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The Cornea Structure and surface modelling

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The human eye

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Standard shape oCentral zone of 1-3 mm closely fits a spherical surface oParacentral zone, 3-4 mm ring, with an outer diameter of 7-8 mm, area of progressive flattening (prolate) oPeripheral zone, outer diameter of 11 mm, greatest flattening and asphericity oLimbus, outer diameter that averages 12 mm, the cornea steepens before joining the sclera

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Standard shape oBecause of its peripheral flattening, an ellipsoid has been suggested as a schematic representation of the front surface of the cornea oConic section, p= 1, circle p= 0, parabola p< 0, hyperbola 0 < p < 1, ellipse p~ 0.6-0.8 (typical cornea)

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Standard shape oThe corneal apex is the point of maximum curvature or height, typically temporal to the center of the pupil oThe corneal vertex is the point located at the intersection of the patient’s line of sight (visual axis) and the corneal surface. It is represented by the corneal light reflex when the cornea is illuminated coaxially with fixation

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Elements in corneal shape

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Structure of the cornea oTransparent avascular tissue oMost anterior surface of the eye oMeasures 11-12 mm horizontally and 10-11 mm vertically oComponents of the normal cornea are the epithelium, stroma and endothelium oThe eye begins to develop during week 4 of gestation as an evagination from the neuroectoderm

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Structure of the cornea oWaves of mesenchymal cells at week 6 and 7 from the neural crest of the surface ectoderm begin forming the corneal endothelium and corneal stroma/sclera, respectively oEpithelium: stratified squamous epithelial cells, basement membrane oStroma: keratocytes (fibroblasts) and extracellular matrix, Bowman layer oEndothelium: mosaic pattern of hexagonal cells, Descemet membrane

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Structure of the cornea oExtracellular matrix Collagen (triple hellix of aminoacids), type I Proteoglycans: GAGs + core proteins oCorneal stroma: 200 lamellae stacked on top of one another oImbibition pressure= IOP-SP oEndothelial pump (Na/K ATPase) oWater content ~ 78% (intact epithelial and endothelial barriers & functioning endothelial pump)

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Structure of the cornea oCollagen fibrils appear to reinforce the ground substance as glass or carbon fibers in synthetic material oGround substance: shear stress about 10 5 N m -2 oHigh proportion of collagen fibrils: tensile stress 10 7 N m -2 oCritical length, lc oStress at which the tissue breaks, σ t

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Structure of the cornea oCorneal thickness: oCentral: 0.52 mm oParacentral: 0.52 mm inferior; 0.57 mm superior oPeripheral: 0.63 mm inferior; 0.67 mm superior oStress/strain oYoung modulus of elasticity of the human cornea= 0.45-10 MPa oPoisson ratio of the human cornea= 0.49

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Aqueous humor dynamics oThe corneal shape is maintained by its elastic properties in conjunction with intraocular pressure (10-21 mm Hg), generated by the continuous production and outflow of aqueous humor in the eye oThe average depth of the anterior chamber is 3.5 mm for an adult eye (s= 0.35 mm), with a diameter of 12.5 mm and a volume of around 260 ml oAqueous humor outflow: trabecular meshwork & uveoscleral

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Aqueous humor dynamics oUnder normal conditions, 2.5 to 3 ml of aqueous leaves the anterior chamber each minute oThe entire volume of the anterior chamber would be emptied in under 2 hours if it were not continually resupplied oThe aqueous humor is renewed 12 to 13 times each day

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Minor elements oEyelid pressure oExtraocular muscles tension oCiliary muscle contraction oAtmospheric pressure

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Optical properties oShape → Curvature → Refractive power oSnell’s law oDioptric power oAverage refractive power= 43 D (49 D - 6 D) on tears,aqueous =1.336; n stroma =1.376

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Corneal Topography

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Keratometry oA keratometer measures the radius of curvature of a small portion of the central cornea assuming to be spheric oRadius is calculated using geometric optics considering the cornea as a spherical reflecting surface

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h h’ d r/ 2 f c x v v=s i u u=s o

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Keratometry oConversion of radius to diopters n’= 1.376 → 1.3375 u=75 mm (Reichert)

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Keratometry oCalculations are based on the geometry of a spherical reflecting surface: the cornea is described as a prolate (flattening) ellipsoid (true apical radius steeper) oQuantitative data are based on only four points within the central 3 millimeters of the cornea (gross qualitative indication of corneal regularity between them) oAssumes paraxial optics (not valid when higher accuracy is required or peripheral areas are measured)

