Method for providing control data for a laser of a treatment device

Abstract

Method for providing control data for a laser (18) of a treatment device (10) for the correction of a cornea (26) of a human or animal eye, the method comprising the following steps carried out by a control device (20): - determining (S10) a corneal geometry of the eye from predetermined examination data, wherein the corneal geometry comprises at least an anterior corneal curvature; - determining (S12) an anterior and posterior interface (14, 16) of a lenticule (12) of the cornea (26) for providing the correction of the cornea (26); - Determining (S14) a cornea (26) deformed by a contact element (28) by means of a corneal deformation model which is determined based on the Euler-Bernoulli beam theory, wherein in the corneal deformation model the cornea (26) with the determined corneal geometry is provided as a volume body, wherein the volume body is formed from respective central corneal surfaces (34, 36) between an anterior corneal surface (30) and a posterior corneal surface (32), wherein in order to determine the deformed cornea (26) in the corneal deformation model the anterior corneal curvature is changed to a predetermined curvature of the contact element (28) and the central corneal surfaces (34, 36) are adapted to the changed curvature of the anterior corneal surface (30) by means of an elastic deformation; - determining (S16) a deformed lenticule (12) by means of the deformed cornea (26), wherein the anterior and posterior boundary surfaces (14, 16) of the lenticule (12) are determined as a function of the adapted central corneal surfaces (34, 36) of the deformed cornea (26), - Providing (S18) the deformed anterior and posterior interfaces (14, 16) of the lenticule (12) as control data for controlling the laser.

Description

The present invention relates to a method for providing control data for a laser of a treatment device for the correction of a cornea. The invention also relates to a control device for carrying out the method, to a treatment apparatus having at least one eye-surgery laser and at least one control device, to a computer program and to a computer-readable medium.Treatment devices and methods for controlling lasers to correct corneal optical deficiency are known in the art. In this case, for example, a pulsed laser and a beam focusing device can be designed such that laser beam pulses cause photodisruption in a focus located within the tissue of the cornea in order to separate a lentivirus from the cornea (cornea) for correction of the cornea. In the treatment with a treatment device, for example for separating a lentivirus, the eye is usually fixed by one or more contact elements of the treatment device. The contact element is a rigid element, for example a planoconcave lens, which is placed on the eye, in particular on the cornea, so that the eye is not moved during the treatment. However, a disadvantage of such a contact element is that a shape of the cornea changes, in particular is compressed, by the contact element. As a result, the shape of the lentivirus to be separated can also change, as a result of which a treatment can be subject to errors.DE 10 2008 017 293 A1 discloses a method for generating control data for an eye surgical treatment apparatus which separates tissue layers in the cornea of the eye by means of a laser device, wherein during operation of the laser device a contact glass having a contact surface deforms the cornea into the shape of the contact surface, for which purpose the contact surface is first placed on a cornea apex by means of a contact surface apex and is then pressed against the cornea in order to deform the cornea. In this case, the control data for the laser device are generated in such a way that they specify coordinates of target points lying in the cornea for the laser device, and the deformation of the cornea, which is present during the operation of the laser device as a result of the contact glass, is taken into account in the generation of the target point coordinates.From DE 10 2020 113 820 A1 and CN 1 13 520 716 A a method for providing control data for an eye surgery laser is known, wherein a correction value is determined for compensating a deformation of a lentivirus to be separated, which is generated by a contact element of the treatment device.EP 3 782 591 A1 discloses systems and methods for lenticular laser cuts based on wavefront maps.DE 10 2016 208 011 A1 discloses a planning device for generating control data for a treatment apparatus, which generates at least one cut surface in the cornea by means of a laser device. The planning device has calculation means for defining the corneal cut surfaces, wherein the calculation means define the corneal cut surfaces based on the data of a LIRIC structure and / or a refraction correction, and a control data set for the corneal cut surfaces for controlling the laser device, wherein the calculation means determine the corneal cut surfaces such that the LIRIC structure is enclosed by the cut surfaces.US 2019 / 0175281 A1 discloses a device for surgical correction of ametropia of an eye.The invention is based on the object of providing control data for controlling a laser, in which a deformation is compensated by a contact element.This object is achieved by the method according to the invention, the apparatuses according to the invention, the computer program according to the invention and the computer-readable medium according to the invention. Advantageous embodiments with expedient developments of the invention are specified in the respective dependent claims, wherein advantageous embodiments of the method are to be regarded as advantageous embodiments of the treatment apparatus, of the control device, of the computer program and of the computer-readable medium and vice versa.A first aspect of the invention relates to a method for providing control data for a laser of a treatment apparatus for the correction of a cornea of a human or animal eye, wherein the method comprises the following steps carried out by a control device. A control device is understood to mean a device, a device component or a device group which is / is configured to receive and evaluate signals, and to provide, for example generate, control data. The control device can be designed, for example, as a control chip, computer program, computer program product or control device. The control device determines a corneal geometry of