The Cornea

Structure and surface modelling

The human eye

Standard shape

o Central zone of 1-3 mm closely fits a spherical surface o Paracentral zone, 3-4 mm ring, with an outer diameter of 7-8 mm, area of progressive flattening (prolate) o Peripheral zone, outer diameter of 11 mm, greatest flattening and asphericity o Limbus, outer diameter that averages 12 mm, the cornea steepens before joining the sclera

Standard shape

o Because of its peripheral flattening, an ellipsoid has been suggested as a schematic representation of the front surface of the cornea o Conic section, y 2  2r o x  px 2 p~ 0.6-0.8 (typical cornea) p= 1, circle p= 0, parabola p< 0, hyperbola 0 < p < 1, ellipse

Standard shape

o The corneal apex is the point of maximum curvature or height, typically temporal to the center of the pupil o The 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

Elements in corneal shape

Structure of the cornea

o Transparent avascular tissue o Most anterior surface of the eye o Measures 11-12 mm horizontally and 10-11 mm vertically o Components of the normal cornea are the epithelium, stroma and endothelium o The eye begins to develop during week 4 of gestation as an evagination from the neuroectoderm

Structure of the cornea

o Waves 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 o Epithelium: stratified squamous epithelial cells, basement membrane o Stroma: keratocytes (fibroblasts) and extracellular matrix, Bowman layer o Endothelium: mosaic pattern of hexagonal cells, Descemet membrane

Structure of the cornea

o Extracellular matrix  Collagen (triple hellix of aminoacids), type I  Proteoglycans: GAGs + core proteins o Corneal stroma: 200 lamellae stacked on top of one another o Imbibition pressure= IOP-SP o Endothelial pump (Na/K ATPase) o Water content ~ 78% (intact epithelial and endothelial barriers & functioning endothelial pump)

Structure of the cornea

o Collagen fibrils appear to reinforce the ground substance as glass or carbon fibers in synthetic material o Ground substance: shear stress about 10 o High proportion of collagen fibrils: tensile stress 10 7 N m -2 o Critical length, lc

l

c 

rσ

f

/

 o Stress at which the tissue breaks, σ t 5 N m -2 σ t  βσ f   1  β  σ g

Structure of the cornea o Corneal thickness:

o Central: 0.52 mm o Paracentral: 0.52 mm inferior; 0.57 mm superior o Peripheral: 0.63 mm inferior; 0.67 mm superior

o Stress/strain

o Young modulus of elasticity of the human cornea= 0.45-10 MPa o Poisson ratio of the human cornea= 0.49

Aqueous humor dynamics

o The 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 o The 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 o Aqueous humor outflow: trabecular meshwork & uveoscleral

Aqueous humor dynamics

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

Minor elements

o Eyelid pressure o Extraocular muscles tension o Ciliary muscle contraction o Atmospheric pressure

Optical properties

o Shape → o Snell’s law Curvature → Refractive power n  sin i  n '  sin i' o Dioptric power F  n' r n o Average refractive power= 43 D (49 D - 6 D) o n tears,aqueous =1.336; n stroma =1.376

Corneal Topography

Keratometry

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

h h' h   x f h' h  v u u d x u=s o v=s i h’ v r/ 2 f c

Keratometry

h' h  r 2 x r   2d h' h h' h  r 2 u r   2u h' h o Conversion of radius to diopters u=75 mm (Reichert) F  n' r n n’= 1.376 → 1.3375

Keratometry

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

Keratometry

o The keratometer assumes that the corneal apex, line of sight, and axis of the true.

o The formula approximates the distance to focal point by the distance to image o Power in diopters depends on an assumed index of refraction o "One-position" instruments, in which it is possible to measure two orthogonal assume regular astigmatism

Videokeratoscopy

o Placido studied the corneal surface by observing the reflected pattern of concentric rings from the cornea: Placido's disk used since 1870 o Until 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 o These devices allow analysis of corneal cur vature in zones both central and peripheral to those measured by keratometry

Videokeratoscopy

o Photokeratoscopy preserves the virtual image of concentric circles on film o Gullstrand developed the first photo keratoscope in 1966, which opened the way for mathematical analysis, and developed algorithms to derive quantitative data from images o Extracting quantitative data for most of the process was too tedious to be clinically

Videokeratoscopy

o Videokeratoscopy stores the reflected corneal mires on video o Modern computerized videokeratoscopes evaluate several thousand points from nearly the entire corneal surface o Advances in video-image processing and microcomputer technology provided a means for immediate acquisition and rapid analysis standard for displaying the output of

Videokeratoscopy o Two types of VK:

o Placido-disk based (reflection based) o Elevation based (projection based)

Placido-disk VK (axial)

o These 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) o Initial 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

Placido-disk VK (axial)

o Salmon & Horner (1995) r a  r 2  e 2 h 2 increase in the periphery in order to Conventionally, normal corneas show decreasing diopters toward the periphery cornea)

Placido-disk VK (tangential)

o Instantaneous 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 o The instantaneous curvature in diopters is estimated from this tangentially determined radius

Placido-disk VK (tangential)

o The 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 r i  r r a 3 2

Placido-disk VK (mean)

o The mean curvature map does not require the perpendicular ray to cross the visual spheres to fit the curvature at that point o The algorithm determines a minimum and maximum size best-fit sphere and from their radii determines an average curvature (arithmetic mean of principal curvatures) of curvature

Elevation based VK

o A 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 o Slit photography o Rasterstereography (grid) o Moiré interference (sets of parallel lines) o Laser interferometry (coherent wavefronts)

Elevation based VK

o In order to represent shape directly, maps may display a z-height from an arbitrary plane (iris, limbal, frontal, or apex plane) using color maps o Geographic 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

Future

o Ideally, researchers hope to develop practical methods for accurately depicting the anterior and posterior surface shapes of the cornea and lens o Then, 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

Future

o With 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