Surgical Device for Supporting Corneal Transplants
Liliane Venturaa, Jean-Jacques De Grootea, Sidney J.F. Sousab
Dept. of Elect. Engineering USP, Av. Trabalhador Saocarlense 400, S. Carlos, SP Brasil 13566-590
Dept. of Opthalmology USP, Av. Bandeirantes 3900, Rib. Preto, SP Brasil 14100-900
A system for supporting corneal suture for minimizing
induced astigmatism, due to irregular manual stitches,
has been designed. The system projects 48 light spots,
from LEDs, displayed in a precise circle at the lachrymal
film of the examined cornea. The displacement, the size
and deformation of the reflected image of these light spots
analysis providies the keratometry and the circularity of
the suture. Measurements in the range of 32D – 55D and
a self-calibration system has been designed in order to
keep the system calibrated. The system has been tested in
13 persons in order to evaluate its clinical applicability
and has been compared to a commercial keratometer
Topcon OM-4. The correlation factors are 0.92 for the
astigmatism and 0.99 for the associated axis. The system
indicates that the surgeon should achieve circularity
≥98% in order to do not induce astigmatisms over 3D.
1. Introduction
For many years, optometrists, ophthalmologists and
researchers of the ocular area have used equipments to
study the eye. Some of these equipments have been in use
simply to observe parts of the eye, subjectively, such as:
magnifying glasses, Slit Lamps and bio-microscopes.
Other instruments referred to as keratometers or
ophthalmology meters have been used to measure the
radii of corneal curvature along the two main meridians
of the eye. The physics principle of such instruments is
already well known [1]. Currently, keratometers already
have technological advancements that allow the
measuring of corneal curvature radii, therefore measuring
the corneal astigmatism, and some are equipped with
rings projection covering the entire surface, showing the
topography of the cornea.
One of the significant factors that induces corneal
astigmatism during the surgical procedure is the
irregularity in suturing the tissue. Sutures are manually
performed on the cornea and systems for monitoring the
circularity of the suturing [2,3,4,5], are not often used.
Most of them are just qualitative.
The intention of the present work is to provide a system
that allows automated keratometry as well as an objective
real-time orientation for the surgeon for suturing the
corneal tissue as most circular as possible, expecting to
reduce the residual corneal astigmatism post- surgery.
A brief description of the optical properties of the human
cornea that concerns this work will be made as well as the
calculus involved for determining the radii of curvature of
the cornea will be described.
1.1 Optical Properties of the Human Cornea. The
cornea has a curved surface with refractive index of 1.376
and thickness of 0.480mm [1,6,7]. The external curvature
radius is approximately 7.8mm (it varies from 7.008.00mm for emmetrope eye) and the internal radius of
curvature varies from 6.2-6.8mm. Hence, the cornea is
equivalent to a positive lens. However it is very thin and
for calculus regarding the central part of the cornea, it is
possible to consider this region of the cornea as having
parallel faces [7,8].
The light rays that strike the cornea refract mainly
because of the relative difference of refractive index
between the air and the corneal surface, rather than
because of its corresponding refraction power (42.95D).
The cornea is not perfectly spherical, actually it is
ellipsoidal, and just the central part of the cornea, the so
called central optical zone of approximately 4,0mm, may
be considered spherical. The central zone is exactly where
keratometry is obtained.
The power of refraction of the small central portion of
that region varies from 41-45D.
In unusual conditions this region may be flattened
down to 37D or may be curved up to 60D. Precisely, it its
well known that the so called regular zone is not always
spherical, actually it is toric, therefore the vertical and
horizontal axes have different values.
1.2 Calculus for obtaining the radii of curvature of the
cornea using a fixed dimension mire target. The human
cornea has specific mechanical properties, which defines
its stability and which are correlated to the stroma
structure, having connections among its layers and
thickness. Hence the cornea may assume different shapes,
being difficult to predict a theoretical model for it. Any
proposed model will present negative and positive
aspects. So, the choice of which model to be used is the
one that is best suitable for the present system.
The cornea may be considered as a convex mirror, which
provides a virtual image of the projected light source
As earlier mentioned, the cornea assumes a spherical
shape in the central optical zone. These features are
relevant for considerations of the model to be used. The
spherical model is a very good approximation for the
mentioned zone, but due to the flattening of the cornea
toward the peripheral zone, we may obtain a small
discrepancy for the keratometric results in this zone when
compared to the actual keratometry measurements
obtained from the corneal topographers, for instance.
However, for a more criterious and accurate study of the
periphery of the cornea, the elliptical model is applied. In
this model, the cornea is treated as an ellipsoid, and
therefore the results of the keratometry obtained for the
cornea are more realistic.
