Device and method for modelling a cornea

Abstract

A patient-specific finite element model of the cornea is generated for the purposes of modeling a cornea for simulating tissue cuts in the cornea. A first group of tissue fibers, with main fibers that extend parallel to the surface of the cornea, is distributed in the finite element model in accordance with a first distribution function. Moreover, a second group of tissue fibers, with inclined cross-linked fibers that do not extend parallel to the surface of the cornea, is distributed in the finite element model in accordance with a second distribution function. Here, the second distribution function distributes the cross-linked fibers with a non-uniform weighting function over the depth of the cornea, from the outer surface of the cornea to the inner surface of the cornea.

Claims

1. A computerized device for modeling a cornea for simulating tissue cuts in the cornea, comprising a processor programmed to load patient-specific corneal data, generate a patient-specific finite element model of the cornea and determine elements in the finite element model which are separated from one another by the tissue cuts on the basis of cut data defining the tissue cuts, wherein the processor is moreover programmed to distribute a first group of tissue fibers, with main fibers that extend parallel to the outer surface of the cornea, in the finite element model in accordance with a first distribution function and to distribute a second group of tissue fibers, with inclined cross-linked fibers that do not extend parallel to the outer surface of the cornea, in the finite element model in accordance with a second distribution function, wherein the second distribution function distributes the cross-linked fibers with a non-uniform, decreasing depth distribution function (.sub.C(s)) over the depth (s) of the cornea, from the outer surface of the cornea to the inner surface of the cornea; and wherein said computerized device further comprises a display for graphically displaying a three-dimensional model of the cornea on the basis of the generated finite element model which is in equilibrium with the intraocular pressure.

2. The device as claimed in claim 1, wherein the processor is programmed to distribute the cross-linked fibers over the depth (s) of the cornea with a depth distribution function (.sub.C(s)) having a sinusoidal profile.

3. The device as claimed in claim 2, wherein the processor is programmed to introduce permeability values for liquid exchange in the corneal tissue into the finite element model, which permeability values are dependent on the depth distribution function (.sub.C(s)), by means of which the cross-linked fibers are distributed over the depth (s) of the cornea.

4. The device as claimed in claim 1, wherein the processor is programmed to introduce permeability values for liquid exchange in the corneal tissue into the finite element model, which permeability values are dependent on the depth (s) of the cornea.

5. The device as claimed in claim 1, wherein the processor is programmed to generate a transition from the patient-specific finite element model of the cornea to a population-based sclera model and to distribute the cross-linked fibers in the transition with a decreasing depth distribution function (.sub.C(t)) over the depth (t) of the transition, from an outer transition surface (MA(R,)), which extends from the outer surface of the cornea to the outer surface of the sclera, to an inner transition surface (MP(R,)), which extends from the inner surface of the cornea to the inner surface of the sclera.

6. The device as claimed in claim 1, wherein the processor is programmed to distribute the cross-linked fibers on a number of layers that extend parallel to the outer surface of the cornea in the finite element model and to distribute the cross-linked fibers in the layers, respectively with a two-dimensional distribution function (2D).

7. The device as claimed in claim 1, wherein the processor is programmed to store different material properties for the first group of tissue fibers and the second group of tissue fibers in the finite element model.

8. The device as claimed in claim 1, wherein the processor is programmed, in the finite element model, to distribute the main fibers uniformly on a plurality of areas that extend parallel to the outer surface of the cornea and to distribute said main fibers on the areas with in each case a two-dimensional distribution function (2D).

9. A computer-implemented method for modeling a cornea for simulating tissue cuts in the cornea, which method comprises an execution of the following steps by a processor: loading patient-specific corneal data, generating a patient-specific finite element model of the cornea, distributing a first group of tissue fibers, with main fibers that extend parallel to the outer surface of the cornea, in the finite element model in accordance with a first distribution function and distributing a second group of tissue fibers, with inclined cross-linked fibers that do not extend parallel to the outer surface of the cornea, in the finite element model in accordance with a second distribution function, wherein the second distribution function distributes the cross-linked fibers with a non-uniform, decreasing depth distribution function (.sub.C(s)) over the depth (s) of the cornea, from the outer surface of the cornea to the inner surface of the cornea, and determining elements in the finite element model which are separated from one another by the tissue cuts on the basis of cut data defining the tissue cuts.

