Characterization of hyperelastic mechanical properties for youth corneal anterior central stroma based on collagen fibril crimping constitutive model

Investigation of the optimal cutting depth in small incision lenticule extraction based on a collagen fibril crimping constitutive model of the cornea

To investigate the optimal cutting depth (Cap) in small incision lenticule extraction from the perspective of corneal biomechanics, a three-dimensional finite element model of the cornea was established using a stromal sub-regional material model to simulate small incision lenticule extraction. The displacement difference PΔ at the central point of the posterior corneal surface before and after lenticule extraction, as well as the von Mises stress at four points of different thicknesses in the center of the cornea, were analyzed using the finite element model considering the hyperelastic property and the difference in stiffness between the anterior and posterior of the cornea. The numerical curves of PΔ-Cap and von Mises Stress-Cap relations at different diopters show that the displacement difference PΔ has a smallest value at the same diopter. In this case, the von Mises stress at four points with different thicknesses in the center of the cornea was also minimal. Which means that the optimal cutting depth exsisting in the cornea. Moreover, PΔ-Cap curves for different depth of stromal stiffness boundaries show that the optimal cap thickness would change with the depth of the stromal stiffness boundary. These results are of guiding significance for accurately formulating small incision lenticule extraction surgery plans and contribute to the advancement of research on the biomechanical properties of the cornea.

Corneal retardation time as an ocular hypertension disease indicator

Objective.A detailed analysis of the corneal retardation timeτas a highly related parameter to the intraocular pressure (IOP), and its plausible role as an indicator of ocular hypertension disease.Approach.A simple theoretical expression forτis derived within the corneal viscoelastic model of Kelvin-Voigt with 3 elements. This retardation time can be easily calculated from the well-known signal and pressure amplitudes of non-contact tonometers like the Ocular Response Analyzer (ORA). Then, a population-based study was performed where 100 subjects aged from 18 to 30 were analyzed (within this group, about 10% had an elevated IOP with more than 21 mmHg).Main results.A clear relationship between the corneal retardation time and the corneal-compensated intraocular pressure (IOPcc) was found, underlying the risk for ocular hypertensive (OHT) subjects with lowerτvalues to develop hypertension illnesses (due to the inability of poorly viscoelastic corneas to absorb IOP fluctuations, resulting in probable optic nerve damage).Significance.Our results might provide an useful tool to systematically discern which OHT patients (and even those with normal IOP values) are more likely to suffer glaucoma progression and, consequently, ensure an early diagnosis.

Biaxial hyperelastic and anisotropic behaviors of the corneal anterior central stroma along the preferential fibril orientations. Part I: Measurement and calibration of personalized stress-strain curves

Lacking specimens is the biggest limitation of studying the mechanical behaviors of human corneal. Extracting stress-strain curves is the crucial step in investigating hyperelastic and anisotropic properties of human cornea. 15 human corneal specimens extracted from the small incision lenticule extraction (SMILE) surgery were applied in this study. To accurately measure the personalized true stress-strain curve using corneal lenticules, the digital image correlation (DIC) method and finite element method were used to calibrate the stress and the strain of the biaxial extension test. The hyperelastic load-displacement curves obtained from the biaxial extension test were performed in preferential fibril orientations, which are arranged along the nasal-temporal (NT) and the superior-inferior (SI) directions within the anterior central stroma. The displacement and strain fields were accurately calibrated and calculated using the digital image correlation (DIC) method. A conversion equation was given to convert the effective engineering strain to the true strain. The stress field distribution, which was simulated using the finite element method, was verified. Based on this, the effective nominal stress with personalized characteristics was calibrated. The personalized stress-strain curves containing individual characteristic, like diopter and anterior surface curvature, was accurately measured in this study. These results provide an experimental method using biaxial tensile test with corneal lenticules. It is the foundation for investigating the hyperelasticity and anisotropy of the central anterior stroma of human cornea.

Patient-specific finite element analysis of human corneal lenticules: An experimental and numerical study

The number of elective refractive surgeries is constantly increasing due to the drastic increase in myopia prevalence. Since corneal biomechanics are critical to human vision, accurate modeling is essential to improve surgical planning and optimize the results of laser vision correction. In this study, we present a numerical model of the anterior cornea of young patients who are candidates for laser vision correction. Model parameters were determined from uniaxial tests performed on lenticules of patients undergoing refractive surgery by means of lenticule extraction, using patient-specific models of the lenticules. The models also took into account the known orientation of collagen fibers in the tissue, which have an isotropic distribution in the corneal plane, while they are aligned along the corneal curvature and have a low dispersion outside the corneal plane. The model was able to reproduce the experimental data well with only three parameters. These parameters, determined using a realistic fiber distribution, yielded lower values than those reported in the literature. Accurate characterization and modeling of the cornea of young patients is essential to study better refractive surgery for the population undergoing these treatments, to develop in silico models that take corneal biomechanics into account when planning refractive surgery, and to provide a basis for improving visual outcomes in the rapidly growing population undergoing these treatments.