the eye from predetermined examination data, wherein the corneal geometry comprises at least one anterior corneal curvature, and determines an anterior and posterior interface of a lentivirus of the cornea in order to provide the correction of the cornea. Furthermore, a cornea deformed by a contact element (patient interface) is determined by means of a corneal deformation model which is determined based on the Euler-Bernoulli beam theory (Euler-Bernoulli beam theory), wherein the cornea with the determined corneal geometry is provided as a volume body in the corneal deformation model, wherein the volume body is formed from respective central corneal surfaces between an anterior corneal surface and a posterior corneal surface, wherein the anterior corneal curvature is changed to a predefined curvature of the contact element in order to determine the deformed cornea in the corneal deformation model, and the central corneal surfaces are adapted to the changed curvature of the anterior corneal surface by means of an elastic deformation. Finally, a deformed lentivirus is determined by means of the deformed cornea, wherein the anterior and posterior boundary surfaces of the lentivirus are determined as a function of the adjusted central corneal surfaces of the deformed cornea, and the deformed anterior and posterior boundary surfaces of the lentivirus are provided as control data for controlling the ophthalmic surgical laser.In other words, it can first be determined which corneal geometry the eye has and which geometry the lentivirus requires in order to achieve correction of the cornea. For this purpose, in particular anterior and posterior boundary surfaces, which delimit the lentivirus in the direction of an optical axis forwards and backwards, can be determined. The anterior and posterior interfaces may have respective predetermined curvatures to achieve corneal correction.However, when using a contact element or a patient interface that is pressed onto the eye, the cornea can deform, as a result of which the corneal geometry changes and also the previously determined anterior and posterior interfaces of the lentivirus. This means that an application of the originally determined anterior and posterior boundary surfaces could lead to a deviating correction. In order to compensate for the effect by the contact element, it is therefore possible to calculate by means of a corneal deformation model which geometry the deformed cornea has, it then being possible to determine, on the basis of the deformed cornea, how the originally planned lentivirus has deformed. This deformed lentivirus may then be used in the control data to perform the originally scheduled correction. For this purpose, the cornea can be described in the corneal deformation model as a volume body which has the corneal geometry. This volume body can be deformed based on Euler-Bernoulli beam theory to obtain the deformed anterior and posterior interface.Euler-Bernoulli beam theory describes elastic bending of a body, it being assumed that a plurality of central corneal surfaces are arranged between the anterior corneal surface and a posterior corneal surface, said central corneal surfaces constituting the volume body. According to the Euler-Bernoulli beam theory, one of the central corneal surfaces is a neutral corneal surface or neutral membrane, the surface of which remains constant during deformation, wherein the further central corneal surfaces can be written on as a function of the neutral corneal surface. In particular, the central corneal surfaces can be compressed under the neutral corneal surface and the surfaces above them are stretched. This neutral corneal surface can be arranged, for example, centrally in the cornea or else at a predetermined thickness or depth (as viewed in the direction of the optical axis). Preferably, the deformation of the central corneal surfaces can be described as a function of the change in the curvature of the neutral membrane, whereby the deformation of the volume body at each surface (corneal surface) can be described.Based on the Euler-Bernoulli beam theory, it can then be mathematically calculated how the central corneal surfaces change during elastic deformation, in particular relative to the neutral corneal surface. In the case of the corneal deformation model, it is assumed as elastic deformation that the anterior corneal curvature changes to the predefined curvature of the contact element, wherein this change can be calculated according to the Euler-Bernoulli beam theory for the respective central corneal surfaces and thus a global change of the volume body can be determined by the contact element.In accordance with the deformation of the volume body thus determined, the anterior and posterior boundary surfaces of the lentivirus can also be calculated on the basis of the changed central corneal surfaces. In this case, for example, the anterior and posterior boundary surfaces can be assigned to respective central corneal surfaces, it being possible to determine how the corneal surfaces assigned to the boundary surfaces change as a result of the deformation. In particular, a deformation value, preferably a single deformation value, can be determined by means of the corneal deformation model, with which deformation value the originally planned lentivirus can be scaled in order to obtain the deformed lentivirus.The control data comprising the deformed lentivirus with the deformed anterior and posterior interfaces may be ultimately provided to the controller for controlling the laser. In other words, the laser of the treatment device can be controlled with the control data for the correction of the cornea, wherein the treatment device can separate the deformed lentivirus provided in the control data from the cornea.The method can be carried out as an analytical method, but also, for example, as a mesh method (discrete point variant). Preferably, it can be additionally taken into account in the corneal deformation model that, on account of incompressibility or minimal compressibility of the cornea, retention of the corneal volume during elastic deformation is assumed. This means that the corneal volume does not change or only changes slightly during the elastic deformation.The invention has the advantage that deformation effects which arise through the contact element can be compensated for, which leads to an improved correction of the cornea.The invention also encompasses embodiments which result