10. The method as claimed in claim 9, characterized by distributing the cross-linked fibers with a depth distribution function .sub.C(s) having a sinusoidal profile over the depth (s) of the cornea by way of the processor.

11. The method as claimed in claim 10, wherein by introducing permeability values for liquid exchange in the corneal tissue, which permeability values are dependent on the depth distribution function .sub.C(s), with which the cross-linked fibers are distributed over the depth (s) of the cornea, into the finite element model by way of the processor.

12. The method as claimed in claim 9, wherein by introducing permeability values for liquid exchange in the corneal tissue, which permeability values are dependent on the depth (s) of the cornea, into the finite element model by way of the processor.

13. The method as claimed in claim 9, wherein by generating a transition from the patient-specific finite element model of the cornea to a population-based sclera model by means of the processor and distributing the cross-linked fibers in the transition with a decreasing depth distribution function .sub.C(t) over the depth (t) of the transition, from an outer transition surface (MA(R,)), which extends from the outer surface of the cornea to the outer surface of the sclera, to an inner transition surface (MP(R,)), which inner transition surface extends from the inner surface of the cornea to the inner surface of the sclera, by way of the processor.

14. The method as claimed in claim 9, wherein by distributing the cross-linked fibers over a plurality of layers that extend parallel to the outer surface of the cornea in the finite element model by way of the processor and by distributing the cross-linked fibers in the layers, respectively with a two-dimensional distribution function, by way of the processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Below, an embodiment of the present invention is described on the basis of an example. The exemplary embodiment is illustrated by way of the following attached figures:

(2) FIG. 1 shows a block diagram of a computerized device for modeling a cornea for simulating tissue cuts in the cornea.

(3) FIG. 2 shows a flowchart with an exemplary sequence of steps of a method for modeling a cornea for simulating tissue cuts in the cornea.

(4) FIG. 3 shows a flowchart with an exemplary sequence of steps for loading eye data.

(5) FIG. 4 shows a flowchart of an exemplary sequence of steps for generating a finite element model of a cornea for simulating tissue cuts in the cornea.

(6) FIG. 5 schematically shows, in a cross section of a corneal segment, the distribution of main fibers that extend parallel to the surface of the cornea over the depth of the cornea (depth distribution) and a corresponding distribution function or depth distribution function or weighting function.

(7) FIG. 6 schematically shows, in a cross section of a corneal segment, the distribution of inclined cross-linked fibers that do not extend parallel to the surface of the cornea over the depth of the cornea (depth distribution) and a corresponding distribution function or depth distribution function or weighting function.

(8) FIG. 7 schematically shows, in a cross section, a transition from a corneal segment to an adjoining sclera segment and the distribution of inclined cross-linked fibers that do not extend parallel to the surface of the cornea over the depth of the cornea and the depth of the transition.

(9) FIG. 8 shows a two-dimensional distribution function for main fibers that extend parallel to the surface of the cornea and inclined cross-linked fibers that do not extend parallel to the surface of the cornea.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(10) In FIG. 1, reference sign 1 relates to a computerized device for modeling a cornea for simulating tissue cuts in the cornea. The device 1 comprises an operational computer with at least one processor 10 and storage 11, connected to the processor 10, for storing data (data storage) and computer program code (program storage). In the embodiment in accordance with FIG. 1, the device 1 moreover comprises a display 12, e.g. an LED or LCD monitor. As depicted schematically in FIG. 1, the device 1 is connected in a variant to a computerized data source 2 external to the device 1, for example by way of a wired or wireless communication interface. The data source 2 comprises one or more processors and it is configured to transmit eye data, including patient-specific corneal data and/or population-based sclera data, to the device 1, as will be described in more detail below. Depending on the embodiment variant, the data source 2 comprises an ophthalmological measuring device for acquiring the patient-specific corneal data from a patient and/or an ophthalmological database with population-based sclera data.

