Determining an implant to be inserted into the cornea of an eye for correcting defective vision

Abstract

The invention relates to a method for producing an implant to be inserted into the cornea of an eye (3) for correcting defective vision, comprising the steps of: a) providing defective vision data concerning the defective vision of the eye to be corrected; b) determining a change in shape of the cornea necessary for correcting the defective vision on the basis of the defective vision data; and c) defining a profile of a thickness of the implant such that the insertion thereof into the cornea brings about the desired defective vision correction, a proportion to which the thickness of the implant changes the shape being determined, the proportion being between zero and one.

Description

[0001]Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena Carl Zeiss Meditec AG May 21, 2025 Attorney File: PAT 9030 / 270-PCT Determining an implant to be inserted into the cornea of ​​an eye for the correction of refractive errors The invention relates to the correction of refractive errors in an eye by inserting an implant into the cornea, which has a thickness gradient that modifies the shape of the cornea in a refractive error-correcting manner. The invention relates in particular to the determination of the thickness gradient. The invention deals with the surgical correction of refractive errors in the eye. For this purpose, the shape of the cornea is to be modified. In most cases, the shape can be described by a curvature. The modification is therefore generally carried out in such a way that the cornea acquires a new curvature (e.g., flatter or more curved at the front). One of the first developments for this was the so-calledLASIK surgery has been extensively implemented in practice. In this surgical principle, known as "laser-assisted in situ keratomileusis" or "LASIK," a flap is detached from the front of the cornea through a lateral incision and folded back. This exposes the interior of the cornea. Tissue is then removed from this interior corneal layer by vaporization using pulsed excimer laser radiation. When the flap is then repositioned over the cornea, it conforms to the underlying corneal bed, resulting in a change in the curvature of the cornea at its front due to the material removal. A later-developed surgical technique, which does not involve detaching a corneal flap, isolates a lenticule within the cornea by precisely applying pulsed laser radiation and then removes it through a small lateral incision.This principle of isolating and then removing a piece of tissue within the cornea requires pulsed laser radiation, which separates tissue within the cornea, something excimer laser radiation cannot do. This pulsed laser radiation must be precisely and three-dimensionally focused on target points within the cornea at a very narrow focal point. The position and shape of the resulting cut surface are crucial for the surgical outcome. This lenticular-extracting surgical technique has been extensively implemented in the technology of Carl Zeiss Meditec AG. K / 22 / K 110103A Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 2 The generation of control data for the lenticular-extracting surgical technique is the subject of EP 2298255 B1. It is also known to insert an implant made of artificial tissue, animal tissue, or human tissue into the cornea for the correction of refractive errors.Tissue refers to a material that consists at least partially of proteins. Materials that are largely composed of water, especially hydrogels, whose elasticity is comparable to that of the human cornea, are particularly suitable. The implant is inserted into a corneal pocket created by a suitable incision. Unlike the lenticule-extracting surgical technique, the location and shape of this incision are often not particularly critical, as the change in corneal shape, and thus the refractive error correction, is determined, among other things, by the thickness profile of the implant. After implantation, external forces can cause the implant to bend, but its thickness, and therefore the corrective effect, remains essentially unchanged due to the low compressibility of the implant material. Determining the thickness profile of the implant is therefore a crucial aspect of this type of refractive error correction.SLAK (Stromal Lenticule Addition Keratoplasty) is a procedure that uses a lenticule cut from donor cornea for the purpose of hyperopia correction. This avoids the explicit calculation of the implant thickness profile by utilizing the reciprocity that the removal of a specific lenticule results in a refractive error correction (e.g., +1 diopter spherical) that is exactly the opposite of the refractive error correction (e.g., -1 diopter spherical) achieved by inserting the same lenticule. US 11406531 B1 further develops the SLAK procedure. It creates a corneal map that quantifies the deviation of an abnormal corneal shape from the optimal shape. WO 2020 / 212199 A1 calculates a difference map based on spatially resolved pachymetry of the eye and typical pachymetry maps of healthy eyes.This is intended to predict the postoperative corneal radius of curvature, the spatially resolved curvature or topography of the postoperative cornea, or to calculate the postoperative refractive power and, in combination with other biometric parameters of the recipient eye, predict the refraction of the recipient eye after implantation. How these functions are technically achieved is not disclosed in detail. WO 2015 / 003779 A2 concerns the refractive modification of a cornea by making deep incisions, which is the basic principle of radial keratotectomy. Patent attorneys GEYER, FEHNERS PARTNER Munich -- Jena 3 employ a finite element model (FEM) calculation, which is extremely computationally intensive. Therefore, the current state of the art still allows for improvements in determining the thickness profile of the implant, both in terms of accuracy and computational efficiency.The invention is therefore based on the objective of improving the accuracy and / or computational efficiency of determining the thickness profile of the implant. The invention is defined in the independent claims. The dependent claims relate to preferred embodiments. A method for producing an implant to be inserted into the cornea of ​​an eye for refractive error correction comprises the steps: a) providing refractive error data about the refractive error of the eye to be