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Analysis of the viscoelastic properties of the human cornea using Scheimpflug imaging in inflation experiment of eye globes.

Lombardo G, Serrao S, Rosati M, Lombardo M - PLoS ONE (2014)

Bottom Line: Upon cyclic stress application, a biomechanical corneal elasticity gradient was found in the front-back direction.The average Young's modulus of the anterior cornea ranged between 2.28±0.87 MPa and 3.30±0.90 MPa in specimens with and without intact epithelium (P = 0.05) respectively.The Young's modulus of the posterior cornea was on average 0.21±0.09 MPa and 0.17±0.06 MPa (P>0.05) respectively.

View Article: PubMed Central - PubMed

Affiliation: CNR-IPCF, Unit of Support of Cosenza, Ponte P. Bucci, 87036 Rende, Italy; Vision Engineering Italy S.r.l., Via Adda 7, 00198 Rome, Italy.

ABSTRACT

Purpose: To demonstrate a Scheimpflug-based imaging procedure for investigating the depth- and time-dependent strain response of the human cornea to inflation testing of whole eye globes.

Methods: Six specimens, three of which with intact corneal epithelium, were mounted in a customized apparatus within a humidity and temperature-monitored wet chamber. Each specimen was subjected to two mechanical tests in order to measure corneal strain resulting from application of cyclic (cyclic regimen) and constant (creep regimen) stress by changing the intra-ocular pressure (IOP) within physiological ranges (18-42 mmHg). Corneal shape changes were analyzed as a function of IOP and both corneal stress-strain curves and creep curves were generated.

Results: The procedure was highly accurate and repeatable. Upon cyclic stress application, a biomechanical corneal elasticity gradient was found in the front-back direction. The average Young's modulus of the anterior cornea ranged between 2.28±0.87 MPa and 3.30±0.90 MPa in specimens with and without intact epithelium (P = 0.05) respectively. The Young's modulus of the posterior cornea was on average 0.21±0.09 MPa and 0.17±0.06 MPa (P>0.05) respectively. The time-dependent strain response of the cornea to creep testing was quantified by fitting data to a modified Zener model for extracting both the relaxation time and compliance function.

Conclusion: Cyclic and creep mechanical tests are valuable for investigating the strain response of the intact human cornea within physiological IOP ranges, providing meaningful results that can be translated to clinic. The presence of epithelium influences the results of anterior corneal shape changes when monitoring deformation via Scheimpflug imaging in inflation experiments of whole eye globes.

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Modified Zener model.A) The Zener model consists of two elements represented by a spring in series with a Kelvin unit. The model was used (B) to approximate the strain response of the cornea (C) to constant stress application. Upon sudden loading (B, black curve), the first element of the model, represented by a spring with stiffness E1, stretches immediately. The dashpot of the second element, with viscosity η, then takes up the stress, transferring the load to the second spring, with stiffness E2, as it slowly opens over time. The strain (ε) should reach a steady constant value (arrow). Upon sudden unloading (B, grey curve), the spring E1 contracts immediately while the spring E2 slowly contracts, being held back by the dashpot. The full response predicted by the model is fairly close to the response of the corneal tissue to physiological IOP variation.
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pone-0112169-g002: Modified Zener model.A) The Zener model consists of two elements represented by a spring in series with a Kelvin unit. The model was used (B) to approximate the strain response of the cornea (C) to constant stress application. Upon sudden loading (B, black curve), the first element of the model, represented by a spring with stiffness E1, stretches immediately. The dashpot of the second element, with viscosity η, then takes up the stress, transferring the load to the second spring, with stiffness E2, as it slowly opens over time. The strain (ε) should reach a steady constant value (arrow). Upon sudden unloading (B, grey curve), the spring E1 contracts immediately while the spring E2 slowly contracts, being held back by the dashpot. The full response predicted by the model is fairly close to the response of the corneal tissue to physiological IOP variation.

Mentions: The time dependency of the anterior and posterior corneal strain to the application of a steady stress [14] was described by means of the creep compliance function derived by the Zener, or standard linear solid, model (Figure 2). The model has been previously shown to well approximate the viscoelastic response of the corneal tissue, whose conformational changes is limited by the network of junction points (e.g., stromal protein cross-linking bonds) [13]. It, however, cannot describe the permanent strain that may be left in the corneal tissue in a creep test. For that reason, we restated the creep compliance function in order to take into account the permanent strain and the relaxation times upon loading and unloading. In particular, the creep compliance function (Φ) was considered to consist of two main components, the unrelaxed compliance (Cu) and the relaxed compliance (C∞), depending on whether the stress is applied (loading creep curve): (6)or relaxed (unloading creep curve):(7)where Cu (either under loading or unloading) characterizes the immediate elastic response and C∞ (either under loading or unloading) characterizes the steady state response, which includes the viscous flow, the retard elastic and the permanent strain responses of the model; these coefficients are proportional to the inverse of the stiffness E1 and E2 of the Zener model respectively. The coefficients τload and τunload are the relaxation times and represent a measure of how quickly the cornea relaxes to loading and unloading respectively; t is time; and T0 is the instant time at which the applied stress is removed. In this work, we used the C∞ and τ parameters to quantify the strain response of the cornea to creep testing.


