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,
p= 1, circle
2
2
p= 0, parabola
y  2ro x  px
p< 0, hyperbola
0 < p < 1, ellipse
p~ 0.6-0.8 (typical cornea)
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 105 N m-2
o High proportion of collagen fibrils: tensile stress
107 N m-2
o Critical length, lc
lc  rσ f/
o Stress at which the tissue breaks, σt
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
o
o
o
Eyelid pressure
Extraocular muscles tension
Ciliary muscle contraction
Atmospheric pressure
Optical properties
o Shape → Curvature → Refractive power
o Snell’s law
nsin i  n'sin i'
o Dioptric power
F  n'- n
r
o Average refractive power= 43 D (49 D - 6 D)
o ntears,aqueous=1.336; nstroma=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'  v
h u
h'   f
h x
h
h’
u
d
x
u=so
v=si
v
r/2
f
c
Keratometry
h'  r
h -2x
h'  r
h -2u
r  2d h'
h
r  2u h'
h
u=75 mm
(Reichert)
o Conversion of radius to diopters
F  n'- n
r
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
instrument coincide, but it is not usually
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
meridians without rotating the instrument,
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 curvature 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 photokeratoscope in 1966, which opened the way
for mathematical analysis, and developed
algorithms to derive quantitative data from
careful measurements of the Placido ring
images
o Extracting quantitative data for most of the
corneal surface was important, but the
process was too tedious to be clinically
useful
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
of the large volume of data
o Color topographic maps have become the
standard for displaying the output of
videokeratoscopes since 1987
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)
ra  r2  e2h2
o Based 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)
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
3
r
ri  a2
r
Placido-disk VK (mean)
o The 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
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)
known as the mean curvature for that point
o Even more sensitivity to peripheral changes
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 bestfit 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