Computational modeling of electromechanical coupling in human cardiomyocyte applied to study hypertrophic cardiomyopathy and its drug response

BACKGROUND AND OBJECTIVE

Knowledge of electromechanical coupling in cardiomyocyte and how it is influenced by various pathophysiological factors is fundamental to understanding the pathogenesis of myocardial disease and its response to medication, which is however hard to be thoroughly addressed by clinical/experimental studies due to technical limitations. At this point, computational modeling offers an alternative approach. The main objective of the study was to develop a computational model capable of simulating the process of electromechanical coupling and quantifying the roles of various factors in play in the human left ventricular cardiomyocyte.

METHODS

A new electrophysiological model was firstly built by combining several existing electrophysiological models and incorporating the mechanism of electrophysiological homeostasis, which was subsequently coupled to models representing the cross-bridge dynamics and active force generation during excitation-contraction coupling and the passive mechanical properties of cardiomyocyte to yield an integrative electromechanical model. Model parameters were calibrated or optimized based on a large amount of experimental data. The resulting model was applied to delineate the characteristics of electromechanical coupling and explore underlying determinant factors in hypertrophic cardiomyopathy (HCM) cardiomyocyte, as well as quantify their changes in response to different medications.

RESULTS

Model predictions captured the major electromechanical characteristics of cardiomyocyte under both normal physiological and HCM conditions. In comparison with normal cardiomyocyte, HCM cardiomyocyte suffered from systemic changes in both electrophysiological and mechanical variables. Numerical simulations of drug response revealed that Mavacamten and Metoprolol could both reduce the active contractility and alleviate calcium overload but had marked differential influences on many other electromechanical variables, which theoretically explained why the two drugs have differential therapeutic effects. In addition, our numerical experiments demonstrated the important role of compensatory ion transport in maintaining electrophysiological homeostasis and regulating cytoplasmic volume.

CONCLUSIONS

A sophisticated computational model has the advantage of providing quantitative and integrative insights for understanding the pathogenesis and drug responses of HCM or other myocardial diseases at the level of cardiomyocyte, and hence may contribute as a useful complement to clinical/experimental studies. The model may also be coupled to tissue- or organ-level models to strengthen the physiological implications of macro-scale numerical simulations.

Biaxial hyperelastic and anisotropic behaviors of the corneal anterior central stroma along the preferential fibril orientations. Part II: Quantitative computational analysis of mechanical response of stromal components

To study the hyperelastic and anisotropic behaviors of the central anterior stroma for patients with myopia, 40 corneal stromal specimens extracted after small incision lenticule extraction (SMILE) surgery were used in the biaxial extension test along two preferential fibril orientations. An improved collagen fibril crimping constitutive model with a specific physical meaning was proposed to analyze the hyperelasticity and anisotropy of the stroma. The effective elastic modulus of the two families of preferentially oriented collagen fibrils and the stiffness of the non-collagenous matrix along all three directions were compared according to the specific physical meaning of the parameters. Anisotropic behavior was found in the hyperelastic properties of the corneal anterior central stroma in the preferential fibril orientations. The stiffness of non-collagenous matrix is significantly larger in the optical axis direction than in the nasal-temporal (NT) and superior-inferior (SI) directions. Moreover, individual differences between males and females slightly impact on hyperelastic and anisotropic behaviors. The differences of these behaviors were significant in the comparison of the left and right eyes. These results have a guiding significance for the accurate design of surgical plans for refractive surgery according to a patient's condition and have a driving value for the further exploration of the biomechanical properties of the whole cornea.

Effectiveness of collagen cross-linking induced by two-photon absorption properties of a femtosecond laser in ex vivo human corneal stroma

This study aimed to investigate the effectiveness of two-photon induced collagen cross-linking (CXL) using femtosecond lasers in human corneal stroma. An 800-nm femtosecond laser optical path for CXL was established. Corneal samples that received two-photon induced CXL and ultraviolet-A (UVA) CXL underwent uniaxial stretching experiments, proteolytic resistance assays and observation of collagen fiber structure changes. Two-photon induced CXL can achieve corneal stiffening effects comparable to UVA CXL and showed better advantages at low strains. The cornea after two-photon induced CXL exhibited high enzymatic resistance and tight collagen fiber arrangement. Two-photon induced CXL promises to be a new option for keratoconus.

Measuring Human Corneal Stromal Biomechanical Properties Using Tensile Testing Combined With Optical Coherence Tomography

Purpose: To investigate the ex vivo elastic modulus of human corneal stroma using tensile testing with optical coherence tomography (OCT) imaging and its correlation with in vivo measurements using corneal visualization Scheimpflug technology.

