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

Depth-dependent mechanical properties of the human cornea by uniaxial extension.

The purpose of this study was to investigate the depth-dependent biomechanical properties of the human corneal stroma under uniaxial tensile loading. Human stroma samples were obtained after the removal of Descemet's membrane in the course of Descemet's membrane endothelial keratoplasty (DMEK) transplantation. Uniaxial tensile tests were performed at three different depths: anterior, central, and posterior on 2 x 6 × 0.15 mm strips taken from the central DMEK graft. The measured force-displacement data were used to calculate stress-strain curves and to derive the tangent modulus. The study showed that mechanical strength decreased significantly with depth. The anterior cornea appeared to be the stiffest, with a stiffness approximately 18% higher than that of the central cornea and approximately 38% higher than that of the posterior layer. Larger variations in mechanical response were observed in the posterior group, probably due to the higher degree of alignment of the collagen fibers in the posterior sections of the cornea. This study contributes to a better understanding of the biomechanical tensile properties of the cornea, which has important implications for the development of new treatment strategies for corneal diseases. Accurate quantification of tensile strength as a function of depth is critical information that is lacking in human corneal biomechanics to develop numerical models and new treatment methods

Orientation and depth dependent mechanical properties of the porcine cornea: Experiments and parameter identification.

The porcine cornea is a standard animal model in ophthalmic research, making its biomechanical characterization and modeling important to develop novel treatments such as crosslinking and refractive surgeries. In this study, we present a numerical model of the porcine cornea based on experimental measurements that captures both the depth dependence and orientation dependence of the mechanical response. The mechanical parameters of the established anisotropic hyperelastic material models of Gasser, Holzapfel and Ogden (HGO) and Markert were determined using tensile tests. Corneas were cut with a femtosecond laser in the anterior (100 μm), central (350 μm), and posterior (600 μm) regions into nasal-temporal, superior-inferior, and diagonal strips of 150 μm thickness. These uniformly thick strips were tested at a low speed using a single-axis testing machine. The results showed that the corneal mechanical properties remained constant in the anterior half of the cornea regardless of orientation, but that the material softened in the posterior layer. These results are consistent with the circular orientation of collagen observed in porcine corneas using X-ray scattering. In addition, the parameters obtained for the HGO model were able to reproduce the published inflation tests, indicating that it is suitable for simulating the mechanical response of the entire cornea. Such a model constitutes the basis for in silico platforms to develop new ophthalmic treatments. In this way, researchers can match their experimental surrogate porcine model with a numerical counterpart and validate the prediction of their algorithms in a complete and accessible environment

Analysis of Biomechanical Response After Corneal Crosslinking with Different Fluence Levels in Porcine Corneas.

PURPOSE To evaluate corneal stiffening of porcine corneas induced by corneal crosslinking (CXL) with constant irradiance as a function of total fluence. METHODS Ninety corneas from freshly enucleated porcine eyes were divided into five groups of 18 eyes. Groups 1-4 underwent epi-off CXL using a dextran-based riboflavin solution and an irradiance of 18 mW/cm2, group 5 served as the control group. Groups 1 to 4 were treated with a total fluence of 20, 15, 10.8, and 5.4 J/cm2, respectively. Thereafter, biomechanical measurements were performed on 5 mm wide and 6 mm long strips using an uniaxial material tester. Pachymetry measurements were performed on each cornea. RESULTS At 10% strain, the stress was 76, 56, 52, and 31% higher in groups 1-4, respectively compared to the control group. The Young's modulus was 2.85 MPa for group 1, 2.53 MPa for group 2, 2.46 MPa for group 3, 2.12 MPa for group 4, and 1.62 MPa for the control group. The difference between groups 1 to 4 and the control group 5 were statistically significant (p = <0.001; p = <0.001; p = <0.001; p = 0.021). In addition, group 1 showed significantly more stiffening than group 4 (p = <0.001), no other significant differences were found. Pachymetry measurements revealed no statistically significant differences among the five groups. CONCLUSION Additional mechanical stiffening can be achieved by increasing the fluence of the CXL. There was no threshold detected up to 20 J/cm2. A higher fluence could compensate the weaker effect of accelerated or epi-on CXL procedures

Oxygen kinetics during corneal crosslinking with and without supplementary oxygen.