in additional advantages.One embodiment provides that a deformation correction value is determined by the corneal deformation model, by means of which deformation correction value the deformed grating is calculated for a planned refractive power correction in order to compensate for the deformation by the contact element. In other words, the anterior and posterior interfaces of the lentivirus can be determined by means of a planned refractive power correction, i.e. a diopter value to be compensated. This planned refractive power correction can be scaled by means of a deformation correction value determined by the corneal deformation model or can be calculated by means of a difference amount by means of the deformation correction value in order to obtain a global transformation of the refractive power correction. Preferably, an individual value can be determined as deformation correction value, by means of which the planned refractive power correction is adapted. This embodiment provides the advantage that a user planning a refractive power correction can adapt it from the corneal deformation model only by means of the deformation correction value, in particular with a scaling with the deformation correction value or a difference amount with the deformation correction value, in order to obtain the deformed grating which is provided as control data for controlling the laser.A further embodiment provides that a deformation correction value is determined by the corneal deformation model, by means of which deformation correction value the deformed grating is calculated for a planned grating diameter in order to compensate for the deformation by the contact element. In other words, a lenticular diameter can be planned for the correction of the cornea, in particular a diameter of an optical zone or a size of the correction. By means of the deformation correction value from the corneal deformation model, the planned grating diameter can then be adapted via a scale or a difference amount with the deformation correction value in order to obtain the deformed grating, which can be provided as control data for controlling the laser. Thus, a global transformation of the lenticular diameter, preferably with a single deformation correction value, can be achieved.A further embodiment provides that in the corneal deformation model a lateral boundary surface of the volume body in a radial direction is freely deformed, in particular obliquely, by the deformation of the volume body. In other words, it can be assumed in the corneal deformation model that the volume body representing the cornea is deformed without boundary conditions. In a real situation in the eye, the corneal area can be limited due to morphological conditions in the eye, in particular in a lateral direction. For example, a body would expand toward the sides under a pressure from above, this lateral expansion at the cornea being limited by the tissue of the eye. In this embodiment, a simplified consideration of the cornea is assumed by assuming it as a free volume body in space. Thus, it can expand or deform unimpeded by deformation, in particular laterally in the radial direction. The lateral boundary surface is understood to mean the surfaces that laterally delimit the volume body in the radial direction. This embodiment has the advantage that a simplification of the corneal deformation model is made possible.In a further embodiment, it is provided that in the corneal deformation model a lateral boundary surface of the solid body in a radial direction is deformed into an intermediate position during the deformation of the solid body, wherein the intermediate position is located between an initial position of the lateral boundary surface and a position of the boundary surface during a free deformation of the boundary surface. In other words, in this embodiment it is taken into account that the cornea is not freely deformable in space and is at least partially bounded at least to the sides, in particular at the lateral boundary surface of the volume body. In particular, a cornea in the eye can be laterally delimited by the sclera or leather hide of the eye, wherein the lateral boundary surface of the solid body can be located at a transition zone between cornea and leather hide, the so-called limbus. In this embodiment, it is assumed that the leather hide can yield by a predefined deformation value, so that the solid body is deformed into an intermediate position, wherein the intermediate position assumes between the position that the lateral boundary surface would assume in the case of free deformation and an initial position that the lateral boundary surface has before deformation. For example, starting from a cornea center and viewed radially, the sclera may begin at 6.5 millimeters and an outer edge point of the lateral boundary surface could be extended to a value of 7.3 millimeters during deformation. The intermediate position can thus preferably be a position between 6.5 millimeters and 7.3 millimeters, preferably between 6.5 millimeters and 6.9 millimeters. In order to take this deformation into account in the corneal deformation model, it can be provided, for example, that the volume body is deformed by a free deformation and subsequently the points of the lateral boundary surface are scaled by means of a deformation value, which preferably takes account of a resistance of the sclera during the deformation, so that the edge points of the boundary surface are displaced into the intermediate position. However, not only do the edge points of the lateral boundary surface change into the intermediate position by the deformation value, but the shape of all central corneal surfaces can also change, whereby this at least partial limitation by the sclera in the corneal deformation model can be taken into account. This embodiment has the advantage that a real situation in the eye can be better taken into account, which can further improve the determination of the deformed lentivirus.A further advantageous embodiment provides that in the corneal deformation model a lateral boundary surface of the solid body in a radial direction is fixed at at least one initial position of the boundary surface during the deformation of the solid body. In other words, the lateral boundary surface, which laterally delimits the volume body in the radial direction, can be fixed at at least one position. Thus, it can be assumed in the corneal deformation model that the sclera