Methods: Twenty-four corneal specimens extracted from stromal lenticules through small incision lenticule extraction were cut into strips for uniaxial tensile tests. In vivo corneal biomechanical responses were evaluated preoperatively using the corneal visualization Scheimpflug technology (CorVis ST). The correlation of the elastic modulus with clinical characteristics and dynamic corneal response parameters were analyzed using Spearman’s correlation analysis.

Results: The mean low strain tangent modulus (LSTM) of the human corneal stroma was 0.204 ± 0.189 (range 0.010–0.641) MPa, and high strain tangent modulus (HSTM) 5.114 ± 1.958 (range 2.755–9.976) MPa. Both LSTM (r = 0.447, p = 0.029) and HSTM (r = 0.557, p = 0.005) were positively correlated with the stress-strain index (SSI). LSTM was also positively correlated with the A1 deflection length (r = 0.427, p = 0.037) and A1 deflection area (r = 0.441, p = 0.031). HSTM was positively correlated with spherical equivalent (r = 0.425, p = 0.038).

Conclusions: The correlation of corneal elastic modulus with A1 deflection parameters and SSI may indicate a relationship between these parameters and tissue elasticity. The HSTM decreased with the degree of myopia. Combining tensile test with OCT may be a promising approach to assess corneal biomechanical properties.

Exploring the Biomechanical Properties of the Human Cornea In Vivo Based on Corvis ST

Purpose: The aim of this study was to provide a method to determine corneal nonlinear viscoelastic properties based on the output data of corneal visualization Scheimpflug technology (Corvis ST).

Methods: The Corvis ST data from 18 eyes of 12 healthy humans were collected. Based on the air-puff pressure and the corneal displacement from the Corvis ST test of normal human eyes, the work done by the air-puff attaining the whole corneal displacement was obtained. By applying a visco-hyperelastic strain energy density function of the cornea, in which the first-order Prony relaxation function and the first-order Ogden strain energy were employed, the corneal strain energy during the Corvis ST test was calculated. Then the work done by the air-puff attaining the whole corneal displacement was completely regarded as the strain energy of the cornea. The identification of the nonlinear viscoelastic parameters was carried out by optimizing the sum of difference squares of the work and the strain energy using the genetic algorithm.

Results: The visco-hyperelastic model gave a good fit to the data of corneal strain energy with time during the Corvis ST test (R² > 0.95). The determined Ogden model parameter μ ranged from 0.42 to 0.74 MPa, and α ranged from 32.76 to 55.63. The parameters A and τ in the first-order Prony function were 0.09–0.36 and 1.21–1.95 ms, respectively.

Conclusion: It is feasible to determine the corneal nonlinear viscoelastic properties based on the corneal contour information and air-puff pressure of the Corvis ST test.

Time-varying regularity of changes in biomechanical properties of the corneas after removal of anterior corneal tissue

Background

The corneal biomechanical properties with the prolongation of time after corneal refractive surgery are important for providing a mechanical basis for the occurrence of clinical phenomena such as iatrogenic keratectasia and refractive regression. The aim of this study was to explore the changes of corneal elastic modulus, and stress relaxation properties from the 6-month follow-up observations of rabbits after a removal of anterior corneal tissue in simulation to corneal refractive surgery.

Methods

The anterior corneal tissue, 6 mm in diameter and 30–50% of the original corneal thickness, the left eye of the rabbit was removed, and the right eye was kept as the control. The rabbits were normally raised and nursed for 6 months, during which corneal morphology data, and both of corneal hysteresis (CH) and corneal resistance factor (CRF) were gathered. Uniaxial tensile tests of corneal strips were performed at months 1, 3, and 6 from 7 animals, and corneal collagen fibrils were observed at months 1, 3, and 6 from 1 rabbit, respectively.

Results

Compared with the control group, there were statistical differences in the curvature radius at week 2 and month 3, and both CH and CRF at months 1, 2, and 6 in experiment group; there were statistical differences in elastic modulus at 1, 3, and month 6, and stress relaxation degree at month 3 in experiment group. The differences in corneal elastic modulus, stress relaxation degree and the total number of collagen fibrils between experiment and control groups varied gradually with time, and showed significant changes at the 3rd month after the treatment.

Conclusions

Corneas after a removal of anterior corneal tissue undergo dynamic changes in corneal morphology and biomechanical properties. The first 3 months after treatment could be a critical period. The variation of corneal biomechanical properties is worth considering in predicting corneal deformation after a removal of anterior corneal tissue.

