GENERALIZED MODELING OF THE CORNEA
A system and method for simulating a corneal reconfiguration in response to laser surgery uses a computer-programmed, biomechanical generalized model. The generalized model has a plurality of elements; with each element being pre-programmed based on diagnostic corneal data obtained from images of respective individual collagen fibers in a cornea. Collectively these pre-programmed elements replicate biomechanical properties of the cornea. In use, designated biomechanical characteristics on a plurality of selected elements are minimized to simulate laser surgery in an actual cornea. A computer then measures the resultant reconfiguration of the cornea model to assess an actual cornea's response to laser surgery.
1 . A system for simulating a reshaping of a model cornea which comprises:
a computer programmed with a generalized model comprising a plurality of elements, wherein each element is pre-programmed to simulate biomechanical characteristics of a collagen fiber in the cornea, and further wherein biomechanical characteristics of the pre-programmed elements are established based on diagnostic corneal data;
a first computer means connected to the generalized model for minimizing designated biomechanical characteristics on at least one selected element; and
a second computer means electronically connected to the generalized model for evaluating a reshaped model cornea in response to operation of the first computer means.
2 . A system as recited in claim 1 wherein the generalized model defines an anterior surface and a posterior surface for the cornea, with an axis perpendicular to the surfaces and passing through respective apexes of the surfaces, and further wherein the curvatures of the anterior and posterior surfaces are approximated by a respective conic section.
3 . A system as recited in claim 2 wherein the conic section for each surface is expressed as:
z
(
x
)
=
1
2
-
1
[
R
2
+
x
2
(
2
-
1
)
-
R
]
.
4 . A system as recited in claim 3 where:
R for the anterior surface is approximately 7.86 mm;
R for the posterior surface is approximately 6.76 mm; and
e for the eccentricity of the cornea is 0.32.
5 . A system as recited in claim 1 wherein the first computer means minimizes an element by reducing its pre-programmed biomechanical characteristics approximately ninety percent in value.
6 . A system as recited in claim 1 wherein each element includes information regarding shape, elasticity and viscosity of the collagen fiber.
7 . A system as recited in claim 1 wherein the first computer means simulates a cut inside the stroma of the cornea, substantially parallel to the axis.
8 . A system as recited in claim 1 wherein the first computer means simulates a cut inside the stroma, substantially perpendicular to the axis.
9 . A system as recited in claim 1 wherein the generalized model is axisymmetric and is based on a nonlinearly elastic, slightly compressible, transversely isotropic formulation with an isotropic exponential Lagrangian strain-energy function based on:
W= ½ C ( e Q −1)+ C compr ( I 3 InI 3 −I 3 +1)
and
Q=b ff E 2 ff +b xx ( E 2 cc +E 2 ss +E s cs +E 2 sc )+ b fx ( E 2 fc +E 2 cf +E 2 fs +E 2 sf )
Where:
I are invariants,
W is the strain potential (strain-energy function),
C is stress-scaling coefficient,
C compr is bulk modulus (kPa),
E is strain,
b ff is fiber strain exponent,
b xx is transverse strain component, and
b fx is fiber-transverse shear exponent.
10 . A system for simulating a reshaping of a model cornea which comprises:
a generalized model having a plurality of individual elements, wherein each element is pre-programmed with biomechanical characteristics based on diagnostic corneal data pertinent to individual collagen fibers in the cornea to collectively replicate biomechanical properties of the cornea, and to represent the cornea in a first configuration;
a means connected to the generalized model for minimizing designated biomechanical characteristics on a plurality of selected elements; and
a means for evaluating a second configuration for the cornea in response to operation of the minimizing means.
11 . A system as recited in claim 10 wherein the generalized model defines an anterior surface and a posterior surface for the cornea, with an axis perpendicular to the surfaces and passing through respective apexes of the surfaces, and further wherein the curvatures of the anterior and posterior surfaces are approximated by a respective conic section expressed as:
z
(
x
)
=
1
2
-
1
[
R
2
+
x
2
(
2
-
1
)
-
R
]
Where:
R for the anterior surface is approximately 7.86 mm;
R for the posterior surface is approximately 6.76 mm; and
e for the eccentricity of the cornea is 0.32.
12 . A system as recited in claim 11 wherein the generalized model is axisymmetric and is based on a nonlinearly elastic, slightly compressible, transversely isotropic formulation with an isotropic exponential Lagrangian strain-energy function based on:
W= ½ C ( e Q −1)+ C compr ( I 3 InI 3 −I 3 =1)
and
Q=b ff E 2 ff +b xx ( E 2 cc +E 2 ss +E 2 cs +E 2 sc ) 30 b fx ( E 2 fc +E 2 cf +E 2 fs +E 2 sf )
Where:
I are invariants,
W is the strain potential (strain-energy function),
C is stress-scaling coefficient,
C compr is bulk modulus (kPa),
E is strain,
b ff is fiber strain exponent,
b xx is transverse strain component,
b fx is fiber-transverse shear exponent, and
wherein the stress-scaling coefficient for Bowman's capsule (C Bowman ) is approximately five times greater than the stress-scaling coefficient for the stroma (C stroma ).
13 . A system as recited in claim 10 wherein elements are minimized by reducing pre-programmed biomechanical characteristics approximately ninety percent in value.
14 . A system as recited in claim 10 wherein data for each collagen fiber is obtained from images of the cornea and includes information pertaining to the shape, elasticity and viscosity of each respective collagen fiber.
15 . A method for simulating a reshaping of a cornea which comprises the steps of:
creating a generalized model comprising a plurality of elements;
pre-programming the plurality of elements to respectively simulate biomechanical characteristics of individual collagen fibers in the cornea, wherein the pre-programmed elements are established for the generalized model according to diagnostic corneal data;
minimizing biomechanical characteristics on selected elements;
measuring a reshaped cornea in response to the minimizing step; and
repeating the minimizing and measuring steps, as required.
16 . A method as recited in claim 15 wherein the creating step further comprises the steps of:
imaging the cornea to obtain a first set of images of collagen fibers therein at a first pressure in the eye;
changing the first pressure in the eye to a second pressure in the eye;
imaging the cornea to obtain a second set of images of collagen fibers therein at the second pressure in the eye; and
comparing the first set of images with the second set of images to obtain the diagnostic corneal data.
17 . A method as recited in claim 16 wherein the diagnostic corneal data includes information regarding the shape, elasticity and viscosity of individual collagen fibers in the cornea.
18 . A method as recited in claim 15 wherein the generalized model defines an anterior surface and a posterior surface for the cornea, with an axis perpendicular to the surfaces and passing through respective apexes of the surfaces, and further wherein the curvatures of the anterior and posterior surfaces are approximated by a respective conic section expressed as:
z
(
x
)
=
1
2
-
1
[
R
2
+
x
2
(
2
-
1
)
-
R
]
.