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Keratometry oThe keratometer assumes that the corneal apex, line of sight, and axis of the instrument coincide, but it is not usually true. oThe formula approximates the distance to focal point by the distance to image oPower in diopters depends on an assumed index of refraction o"One-position" instruments, in which it is possible to measure two orthogonal meridians without rotating the instrument, assume regular astigmatism

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Videokeratoscopy oPlacido studied the corneal surface by observing the reflected pattern of concentric rings from the cornea: Placido's disk used since 1870 oUntil recently, keratoscopy instruments provided only a qualitative assessment of the cornea. In general, the reflected mires appear closer together on steeper parts of the cornea oThese devices allow analysis of corneal cur- vature in zones both central and peripheral to those measured by keratometry

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Videokeratoscopy oPhotokeratoscopy preserves the virtual image of concentric circles on film oGullstrand developed the first photo- keratoscope in 1966, which opened the way for mathematical analysis, and developed algorithms to derive quantitative data from careful measurements of the Placido ring images oExtracting quantitative data for most of the corneal surface was important, but the process was too tedious to be clinically useful

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Videokeratoscopy oVideokeratoscopy stores the reflected corneal mires on video oModern computerized videokeratoscopes evaluate several thousand points from nearly the entire corneal surface oAdvances in video-image processing and microcomputer technology provided a means for immediate acquisition and rapid analysis of the large volume of data oColor topographic maps have become the standard for displaying the output of videokeratoscopes since 1987

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Videokeratoscopy oTwo types of VK: oPlacido-disk based (reflection based) oElevation based (projection based)

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Placido-disk VK (axial) oThese units assume the angle of incidence to be nearly perpendicular and the radius of curvature to be the distance from the surface to the intersection with the line of sight or visual axis (axial distance) oInitial shape by triangulation or other methods and then calculate the power map from the shape. Axial curvature values closely approximate the power of the central cornea but fail to describe the true shape & power of the peripheral cornea

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Placido-disk VK (axial) oSalmon & Horner (1995) oBased on Snell’s law, corneal power must increase in the periphery in order to refract the light into the pupil. Conventionally, normal corneas show decreasing diopters toward the periphery as displayed by these devices (intuitive sense of the normal flattening of the cornea)

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Placido-disk VK (tangential) oInstantaneous radius of curvature (and derived tangential power) at a certain point: taking a perpendicular path through the point, that intersects the point and the visual axis, but allowing the radius to be the length necessary to correspond to a sphere with the same curvature at that point oThe instantaneous curvature in diopters is estimated from this tangentially determined radius

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Placido-disk VK (tangential) oThe tangential map typically shows better sensitivity to peripheral changes with less smoothing of the curvatures than the axial map. In these maps, the diopters are relative units of curvature and not the equivalent of diopters of corneal power

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Placido-disk VK (mean) oThe mean curvature map does not require the perpendicular ray to cross the visual axis, allowing for an infinite number of spheres to fit the curvature at that point oThe algorithm determines a minimum and maximum size best-fit sphere and from their radii determines an average curvature (arithmetic mean of principal curvatures) known as the mean curvature for that point oEven more sensitivity to peripheral changes of curvature

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Elevation based VK oA more accurate way to describe curvature would be to use the true shape of the cornea: some systems directly derive corneal shape by means of scanning slits or rectangular grids and then determine power from that shape oSlit photography oRasterstereography (grid) oMoiré interference (sets of parallel lines) oLaser interferometry (coherent wavefronts)

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Elevation based VK oIn order to represent shape directly, maps may display a z-height from an arbitrary plane (iris, limbal, frontal, or apex plane) using color maps oGeographic maps show land elevation relative to sea level. Similarly, corneal surface maps are plotted to show differences from best- fit spheres or other objects that closely mimic the normal corneal shape

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Future oIdeally, researchers hope to develop practical methods for accurately depicting the anterior and posterior surface shapes of the cornea and lens oThen, ray tracing can be used to plot an accurate refractive map of the eye, to establish the effects of the cornea and lens surfaces on the wavefront of light

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Future oWith such information, alterations of the shape of the eye structures can be planned to maximize the refractive effect and minimize the aberrations of keratorefractive and other surgeries

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