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, wherein the method comprises the following steps performed by at least one control device (20): - Determining (S10) an effect of a deformation of the cornea (26) on predetermined corneal parameters by means of a corneal deformation model, wherein the corneal deformation model allows the cornea (26) to be modeled in a deformed and undeformed state, wherein, to determine the effect of the deformation, values ​​of several predetermined corneal parameters are varied in the undeformed state of the cornea (26) and the effect of this variation on values ​​of the corneal parameters in the deformed state of the cornea (26) is determined;- Determining (S12) the at least two most important predefined corneal parameters for treatment and / or corneal deformation (26) depending on the magnitude of the determined effect; - Adapting (S14) one or more predefined fit functions to the values ​​of the at least two most important predefined corneal parameters, wherein the one adapted fit function provides a compensation function to compensate for the deformation or the several adapted fit functions are combined to form the compensation function; - Calculating (S16) a deformation-corrected treatment value using the compensation function and preoperative values ​​of the at least two most important predefined corneal parameters; - Providing (S18) the deformation-corrected treatment value as control data for the treatment device (10);- wherein the one or more respective predefined fit functions are polynomial functions of the form z(x,y)=ax2+b*xy+cy2+dx+ey+fs, where z(x, y) is a treatment value of a corneal parameter to be deformation-corrected, x and y are values ​​of at least the two most important predefined corneal parameters to be used as preoperative values ​​in the compensation function, and a, b, c, d, e and f are coefficients obtained by fitting to the values ​​of the most important corneal parameters from the corneal deformation model.

Description

The present invention relates to a method for providing control data for a laser of a treatment device for corneal correction. The invention further relates to a control unit for carrying out the method, a treatment device comprising at least one ophthalmic surgical laser and at least one control unit, a computer program, and a computer-readable medium. Treatment devices and methods for controlling lasers to correct corneal refractive errors are known in the prior art. For example, a pulsed laser and a beam focusing device can be configured such that laser pulses create an optical breakthrough at a focus located within the corneal tissue, thereby removing a lenticule from the cornea to correct the refractive error. During treatment with such a device, for example, to remove a lenticule, the eye is typically fixed in place by one or more contact elements of the device. The contact element is a rigid element, such as a plano-concave lens, which is placed on the eye, particularly on the cornea, to prevent eye movement during treatment.A disadvantage of such a contact element, however, is that it alters the shape of the cornea, particularly by compressing it. This can also change the shape of the lenticule to be removed, potentially rendering a planned treatment inaccurate. Furthermore, determining the geometry of the lenticule to be removed is usually carried out using established standard methods. For example, a refractive power or diopter value to be corrected is specified, which is then used to determine the shape of the lenticule to be removed. In particular, the "collapse" or closure of the cornea after removal of the lenticule results in the desired correction. However, when determining the corneal correction, especially for refractive correction, using standard methods, slight deviations from the intended result can occur, as the corneal closure is based on an idealized cornea. The aforementioned corneal deformation effects, particularly those caused by the contact element or by imprecise corneal closure after lenticule removal, can lead to undesirable deviations in the treatment outcome if these errors accumulate. Therefore, every effort is made to consider and compensate for these effects beforehand, although determining the necessary compensation is often very complex and time-consuming. Furthermore, the publication by Kehrer, Tobias; Mosquera, Samuel Arba: “A simple cornea deformation model”. In: Advanced optical technologies, Vol. 10, 2021, No. 6, pp. 433-450; ISSN 2192-8576 reveals a corneal deformation model based on the idea of ​​extending the “neutral axis” model to two-dimensional deformations. The invention is therefore based on the objective of simplifying the compensation of deformation effects of the cornea. This problem is solved by the inventive method, the inventive devices, the inventive computer program, and the inventive computer-readable medium. Advantageous embodiments with expedient further 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 device, the control device, the computer program, and the computer-readable medium, and vice versa. A first aspect of the invention relates to a method for providing control data to a laser of a treatment device for correcting the cornea of ​​a human or animal eye, wherein the method comprises the following steps, which are carried out by at least one control device. A control device is understood to be a device, a device component, or a group of devices that is configured to receive and