corrected, b) determining a necessary change in corneal shape to correct the refractive error based on the refractive error data, c) defining a lateral thickness profile of the implant such that its insertion into the cornea achieves the desired refractive error correction, whereby a proportion is determined and taken into account to which the thickness of the implant changes the shape of the anterior surface of the cornea, wherein the proportion lies between zero and one.Similarly, a method for determining control data for a processing device for producing an implant to be inserted into the cornea of ​​an eye for refractive error correction comprises steps a) to c). It further comprises: d) defining control data such that the processing device, during operation, produces the implant with a lateral thickness profile from the implant material. Likewise, a method for producing an implant for refractive error correction of an eye comprises steps a) to d), and additionally: e) producing the implant with a lateral thickness profile using the processing device and the control data. Finally, a method for refractive error correction of an eye comprises steps a) to e), and additionally: f) inserting the implant into the cornea of ​​the eye.Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 4 A planning device for determining control data for a processing device for producing an implant to be inserted into the cornea of ​​an eye for refractive error correction has an interface for providing refractive error data about the refractive error of the eye to be corrected and a processor configured to perform steps b) and c). A processing device for producing an implant to be inserted into the cornea of ​​an eye for refractive error correction comprises a laser device for processing implant material as well as this planning device. The determination of the implant thickness profile requires that the proportion to which the implant thickness changes the shape of the anterior surface of the cornea be explicitly taken into account.Previously, it was either assumed that the thickness of the implant directly altered the shape of the anterior cornea, or other complex calculations were used. The realization that explicitly determining and then taking this proportion into account improves accuracy and is computationally efficient is a discovery that can be attributed to the inventors. The term "lateral thickness profile" is used here to clarify that the thickness varies perpendicular to the depth along which it is measured. The adjective "lateral" emphasizes this fact, even though it is, strictly speaking, overriding. The proportion can be defined in various ways, which can be used individually or in combination. In one variant, a distribution factor RAD is defined to calculate the proportion to which the thickness of the implant alters the shape of the anterior cornea.This ratio is called "Relative Anterior Deformation" (RAD) and represents a factor indicating what proportion of the implant thickness affects a change in the anterior surface of the cornea. The distribution factor RAD for the thickness profile of the implant I(x,y) (exemplarily in Cartesian coordinates) multiplied by the implant thickness, i.e., RAD*I(x,y), quantifies the change in the shape of the anterior surface of the cornea, while the remainder (1-RAD)*I(x,y) quantifies the change in the shape of the posterior surface. In this variant 1, the distribution factor can be chosen depending on a thickness h, which is the thickness of the cornea above the implant inserted into the cornea, i.e., above the pocket incision; in particular, the distribution factor is a function of h / d, where d is the total thickness of the cornea.Furthermore, a function can be used that is defined by the boundary points at h=0 and h=d, as well as an intermediate support point. In a simple implementation, the relationship between the boundary points and this additional support point can be assumed to be linear; a (e.g., quadratic) fit function is also possible. It was found that at an implantation depth h of 120 µm, the partitioning factor preferably has a value between 0.3 and 0.7, and particularly preferably a value between 0.4 and 0.6. This can be used as a support point. Preferably, it is taken into account that the mechanical properties of the epithelial layer on the anterior surface of the cornea differ significantly from those of the stroma. For this purpose, the approximately 50 to 60 µm thick epithelial layer is subtracted from the depths and thicknesses used for the calculation. This is particularly advantageous at shallower implantation depths.Furthermore, the distribution factor can be a function of the locally varying thickness I of the implant. Finally, the distribution factor can also be a function of the locally varying elasticity of the cornea. Generally, it is preferable to choose a locally varying RAD. Combinations of individual or all options are possible. In variant 2, the damping is calculated to determine the proportion. This damping is determined by the cornea in the lateral area where the implant is to be inserted and indicates how the lateral thickness profile is transferred to the shape of the anterior cornea. In variant 3, the proportion is determined from a finite element method (FEM) simulation.A finite element method (FEM) simulation can also be used for further improvement by calculating a starting value for the lateral thickness of the implant based on the proportion. From this starting value, the lateral thickness of the implant is then iteratively optimized. In each iteration, the FEM calculates a change in corneal shape resulting from the lateral thickness of the implant. Any deviation from a target value for the change in corneal shape is used to modify the lateral thickness of the implant. The definition of the proportion makes it particularly easy to account for the deformation of the posterior cornea caused by the implant. This is achieved by determining the proportion to one, which indicates the degree to which the implant thickness influences the shape of the posterior cornea.When defining the thickness profile, it can be taken into account, in particular, that a change in the shape of the back surface contributes to the correction of refractive errors only a fraction of the contribution of the change in shape of the front surface. Preferably, this fraction lies between 5 / 100 and 15 / 100. Where the shape of the cornea at its front or back surface is mentioned