(11) The processor 10 is configured or programmed to execute a method for modeling a cornea for simulating tissue cuts in the cornea. To this end, the device 1 comprises a computer program product with a computer-readable medium, which is permanently or removably connected to the processor 10 and which comprises computer program code stored thereon, said computer program code being configured to control the processor 10 in such a way that the latter executes the method. In the following paragraphs, possible sequences of steps for executing the method are described with reference to FIGS. 2, 3 and 4.

(12) As depicted in FIG. 2, eye data are loaded into the storage 11 in step S1.

(13) As can be seen in FIG. 3, population-based sclera data are loaded into the storage 11 in the optional step S11 in this case. The population-based sclera data define a geometric average model of the sclera, including three-dimensional geometry and dimensions of an average sclera on a statistical data basis. In one embodiment variant, the sclera data define at least the geometry and the dimensions of a boundary region of the sclera, which adjoins the transition to the cornea. By way of example, the sclera data are acquired from an Internet-based data source or are permanently stored in the data storage 11.

(14) In step S12, patient-specific corneal data are loaded into the storage 11. The patient-specific corneal data define a patient-specific geometric model of the cornea, including three-dimensional geometry and dimensions of the cornea of a patient on a data basis acquired by measurement. The patient-specific corneal data are preferably acquired by means of an ophthalmological measuring device and stored in the data storage 11 in a manner assigned to the relevant patient.

(15) As depicted schematically in FIG. 2, the processor 10 generates an initial finite element model in step S2 on the basis of the loaded eye data, in particular a patient-specific finite element model of the cornea on the basis of the patient-specific corneal data.

(16) In an embodiment variant, a spherical finite element grid is initially produced, which is transformed by means of a transformation method (warping method) into the patient specific geometry of the cornea 34 (which is defined by the patient-specific corneal data), for example by means of a transformation method as described in Studer H P, Riedwyl H, Amstutz C A, Hanson V M, Bchler P, (2013) Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery; Journal of Biomechanics, 46(4): 751-758.

(17) As can be seen in FIG. 4, a transition from the patient-specific cornea to the population-based sclera is generated by the processor 10 in the optional step S21. This is advantageous because part of the sclera is also simulated for a precise simulation of surgical interventions. As illustrated in FIG. 7, a smooth geometric transition 36 is generated from the patient-specific cornea 34 to the population-based sclera 35. In particular, mathematical functions for geometric surfaces are defined for the transition 36 from the patient-specific cornea 34 to the population-based sclera 35, namely a function M.sub.A(R,) for the front/outer transition surface (anterior) and a function M.sub.P(R,) for the back/inner transition surface (posterior). The front/outer transition surface M.sub.A(R,) is realized as a smooth surface and it extends continuously from the front/outer surface 30 of the cornea 34 to the front/outer surface 350 of the sclera 35. The back/inner transition surface M.sub.P(R,) is realized as a smooth surface and it extends continuously from the back/inner surface 33 of the cornea 34 to the back/inner surface 351 of the sclera 35. Depending on the embodiment variant, the transition 36 is generated on the basis of the patient-specific geometry model of the cornea 34, loaded in step S1, or on the basis of the corresponding finite element model of the cornea 34.

(18) In step S22, the processor 10 distributes the main fibers 31 that extend parallel to the surface 30 of the cornea, as depicted in FIG. 5, in the patient-specific finite element model of the cornea 34. Optionally, the main fibers 31 are accordingly also distributed in the transition 36 from the patient-specific cornea 34 to the population-based sclera 35.