evaluate signals and to provide, for example, generate control data. The control device can be configured, for example, as a control chip, computer program, computer program product, or control unit.In this procedure, the control unit determines the effect of corneal deformation on predefined corneal parameters using a corneal deformation model, whereby the cornea can be modeled in a deformed and undeformed state by means of the corneal deformation model, whereby to determine the effect of the deformation, values ​​of several predefined corneal parameters are varied in the undeformed state of the cornea and the effect of this variation on values ​​of the corneal parameters in the deformed state of the cornea is determined.Subsequently, at least two of the most important predefined corneal parameters for treatment and / or corneal deformation are determined, depending on the magnitude of the determined effect. One or more predefined fit functions are then adapted to the values ​​of these two most important predefined corneal parameters. One adapted fit function provides a compensation function to correct the deformation, or the multiple adapted fit functions are combined to form the compensation function. Finally, a deformation-corrected treatment value is calculated using the compensation function and the preoperative values ​​of the two most important predefined corneal parameters. This deformation-corrected treatment value is then provided as control data for the treatment device.Here, the one or more predefined fit functions are polynomial functions of the form z(x, y) = ax2+ b*xy + cy2+ dx + ey + f, where z(x, y) is a treatment value of a corneal parameter to be deformation-corrected, x and y are values ​​of at least the two most important predefined corneal parameters to be used as preoperative values ​​in the compensation function, and a, b, c, d, e and f are coefficients obtained by fitting to the values ​​of the most important corneal parameters from the corneal deformation model. In other words, the process begins by modeling how corneal parameters change due to corneal deformation. This can be calculated or simulated using a corneal deformation model. The corneal deformation model allows the cornea to be modeled in both a deformed and an undeformed state. For example, the deformation caused by a contact element can be modeled, as well as the corneal closure after lenticule removal and the resulting deformation from the collapse of the remaining corneal layers. This means that a value (corneal value) of a corneal parameter, such as the corneal radius of curvature, can be specified in the undeformed state. The corneal deformation model can then be used to determine the effect of corneal deformation on this value and the values ​​of other corneal parameters, and thus on the planned treatment outcome. Corneal parameters can include, for example, geometries of the cornea and / or the lenticule to be separated, which may change before and after deformation. The deformation or the degree of deformation can be predetermined or specified, for example, by a known radius of curvature of a contact element. The contact element can, for example, have a plano-concave, a plano-parallel, or a convex-concave shape.Determining the effect of corneal deformation on the specified corneal parameters can be done, for example, in the form of a table in which a specified corneal parameter, preferably several corneal parameters, are varied, wherein the respective values ​​of the other corneal parameters for the deformed state in the cornea are determined by the corneal deformation model and are stored for each variation, preferably in a ratio showing how the respective values ​​change in the deformed and non-deformed states. For example, a corneal parameter could be the radius of curvature of the anterior corneal surface, for which a value, such as 7 mm, is initially assumed. Using the corneal deformation model, it can then be determined how other corneal parameters, such as the radius of curvature of the anterior lenticule's interface, change when the cornea is deformed, starting with the 7 mm radius of curvature of the anterior corneal surface. Next, the radius of curvature of the anterior corneal surface can be varied, meaning a second value, such as 8 mm, is assumed, and the corresponding values ​​are then determined and stored. This variation can preferably be performed for multiple values, particularly a predefined range of values, to determine the effect of deformation on the specified corneal parameters. Any model capable of describing the cornea, and in particular its parameters, in both deformed and undeformed states can be used as a corneal deformation model. Preferably, the cornea is described as a solid volume that is deformed based on the Euler-Bernoulli beam theory to determine the respective corneal parameters and their effects on the corneal values. A corneal deformation model based on the Euler-Bernoulli beam theory has proven particularly suitable for replicating these deformation effects. The control device used to determine the effect of the deformation can be part of the treatment device or a separate control device. Subsequently, the determined effect of the deformation can be used to identify which corneal parameters have the greatest influence on a given treatment and / or corneal deformation, thus determining the most important corneal parameters. This means that a ranking can be created based on the deviation determined by the corneal