here, the curvature is preferably used in embodiments. It is understood that the features mentioned above and those to be explained below can be used not only in the combinations specified, but also in other combinations or individually, without departing from the scope of the present invention. The invention is explained in more detail below with reference to exemplary embodiments and the accompanying drawings, which also disclose essential features of the invention.These exemplary embodiments serve only for illustration and are not to be interpreted as restrictive. For example, a description of an exemplary embodiment with a large number of elements or components should not be interpreted as meaning that all of these elements or components are necessary for implementation. Rather, other exemplary embodiments may also contain alternative elements and components, fewer elements or components, or additional elements or components. Elements or components from different exemplary embodiments may be combined with one another unless otherwise specified. Modifications and variations described for one of the exemplary embodiments may also be applicable to other exemplary embodiments. To avoid repetition, identical or corresponding elements in different figures are designated with the same reference numerals and are not explained multiple times.The figures show: Fig. 1 a block diagram of a processing device, Fig. 2 a schematic representation of a cornea with an implant inserted for refractive error correction, Fig. 3 an illustration of surfaces and their mathematical description that are important for determining the geometry of an implant for refractive error correction, Fig. 4 a relationship between elevation and the Cartesian coordinate system, and patent attorneys GEYER, FEHNERS PARTNER Munich -- Jena 7 Fig. 5 a block diagram of a method for determining the geometry of the implant for refractive error correction. Fig. 1 shows, as a block diagram, a processing device 2 comprising a laser device 4 which emits a laser beam 6 for processing material. The material can be implant material 8 for an implant to be inserted, which is arranged on a table 10.The processing of the implant material 8 using laser radiation is purely an example. Depending on the material used, other processes are also possible, e.g., those that do not use laser radiation, particularly when using a hydrogel implant material 8. Optionally, the processing device 2 can also process the cornea of ​​an eye 12, for example, to create a pocket incision into which the prepared implant can be inserted. The device 2 further comprises a planning device 14, which can be connected to the laser unit 4, but can also be independent or an integral part of the laser unit 4. It has a processor (not shown) for performing calculations and a memory. Measurement and refractive error data, which describe parameters of the eye as well as a refractive error to be corrected, can be directly supplied via an interface 16, which is optional.An operator can interact with the planning device via input interface 18 and output interface 20. Fig. 2 shows a cornea 22 of the eye 12. An implant 24, which is essentially incompressible, is inserted into this cornea 22 and thereby alters the curvature of both the anterior surface 26 and the posterior surface 28 of the cornea 22. This alteration is designed by appropriately selecting the geometry of the implant 24 so that a previously existing refractive error is at least partially corrected. To manufacture the refractive error-correcting corneal implant 24, its shape (implant shape) is defined such that the cornea 22 into which it is inserted changes its shape in a predetermined manner. This is based on refractive error data describing the refractive error of the eye to be corrected.This can involve a spherical refractive error to be corrected (usually expressed in diopters), astigmatism, and / or higher-order refractive errors. The refractive error data is derived from known measuring devices. Patent attorneys GEYER, FEHNERS PARTNER Munich -- Jena 8 The term "shape" here means that the cornea 22 has a front surface 26 (anterior surface) and a back surface 28 (posterior surface), which are two-dimensional surfaces in three-dimensional space. The absolute position of these surfaces in space can be determined, for example, by measuring the cornea 22 (e.g., with optical coherence tomography). Their position is then recorded in relation to the measuring device, but preferably also in relation to other anatomical structures of the eye (e.g., fovea, iris, limbus, scleral structures).The surfaces thus also have a specific position relative to each other, whereby their distance can be described using a pachymetry map ^^ (distance as a function of location) and their anterior or posterior surface shape (topography) as elevation ^. In the following, surfaces are generally denoted by the symbol ^ as an example. The "implant shape" represents a volume ^. ^^^This is represented by a surface which is typically bounded in space by at least an anterior and a posterior surface, but often also by a lateral surface. It has a thickness profile, which is denoted by ^^^^ ^^, where the reference to Cartesian coordinates ^^^ ^^ is purely exemplary. The thickness profile of the implant is typically three-dimensional and, in cross-sectional view, represents an implant profile. Therefore, the terms "implant shape" and "implant profile" are used interchangeably here. The thickness of the implant is thus location-dependent. The explicit reference "^^^ ^^" to the location dependency is sometimes omitted in this description for the sake of simplicity. The absolute position of the implant 24 results from its implantation into a corneal pocket (created by a pocket incision). A pocket is a cavity in the stroma of the cornea 22 that serves to receive the implant 24. It is created by a cut surface within the cornea 22 (i.e.,(dR perpendicular to the optical axis). Furthermore, a pocket typically has at least one opening (incision) to the surface 26 of the cornea 22, through which the implant 24 is inserted into the pocket. The pocket incision can be understood as a two-dimensional surface in three-dimensional space, the position of which is determined, for example, by the distance to the anterior 26 or posterior 28 of the cornea 22. A pocket also remains in the cornea 22 during lenticule extraction, which can be used in the same way. It is then typically located very close to the surface 26. In common applications, a pocket incision is preferably located at a constant distance from the anterior corneal surface 26. However, a different surface position is also conceivable. In the case of a very irregular surface profile (e.g., in advanced keratoconus), the distance to the anterior surface 26 is only approximately constant.To account for this effect when calculating the implant shape, a deviation from the usual position is preferably considered. Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 9 The depth h of the implant's position is specified in terms of the thickness of the corneal layer above the implant. This corresponds to the distance to the anterior corneal surface 26. If, exceptionally, the pocket incision is not at a constant distance from the anterior corneal surface 26, the minimum thickness can be used as the depth h. For refractive error correction, the shape of the cornea 22 is to be changed in the intended manner in terms of the position and shape of the corneal surfaces by inserting the implant 24 into the pocket. This constitutes a topographic correction. The front surface 26 (anterior surface) is covered by the surface ^ before implantation. ^ described and after implantation through the area ^ ^ ^(Generally, postoperative dimensions are indicated here by the addition of *), as well as analogously the area of ​​the back 28 (posterior surface) with ^ ^ ^and ^ ^ ^ The operational changes of the areas ^ ^ and ^ ^ ^can be described by a thickness correction: ^^ ^ ^^ ^ ^ ^^ and ^^ ^ ^^^ ^ ^^. ^^ and ^^ are each a difference between the respective pre- and postoperative areas and can therefore each be understood as a contribution to the change in thickness, namely ^ ^ as a contribution caused by the changes of the front 26 (anterior surface), and ^ ^ as a contribution caused by changes to the area of ​​the back surface 28 (posterior surface). Therefore, they are denoted here with an italic ^. The desired target corrections are then specified for the intended method of change ^. ^ and ^ ^, which are generally to be distinguished from the changes achieved in practice (marked with a tilde): ^ ^ ^ and ^ ^ ^ Since the outermost solid layer of the eye consists of a cell layer (epithelial cells) that can change its shape within hours through moisture absorption or release, but especially through the natural regeneration process, it is expedient to consider the anterior topography instead of this outer boundary surface. ^, to consider the underlying surface (Bowman's membrane). The corresponding topography is then the stromal topography. The relationships and calculations described apply analogously, which is why no new symbol is introduced here. The epithelial layer virtually removed by reference to Bowman's membrane can be virtually added back in a final step. The change in the topographies of the anterior surface 26 and / or the posterior surface 28 of the cornea 22 upon implantation is predicted as follows. This can be done in various ways using a device (planning device) with an integrated calculation core (predictor) and a specific prediction procedure executed by the device.Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 10 The aforementioned surfaces of the cornea 22 are mathematically described by mappings that refer to the same Cartesian coordinate system. The relationships are shown in Fig. 3. The z-direction of the coordinate system is identical to the optical axis of the eye 12, and the origin of the coordinate system at z = 0 is the vertex of the cornea 22. A line connecting a fixation light point in a diagnostic device and the fovea coincides with the optical axis of the eye 12 when the eye is fixating. The xy-plane, perpendicular to the optical axis, represents the domain of definition. The surface (topography) can be described by a Cartesian mapping ^ or by an elevation ^, the thickness (pachymetry map) by a thickness mapping ^. Furthermore, Fig. 3 shows the Cartesian coordinate system and the reference sphere 30 for the elevation specification (dashed line).Two representations are common for describing a surface (topography): - Cartesian mapping ^: axial height mapping ^^ ^ ^^^^^ ^^, which provides the ^-coordinate of a point ^^^ ^^ on the surface. - Elevation ^^^: radial height mapping ^^ ^ ^^^^^^^ ^^, which gives the position ^ of the point (x,y) perpendicular to the surface of a fixed reference sphere 30 with a radius ^. ref and a center point ^ ref The specification of the reference sphere 30 is required. The surfaces described above in general terms ^ ^ and ^ ^Elevations are specified in a concrete radial coordinate system, which is why the suffix "_r" was added to the letters ^. Thickness profiles are also used: - A pachymetry map ^^^^ ^^ measures the thickness of the cornea 22 (or the epithelium) at the point ^^^ ^^ perpendicular to the anterior corneal surface (see Fig. 3). It can be defined by the difference between the anterior and posterior elevation ^ ^ ^^ ^ ^^ - The implant profile ^^^^ ^^^ represents the thickness of the implant at the point ^^^ ^^, i.e., the thickness profile of the implant. - A thickness correction ^^^ ^ ^^^^ ^^ quantifies the desired target corrections of the anterior or posterior surface at the point ^^^ ^^. The reference sphere 30 is optimally fitted to the Cartesian representation (^ ^ ) of the anterior surface ^ ^ adapted. The sphere 30 is defined by its radius ^ ref and its center defined. Patent attorneys GEYER, FEHNERS PARTNER Munich -- Jena 11 Fig. 4 shows the conversion between Cartesian coordinates ^ and elevation ^. In this example, the reference sphere 30 (dashed line) lies "above" or in front of the cornea 22 (solid line). Therefore, ^ is negative in this example. ^ ref The center of sphere 30 is the point. The elevation ^ is defined as the distance between a point on the cornea 22 and a perpendicular point on the reference sphere 30. The conversion between elevation ^ and coordinates ^ is given by: The correction zone (CZ) is an area in the xy-plane centered around the optical axis (at ^^^^^). Within this area, the cornea 22 is to be reshaped as intended. The correction zone is typically circular with radius ^ ^^ The planning device 14 includes the processor, which performs a mathematical mapping ^ ^The planning device 14 uses a system that calculates the anterior thickness correction from the thickness profile of the implant and a set of other parameters (patient data, implantation depth, etc.). The predictor