(19) The main fibers 31 are distributed on layers or areas of the cornea 34, which respectively extend at different depths, parallel to the corneal surface 30. Here, use is made of a two-dimensional distribution function .sub.2D (see the example in FIG. 8) to distribute the main fibers 31 within respectively one of these corneal layers (in plane). Here, this two-dimensional distribution function .sub.2D consists of two parts:
.sub.a(R,;)=cos.sup.2n+sin+c.sub.1,
.sub.b(R,;)=sin.sup.2n()+c.sub.2(1)
which are combined as follows:
.sub.2D(R,;)=w.Math..sub.a(R,;)+(1w).Math..sub.b(R,;).(2)

(20) The weighting w between the two parts depends on the location of a material point P.sub.R on the corneal layer and it is given by:

(21) $\begin{array}{cc}w=\{\begin{array}{cc}1.0& \mathrm{if}0<R<4.0\\ \frac{1}{2}\cos \left[\frac{}{1.5}\left(R-4.0\right)\right]+\frac{1}{2}& \mathrm{if}4.0<R<5.5\\ 0.0& \mathrm{otherwise}\end{array},& \left(3\right)\end{array}$

(22) where R is the distance of the material point P.sub.R from the corneal center (0, 0), is the angle between the positive x-axis in the model and the link between the material point P.sub.R and the corneal center, and defines the fiber direction in the local coordinate system of the material point P.sub.R.

(23) A first depth distribution function .sub.H(s) is used for the distribution (weighting) of the main fibers 31 on the individual corneal layers. In the example of FIG. 5, the first depth distribution function .sub.H(s) is uniform (constant), i.e. the main fibers 31 are distributed uniformly over the depth s, from the front corneal surface 30 to the back corneal surface 33, and there are the same number of main fibers 31 at each corneal depth (in each corneal layer):
.sub.H(s)=1.(4)

(24) Accordingly, the main fibers 31 are distributed independently of the depth and parallel to the surface 30 in accordance with equations (1) to (3), as illustrated in FIG. 8. A person skilled in the art will understand that a different depth distribution function .sub.H(s) can also be used for the main fibers 31 on account of different anatomical circumstances.

(25) Since parts of the transition 36 from the cornea to the sclera 35 are corneal tissue, the fiber distribution is also applied in the transition 36. In the transition 36 from the patient-specific cornea 34 to the population-based sclera 35, the main fibers 31 are also distributed in the same manner as in the cornea 34, within the parallel layers (areas) by means of the two-dimensional distribution function .sub.2D and over the depth s in accordance with the uniform first depth distribution function (weighting function) .sub.H(s). The homogeneous depth distribution of the main fibers 31 is depicted schematically in FIGS. 5 and 7 in such a way that the main fibers 31 are depicted as layers or areas extending parallel to the corneal surface 30.

(26) In step S23, the processor 10 distributes the inclined cross-linked fibers 32 that do not extend parallel to the surface 30 of the cornea, as depicted in FIG. 6, in the patient-specific finite element model of the cornea 34. Optionally, the cross-linked fibers 32 are accordingly also distributed in the transition 36 from the patient-specific cornea 34 to the population-based sclera 35.

(27) Hence, the cross-linked fibers 32 are a fiber family differing from the main fibers 31, which cross-linked fibers are inclined by approximately 15 (wherein the inclination should be understood to mean a deviation from the direction of the main fibers), alternately toward the inside, i.e. inclining toward the surface 33, and toward the outside, i.e. inclining toward the surface 30. In a variant, different material properties are assigned to the main fibers 31 and the cross-linked fibers 32.

(28) Like the main fibers 31, the cross-linked fibers 32 are distributed within the corneal layers or areas extending parallel to the corneal surface 30 (in plane) by means of the two-dimensional distribution function .sub.2D in accordance with equations (1) to (3) described above.

(29) A second depth distribution function .sub.C(s) is used for the distribution (weighting) of the cross-linked fibers 32 on the individual corneal layers. In the example of FIG. 6, the second depth distribution function (weighting function) .sub.C(s) has a profile decreasing with depth s. That is to say, the cross-linked fibers 32 are distributed with a decreasing number over the depth s from the front corneal surface 30 to the back corneal surface 33. In contrast to the depth distribution of the main fibers 31, the cross-linked fibers 32 are therefore not distributed uniformly (i.e. not in a constant manner) but with a specific depth distribution function or weighting function over the depth s. In the example of FIG. 6, the second depth distribution function .sub.C(s) has a sinusoidal profile (at least in a defined portion of the thickness or depth s of the cornea 34) and it is defined as follows:

(30) $\begin{array}{cc}{}_C\left(s\right)=\{\begin{array}{cc}1.0& \mathrm{if}s<1/3\\ \frac{1}{2}\left[\sin \left[3\left(s-\frac{1}{3}\right)\frac{}{2}\right]+1\right]& \mathrm{if}1/3<s<2/3\\ 0.0& \mathrm{otherwise}\end{array}& \left(5\right)\end{array}$

(31) In contrast to the uniform depth distribution .sub.H(s) of the main fibers 31, the number of cross-linked fibers 32 continuously decreases with the depth s in the cornea 34. A person skilled in the art will understand that a different depth distribution function .sub.C(s) which decreases with depth s can also be used for the cross-linked fibers 32 on account of different anatomical circumstances.

(32) Since parts of the transition 36 from the cornea to the sclera 35 are corneal tissue, the fiber distribution and the consideration of the depth inhomogeneity is also applied in the transition 36. In the transition 36 from the patient-specific cornea 34 to the population-based sclera 35, the cross-linked fibers 32 are also distributed in the same manner as in the cornea 34. Within the layers extending parallel to the front/outer surface of the transition 36 defined by the function M.sub.A(R,), the cross-linked fibers 32 are distributed (in plane) by means of the two-dimensional distribution function .sub.2D, described above, in accordance with equations (1) to (3). The inhomogeneous depth distribution is derived from the depth distribution in accordance with equation (5). Here, t(R,)=M.sub.A(R,)M.sub.P(R,) and hence

(33) $\begin{array}{cc}{}_C\left(t\right)=\{\begin{array}{cc}0.0& \mathrm{if}t<1/3\\ \frac{1}{2}\left[\sin \left[3\left(t-\frac{1}{3}\right)\frac{}{2}\right]+1\right]& \mathrm{if}1/3<t<2/3\\ 1.0& \mathrm{otherwise}\end{array}& \left(6\right)\end{array}$
applies. The inhomogeneous depth distribution of the cross-linked fibers 32 is depicted schematically in FIGS. 6 and 7 in such a way that the cross-linked fibers 32 are depicted as inclined arrows, the length of which symbolizes the weighting (number, frequency) thereof.

(34) Refractive surgical treatments, such as e.g. phototherapeutic keratectomy (PTK) and laser-assisted in situ keratomileusis (LASIK), are known to lead to peripheral corneal thickening. It is assumed that the incisions of the treatment lead to relaxation in the tissue. This relaxation in turn leads to changes in the physiological imbibition pressure of the cornea, leading to liquid displacements and the swelling of the tissue. Liquid displacements through the tissue structure of the cornea can be formulated as a poroelastic problem and it can be modeled by means of two-phase finite elements. Here, it is possible to image both the linear and the nonlinear case (in the latter case, the material permeabilityi.e. the permeability of the material to liquidsdepends on the deformation).

(35) In step S24, the processor introduces permeability values into the finite element model of the cornea 34 and optionally of the transition to the sclera 35. The permeability values P(s) characterize the liquid exchange in the corneal tissue and are set dependent on the depth s of the cornea 34. The permeability values P(s) specify the permeability of the corneal tissue to liquids, dependent on the depth s of the cornea 34. Since the depth distribution function for inclined fibers is related directly to the degree of adhesion of the collagen fibers and hence to the impermeability of the tissue, the change in the permeability P(s) dependent on the depth s can be modeled in accordance with the following equation (7) as a function of the depth distribution function .sub.C(s) of the cross-linked fibers 32:
P(s)=1.sub.C(s).(7)

(36) Hence, the change in the permeability in the two-phase finite elements with the depth s in the cornea, and hence the depth-dependent swelling of the cornea, can be modeled.

(37) The individual elements of the finite element model produced in step S2, with the initial geometry of the cornea 34 and the transition 36 to the sclera 35, each comprise a plurality of integration points with element values such as stress, strain, deformation, reaction force, plastic deformation, strain energy, etc. Here, these element values are directionally dependent values, which are calculated at the integration points from the parts contributed by the fibers. In one embodiment variant, different material properties are provided and stored in the elements for the main fibers 31 and the cross-linked fibers 32.

