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The cornea is the transparent soft tissue located in the outer layer of the eyeball and provides 70% ocular refractive power [

Similar to most biological tissues, corneal biomechanics include its anisotropic, nonlinear elastic properties and viscoelastic properties [

As one knows some anatomical and histological properties of cornea change with the increase of age. There should also be some changes in corneal biomechanical parameters with the increase of age. A large number of clinical studies found that corneal clinical biomechanical parameters are correlated with age [

In this study, corneal strip tensile and stress relaxation experiments were carried out on rabbits with different ages to obtain corneal biomechanical properties. The results of the relationship between ORA parameters and age based on the same rabbits were reported in our last research [

Twenty-Four New Zealand rabbits aged 3, 12, 18, and 24 months (6 for each age) with healthy eyes were enrolled in the study. All of the rabbits were provided by Animal Laboratory Center of Capital Medical University, and the experiments followed with the ARRIVE guidelines and NIH guidelines.

Central Corneal Thickness (CCT) was measured using Pachymeter SP 3000 before the animals were killed, and the result was showed in Table

Information of corneal strips with different ages.

Age/months | CCT/ | Length/mm | Width/mm |
---|---|---|---|

3 | 349±14 | 15.17±1.13 | 3.21±0.14 |

12 | 375±26 | 15.27±2.13 | 3.33±0.10 |

18 | 389±20 | 16.25±0.94 | 3.42±0.18 |

24 | 373±28 | 16.28±1.29 | 3.38±0.12 |

All rabbits were anesthetized with 3% pentobarbital sodium (Merck, Germany) at a dose of 1ml/kg and measured with ORA in vivo for 4 times. The details of the methods for ORA measurements on rabbits have been reported in our previous study [

Clamping and water bath system of corneal strip.

The load-displacement data obtained from the corneal strip tensile tests were converted to stress-strain data by Eq (_{0} is the initial sectional area at the center point of the strips from the start, _{0} is the initial length of corneal strip.

The stress-strain curve was nearly linear under a lower stress of 0.015MPa-0.03MPa and a higher stress of 0.06MPa-0.1MPa (Figure _{1}, and elastic modulus under higher stress, denoted by_{2}. Researches have shown that exponential model can characterize the stress-strain relationship of soft tissue well [

Stress-strain curve of corneal strip and regional division for the curve. The red, green, and blue line represent the physiological range, higher stress state, and nonlinear range, respectively.

which gives the linear relation between corneal tangent modulus,

where_{1},_{1},_{2},_{2},_{3},_{3} were constants,_{0} is the normalized stress-relaxation function, _{0} is the initial stress. Corneal stress relaxation limit (

After obtaining above corneal biomechanical parameters, one-way ANOVA analysis was used to analyze the correlation between these parameters and age. Pearson’s correlation was used to get the correlation between corneal clinical and traditional biomechanical parameters. All of the statistical analyses were produced on SPSS 21.0 and

To obtain the correlation between ORA parameters and corneal biomechanical parameters quantitatively in further detail, we simulated ORA measurements with different corneal biomechanical parameters by finite element method. The geometrical model (Figure

Finite element models of ORA measurements (a) and the output central corneal coordinate (b).

As the difference between corneal biomechanical parameters in vivo and in vitro, corneal tangent modulus and parameters of the 3-order Prony model were adjusted to make the simulated ORA parameters have the same magnitude with experimental parameters. Besides, linear regression analysis was used to obtain the quantitative relation between ORA parameters and corneal biomechanical parameters preliminary.

Table

The results of the linear fitting and exponential fitting for stress-strain data were showed in Table _{1} and_{2} represent corneal physiological elastic modulus and corneal elastic modulus under higher stress, respectively. Results of the one-way ANOVA analysis were listed in the last line of the table. From the results we can see that there was no significant variation in corneal physiological elastic modulus with the increase of age (_{1} and_{2} with the increase of age.

Linear and exponential fitting results of the stress-strain data.

Age/month | Linear fitting | Exponential fitting | |||||
---|---|---|---|---|---|---|---|

_{1}/MPa | R^{2} | _{2}/MPa | R^{2} | | | R^{2} | |

3 | 0.97±0.24 | 0.929±0.027 | 3.01±0.59 | 0.988±0.005 | 0.0070±0.0048 | 37±8 | 0.998±0.001 |

12 | 1.04±0.22 | 0.939±0.020 | 4.13±1.31 | 0.989±0.002 | 0.0013±0.0020 | 53±18 | 0.998±0.001 |

18 | 0.978±0.079 | 0.972±0.008 | 3.66±0.42 | 0.993±0.002 | 0.0021±0.0020 | 47±6 | 0.999±0.001 |

24 | 1.124±0.263 | 0.949±0.017 | 4.93±1.03 | 0.988±0.017 | 0.0002±0.0001 | 64±13 | 0.998±0.002 |

| 0.256 | <0.001 | <0.001 | <0.001 |

_{1}: physiological elastic modulus; _{2}: elastic modulus under higher stress.

Variation of corneal elastic modulus with age (_{1}: physiological modulus;_{2}: elastic modulus under higher stress).

Corneal nonlinear elastic properties with different ages were showed in Table

Stress-strain curve (a) and

The results of corneal stress relaxation were showed in Table _{1} (_{3} (

Results of the stress relaxation with different ages.