function can be expressed mathematically as follows: Furthermore, the planning device 14 also provides the posterior thickness correction: This is the contribution of the change in the posterior area to the thickness correction, which is why it is subsequently referred to as posterior (or anterior) thickness correction. Fig. 5 schematically shows a block diagram of a method for generating control data for the processing device 4, which can be executed, for example, by the planning device 14. In step S1, measurement and refractive error data about the eye 12 are provided.In step S2, the geometry of the implant 24 to be inserted, which is to be produced from the implant material 8, is determined. In step S3, control data is then provided for this geometry, which controls the processing device 4 so that it produces the defined implant 24 from the implant material 8. Optionally, the control data also includes the corresponding information so that the processing device 4 creates the pocket incision for inserting the implant 24 in the cornea 22 of the eye 12. However, this is not mandatory; in particular, it is not mandatory that the processing device 4 even processes the eye 12. Possible variants of the determination performed by the planning device in step S2, which defines the exact shape of ^, are described below. ^ and ^ ^Determine. All variants take into account that the implant 24 simultaneously deforms the anterior and posterior surfaces 26, 28 of the cornea 22. The variants can also be combined with each other, which is discussed purely as an example. 1. Variant 1 Variant 1 improves the calculation through a radically simple approach. For this purpose, the profile ^^^^ ^^ of the implant is decomposed into a constant ratio. This ratio is called "Relative Anterior Deformation" (RAD) and represents a proportion factor. The proportion^^^ ^ ^^^^ ^^ of the profile quantifies the change in the anterior elevation EA, the remainder ^^ ^^^^^ ^ ^^^^ ^^ the change in the posterior elevation EP. From this, the anterior and posterior thickness corrections result: The negative sign in the last equation results from the fact that the posterior surface is shifted to smaller radii by the implant (see Fig. 3). The reverse of this calculation leads from a target correction to a profile. For determining the RAD factor, several options are possible in Variant 1. In one option for Variant 1, RAD is calculated from the depth h of the pocket. For a cornea of ​​stromal thickness d, the following applies: If the depth h and the corneal thickness d are not constant laterally, this leads to a location-dependent RAD variant: A direct further development of the model is a piecewise linear function, which can be derived from the knowledge of another support point between the two extreme points of the upper of the two equations, namely the values ​​RAD(h=0) = 1 and RAD(h=d) = 0. An example of this is the case where an implant with thickness I(x,y) is implanted and the anterior surface of the cornea is thereby altered such that this change can be approximately described by 0.5*I(x,y). The parameter RAD is approximately 0.5 in this case, and this value will change depending on the implantation depth. For example, if the implantation took place at a depth of 120 µm in a cornea 400 µm thick, then h / d = 120 µm / 400 µm = 0.3 and therefore RAD(0.3) = 0.5.In a simplified implementation, the function's behavior between the extreme points and this further support point can be assumed to be linear. Such a piecewise linear approach already allows for a good prediction of an implantation depth that deviates from the experimentally determined support value. For example, if the attenuated effect of the implantation at a depth of 130 µm on the anterior corneal surface is to be determined, the linear approximation for the value h / d = 130 µm / 400 µm = 0.325 yields the predictive value RAD(0.325) = RAD(0.3) * (1 - (0.325 - 0.3) / (1 - 0.3)) = 0.482. Using a quadratic fit function through the known three points, which better reflects the nonlinear nature of the underlying mechanical problem, it is found that RAD would have been reduced from 0.5 to approximately 0.47 if the implantation in this case had been performed at a depth of 130 µm instead of 120 µm.Since the mechanical properties of the epithelial layer on the anterior corneal surface and in the stroma differ significantly, it is generally advisable to account for this in the mathematical model by subtracting the approximately 50 to 60 µm thick epithelial layer from the depths and thicknesses used for the calculation. For example, a 50 µm thick epithelial cell layer is assumed for simplification, resulting in a baseline value of RAD(0.2) = 0.5 in the aforementioned example. In this example, no significant differences yet arise, but the effect would be considerable at shallower implantation depths. Based on our own clinical data, we deduce that at an implantation depth h of 120 µm, the parameter RAD preferably has a value between 0.3 and 0.7, and particularly preferably a value between 0.4 and 0.6.In a more precise, second option for variant 1, the functional relationship between RAD and the implantation depth h is no longer assumed to be linear, but is determined from a nomogram developed through clinical studies. ^^^ ^ ^^^^ is then defined as the spatial mean calculated within the correction zone (CZ) from the ratio of the practically achieved anterior correction thickness ^^^^^^ ^^ and the profile used in the calculation of an implant ^^^^ ^^ Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 14 ^^^ ^ ̂^^^ ^^^^^^^^^^^ ̂. ^^For each treatment, a new data point ^^^^^ ^ ^^^ is entered into the nomogram. With more and more treatments, a functional relationship eventually emerges, which can be approximately described (fitted) using a polynomial. This function ultimately yields the ^^^ to be used in a calculation as a function of the depth ^. If many treatments have been performed, the dimensionality of the nomogram can be increased, thus further improving the determination of RAD. For example, the nomogram ^^^ ^ The achieved mean correction thickness is defined by the spatial mean calculated within the correction zone (CZ). For each treatment i, a data point is added, and the exact functional relationship is derived from many treatments. ^^ from a fit of a two-dimensional polynomial to the data points. A third option for variant 1 takes into account that the thickness of the implant I(x,y) also influences