deformation model, whereby the most important corneal parameters may vary depending on the treatment and / or type of deformation. For example, in the case of a deformation caused by a contact element, an anterior corneal surface and / or an anterior lenticule interface may have the greatest impact on the other corneal parameters. Preferably, at least the two most important corneal parameters can be determined. Furthermore, one or more fitting functions can be adapted to the values ​​of the most important corneal parameters. In other words, for example, a single fitting function can be fitted to the values ​​of the most important corneal parameters, or a separate fitting function can be used for each of the most important corneal parameters, with the respective fitting functions then subsequently being combined into a compensation function. A polynomial function, in particular a second-order polynomial, can preferably be used as the fitting function for this purpose. One or more fitting functions can then be provided to the treatment device as a compensation function to counteract the deformation. Preoperative values ​​of the corneal parameters, derived from predetermined examination data, can be inserted into the compensation function to obtain deformation-corrected treatment values ​​for the respective corneal parameters. Preferably, this compensation function is provided to the control unit of the treatment device, so that the treatment device only requires the compensation function and the determination of the effect of the deformation and the determination of the most important corneal parameters can be performed only once, particularly on a control unit separate from the treatment device. This means that, after determining the compensation function, a treatment plan for an individual cornea can be created on the treatment device by first determining one or more preoperative values ​​of the most important corneal parameters that the cornea to be treated actually possesses. The determination of these preoperative values ​​can be carried out using known methods, and these preoperative values ​​can then be used in the compensation function to calculate a deformation-corrected treatment value for another corneal parameter to be achieved. Determining the deformation-corrected treatment value does not need to be performed immediately after determining the compensatory function, but can take place at any time thereafter. For example, the preoperative values ​​of the key corneal parameters can be determined from predetermined examination data. These preoperative values ​​are preferably those that were varied to determine the effect in the deformed and undeformed states, and for which the greatest effect was determined for the treatment and / or corneal deformation to be performed. Finally, control data containing the deformation-corrected treatment value can be provided to the treatment device to control the laser.The control data can be determined or provided, for example, for ablative procedures, photodisruptive procedures, in particular for lenticule extraction, corneal crosslinking (CXL) and / or laser-induced refractive index change (LIRIC) procedures. The compensation function thus allows simultaneous compensation for several corneal parameters, preferably the most important corneal parameters, especially for cross-effects that occur during corneal deformation. Corneal parameters include, for example, a radius of curvature of an anterior corneal surface and / or an optical distance between the anterior corneal surface and a posterior corneal surface and / or a corneal thickness and / or a radial distance from a limbus to a center of the cornea and / or an optical distance between the anterior corneal surface and an anterior interface of a lenticule to be separated and / or a radius of the anterior interface of the lenticule to be separated and / or a transition zone and / or a lenticule thickness and / or a planned refractive correction and / or a radius of curvature of a contact element and / or a relative corneal thickness and / or an incision angle of an incision. This aspect of the invention offers the advantage that deformation effects can be easily compensated for, thus leading to better treatment results. Furthermore, it is not necessary to perform a complex and time-consuming calculation or simulation for each individual patient, which describes a change in the coordinate system during deformation. Instead, a single determination of the compensation function can be made, which can then be used for any treatment device to compensate for the deformation. The invention also includes embodiments that offer additional advantages. One interpretation of the corneal deformation model is based on the Euler-Bernoulli beam theory. In other words, the cornea can be described as a solid volume that deforms according to the Euler-Bernoulli beam theory to represent the deformed cornea. The Euler-Bernoulli beam theory describes the elastic bending of a body, assuming that several central corneal surfaces are located between an anterior and a posterior corneal surface, forming the solid volume. According to the Euler-Bernoulli beam theory, one of the central corneal surfaces is a neutral corneal surface or membrane, whose area remains constant during deformation. The other central corneal surfaces can be described in terms of their size relative to the neutral corneal surface.When modeling deformation caused by the contact element, for example, the