Analysis of the viscoelastic properties of the human cornea using Scheimpflug imaging in inflation experiment of eye globes.

Lombardo G, Serrao S, Rosati M, Lombardo M - PLoS ONE (2014)

Modified Zener model.A) The Zener model consists of two elements represented by a spring in series with a Kelvin unit. The model was used (B) to approximate the strain response of the cornea (C) to constant stress application. Upon sudden loading (B, black curve), the first element of the model, represented by a spring with stiffness E1, stretches immediately. The dashpot of the second element, with viscosity η, then takes up the stress, transferring the load to the second spring, with stiffness E2, as it slowly opens over time. The strain (ε) should reach a steady constant value (arrow). Upon sudden unloading (B, grey curve), the spring E1 contracts immediately while the spring E2 slowly contracts, being held back by the dashpot. The full response predicted by the model is fairly close to the response of the corneal tissue to physiological IOP variation.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4232387&req=5

pone-0112169-g002: Modified Zener model.A) The Zener model consists of two elements represented by a spring in series with a Kelvin unit. The model was used (B) to approximate the strain response of the cornea (C) to constant stress application. Upon sudden loading (B, black curve), the first element of the model, represented by a spring with stiffness E1, stretches immediately. The dashpot of the second element, with viscosity η, then takes up the stress, transferring the load to the second spring, with stiffness E2, as it slowly opens over time. The strain (ε) should reach a steady constant value (arrow). Upon sudden unloading (B, grey curve), the spring E1 contracts immediately while the spring E2 slowly contracts, being held back by the dashpot. The full response predicted by the model is fairly close to the response of the corneal tissue to physiological IOP variation.
Mentions: The time dependency of the anterior and posterior corneal strain to the application of a steady stress [14] was described by means of the creep compliance function derived by the Zener, or standard linear solid, model (Figure 2). The model has been previously shown to well approximate the viscoelastic response of the corneal tissue, whose conformational changes is limited by the network of junction points (e.g., stromal protein cross-linking bonds) [13]. It, however, cannot describe the permanent strain that may be left in the corneal tissue in a creep test. For that reason, we restated the creep compliance function in order to take into account the permanent strain and the relaxation times upon loading and unloading. In particular, the creep compliance function (Φ) was considered to consist of two main components, the unrelaxed compliance (Cu) and the relaxed compliance (C∞), depending on whether the stress is applied (loading creep curve): (6)or relaxed (unloading creep curve):(7)where Cu (either under loading or unloading) characterizes the immediate elastic response and C∞ (either under loading or unloading) characterizes the steady state response, which includes the viscous flow, the retard elastic and the permanent strain responses of the model; these coefficients are proportional to the inverse of the stiffness E1 and E2 of the Zener model respectively. The coefficients τload and τunload are the relaxation times and represent a measure of how quickly the cornea relaxes to loading and unloading respectively; t is time; and T0 is the instant time at which the applied stress is removed. In this work, we used the C∞ and τ parameters to quantify the strain response of the cornea to creep testing.

Bottom Line: Upon cyclic stress application, a biomechanical corneal elasticity gradient was found in the front-back direction.The average Young's modulus of the anterior cornea ranged between 2.28±0.87 MPa and 3.30±0.90 MPa in specimens with and without intact epithelium (P = 0.05) respectively.The Young's modulus of the posterior cornea was on average 0.21±0.09 MPa and 0.17±0.06 MPa (P>0.05) respectively.

View Article: PubMed Central - PubMed

Affiliation: CNR-IPCF, Unit of Support of Cosenza, Ponte P. Bucci, 87036 Rende, Italy; Vision Engineering Italy S.r.l., Via Adda 7, 00198 Rome, Italy.

ABSTRACT

Purpose: To demonstrate a Scheimpflug-based imaging procedure for investigating the depth- and time-dependent strain response of the human cornea to inflation testing of whole eye globes.

Methods: Six specimens, three of which with intact corneal epithelium, were mounted in a customized apparatus within a humidity and temperature-monitored wet chamber. Each specimen was subjected to two mechanical tests in order to measure corneal strain resulting from application of cyclic (cyclic regimen) and constant (creep regimen) stress by changing the intra-ocular pressure (IOP) within physiological ranges (18-42 mmHg). Corneal shape changes were analyzed as a function of IOP and both corneal stress-strain curves and creep curves were generated.

Results: The procedure was highly accurate and repeatable. Upon cyclic stress application, a biomechanical corneal elasticity gradient was found in the front-back direction. The average Young's modulus of the anterior cornea ranged between 2.28±0.87 MPa and 3.30±0.90 MPa in specimens with and without intact epithelium (P = 0.05) respectively. The Young's modulus of the posterior cornea was on average 0.21±0.09 MPa and 0.17±0.06 MPa (P>0.05) respectively. The time-dependent strain response of the cornea to creep testing was quantified by fitting data to a modified Zener model for extracting both the relaxation time and compliance function.

Conclusion: Cyclic and creep mechanical tests are valuable for investigating the strain response of the intact human cornea within physiological IOP ranges, providing meaningful results that can be translated to clinic. The presence of epithelium influences the results of anterior corneal shape changes when monitoring deformation via Scheimpflug imaging in inflation experiments of whole eye globes.

Show MeSH
Related in: MedlinePlus