RAD. This is accounted for by a dependency of RAD on the thickness I(x,y). For example, the combination of this property with the depth dependency is shown here: Here, I is a normalization factor, for example, the maximum value 0 of 0. The term 0. ^ leads to a quadratic component in the thickness correction ^ ^For this reason, the above expression can be understood as a Taylor series expansion of the figure ^^^^^^^ ^^^ ^^^^^ in powers of the thickness^^^^ ^^ and can also be further developed with higher orders. This concept can be applied analogously to Taylor series expansions in powers of other parameters of the material 22 or the process (e.g., elastic modulus). Furthermore, the higher-order terms can also be combined with other variants of the predictor. A fourth option takes into account that, especially in the presence of dystrophy of the eye, local changes in elasticity, more precisely in the elastic modulus ^%^^^ ^^ of the cornea 22, occur. Strictly speaking, this is a 4th-rank tensor with 81 components. However, due to existing symmetries and possible simplifications through the specific interaction situation, a characteristic scalar quantity^%^^^ ^^ can be derived, at least approximately.For example, the tensile modulus is well suited to characterize the resistance of a cornea to elastic deformation. The tensile modulus of the cornea 22 of a patient's eye can be approximately calculated from experimental data of possible elasticity measurements, because although cornea 22 is anisotropic, one can simplify by using the relationship between shear modulus G and tensile modulus E that is valid for isotropic materials: G = E / (2(1+v)), where v is the Poisson's ratio. The Poisson's ratio for cornea 22 is approximately 0.47. The RAD can thus be defined as follows: or in combination with the first option: Here, EL0 is a normalization factor, for example, the value of EL for cornea 22 of a healthy eye. Variant 2: In Variant 2, it is assumed that the tissue layers between the implant and the corneal surface have a damping effect, particularly on those parts of the implant shape that exhibit high spatial frequencies. This damping effect when transferring the implant profile to the topography can be calculated using various signal processing methods (forward and inverse transformation into spatial frequency space and attenuation of selected spatial frequencies, convolution, windowed moving average), whereby the depth h of the pocket, as well as a tissue-specific attenuation parameter that generally depends on the spatial frequency, are included in the calculation. One option for Variant 2 is a calculation using convolution within the correction zone (CZ).Since the convolution kernel used in this process, which expresses the attenuation of higher spatial frequencies, has a finite extent, the integration is performed over a surface that must be larger than the CZ by this extent. This surface is called the convolution zone (FZ). ^^^^^ ^^ is the reduced effect of the implant on the corneal surface due to the damping effect of the tissue layers between the implant and the corneal surface. ^^^^^ ^^^ denotes the folding nucleus, which generally depends on the depth h of the pocket. For example, a standardized nucleus in Gaussian shape is given by: Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 16 The dependence of the damping on the thickness of the tissue layer above the implant is then parameterized by a depth dependence of the width of the Gaussian curve, i.e. .The simplest conceivable form here is )^^^ ^ )^ ^ ^^ ^ ^^ ^ ^^^^^, where d is again the thickness of the cornea 22. For h=0, the Gaussian function becomes a delta function, and the convolution integral yields the unchanged thickness profile of the implant. The use of the factor RAD and smoothing can be combined by multiplying a normalized convolution kernel with one of the variants of the factor RAD described above: ^^^^^^^^ ^^^ ^ ^^^^^^^^^ ^^^ ^^^^^ ^^^ The damping effect generally depends not only on the depth of the implant but also on its absolute position in the cornea. Epithelial dynamics play an important role in the location-dependent damping, but this does not need to be considered when calculating the stromal topography (see later section). Furthermore, due to the collagen fibril arrangement in the cornea, the elasticity across the cornea 22 is generally not isotropic.This parameter also has a spatially variable influence on the attenuation of the components with high spatial frequencies. Therefore, in a second option for variant 2, the high-frequency attenuating component (convolution core) is parameterized spatially, i.e., ^^ ^^^^ ^^^ ^^ ^^^. For example, by: ^^ This allows the difference in corneal elasticity 22 between the central and peripheral areas to be taken into account by modifying a technically simple heuristic model. 3. Variant 3 Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 17 The aforementioned variants 1 and 2 are, with the exception of the higher-order terms, linear methods, i.e., the thickness correction ^ ^ depends linearly on the implant profile ^. If the nonlinear effects are small in the case of a real cornea 22, then in one variant 3 the predictor ^ ^ about the determination of an impulse response function to be determined. It describes the deformation of the anterior surface 26 after implantation of a very localized, point-shaped implant ^^^^ ^^ ^ ^^^^^ ^^ ^ ^^^^ ^^^^ at the location (^^^^^^). If, furthermore, the impulse response ^^^^^ ^^^ ^^ ^^^ ^^^ is the same for each position (^^^ ^^^), then the anterior thickness correction results from the following folding: This can be inverted by unfolding (e.g. in Fourier space) and thus the implant profile I(x,y) can be derived from the desired thickness correction ^ ^ The information about the behavior of the cornea 22 is contained in the impulse response function. This can be determined empirically, by FEM, or experimentally on donor cornea 8. A comparison of the above convolution with the formula in the section on variant 2 makes it clear that the impulse response function is identical to the convolution kernel ^^^^^ ^^^. Since the methods for determining the anterior impulse response function ^ ^ ^^^By measuring the entire cornea 22, the shape of the posterior corneal surface 28 can also be determined, and a posterior impulse response function can be calculated from its deformation. ^ ^^^ This can be found. This describes the deformation of the posterior surface after implantation of a very localized, point-shaped implant. The posterior thickness correction is then Should the impulse response depend strongly on the position (), a mean impulse response can be found by suitable averaging within the correction zone, and the convolution formalism can be used further. The averaging can, for example, be the spatial mean calculated within the correction zone (CZ). Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 18 4. Variant 4 In a particularly precise variant 4, an implant shape is first defined. ^The implant shape is taken as a starting value, for example by using a standard value or one of the previously described simple methods. The implant shape is optimized in an iteration, now also taking into account the elastic material properties of the implant 8. In a first option, the refractive error data and the implant shape assumed as a starting value are used. ^ the postoperative topography ^ ^ ^ ^^ Simulated using FEM. From this, the achieved topography correction is calculated, and the difference to the target correction is determined. The function is then squared, averaged over the correction zone CZ, and the square root of the calculated value is taken. The value calculated in this way is the standard deviation. ^^^of the first iteration between achieved and desired topography correction. The described method is thus a local optimization method using the least squares method. Other measures are possible. In the next iteration, the shape of the implant is modified using ^^^^^^^ ^^, for example as follows: ^^^^^ ^^ ^ ^^^^^ ^^ ^ ^^^^^^^ ^^, resulting in a new implant shape ^ ^ results; from this a second topography correction is performed using FEM ^ ^ ^^^ determined, and thus finally the second standard deviation ) ^^^The iteration continues until the standard deviation reaches a local minimum, i.e., the change achieved in one iteration is below a threshold (example of a termination criterion), ideally zero. It is possible that this will not be reached; in that case, the iteration is terminated after a certain number of iterations (second termination criterion). This would be the case, for example, if the target correction exhibits particularly high spatial frequencies that cannot be achieved due to the stiffness of the cornea. However, the implant profile found through the iteration approximates the desired target correction in the best possible way.Since the FEM simulation is based on a comprehensive model of the eye, material properties (tensile modulus, shear modulus, flexural modulus) or other surfaces (including pocket surfaces) can also be considered, and corresponding target corrections and iterations for these surfaces can be defined and combined. The posterior surface ^ is of particular importance here. ^ ^ named. Patent attorneys GEYER, FEHNERS^^ PARTNER Munich -- Jena 19 To the implant profile ^ ^ To change, a deviation from the target correction will be observed in each iteration. calculated. Positive values ​​of this function indicate the position of the implant profile ^ ^ If it is too thick, negative values ​​are used where it is too thin. Based on this knowledge, the implant profile of the next iteration ( ^ ^) is corrected by exactly this amount. Through the calculation of differences, negative values ​​for ^ can also be mathematically possible. ^This results in a result. However, since there are no negative thicknesses, the boundary condition ^^ ! ^ must also be met. This can be achieved, for example, by setting areas of the implant profile with negative values ​​to zero. This iterative method converges very quickly, so that after a few cycles the difference is sufficiently small to terminate the calculation process. In the case of discontinuous and therefore slow convergence, the convergence can be improved by linearly blending the implant profiles. ^^^^ ^ +^^^ ^ ^^^^^ ^ ^^ ^ +^^^^ . Here, ^ " + " ^ is a constant optimized for the process. In a second option, the volume between the anterior boundary surface ^ is used for the implant profile. ^ and the posterior boundary surface ^ ^The shape of these surfaces within the correction zone is considered. It is parameterized by expansion using suitable basis functions (e.g., Zernike functions) or by representation with finite elements or on a regular grid. The most suitable representation is the one also used within the FEM simulation. The surfaces are then defined by a parameter set corresponding to the representation method. ^ $ and # ^ $. To start the iteration, the initial value ^ is used again. ^ used for the implant shape (like this). Its parameter # ^^^ $and # ^^^ $ are determined. In each iteration, the parameters # ^^^ $ and # ^^^ $ is modified according to a suitable local optimization method (conjugate gradient method, quasi-Newton method, etc.) and a new parameter set is derived from it. ^^^^^ $ and generated. The iteration continues until the termination criterion described above is met. 5. Variant 5 Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 20 While FEM-based calculations require many diagnostic parameters with high accuracy, they can then be superior to simpler approaches even in difficult cases. Their biggest disadvantage, however, lies in the high computational effort, which currently translates into a significant time investment for the user when employing the predictor. This can be reduced by using pre- and post-operative datasets together with implant designs to train an AI. In a special implementation variant, a set of FEM-based simulation calculations, which can be performed without time constraints, are used as training data.Preoperative or fabricated preoperative data are fed into a finite element method (FEM) calculation, and the implant profile and postoperative data are calculated. The entire dataset is used as training data for the AI. The trained AI is then available to perform predictions as a planning tool or procedure, significantly reducing the execution time compared to computationally intensive methods like FEM. This results in a more manageable tool for the user, as they can experiment with different boundary conditions or treatment goals using a near-instantaneous planning tool before deciding on their preferred option. This approach can also be combined with FEM calculations by subsequently verifying an AI-calculated solution using FEM.In this way, an implant shape that better meets the user's objectives can be calculated than would be possible without combining both methods.