The results presented by the elliptical model differ from
the ones obtained by the spherical model, especially at the
periphery of the cornea.
For keratometry purposes it can be said that, since just the
central optical zone will be analyzed, the spherical model,
which is much simpler to be implemented than the
elliptical model, is sufficient and accurate, but for small
radii of curvature, no approximations should be made, as
we have learned from the development and tests of our
first keratometry system for slit lamps [9].
1.3 Spherical Model Without Approximations. The
central zone of the cornea where the circular light mire is
projected (3mm in diameter) is spherical and therefore the
cornea may be considered as a convex mirror.
Figure 1 shows a schematic diagram of the keratometric
An object of size h (radius of the circular target mire) is
positioned at a distance a from the cornea, where it is
perfectly focused onto the cornea.
The reflection of object h provides a virtual image y,
which is half of the dimension of the projected target on
the cornea (around 1.5mm) and is at a distance b from the
corneal surface.
Distance d is 200mm for the surgical ocular microscope
that we have used. Dimension b is the distance between
the corneal surface and the actual position of the virtual
image of the object (projected target).
Figure 1: Schematic diagram of the keratometric principle
Considering that the light rays coming from h reach the
optical axis at small angles, it is possible to say that the
focusing distance is one half of the curvature radius of the
cornea (R).
Observing triangles HOV and VIM and since
d =a+b
The radius of curvature of the surface to be determined is:
2d h y
h2 − y2
The keratometric results are usually presented in
“Refraction Power” (F), given by expression (5) and the
unit is expressed in diopters (D).
nc − 1
nc (1.3375) is the corneal refractive index .
This paraxial equation (3) provides the refractive power
of the corneal surface for incident rays that are
approximately normal to the cornea and it is validated just
for the central optical zone.
2. The developed module
The system consists of a projected light ring onto the
cornea in such manner that any distortion of the reflected
image is analyzed for keratometric measurements.
The keratometry system can be divided in two distinct
portions: the projection system and the image capturing
The projection system consists in projecting onto the
patient’s cornea a mire with 36 red LEDS displayed in a
perfect circle, which is to be held by the surgeon as
shown in figure 2. The mire has 5 extra LEDS (one for
center alignment of the system and 4 others for angular
alignment). The mire has a special design that projects the
light spots homogeneously and in a precise circle of 3mm
of diameter in a standard cornea, i.e., with radius of
curvature of 7.895mm (a stainless steal sphere with
precision of 0.0025mm for its radius of curvature has
been used as a standard cornea for calibrating the system,
as shown in figure 3a). Figure 3b shows the target’s mire
projected onto a patient’s cornea.
Figure 3: Target’s mire projected onto: (a) a stainless
steal sphere; (b) the patient’s cornea during
Figure 4: Devices for assisting regular corneal suturing.
The digitized image is processed by dedicated
software for the system.
The software is based on the information provided by
the structure of the projecting target, determining its
distortion as its image is reflected back from the cornea.
The distortions analyzed between the original shape of
the projected target and its reflected image contains
information to provide the keratometric data.
Figure 2: The projection system: Mire with 36 LEDS
displayed in a perfect circle to be used during a
corneal suture.
The image of the target projected onto the patient’s
cornea is reflected back to the microscope and passes
through the observation system. A beam-splitter is placed
between the magnification system and the eyepiece lenses
of the slit lamp, where 70% of the reflected light is
deviated to the eyepiece lenses. A regular video optical
adapter for slit lamps (lenses, pin-holes and prisms) is
coupled to the beam-splitter and a CCD camera WATEC
221S is attached to it. The reflected image is analyzed by
the software at a micro computer OQO – model 2 coupled
to the CCD camera via a video bus cable, as show in
figure 4.
Unlikely the usual keratometers, the keratometric
module for the ocular microscope is not usually operated
in an environment free from external disturbances, as
light, for example. Hence, the developed algorithm is
capable to avoid these kinds of interferences in the image
The image provided by the system is initially
described in a matrix Im[x,y], which gives the position of
the image in pixels and its brightness value in grayscale,
0 ≤ Im[ x, y ] ≤ 255
The result of the non-uniformity of the brightness
distribution in the image of the light spots that reach the
examined surface is loss of information in the
identification process of the target’s shape. The
developed algorithm considers this possibility, once it
provides the keratometric results even if some light spot
is missing in the identification process.
The image to be processed is composed by the 36
spots of light displayed in a highly accurate circular form,
where the size of the target mire as well as the focusing
distance is accurately known. The reflected image
captured by the optical system will carry the distortions of
the examined surface, the cornea.
As the intensities of the light spots are not
homogeneously distributed, a convolution process is used
having a circular mask with a radius of the size of the
average radius obtained by the light spots.