(38) In step S3, the processor 10 calculates a solution to the finite element model. Here, the finite element model, produced in step S2, of the initial geometry of the cornea 34 and of the transition 36 to the sclera 35 is exposed (computationally) to the intraocular pressure (which is e.g. measured in a patient-specific manner). This leads to a (calculated) mechanical imbalance in the finite element model. As a consequence, the cornea as represented by the finite element model is deformed (inflated) and the individual elements in the model are deformed. Thus, a (calculated) strain in the elements of the model is created. The strain is connected with a defined material function which determines how much stress is created due to a calculated strain. In fact, the fibers and distribution functions are included in this material function, which is calculated at each integration point. The material function relates strain and energy (stress). The material function is defined by

(39) $\begin{array}{cc}=U+{\stackrel{\_}{}}_m\left[C_{10}\right]+\frac{1}{}\left({\stackrel{\_}{}}_{f1}\left[{}_m,{}_m\right]+{\stackrel{\_}{}}_{f2}\left[{}_k,{}_k\right]\right)d& \left(8\right)\end{array}$

(40) where is the energy, .sub.f1 are the main fibers 31, .sub.f2 are the cross-linked fibers 32 and are the distribution functions. .sub.m is a tissue part which does not consist of fibers and U is a penalty function for changes in volume (this leads to an incompressibility of the tissue). The calculated stress is then in turn stored in the element. This sequence deformation.fwdarw.strain.fwdarw.stress is repeated iteratively in step S3 until the strain configuration at which the applied intraocular pressure is compensated for by the calculated stresses is reached. When the deformation state or the strain configuration for compensating the intraocular pressure is found for each element, there is a calculated equilibrium between stresses in the elements, which emerge from the deformation and the strain, and the intraocular pressure, i.e. a solution of the finite element model is present.

(41) In step S4, the processor 10 graphically displays on the display 12 a three-dimensional model of the cornea 34 on the basis of the generated finite element model which is in equilibrium with the intraocular pressure. The graphical display of the corneal model can be modified by a user of the device 1, preferably by entering user commands (e.g. via mouse, keyboard and/or touchscreen), for example in respect of the orientation by means of a free rotation in space and/or in respect of the size or resolution by means of a zoom function, like in a CAD system.

(42) In step S5, the processor 10 receives cut data, for example from a user of the device 1 in accordance with user commands and/or from a selected file with stored cut data. The user commands for defining cuts or corresponding cut data can be introduced into the displayed model by the user, for example by means of a computer mouse, a keyboard and/or by way of a touchscreen. The cut data define the three-dimensional geometry, the dimensions and the position of one or more cuts into the cornea 34 and/or in the region of the sclera 35 adjoining the cornea 34 by way of the transition 36. Here, the cuts can also be positioned in the interior of the eye tissue, with or without severing of the front/outer surface 30 of the cornea 35 or the transition surface M.sub.A(R,) of the transition 36 and the front/outer surface 350 of the sclera 35.

(43) In step S6, the cut data are applied to the finite element model of the cornea 34 and of the transition 36 by the processor 10. That is to say, the processor 10 determines the elements in the model affected by the cut data, which elements are separated from one another by a cut carried out in accordance with the cut data.

(44) In step S3, the processor 10 again calculates the solution to the finite element model, as described above, for the finite element model modified by the cut data. On the basis of the modified finite element model, which again is in equilibrium with the intraocular pressure, the processor 10 generates a graphical display of the corneal model modified by the cut on the display 12 in step S4.

(45) The finite element model therefore enables the modeling of the cornea 34 and the simulation of tissue cuts in the cornea 35. Here, the degree of iteration of steps S3.fwdarw.S4.fwdarw.S5.fwdarw.S6.fwdarw.S3, or the length of cuts per iteration step, can be set e.g. by the user.

(46) Finally, it should be noted that although the description depicts steps as being carried out in a specific sequence, a person skilled in the art will understand that the sequence of at least some steps can be modified, without in the process departing from the subject matter for which protection is sought.