Table 1.
Right healthy eye data provided by the Pentacam.
Fig 1.
Three-dimensional eyeball model, collagen fiber distribution, pachymetry and patient-specific validation.
a) Finite element model of the eye. Light blue mesh corresponds to the patient-specific cornea obtained by means of the Pentacam system; the limbus is shown as dark blue area, whereas sclera is white; b) Corneal Collagen Fiber Distribution (nasal-temporal fibers in green and superior-inferior fibers in red) and Limbo Fiber orientation (blue fibers distributed circumferentially); c) Actual patient’s pachymetry given by the Pentacam topographer (grey area shows the average corneal size considered for the 3D FE model); d) Error difference (%) between the actual patient’s pachymetry and the pachymetry of the numerical model. Blue values represent a truly patient-specific corneal thickness (green area belongs to the quadric surface necessary to extend corneal data to the average desired diameter).
Table 2.
Mesh sensitivity analysis.
Table 3.
Material parameters for cornea, limbus, and sclera.
Fig 2.
Human corneal response of the constitutive model.
a) IOP (mmHg) vs. Apical Rise (mm). Human range (grey shadow) obtained from inflation test in human corneas [23,24]. Colored lines correspond to inflation response for the three material selected for the numerical simulation: low(material A)—red, intermediate(material B)—blue, large(material C)—green); b) Uniaxial stress-stretch behavior for the three studied materials.
Fig 3.
Non-contact tonometer air-puff loading and CFD results.
a) Temporal pressure profile applied on the center of the cornea (corneal apex region). Solid black line represents the temporal profile used in the simulations. Dashed black line was no considered since only the maximum displacement of the corneal apex was studied; b) Spatial profile of pressure applied on cornea obtained with the CFD simulation shown in c) and d); c) Symmetrical pressure profile obtained from the CFD simulation; d) Symmetrical velocity streamline plot result from the CFD simulation.
Fig 4.
Displacement—Pressure response of the corneal apex.
Vertical displacement of the corneal apex (mm) as a function of IOP (10, 12, 19 and 28 mmHg) for the three material models: low (material A), intermediate (material B), large (material C) stiffness.
Fig 5.
Displacement—Pressure: response overlapping.
Overlapping zone in the corneal response (grey zone) where different combinations of IOP and material lead to the same displacement.
Fig 6.
Displacement—Time response of the corneal apex.
Time course of the apex displacement for the conducted simulations. Displacement’s region 10–28 mmHg (mat. A) (red colored area) are the results for low stiffness material (A) for all three different IOP (10, 19 and 28 mmHg); Displacement’s region 10–28 mmHg (mat. B) (blue colored area) are the results for intermediate stiffness material (B) for all three different IOP (10, 19 and 28 mmHg); Displacement’s region 10–28 mmHg (mat. C) (green colored area) are the results for large stiffness material (C) for all three different IOP (10, 19 and 28 mmHg). Different overlapping zones, at different loading time, can be observed in figure. Inverted triangles correspond to simulations performed with the real IOP (12 mmHg) and the three different corneal material models.
Fig 7.
Displacement of the corneal apex (mm) as a function of the corneal thickness (CCT).
Patient’s pachymetry was constantly decreased for the simulations. Results show a cubic relation between displacement and pachymetry (CCT) when the material was fixed (large stifnees material—C) and three levels of IOP were considered: 10 mmHg (dotted-dashed green line), 19 mHg (solid green line), and 28 mmHg (doted green line). Results also show a cubic relation between displacement and pachymetry (CCT) when the IOP was kept at 19 mmHg and the three corneal stiffnesses were considered: low (material A) solid red line, intermediate (material B) solid blue line, and large (material C) solid green line. The right panel shows the accuracy of the fit (minimum mean squares) and the constants of the cubic polynomial.
Fig 8.
Corneal response in the meridional plane (FE results).
Meridional cutting plane of the cornea. a) Displacement field along the optical axis at first applanation time (mm), b) Vertical displacement field at high concavity time (mm), c) Circumferential logarithmic strain field (-) at first applanation time, d) Hoop stress field (MPa) at first applanation time (spherical coordinate system). c) and d) show the bending mode of deformation at which the cornea is subjected during a non-contact tonometry test. Results correspond to IOP = 19 mmHg and material C.
Fig 9.
Stress strain response of anterior and posterior apical points during non-contact tonometry.
Normal Cauchy Stress vs. stretch path along the meridional direction followed by two points on the anterior and posterior surface of the cornea during air-puff for an IOP = 19 mmHg and the stiffest material (C). Blue color is associated with compression whereas red color is associated with tension. At the physiological configuration when the eye is subjected to IOP (open circle at the beginning of the air jet profile, shown in the inset) the cornea only experiences traction (membrane tensional state). As the air-pulse progresses (black filled circle in the pressure profile inset), the anterior corneal surface (inverted open triangle) experiences compression (λ<1) whereas, the posterior corneal surface (open square) experiences a larger tensional stress (λ>1).