PURPOSE To measure and simulate oxygen kinetics during corneal crosslinking (CXL) at different irradiances with and without supplementary oxygen. DESIGN Experimental, laboratory study. METHODS In de-epithelialized porcine eyes, a femtosecond-laser generated tunnel was used to place a fiber-probe in corneal depths of 100, 200 and 300μm to measure the local oxygen concentration. After riboflavin imbibition, the corneas were irradiated at 3, 9, 18 and 30mW/cm2 while the oxygen concentration was measured. All experiments were performed under normoxic (21%) and hyperoxic (>95%) conditions. The obtained data were used to identify parameters of a numerical model for oxygen consumption and diffusion. RESULTS The equilibrium stromal oxygen concentration under atmospheric oxygen at 3mW/cm2 was 2.3% in 100μm decreasing to <1% in 300μm. With 9, 18 and 30mW/cm2, no oxygen was available in 200μm respectively 100μm or deeper. Using a hyperoxic environment, the concentration was 50% using 3mW/cm2 in 100μm, decreasing to 40% in 300μm. At 9mW/cm2 the concentrations were 5%, 3% and 1% in 100, 200 and 300μm, respectively. Using 18 and 30mW/cm2 all oxygen was depleted at 100μm, however, oxygen half-lives were longer at 18mW/cm2 than at 30mW/cm2. The oxygen model was able to reproduce the experiments and indicated an exponential decay with increasing distance to the anterior surface. CONCLUSION Supplementary oxygen increases the oxygen-availability during CXL. At higher irradiances, supplementary oxygen is beneficial and eliminates the bottleneck of oxygen allowing a potentially more efficient crosslinking. The calibrated numerical model can quantify the spatial oxygen concentration related to different scenarios such as irradiance or environmental oxygen concentration

Oxygen kinetics during CXL using symmetrically and asymmetrically pulsed UV-irradiation

Purpose To investigate oxygen kinetics during symmetrically pulsed and asymmetrically pulsed crosslinking (p-CXL) with and without supplementary oxygen at different irradiances and corneal depths. Design Experimental, laboratory study Methods In de-epithelialized porcine eyes, a femtosecond-laser generated tunnel was used to place a fibre-probe in corneal depths of 200 and 300 µm to measure the local oxygen concentration. After riboflavin imbibition, the corneas were irradiated at 9, 18 and 30 W/cm2 for 10 seconds On and 10 seconds Off; while the oxygen concentration was continuously measured until oxygen levels depleted below the oxygen sensor’s threshold (1%) or until stabilized. All experiments were performed under normoxic (21%) and hyperoxic (>95%) conditions and the obtained data were used to identify parameters of a numerical algorithm for oxygen consumption and diffusion. Following the algorithm’s development, the suggested asymmetrical pulsing values were experimentally tested. For 9, 18 and 30 mW/cm2 the suggested tested pulsing schemes were 3 seconds On : 9 seconds Off, 2 seconds On : 9 seconds Off and 1 second On : 9 seconds Off respectively. Results The minimum, available stromal oxygen for p-CXL in normoxic environment was decreasing <1% for 9, 18 and 30 mW/cm2 in 200 and 300 μm. Using optimized p-CXL, the minimum available oxygen increased to 3.8, 1.8 and 2.8 % at 200 μm, for irradiances of 9, 18 and 30 mW/cm2, respectively, where the periods exhibited an equilibrium state. At 300 μm, 1.1 % of oxygen was available for 30 mW/cm2. Using a hyperoxic environment, the oxygen concentration was 19.2% using 9 mW/cm2 in 200 μm, dropping to 17.0% in 300 μm. At 18 mW/cm2, the concentrations were 3.9% and 1% in 200 and 300 μm, respectively. Using 30 mW/cm2, all oxygen was depleted below the threshold limit (1% O2) for both depths. Using optimized pulsing in combination with hyperoxic environment, the oxygen concentration was 42.0% using 9 mW/cm2 in 200 μm and 43.3% in 300 μm. At 18 mW/cm2, the concentrations were 24.7% and 16.1% in 200 and 300 μm, respectively. Using 30 mW/cm2, the minimum oxygen availability was 25.7% and 13.7% in 200 and 300 μm, respectively. Conclusion Supplementary oxygen during symmetrical and asymmetrical p-CXL increased the oxygen availability during corneal cross-linking. The pulsed irradiance and the hyperoxic environment potentially increased the efficacy of corneal cross-linking in deeper corneal layers and higher irradiances. The numerical algorithm for asymmetrical pulsing led to the quantification of “On” and “Off” times related to different scenarios such as irradiances

Spatio-temporal characterization of fracture healing patterns and assessment of biomaterials by time-lapsed in vivo micro-computed tomography

Thorough preclinical evaluation of functionalized biomaterials for treatment of large bone defects is essential prior to clinical application. Using in vivo micro-computed tomography (micro-CT) and mouse femoral defect models with different defect sizes, we were able to detect spatio-temporal healing patterns indicative of physiological and impaired healing in three defect sub-volumes and the adjacent cortex. The time-lapsed in vivo micro-CT-based approach was then applied to evaluate the bone regeneration potential of functionalized biomaterials using collagen and bone morphogenetic protein (BMP-2). Both collagen and BMP-2 treatment led to distinct changes in bone turnover in the different healing phases. Despite increased periosteal bone formation, 87.5% of the defects treated with collagen scaffolds resulted in non-unions. Additional BMP-2 application significantly accelerated the healing process and increased the union rate to 100%. This study further shows potential of time-lapsed in vivo micro-CT for capturing spatio-temporal deviations preceding non-union formation and how this can be prevented by application of functionalized biomaterials. This study therefore supports the application of longitudinal in vivo micro-CT for discrimination of normal and disturbed healing patterns and for the spatio-temporal characterization of the bone regeneration capacity of functionalized biomaterials