Claims

Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 21 Carl Zeiss Meditec AG Attorney File: PAT 9030 / 270-PCT Claims 1. A method for producing an implant to be inserted into the cornea of ​​an eye (3) for the purpose of correcting refractive error, comprising the steps a) providing refractive error data about the refractive error of the eye (3) to be corrected, b) determining a change in the shape of the cornea necessary to correct the refractive error based on the refractive error data, c) defining a thickness profile of the implant such that its insertion into the cornea (5) effects the desired refractive error correction, wherein a proportion is determined to which the thickness of the implant changes the shape of the front surface of the cornea, the proportion being between zero and one.

2. The method according to claim 1 further comprising d) producing the implant with the thickness profile using the processing device. 3.A method for determining control data for a processing device for producing an implant to be inserted into the cornea of ​​an eye (3) for refractive error correction, comprising the steps: a) providing refractive error data about the refractive error of the eye (3) to be corrected; b) determining a change in the shape of the cornea necessary to correct the refractive error based on the refractive error data; c) defining a thickness profile of the implant such that its insertion into the cornea (5) produces the desired refractive error correction, whereby a proportion is determined to which the thickness of the implant changes the shape of the anterior surface of the cornea, wherein the proportion is between zero and one; and d) specifying control data such that the processing device, in operation, produces the implant with the thickness profile from implant material. 4.Method according to one of the above claims, wherein a division factor (RAD) is determined to determine the proportion to which the thickness of the implant changes the shape of the front of the cornea, and wherein the division factor Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 22 between zero and one, and the addition of the division factor (RAD) to one determines the proportion to which the thickness of the implant alters the shape of the posterior surface of the cornea.

5. Method according to claim 4, wherein the division factor (RAD) depends on a thickness h that the cornea has over the implant inserted into the cornea, in particular the division factor (RAD) is a function of h / d, where d is the thickness of the cornea.

6. Method according to one of claims 4 or 5, wherein the division factor (RAD) has a value between 0.3 and 0.7 at an implantation depth (h) of 120 µm, particularly preferably a value between 0.4 and 0.

6.

7. Method according to one of claims 4 to 6, wherein the division factor (RAD) is a function of the thickness profile of the implant.

8. A method according to any one of claims 4 to 7, wherein the division factor (RAD) is a function of the elasticity of the cornea. 9.A method according to any one of the preceding claims, wherein, to determine the proportion, a damping is calculated which the cornea has over the lateral area into which the implant is to be inserted and which indicates how the thickness profile is transferred to the shape of the anterior cornea.

10. A method according to any one of the preceding claims, wherein a supplement to the proportion to one determines the proportion to which the thickness of the implant influences the shape of the posterior cornea, and wherein this influence is taken into account when defining the thickness profile. 11.A method according to any of the above claims, wherein a starting value for the thickness D profile of the implant is calculated based on the proportion, and the thickness D profile of the implant is iteratively optimized from this starting value, wherein in each iteration a change in the shape of the cornea resulting from the thickness D profile of the implant is calculated using FEM, and wherein a deviation from a target value of the change in the shape of the cornea is used to change the thickness profile of the implant.

12. A method for correcting refractive errors in an eye comprising the steps a) providing refractive error data about the refractive error of the eye to be corrected (3). Patent Attorneys GEYER, FEHNERS PARTNER Munich -- Jena 23 b) Determining a change in the shape of the cornea necessary to correct the refractive error based on the refractive error data, c) Defining a thickness profile of the implant such that its insertion into the cornea (5) effects the desired refractive error correction, whereby a proportion is determined to which the thickness of the implant changes the shape of the front of the cornea, wherein the proportion lies between zero and one, d) Producing the implant with the thickness profile using the processing device and f) Inserting the implant into the cornea of ​​the eye. 13.Planning device for determining control data for a processing device for producing an implant to be inserted into the cornea of ​​an eye (3) for refractive error correction, wherein the planning device has an interface for providing refractive error data about the refractive error of the eye (3) to be corrected and a processor configured to perform steps b) and c) of a method according to claim 2 or any one of claims 3 to 9, insofar as it relates back to claim 2.

14. Processing device for producing an implant to be inserted into the cornea of ​​an eye for refractive error correction, comprising a laser device for processing implant material and a planning device according to claim 10.

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