using scanning electron microscopy (SEM) of the corneal biopsy samples. Our empirical results indicate that the THz-TDS can be used to track IOP levels through the changes in corneal hydration.

Indentation of the cornea: A Bi-layer contact problem

Histological observations of the cornea have identified the presence of multiple layers with differing thickness and function. The composition of the cornea consists primarily of collagen fibrils held together with proteoglycans but with an aqueous interstitial component being dominant. Indentation provides a means to quantify the spatial variation of the mechanical properties of the cornea, however the role of the different layers on the indentation response has barely been addressed. In addition, the response of the fluid content and its displacement during indentation has not been adequately considered. In this study indentation of the cornea with a relatively large spherical tipped indenter (R = 500 μm) is considered. It was observed that the initial phase of loading did not fit a classic Hertz elastic response but showed an initial steeper slope that gradually declines with increasing force and displacement. A relatively simple approach is developed that initially considers the cornea as a poro-elastic bi-layer contact problem, that is the presence of an outer thin stiffer Bowman's layer overlaying the thicker less stiff stroma.

Inverse solution of corneal material parameters based on non-contact tonometry: A comparative study of different constitutive models

Assessing the biomechanical properties of the cornea in vivo is important for predicting the outcome of refractive surgery, and for controlling the risk of postoperative complications. In this study, we examined the impact of corneal mechanical properties (nonlinearity and anisotropy) on the inverse solution of corneal material parameters based on the non-contact tonometry ("air puff") test. Finite element models with different constitutive models (linear-elastic, isotropic hyperelastic, and fiber-dependent) were established to simulate the non-contact tonometry test. The results showed that the corneal nonlinear mechanical property and fiber distribution had significant effects on the corneal deflection profile. These findings may help in constructing an appropriate inverse solution strategy when using the inverse finite element method and in identifying individual differences in the corneal matrix shear modulus and fiber stiffness.

The best optical zone for small-incision lenticule extraction in high myopic patients

Small-incision lenticule extraction (SMILE) is an effective and safe procedure for the correction of myopia due to minimally invasive and noncorneal flap surgery. However, the SMILE procedure has certain requirements for corneal cap thickness, attempted refractive correction, residual stromal bed thickness, and optical zone diameter, which sometimes make surgeons hesitant to choose SMILE or other refractive surgeries. The requirements limit its use in patients with high myopia. The purpose of this review was to find the optimal parameters of SMILE through discussing the best optical zone for high myopic patients, the visual quality of different optical zones, the choice of corneal cap thickness, and their effects on corneal biomechanical parameters, so surgeons can provide reference recommendations for patients with high myopia in choosing a reasonable and safe procedure.

Investigation of water diffusion dynamics in corneal phantoms using terahertz time-domain spectroscopy

Perturbation of normal corneal water content is a common manifestation of many eye diseases. Terahertz (THz) imaging has the potential to serve as a clinical tool for screening and diagnosing such corneal diseases. In this study, we first investigate the diffusive properties of a corneal phantom using simultaneous THz time-domain spectroscopy (THz-TDS) and gravimetric measurements. We will then utilize a variable-thickness diffusion model combined with a stratified composite-media model to simulate changes in thickness, hydration profile, and the THz-TDS signal as a function of time. The simulated THz-TDS signals show very good agreement with the reflection measurements. Results show that the THz-TDS technique can be used to understand water diffusion dynamics in corneal phantoms as a step towards future in vivo quantitative hydration sensing.

A Review of Structural and Biomechanical Changes in the Cornea in Aging, Disease, and Photochemical Crosslinking

The study of corneal biomechanics is motivated by the tight relationship between biomechanical properties and visual function within the ocular system. For instance, variation in collagen fibril alignment and non-enzymatic crosslinks rank high among structural factors which give rise to the cornea's particular shape and ability to properly focus light. Gradation in these and other factors engender biomechanical changes which can be quantified by a wide variety of techniques. This review summarizes what is known about both the changes in corneal structure and associated changes in corneal biomechanical properties in aging, keratoconic, and photochemically crosslinked corneas. In addition, methods for measuring corneal biomechanics are discussed and the topics are related to both clinical studies and biomechanical modeling simulations.

Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method

The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

Cap morphology after small-incision lenticule extraction and its effects on intraocular scattering

AIM

To investigate cap morphology after small-incision lenticule extraction (SMILE) and its effects on intraocular scattering.

METHODS

Sixty-five eyes of 33 patients undergoing SMILE were enrolled. In addition to regular evaluation, Fourier-domain optical coherence tomography was used to investigate cap thickness at 1d, 1wk, 1 and 3mo postoperatively. The optical quality including modulation transfer function cutoff frequency, Strehl ratio, Optical Quality Analysis System (OQAS) values, and objective scattering index (OSI), were evaluated using OQAS™.

RESULTS

Cap thickness decreased from 1d to 1wk (P<0.001), but remained higher than intended thickness of 120 µm after 3mo (P<0.001). Cap thickness in central area was thinner than that of in the paracentral and peripheral areas (P<0.0001). Total number of microdistortions decreased from 1d to 3mo (P<0.0001). Pearson analysis revealed a weak correlation between OSI and standard deviation of cap thickness at 1d and 1mo, as well as between range of cap thickness and OSI at 1mo. No correlation was found between microdistortion and OSI, but a negative correlation existed between microdistortion and range at 1d and 1moafter surgery.

CONCLUSION

The corneal cap tends to be more accurate and regular with time lapse. Better cap morphology tends to contribute less intraocular scattering in the eyes undergoing SMILE.

The structural response of the cornea to changes in stromal hydration

The primary aim of this study was to quantify the relationship between corneal structure and hydration in humans and pigs. X-ray scattering data were collected from human and porcine corneas equilibrated with polyethylene glycol (PEG) to varying levels of hydration, to obtain measurements of collagen fibril diameter, interfibrillar spacing (IFS) and intermolecular spacing. Both species showed a strong positive linear correlation between hydration and IFS² and a nonlinear, bi-phasic relationship between hydration and fibril diameter, whereby fibril diameter increased up to approximately physiological hydration, H = 3.0, with little change thereafter. Above H = 3.0, porcine corneas exhibited a larger fibril diameter than human corneas (p < 0.001). Intermolecular spacing also varied with hydration in a bi-phasic manner but reached a maximum value at a lower hydration (H = 1.5) than fibril diameter. Human corneas displayed a higher intermolecular spacing than porcine corneas at all hydrations (p < 0.0001). Human and porcine corneas required a similar PEG concentration to reach physiological hydration, suggesting that the total fixed charge that gives rise to the swelling pressure is the same. The difference in their structural responses to hydration can be explained by variations in molecular cross-linking and intra/interfibrillar water partitioning.

Peripheral Endothelial Cell Count Is a Predictor of Disease Severity in Advanced Fuchs Endothelial Corneal Dystrophy

PURPOSE

In advanced Fuchs endothelial corneal dystrophy (FECD), central endothelial changes do not correlate with disease severity. The peripheral endothelial cell count (ECC) has not been studied as a marker of FECD severity. The goal of this study was to determine the relationship between the peripheral ECC and known clinical markers of FECD in advanced cases.

METHODS

Patients with FECD examined between January 1, 2013, and September 1, 2016, by 1 cornea specialist were identified. Medical records from all previous visits were reviewed to include eyes with high-quality central and peripheral in vivo confocal microscopy images performed on the same day as a clinical evaluation. Endothelial photographs were used to perform manual cell counts centrally and peripherally. Clinical grading of FECD from 1 to 4 was performed at the slit-lamp.

RESULTS

We identified 154 eyes of 126 patients that met criteria for inclusion. With higher disease grades, central ECC and peripheral ECC decreased, visual acuity worsened, and central corneal thickness (CCT) increased (all P < 0.05). In patients with advanced disease (defined as either grade 3 or 4, CCT >700, or central ECC <350), the peripheral ECC was the best predictor of disease severity and had the highest number of statistically significant correlations with other clinical markers compared with competing variables.

CONCLUSIONS

In advanced FECD, severity is best determined by the peripheral ECC compared with the central ECC, visual acuity, clinical disease grade, and CCT. The peripheral ECC should be added to the clinical parameters used to evaluate FECD severity.