Age/months | 3 | 12 | 18 | 24 | |
---|---|---|---|---|---|

_{1} | 0.40±0.09 | 0.42±0.07 | 0.39±0.11 | 0.45±0.10 | 0.499 |

_{1}/s | 3.07±0.39 | 2.89±0.34 | 3.01±0.25 | 2.63±0.27 | 0.008 |

_{2} | 0.16±0.03 | 0.18±0.04 | 0.15±0.02 | 0.16±0.02 | 0.155 |

_{2}/s | 61±58 | 29±13 | 86±84 | 55±47 | 0.282 |

_{3} | 0.16±0.02 | 0.19±0.01 | 0.15±0.02 | 0.17±0.01 | <0.001 |

_{3}/s | 238±117 | 286±139 | 207±141 | 209±95 | 0.344 |

^{2} | 0.995±0.001 | 0.999±0.001 | 0.999±0.001 | 0.999±0.001 | |

_{∞} | 0.27±0.07 | 0.21±0.05 | 0.30±0.10 | 0.22±0.09 | 0.045 |

| 2.15±0.73 | 1.86±0.61 | 2.27±0.86 | 1.68±0.74 | 0.224 |

Figure

Stress relaxation curve (a) and corneal viscoelastic parameters (relaxation limit (b) and relaxation time (c)) of corneal strips with different ages.

Comparing the age-related variations of ORA parameters (Figure _{2}), and both CRF and CH showed similar trend with relaxation limit (_{2} (

Age-related variations of ORA parameters.

CH, CRF, and other 15 ORA waveform parameters (

Explicit finite element method was used to explore the quantitative relation between ORA parameters and corneal biomechanical parameters. Figure

Cornea displacements distribution of the initial (a), the first applanation (b), the maximum indentation (c), and the second applanation state.

As the difference between corneal biomechanical parameters in vivo and in vitro, corneal tangent modulus and parameters of the 3-order Prony model were adjusted to make the simulated ORA parameters have the same magnitude with experimental parameters. Results showed that the simulated and experimental ORA parameters (CH and CRF) showed similar magnitude when corneal tangent modulus was set to be 1/3 of the corneal physiological tangent modulus and_{1},_{2},_{3} of the 3-order Prony model parameters was set to be 1/10 of the experimental results obtained from corneal strips extension experiments (Table

Results of finite element analysis of ORA measurements.

age/months | 3 | 12 | 18 | 24 |
---|---|---|---|---|

Experimental CH/mmHg | 5.32 | 4.86 | 5.13 | 4.53 |

Simulated CH/mmHg | 6.10 | 5.98 | 6.04 | 5.64 |

Experimental CRF/mmHg | 4.49 | 3.64 | 4.12 | 3.41 |

Simulated CRF/mmHg | 6.25 | 4.83 | 5.70 | 4.31 |

To explore the relation between ORA parameters quantitatively, we maintain_{2},_{2},_{3},_{3} to be fixed and make_{1},_{1} varied from 0.3-0.4MPa, 0.3-0.4, and 0.2-0.5s, respectively, when simulating ORA measurements. Corneal stress relaxation limit (

In this study, mechanical interpretation of ORA parameters was cognized preliminarily by comparing the variation of ORA parameters and corneal biomechanical parameters with age. And explicit finite element analysis of ORA measurements was used to get the quantitative relations further. CRF was found to vary oppositely with increase of age compared to corneal tangent under higher stress (_{2}), and both CRF and CH showed similar trend with relaxation limit (

Exponential model [^{2}) for the two linear fittings, exponential fitting, and Prony model fitting was larger than 0.92, 0.98, 0.99, and 0.99, respectively, which indicated that our fitting methods were effective. Results of corneal inflating tests also showed a linear corneal apex increase with pressure of 15-30 mmHg [_{1}) was 0.7-1.5MPa in this study, the ranges of parameters of exponential model (_{∞}) was 0.13-0.45. These results are coincident with these parameters reported by Wang (_{1}=1.60±0.38MPa) [_{∞}=0.3-0.5 for porcine cornea and 0.6-0.8 for human cornea [

From Table

From Figures _{2}), and both CRF and CH showed similar trend with corneal stress relaxation limit (_{∞}) and relaxation time (_{∞}. Besides, explicit finite element analyses of ORA measurements also show positive correlations between ORA parameters (CH, CRF) and corneal tangent modulus_{∞}) and relaxation time (

The limitations of this study lied in 2 aspects. Cornea is an anisotropic material and its biomechanical properties should be characterized by the biomechanical properties of corneal strips in different directions (such radial and circumferential corneal strips). As it is difficult to obtain circumferential corneal strips for tensile tests, we selected corneal strips in nasal-temporal direction and superior-inferior direction. But no significant difference was found between the two directions. Tests on more directions may be needed to characterize corneal biomechanical properties more comprehensively. Another limitation of this study is that when we simulate ORA measurements, we calculated CH and CRF according to Eq (_{1},_{2}. While the relationship has not been determined at present, researches have reported that experimental CH and CRF are linear positive correlation with the calculated CH and CRF [

Mechanical interpretation of ORA parameters was cognized preliminarily by comparing the variation of ORA parameters and corneal biomechanical parameters with age. Explicit finite element analysis of ORA showed a similar correlation between ORA parameters and corneal biomechanical parameters. Both CRF and CH are positively linearly related to corneal elastic modulus and negatively linearly depend on relaxation limit and relaxation time and relaxation limit (

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was financially supported by the National Natural Science Foundation of China (nos. 31370952, 31470914).