As the center of the mask has a well defined position
it identifies its center and stores its position as Px[1],
Py[1]. Proceeding similarly, structures with lower
intensities are identified.
When all the Ne structures have been identified, as
well as the position of their center of mass (Px[i],Py),
(xcm0, ycm0) may be determined, which defines the position
of the center of mass of the image by:
xcm0 = ∑Px[i] / Ne e ycm0 = ∑Py[i] / Ne
The mathematical fitting expression for representing
the reflected image of the target onto the cornea is an
ellipse, with an inclination angle of θ related to the x axis
of the coordinate system, as represented in figure 5. The
coordinate system is X,Y and a and b are the minor and
major axis of the ellipse, respectively.
It should be noted that for the ellipse 0<e<1, therefore
circularity varies from 0% - 100%.
A real time image is displayed at the OQO monitor
with orientations for adjusting the target mire axis and
center. Figure 6 presents the interface screen. There is a
center guide denoted by 1 (small circle at the center of the
image screen), as well as an angular guide, denoted by 2
(two rectangles orthogonally placed in the center of the
image capturing screen). Region denoted by 3 is where
the 36 reflected spots should be.
There is a calibration button for calibrating the
system. The calibration of the system should be
performed every time its optical components are removed
and then replaced back in the microscope.
It consists in placing a standard stainless sphere with
radius of curvature of 7,895mm± 0,0025mm, in the fixed
focusing position provided by every slit lamp; set the
microscope to a desired magnification and capturing its
reflected image from the 36 light spots.
Keratometry and circularity (eccentricity) are
presented every time that the image is capture (either by
the mouse, voice command, or stepping pedal).
Figure 5: Representation of the ellipse used in the
software’s algorithm.
The eccentricity is a function added to the software to
acquaint the surgeon with the circularity of the suturing,
indicating whether the surgeon should stiffen the stitch or
relax it.
The eccentricity, denoted e, is a parameter associated
with every conic section. It can be thought of as a
measure of how much the conic section deviates from
being circular. [10]:
For any ellipse,
let a be the
length of its semi-major axis, b be the length of its semiminor axis and K=1.
Therefore, the circularity has been defined in our software
C = 100 (1 – e)%
Figure 6: Screen presented for the surgeon during
Figure 7 presents a measurement performed in a
patient during suturing. A 98% of eccentricity has been
achieved by the surgeon, however, it shows that almost
1D of astigmatism remains for this circularity.
correlation between our system and the Topcon OM-4 is
r2=0.97 for the axis.
4. Discussions and Conclusion
Regarding figure 7, it may be noticed that high postoperatory astigmatisms are usually induced by the
irregular manual suturing of the tissue. Even a high
eccentricity (98% of circularity) achieved during the
suture indicates that an astigmatism of the order of 1D
still remains.
Figure 7: Real time surgery measurement of keratometry
and eccentricity of a cataract surgery.
3. Results
In order to know the accuracy of our system, 21
standard steal spheres have been analyzed.
Figure 8 shows the correlation curve between our
system and the data provided by the manufacturer of the
standard spheres, in a range of 3.0000mm – 17.0000mm
Spheres with radius of curvature of 7.8mm, which are
the best representative for the corneal model, is 90%
Around 290 patients have been tested and it has been
observed that circularity is corneal geometrical structure
dependent. For instance, in order to remain astigmatisms
lesser then 3D, for patients with corneas having radii of
curvature around 7.8mm, a 97% of eccentricity should be
achieved; for flatter corneas (refractive power of 38D)
and more warped corneas (refractive power of 55D),
eccentricities of 95% and 99%, respectively should be
This may lead to an awareness that manual suture
should be carefully performed in order to obtain better
post-operatory results related to remaining astigmatism.
Maybe automated systems for suturing should be
considered in the near future.
5. Acknowledgements
The authors would like to thank CNPq (477226/2003-5)
for all the financial support for this research and for some
of the researchers, and Hospital das Clínicas de Ribeirão
Preto (São Paulo – BRASIL), which is the Hospital that
has always been contributing for the success of our
6. References
Figure 8: Correlation curve between our system and the
data provided by the manufacturer of the standard
spheres, in a range of 3,0mm – 17,0mm.
Patients have been submitted to our system and the
obtained results have high correlation factors (r2=0.96)
with the keratometers available on the market (Topcon
In order to know the accuracy of the axis component
of our system a device for distorting a contact lens
coupled to a precise angular ruler was developed. It
consisted of a vertical wedge, where the lens was placed
and slightly pushed to be vertically deformed. Three
different deformations were performed and they were
precisely rotated at steps of 10 for the 3600. The
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Surgical Device for Supporting Corneal Transplants