cannot be compressed at this position and thus the volume body cannot escape to the sides at this position when it is deformed by the contact element. The initial position here means the position of the boundary surface which it has before the deformation of the volume body. That is, the position of the boundary surface before deformation is equal to the lateral boundary surface after deformation in this embodiment. This embodiment provides the advantage that the corneal deformation model better describes a situation in a real eye, whereby the determination of the deformed lentivirus can be further improved.It is preferably provided that in the corneal deformation model a lateral boundary surface of the solid body in a radial direction is fixed at an initial position of the entire lateral boundary surface during the deformation of the solid body. This means that the lateral boundary surface is fixed not only in an initial position, i.e. at at least one point of the boundary surface, but at all points that the lateral boundary surface initially exhibited before the deformation. This means that the volume body is viewed as laterally fixed and incompressible in the eye.Preferably, it is provided that for fixing the volume body at the at least one position of the boundary surface, a transformation point is specified on the respective corneal surface, which transformation point, viewed in the radial direction, is located outside the initial position of the boundary surface, wherein the transformation point after the elastic deformation is reset by a scaling factor to an initial position of the transformation point before the elastic deformation, wherein after the transformation point is reset to the initial position, only the region of the corneal surface which is located inside the boundary surface in the radial direction is taken into account. In other words, a transformation point or support point can be defined which, viewed in the radial direction, is located outside the lateral boundary surface and which, after the elastic deformation of the solid body, is reset by means of a scaling factor to an initial position which the transformation point had before the elastic deformation. Subsequently, only the region of the volume body, in particular only the central corneal surfaces of the volume body, which are located within the fixed lateral boundary surface is taken into account. The transformation point can be predefined for a respective corneal surface of the volume body. By means of the scaling factor, after the elastic deformation, the transformation point or points displaced by the deformation can thus be brought back to the initial position, wherein at the same time the respective central corneal surfaces can be adjusted accordingly. The effect of fixing the solid body can thus be described by mathematical methods, wherein edge effects can be prevented in an improved manner by means of the transformation point outside the lateral boundary surface, in particular wrinkling, which could otherwise occur at the lateral boundary surface during the scaling by the scaling factor.In a further advantageous embodiment, it is provided that, for fixing the volume body at the initial position of the entire lateral boundary surface, the corneal surfaces are adapted by a scaling factor, wherein edge points of the respective corneal surfaces which are located on the initial position of the lateral boundary surface before the deformation are transformed back to the initial position of the lateral boundary surface after the deformation by the scaling factor. In other words, for the fixation of the volume body at the initial position of the entire lateral boundary surface, a free deformation of the cornea is carried out, in which the edge points of the lateral boundary surface deform, wherein subsequently a reverse transformation to the initial position of the edge points is achieved by the scaling factor and simultaneously an associated adaptation of the respective corneal surfaces, in particular the anterior, posterior and / or the central corneal surfaces. This embodiment has the advantage that a deformation can be carried out taking into account a fixing of the solid body at the entire lateral boundary surface, which can better reproduce the situation in the real eye.Preferably, it is provided that the lateral boundary surface is predetermined at a beginning (limbus) of a leather hide (sclera) of the eye. The leather hide can be, for example, approximately 6.5 millimeters from a center of the cornea in the radial direction. Preferably, the beginning of the leather hide defines the lateral interface, the lateral interface preferably being fixed at this position in the corneal deformation model.A further embodiment provides that in the corneal deformation model the volume body is described on the anterior corneal surface by an anterior corneal ellipsoid and on the posterior corneal surface by a posterior corneal ellipsoid, wherein for the predetermined curvature of the contact element a predetermined contact element ellipsoid is provided, to which the anterior corneal ellipsoid is changed for the elastic deformation. In other words, it is assumed for the volume body that it is delimited upward or forward by an anterior corneal surface which is formed as an anterior corneal ellipsoid and downward or rearward by a posterior corneal surface which is formed as a posterior corneal ellipsoid. In a corresponding manner, the central corneal surfaces can be described as respective corneal surface ellipsoids. The ellipsoids may be rotationally symmetric to define a three-dimensional body. The ellipsoids can, however, also be rotationally asymmetrical, in order to describe, for example, a keratoconus. It is preferably provided that the respective ellipsoids are designed as paraboloid or spheroid. By describing the respective corneal surfaces as ellipsoids, a preferred configuration of the corneal deformation model, in particular the change of the volume body by the Euler-Bernoulli beam theory, can be described.A second aspect of the present invention relates to a control device which is configured to carry out the method described above. The advantages listed above are obtained. The control device can be designed, for example, as a control chip, control device or user program ("app"). The control device can preferably have a processor device and / or a data memory. A processor device is understood to mean an apparatus or an