Biomechanical Simulation of Stress Concentration and Intraocular Pressure in Corneas Subjected to Myopic Refractive Surgical Procedures

Recent advances in the analysis of corneal biomechanical properties remain difficult to predict the structural stability before and after refractive surgery. In this regard, we applied the finite element method (FEM) to determine the roles of the Bowman’s membrane, stroma, and Descemet’s membrane in the hoop stresses of cornea, under tension (physiological) and bending (nonphysiological), for patients who undergo radial keratotomy (RK), photorefractive keratectomy (PRK), laser-assisted in situ keratomileusis (LASIK), or small incision lenticule extraction (SMILE). The stress concentration maps, potential creak zones, and potential errors in intraocular pressure (IOP) measurements were further determined. Our results confirmed that the Bowman’s membrane and Descemet’s membrane accounted for 20% of the bending rigidity of the cornea, and became the force pair dominating the bending behaviour of the cornea, the high stress in the distribution map, and a stretch to avoid structural failure. In addition, PRK broke the central linking of hoop stresses and concentrated stress on the edge of the Bowman’s membrane around ablation, which posed considerable risk of potential creaks. Compared with SMILE, LASIK had a higher risk of developing creaks around the ablation in the stroma layer. Our FEM models also predicted the postoperative IOPs precisely in a conditional manner.

A nonlinear poroelastic theory of solid tumors with glycosaminoglycan swelling

Mechanics plays a crucial role in the growth, development, and therapeutics of tumors. In this paper, a nonlinear poroelastic theory is established to describe the mechanical behaviors of solid tumors. The free-swollen state of a tumor is chosen as the reference state, which enables us to avoid pursuing a dry and stress-free state that is hard to achieve for living tissues. Our results reveal that the compression resistance of a tumor is primarily attributed to glycosaminoglycan (GAG) swelling, and the compactness of cell aggregates is found to affect tumor consolidation. Over-expressed GAGs and dense cell aggregates can stiffen the tumor, a remodeling mechanism that makes the tumor with higher elastic modulus than its surrounding host tissues. Glycosaminoglycan chains also influence the transient mechanical response of the tumor by modulating the tissue permeability. The theoretical results show good agreement with relevant experimental observations. This study may not only deepen our understanding of tumorigenesis but also provide cues for developing novel anticancer strategies.

Comparison of Patient-Specific Computational Modeling Predictions and Clinical Outcomes of LASIK for Myopia

Purpose

To assess the predictive accuracy of simulation-based LASIK outcomes.

Methods

Preoperative and 3-month post-LASIK tomographic data from 20 eyes of 12 patients who underwent wavefront-optimized LASIK for myopia were obtained retrospectively. Patient-specific finite element models were created and case-specific treatment settings were simulated. Simulated keratometry (SimK) values and the mean tangential curvature of the central 3 mm (Kmean) were obtained from the anterior surfaces of the clinical tomographies, and computational models were compared. Correlations between Kmean prediction error and patient age, preoperative corneal hysteresis (CH), and corneal resistance factor (CRF) were assessed.

Results

The mean difference for Kmean between simulated and actual post-LASIK cases was not statistically significant (-0.13 ± 0.36 diopters [D], P = 0.1). The mean difference between the surgically induced clinical change in Kmean and the model-predicted change was -0.11 ± 0.34 D (P = 0.2). Kmean prediction error was correlated to CH, CRF, and patient age (r = 0.63, 0.53, and 0.5, respectively, P < 0.02), and incorporation of CH values into predictions as a linear offset increased their accuracy. Simulated changes in Kmean accounted for 97% of the variance in actual spherical equivalent refractive change.

Conclusions

Clinically feasible computational simulations predicted corneal curvature and manifest refraction outcomes with a level of accuracy in myopic LASIK cases that approached the limits of measurement error. Readily available preoperative biomechanical measures enhanced simulation accuracy. Patient-specific simulation may be a useful tool for clinical guidance in de novo LASIK cases.

The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium

The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments. The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges. The steady-state analysis on active membranes suggests a new pressure mechanism which balances the fluid pressure together with the osmotic pressure. The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport. We apply the proposed theory to study the transendothelial fluid pressure in the in vivo cornea, which is a crucial factor maintaining the hydration and transparency of the tissue. The results show the importance of the proposed pressure mechanism in mediating stromal fluid pressure and provide a new interpretation of the pressure modulation mechanism in the in vivo cornea.