Changes and quantitative characterization of hyper-viscoelastic biomechanical properties for young corneal stroma after standard corneal cross-linking treatment with different ultraviolet-A energies

Corneal collagen cross-linking (CXL) treatment can restore vision in patients suffering from keratoconus and corneal injury, by improving the mechanical properties of the cornea. The correlation between ultraviolet-A (UVA) irradiant energies of standard CXL (SCXL) and corneal visco-hyperelastic mechanical behavior remains unknown. In this study, SCXL with four different UVA irradiant energy doses (0-5.4 J/cm²) were administered as part of quantitative treatments of corneal stromal lenticules extracted from young myopic patients via small incision lenticule extraction (SMILE) corneal refractive surgery. Double-strip samples with symmetric geometries were cut simultaneously for SCXL treatment and non-treated control. First, 40 pairs of strips were loaded to failure to assess the mechanical parameters of the material. Then, another 40 pairs were tested using a special uniaxial tensile test including quasi-static loading-unloading, instantaneous loading, and stress relaxation, to determine the visco-hyperelastic mechanical behavior. Upon combining the collagen fibril crimping constitutive model with the quasi-linear viscoelastic model, it was observed that with increasing UVA energy dose, the corneal strength and hyperelastic stiffness were significantly enhanced, while the maximum stretch and viscosity of the cornea were significantly reduced. Considering the quantitative analysis of SCXL and the rehabilitation prediction of keratoconus treatment, the results clarify the biomechanical behavior of human corneal stroma in SCXL clinical surgery. STATEMENT OF SIGNIFICANCE: This study quantitatively analyzes the improvement in the biomechanical properties of young central corneal stroma, due to SCXL treatment with different energies. Furthermore, the correlation between the hyper-viscoelastic mechanical parameters and UVA irradiant energy doses of SCXL are clarified. The contribution of this study fills the knowledge gap of the CXL on corneal biomechanics. It can not only clarify this mechanism better but also assist with guiding SCXL surgery for individualized patient corneas.

Characterization of non-linear mechanical behavior of the cornea

The objective of this study was to evaluate which hyperelastic model could best describe the non-linear mechanical behavior of the cornea, in order to characterize the capability of the non-linear model parameters to discriminate structural changes in a damaged cornea. Porcine corneas were used, establishing two different groups: control (non-treated) and NaOH-treated (damaged) corneas (n = 8). NaOH causes a chemical burn to the corneal tissue, simulating a disease associated to structural damage of the stromal layer. Quasi-static uniaxial tensile tests were performed in nasal-temporal direction immediately after preparing corneal strips from the two groups. Three non-linear hyperelastic models (i.e. Hamilton-Zabolotskaya model, Ogden model and Mooney-Rivlin model) were fitted to the stress–strain curves obtained in the tensile tests and statistically compared. The corneas from the two groups showed a non-linear mechanical behavior that was best described by the Hamilton-Zabolotskaya model, obtaining the highest coefficient of determination (R² > 0.95). Moreover, Hamilton-Zabolotskaya model showed the highest discriminative capability of the non-linear model parameter (Parameter A) for the tissue structural changes between the two sample groups (p = 0.0005). The present work determines the best hyperelastic model with the highest discriminative capability in description of the non-linear mechanical behavior of the cornea.

Biomechanical effect of ultraviolet-A-riboflavin cross-linking on simulated human corneal stroma model and its correlation with changes in corneal stromal microstructure

In this study, we established an experimental human corneal stroma model of simulated cornea tissue composed of thin anterior cornea strips layers obtained from small incision lenticular extraction (SMILE) surgery. We investigated the biomechanical effect of ultraviolet-A- riboflavin cross-linking at different depths of corneal stroma model and correlated it with stromal microstructural changes examined by transmission electron microscopy (TEM). Corneal strips were harvested from fresh human corneal lenticules obtained after SMILE surgery. Experimental models (n = 34) were established by superimposing the corneal lenticule strips until their thickness reached close to 500 μm. Corneal cross-linking (CXL) was performed subsequently using standard or accelerated protocol. Elasticity and viscosity were quantified using stress-strain extensometer. TEM was used to visualize the collagen fiber diameter and interfibrillar spacing. The relative change in Young's modulus (rel. ΔE) decreased nonlinearly with increasing stromal depth both in the standard and accelerated groups. Compared to the sham controls, the rel. ΔE in standard and accelerated CXL groups increased significantly in the anterior 400 μm and 275 μm depth, respectively. Also, the relative change in stress (rel. ΔS) was significantly lower after standard and accelerated CXL compared to sham controls. Depth analysis showed similar results for the elastic effect. TEM images showed a small, non-significant increase in fibril diameter. The interfibrillar spacing decreased significantly after standard and accelerated CXL in the anterior-mid stromal region. We noted that the increase of corneal stiffness correlated with decrease in interfibrillar spacing after CXL. The stiffening effect was depth dependent. The effect of accelerated CXL was less in the deep corneal stromal regions compared to standard CXL.