apparatus component for electronic data processing. The processor device can have, for example, at least one microcontroller and / or at least one microprocessor. The optional data memory can preferably store a program code for carrying out the method according to the invention. The program code can then be designed to cause the control device, when executed by the processor device, to carry out one of the above-described embodiments of one or both methods according to the invention.A third aspect of the present invention relates to a treatment apparatus having at least one eye-surgery laser for the separation of a lentivirus with predefined interfaces from a human or animal eye by means of photodisruption and / or ablation, and at least one control device for the laser or lasers, which is designed to carry out the steps of the method according to the first aspect of the invention.In a further advantageous embodiment of the treatment device according to the invention, the laser can be suitable for emitting laser pulses in a wavelength range between 300 nm and 1400 nm, preferably between 900 nm and 1200 nm, at a respective pulse duration between 1 fs and 1 ns, preferably between 10 fs and 10 ps, and a repetition frequency greater than 10 kilohertz (KHz), preferably between 100 KHz and 100 megahertz (MHz). The use of such lasers in the method according to the invention also has the advantage that the irradiation of the cornea does not have to take place in a wavelength range below 300 nm. This region is subsumed in laser technology under the term "deep ultraviolet". This advantageously prevents unintentional damage to the cornea from occurring due to these very short-wave and high-energy beams. Photodisruptive and / or ablative lasers of the type used here usually introduce pulsed laser radiation with a pulse duration between 1 fs and 1 ns into the corneal tissue. As a result, the power density of the respective laser pulse required for the optical breakdown can be spatially narrowly limited, so that a high cutting accuracy is made possible during the generation of the boundary surfaces. The wavelength range selected can also be, in particular, the range between 700 nm and 780 nm.In further advantageous embodiments of the treatment apparatus according to the invention, the control device can have at least one storage device for at least temporarily storing at least one control data set, wherein the control data set or sets comprise control data for positioning and / or for focusing individual laser pulses in the cornea / cornea; and can have at least one beam device for beam guidance and / or beam shaping and / or beam deflection and / or beam focusing of a laser beam of the laser.Further features and their advantages can be gathered from the descriptions of the first aspect of the invention, wherein advantageous configurations of each aspect of the invention are to be regarded as advantageous configurations of the respective other aspect of the invention.A fourth aspect of the invention relates to a computer program comprising instructions which cause the control device according to the second aspect of the invention to execute the method steps according to the first aspect of the invention.A fifth aspect of the invention relates to a computer-readable medium on which the computer program according to the fourth aspect of the invention is stored. Further features and their advantages can be gathered from the descriptions of the first to fourth aspects of the invention, advantageous configurations of each aspect of the invention being regarded as advantageous configurations of the respective other aspect of the invention.Further features of the invention are evident from the claims, the figures and the description of the figures. The features and combinations of features mentioned above in the description, and the features and combinations of features mentioned below in the description of the figures and / or shown alone in the figures, can be used not only in the respectively specified combination but also in other combinations without departing from the scope of the invention. Therefore, embodiments of the invention are also to be considered as included and disclosed which are not explicitly shown and explained in the figures, but which emerge from the explained embodiments and can be generated by separate combinations of features. Embodiments and combinations of features are also to be considered as disclosed, which therefore do not have all features of an originally formulated independent claim. Furthermore, embodiments and combinations of features, in particular by the embodiments set forth above, are to be considered as disclosed which go beyond or deviate from the combinations of features set forth in the references of the claims. The following shows:The following shows: FIG. 1 shows a schematic illustration of a treatment apparatus according to an exemplary embodiment; FIG. 2 shows a schematic method diagram for providing control data according to an exemplary embodiment; FIG. 3 ashows a schematically illustrated volume body in a non-deformed state; FIG. 3 b shows the volume body in a freely deformed state; FIG. 3 cshows the volume body in the deformed state with fixation at the lateral boundary surfaces.In the figures, identical or functionally identical elements are provided with the same reference numerals.FIG. 1 shows a schematic representation of a treatment device 10 with an eye-surgery laser 18 for separating a lentivirus 12 defined by control data from a cornea (cornea) 26 by means of photodisruption and / or ablation, wherein the cornea 26 is bounded in the direction of an optical axis by an anterior corneal surface 30 and a posterior corneal surface 32. For separating the lentivirus 12, a posterior interface 14 and an anterior interface 16 of the lentivirus 12 are specified in the control data, on which a cavitation bubble path for separating the lentivirus 12 from the cornea 26 can be generated. It can be seen that, in addition to the laser 18, a control device 20 for the laser 18 can be formed, so that this can emit pulsed laser pulses, for example, in a predefined pattern for generating the boundary surfaces 14, 16. Alternatively, the control device 20 can be a control device 20 external with respect to the treatment apparatus 10.Furthermore, FIG. 1 shows that the laser beam 24 generated by the laser 18 is deflected in the direction of the cornea 26 by means of a beam device 22, namely a beam deflection device, such as a rotation scanner. The beam deflection device 22 is likewise controlled by the control device 20 in order to generate the boundary surfaces 14, 16, preferably also incisions or cuts, along predetermined incision profiles.The laser 18 illustrated can preferably be a photodisruptive and / or ablative laser which is designed to emit laser pulses in a wavelength range between 300 nm and 1400 nm, preferably between 700 nm and 1200 nm, at a respective pulse duration between 1 fs and 1 ns, preferably between 10 fs and 10 ps, and a repetition frequency greater than 10 KHz, preferably between 100 KHz and 100 MHz. The control device 20 optionally also has a storage device (not shown) for at least temporarily storing at least one control data set, wherein the control data set or sets comprise control data for positioning and / or focusing individual laser pulses in the cornea. The position data and / or focusing data of the individual laser pulses, that is to say the lenticular geometry of the lenticular 12 to be separated, is generated on the basis of predetermined control data, in particular from a previously measured topography and / or pachymetry and / or the morphology of the cornea or the optical refractive error correction to be generated.For detecting the vision deficiency data, which may indicate a value in diopters, for example, appropriate examination data for describing the vision deficiency may be received by the controller 20 from a data server, or the examination data may be directly input to the controller 20.Furthermore, a contact element 28 may be provided, which may belong to the treatment apparatus 10. Alternatively, the contact element 28 can also be provided separately from the treatment device 10. The contact element 28, which can also be referred to as a patient interface or fixation system, serves to fix the eye or the cornea 26 for the treatment. For this purpose, the contact element 28 can have a planoconcave lens, which is adapted to the cornea 26 for fixation. However, by the fixation by means of the contact element 28, the cornea 26 can deform and thus the geometry of the lentivirus 12 no longer has the originally planned dimensions. It may therefore occur that, for example, a planned or to be corrected refractive power value deviates from a reached refractive power value after treatment with the treatment device 10.FIG. 2 shows a schematic method diagram for providing control data for the laser 18 of the treatment apparatus 10 for correcting the cornea 26, wherein the deformation of the cornea 26 by the contact element 28 can be taken into account by the method. The method steps can preferably be carried out by the control device 20, which is separate from the treatment apparatus 10 and / or which can be integrated into the treatment apparatus 10. In a step S 10, a corneal geometry of the eye can be determined from predetermined examination data, wherein the corneal geometry comprises at least one anterior corneal curvature of the anterior corneal surface 30. In a step S 12, an anterior interface 16 and a posterior interface 14 of a lentivirus 12 of the cornea 26 can be determined, which is to be removed for correction of the cornea. The anterior and posterior interfaces 14, 16 may preferably be determined based on the previously determined corneal geometry.Since the anterior and posterior boundary surfaces 14, 16 change as the cornea 26 is deformed by the contact element 28, a deformed cornea can be modeled by means of a corneal deformation model in a step S 14 in order to compensate for this deformation, wherein the corneal deformation model is based on the Euler-Bernoulli beam theory and it is determined here how corneal surfaces within the cornea 26 change by deformation. In this case, the cornea 26 can be modeled as a volume body which is formed from respective central corneal surfaces 34, 36, wherein, in order to determine the deformed cornea in the corneal deformation model, the anterior corneal curvature is changed to a predefined curvature of the contact element 28 and the central corneal surfaces 34, 36 are adapted to the changed curvature of the anterior corneal surface 30 by means of an elastic deformation.To illustrate the corneal deformation model, the deformation of the corpuscle of the cornea 26 is illustrated in FIGS. 3a to 3c. In this case, FIG. 3 ashows, for example, the volume body of the cornea 26 in a free state before the deformation by the contact element 28. the volume body can be bounded in the direction of the optical axis by the anterior corneal surface 30 and the posterior corneal surface 32 and in the radial direction (laterally) by lateral boundary surfaces 38. the anterior corneal surface 30 and the posterior corneal surface 32 can be provided as a corneal ellipsoid, wherein in this figure, for the purposes of illustration, a two-dimensional cross section through the volume body is shown and the volume body can be present in a three-dimensional shape, in particular rotationally symmetrical. Alternatively, the solid body can also deviate from the rotational symmetry and have an irregular shape.In addition to the anterior and posterior corneal surfaces 30, 32, central corneal surfaces 34, 36 of the volume body are also shown, wherein a central corneal surface can be provided for each position in the z direction (direction of the optical axis) within the volume body, which is not shown here for reasons of clarity. One of the central corneal surfaces, for example the central corneal surface 36, can be a neutral corneal surface or neutral membrane which, according to the Euler-Bernoulli beam theory, has the same surface before and after the deformation, which is taken into account in the modelling of the cornea 26 on the basis of the corneal deformation model. Preferably, a respective central corneal surface 34 can be described in relation to this neutral corneal surface 36 in the corneal deformation model.Preferably, a radius of curvature of a respective central corneal surface 34 can thus be described by means of the corneal deformation model according to the formula, wherein said model provides the radius of curvature of the central corneal surface 34 before the deformation (r cent,pre). Here, r ca describes the radius of curvature of the anterior corneal surface 30 and r cp describes the radius of curvature of the posterior corneal surface 32. the variable q describes a relative position of the central corneal surface 34 to the neutral corneal surface 36, wherein q can assume a value between 0 and 1.Similarly, a position in the z direction, which is dependent on the radial position, can also be described with respect to the radius of curvature, wherein the z direction runs in the direction of the optical axis. This can be described for the respective central corneal surface 34 with the formula wherein r X describes a radial position starting from the center of the cornea 26 and dcc describes a central thickness of the cornea 26 at the highest point or inflection point of the cornea 26.During the deformation of the cornea 26 by the contact element 28, it can be provided in the corneal deformation model that the radius of curvature of the anterior corneal surface 30 is adapted to a radius of curvature of the contact element 28. This situation is illustrated, for example, in FIG. 3 b, wherein the contact element 28 is not shown here for reasons of clarity. It can be seen that the anterior corneal surface 30 is depressed and thus the central corneal surfaces 34 and 36 as well. however, it still remains considered according to Euler-Bernoulli beam theory that the neutral corneal surface 36 has the same area as before deformation.During this deformation, it is assumed that the volume body can freely deform and is not limited toward the sides. Therefore, during the deformation, the lateral boundary surfaces 38 are also deformed obliquely outwards, in comparison with the non-deformed cornea 26 in FIG. 3 a. Since the central corneal surfaces 34 change according to the formulae given above from the corneal deformation model in their radius of curvature and their position in the z direction, it follows that the lentivirus 12 defined in step S 12, which is not shown in these figures, also changes because the radii of curvature of the anterior boundary surface 16 and of the posterior boundary surface 14 of the lentivirus deform as well. This deformation can preferably be determined in a step S 16 of the method by ascertaining these from the adapted corneal surfaces 34, 36 of the deformed cornea.Subsequently, the deformed anterior and posterior interfaces 14, 16 of the lentivirus 12 may be provided as control data for controlling the laser in a step S18 to compensate for the deformation of the cornea by the contact element 28.However, the situation shown in FIG. 3 bis only a theoretical assumption and in particular the lateral boundary surfaces 38 cannot freely deform in a real eye, but are fixed by morphological characteristics of the eye. This boundary condition can preferably also be taken into account in the corneal deformation model, which is illustrated for example in FIG. 3 c.In this case, the volume body of the cornea 26 is illustrated after the deformation by the contact element 28, wherein the lateral boundary surfaces 38 cannot escape laterally as in the case of the free cornea, but are at least partially fixed at the lateral boundary surface 38. It can be assumed here that the lateral boundary surface 38 represents a beginning (limbus) of a leather hide (sclera) which is not compressible or is only very slightly compressible. The limbus can be assumed here, for example, at a radial position (r X) of 6.5 millimeters.In order to take this fixation at the lateral boundary surface 38 into account, it can be provided that a deformation of the cornea 26 is carried out in the free state, that is to say a deformation as shown in FIG. 3 b, wherein respective edge points of the respective corneal surfaces 34, 36 are transformed back after the deformation by means of a scaling factor to the initial position of the lateral boundary surface 38 and thus the oblique lateral boundary surface (as in FIG. 3 b) is transformed back again to the laterally fixed (perpendicular boundary surface as in FIGS. 3 aand 3 c ). This has the advantage that it is also possible to take account of morphological boundary conditions in the cornea 26, which improves the corneal deformation model and the anterior and posterior boundary surfaces 14, 16 of the lentivirus 12 determined therefrom.Alternatively or additionally, for fixing the lateral boundary surfaces 38, a transformation point can also be provided on the respective corneal surfaces 34, 36, which transformation point is located outside the initial position of the boundary surfaces 38, for example on the left and right of the boundary surfaces 38 in FIG. 3 a, wherein the transformation point is co-deformed and, after the deformation, is transformed back to the initial position of the respective transformation point by means of the scaling factor, wherein subsequently only the region which is located within the lateral boundary surfaces 38 is taken into account. In other words, the scaling may be performed at a transformation point that is outside the lateral interfaces 38, thereby reducing artifacts at the lateral interfaces 38.Partial deformations of the lateral boundary surfaces 38 can preferably also be taken into account, wherein the edge points are not transformed back to the initial position here by the scaling factor, but to an intermediate position, that is to say a point of the lateral boundary surface 38 which is located between the lateral boundary surface 38 shown in FIG. 3 aand FIG. 3 b. For example, the initial position of the lateral boundary surface 38 may be 6.5 millimeters and a maximum extension of the freely deformed lateral boundary surface 38 may be 7.3 millimeters, wherein the respective edge points may be transformed back to an intermediate position between these values. In this case, it is taken into account, for example, that the leather hide can be at least partially compressed, which describes the cornea 26 even better in the corneal deformation model.In practical application for taking into account the deformation by the contact element 28, a deformation correction value can thus be determined, for example, by means of which a planned refractive power correction can be scaled in order to calculate a compensation of the deformation by the contact element. Thus, instead of point-by-point scaling, a global transformation may be performed which provides a compensation for deformation by the contact element 28 and thus contributes to an improvement in the correction of the cornea 26.Overall, the examples show how a deformation model can be provided by the invention, with which a deformation of the cornea 26 by the contact element 28 can be taken into account.

Claims

Method for providing control data for a laser (18) of a treatment apparatus (10) for the correction of a cornea (26) of a human or animal eye, wherein the method comprises the following steps, carried out by a control device (20): - determining (S10) a corneal geometry of the eye from predetermined examination data, wherein the corneal geometry comprises at least one anterior corneal curvature; - determining (S12) an anterior and posterior interface (14, 16) of a lentivirus (12) of the cornea (26) for providing the correction of the cornea (26); determining (S14) a cornea (26) deformed by a contact element (28) by means of a corneal deformation model which is determined based on the Euler-Bernoulli beam theory, wherein the cornea (26) with the determined corneal geometry is provided in the corneal deformation model as a volume body, wherein the volume body is formed from respective central corneal surfaces (34, 36) between an anterior corneal surface (30) and a posterior corneal surface (32), wherein the anterior corneal curvature is changed to a predetermined curvature of the contact element (28) and the central corneal surfaces (34, 36) are adapted to the changed curvature of the anterior corneal surface (30) by means of an elastic deformation for determining the deformed cornea (26) in the corneal deformation model; determining (S16) a deformed lens (12) by means of the deformed cornea (26), wherein the anterior and posterior boundary surfaces (14, 16) of the lens (12) are determined depending on the adapted central corneal surfaces (34, 36) of the deformed cornea (26), providing (S18) the deformed anterior and posterior boundary surfaces (14, 16) of the lens (12) as control data for controlling the laser.Method according to claim 1, wherein a deformation correction value is determined by the corneal deformation model, by means of which deformation correction value the deformed grating (12) is calculated for a planned refractive power correction in order to compensate for the deformation by the contact element (28).Method according to claim 1, wherein a deformation correction value is determined by the corneal deformation model, by means of which deformation correction value the deformed grating (12) is calculated for a planned grating diameter in order to compensate for the deformation by the contact element (28).Method according to one of the preceding claims, wherein in the corneal deformation model a lateral boundary surface (38) of the volume body in a radial direction is freely deformed by the deformation of the volume body.Method according to one of the preceding claims, wherein in the corneal deformation model a lateral boundary surface (38) of the volume body in a radial direction is deformed into an intermediate position during the deformation of the volume body, wherein the intermediate position is located between an initial position of the lateral boundary surface (38) and a position of the lateral boundary surface (38) during a free deformation of the lateral boundary surface (38).Method according to one of the preceding claims, wherein in the corneal deformation model a lateral boundary surface (38) of the volume body in a radial direction is fixed at at least one initial position of the lateral boundary surface (38) during the deformation of the volume body.Method according to one of the preceding claims, wherein in the corneal deformation model a lateral boundary surface (38) of the volume body in a radial direction is fixed at an initial position of the entire lateral boundary surface (38) during the deformation of the volume body.Method according to one of Claims 6 or 7, wherein, in order to fix the volume body at the at least one position of the lateral boundary surface (38), a transformation point is specified on the respective corneal surface (30, 32, 34, 36), which transformation point, as viewed in the radial direction, is located outside the initial position of the lateral boundary surface (38), wherein the transformation point is reset after the elastic deformation by a scaling factor to an initial position of the transformation point before the elastic deformation, wherein after the transformation point is reset to the initial position, only the region of the respective corneal surface (30, 32, 34, 36) which is located inside the initial lateral boundary surface (38) in the radial direction is taken into account.Method according to one of claims 6 or 7, wherein, for fixing the volume body at the initial position of the entire lateral boundary surface (38), the corneal surfaces (30, 32, 34, 36) are adapted by a scaling factor, wherein edge points of the respective corneal surfaces (30, 32, 34, 36) which are located on the initial position of the lateral boundary surface (38) before the deformation are transformed back to the initial position of the lateral boundary surface (38) after the deformation.The method according to any one of claims 4 to 9, wherein the lateral boundary surface (38) is defined at a beginning of a sclera of the eye.Method according to one of the preceding claims, wherein in the corneal deformation model the volume body is described on the anterior corneal surface (30) by an anterior corneal ellipsoid and on the posterior corneal surface (32) by a posterior corneal ellipsoid, wherein for the predetermined curvature of the contact element (28) a predetermined contact element ellipsoid is provided, to which the anterior corneal ellipsoid is changed for the elastic deformation.Control device (20) which is designed to carry out a method according to one of Claims 1 to 11.Treatment device (10) having at least one eye-surgery laser (18) for the separation of a lentivirus (12) having predefined boundary surfaces (14, 16) from a human or animal eye by cavitation bubbles and at least one control device (20) according to Claim 12.Treatment device (10) according to claim 13, characterised in that the laser (18) is suitable for emitting laser pulses in a wavelength range between 300 nm and 1400 nm, preferably between 900 nm and 1200 nm, at a respective pulse duration between 1 fs and 1 ns, preferably between 10 fs and 10 ps, and a repetition frequency greater than 10 KHz, preferably between 100 KHz and 100 MHz.Treatment apparatus (10) according to Claim 13 or 14, characterized in that the control device (20) - has at least one storage device for at least temporarily storing at least one control data record, wherein the control data record or records comprise control data for positioning and / or for focusing individual laser pulses in the cornea; and - comprises at least one beam device (22) for beam guidance and / or beam shaping and / or beam deflection and / or beam focusing of a laser beam (24) of the laser (18).A computer program comprising instructions for causing the controller (20) of claim 12 to perform the method steps of any one of claims 1 to 11.A computer readable medium having stored thereon the computer program of claim 16.

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