central corneal surfaces below the neutral corneal surface can be compressed, while those above it are stretched. When modeling corneal closure after lenticule removal, the corneal surfaces above the lenticule can be stretched. Based on Euler-Bernoulli beam theory, it is mathematically possible to calculate how the central corneal surfaces change during elastic deformation, particularly relative to the neutral corneal surface. Using Euler-Bernoulli beam theory as a corneal deformation model has proven particularly suitable because it describes corneal deformation with exceptional accuracy. This allows for the modeling of improved corneal values ​​for the respective corneal parameters, from which the compensation function can be determined. Preferably, to determine the effect of the deformation, the values ​​of the specified corneal parameters are varied within predefined ranges, each range containing standard values ​​for the respective corneal parameter. In other words, the value of a given corneal parameter can be varied within a range containing standard values ​​to determine the effect of the deformation. These standard values ​​may, for example, be known from a patient cohort. This allows, preferably, only values ​​for the respective corneal parameter that are typically found in a patient's eye to be considered. Particularly preferably, not all values ​​from this range are checked using the corneal deformation model, but only a predefined number of reference points that allow for a sufficiently accurate determination of the deformation compensation.This design reduces the effort required to model the deformation. It is particularly preferred that the specified fitting function be a polynomial function, especially a second-order polynomial. For example, for a corneal parameter, only a finite number of values ​​may be determined by the corneal deformation model, such as five values ​​within the range of standard values. The values ​​between these limits can then be determined, for example, by fitting the available values ​​using a fitting function, for which a second-order polynomial has proven particularly suitable. In particular, the adjustment function can be composed of several polynomial functions, with the polynomial functions being fitted for each of the most important corneal parameters.Thus, the compensation function, which is composed of several polynomial functions, can compensate for multiple corneal parameters simultaneously, thereby also taking into account cross-effects between the different corneal parameters. A second-order polynomial can, for example, be of the form z(x) = ax² + bx + c, where z(x) can be a treatment value of a corneal parameter to be deformation-corrected, and x is a value of one of the corneal parameters identified as important, which is to be used as a preoperative value in the compensation function. In this case, a, b, and c are coefficients obtained by fitting the values ​​of the most important corneal parameters from the corneal deformation model.Alternatively, the polynomial function can be of the form z(x, y) = ax2+ b*xy + cy2+ dx + ey + f, where z (x, y) can be the treatment value to be achieved, which is to be deformation-corrected by the compensation function, x a preoperative value of a first important corneal parameter and y a preoperative value of a second important corneal parameter and a, b, c, d and f the coefficients that were determined from fitting the fit functions to the most important corneal parameters from the corneal deformation model. Preferably, the compensation function is obtained by multiplying or summing the adapted fit functions of at least two of the most important predefined corneal parameters. In other words, if there are several important corneal parameters, multiple fit functions can be adapted to the respective corneal parameters. To obtain the compensation function from the respective fit functions, they can be combined by multiplication or summation. For example, z(x) can be a fit function of a first corneal parameter and z(y) the fit function of a second parameter, where the compensation function can be z(x, y) = z(x) z(y) or z(x) + z(y). In an advantageous embodiment, the compensation function is used to adjust a planned refractive correction and / or a planned lenticule diameter. In other words, the anterior and posterior interfaces of a lenticule can be determined by means of a planned refractive correction, i.e., a diopter value to be compensated. This planned refractive correction can be scaled or adjusted by means of a correction value obtained from the compensation function, or the compensation function can provide a global value that is used as a deformation-corrected refractive correction. Alternatively or additionally, a lenticule diameter can be planned for corneal correction, in particular a diameter of an optical zone or a correction magnitude.Using the compensation function, the planned lenticule diameter can then be adjusted via scaling or a difference value to obtain the deformation correction. Alternatively, a global value for the planned lenticule diameter can be calculated from the compensation function. This design offers the advantage that a user planning a refractive power correction and / or a lenticule diameter can easily adjust these using the compensation function to compensate for the deformation. Preferably, the compensation function is designed to compensate for corneal deformation caused by a contact element and / or to compensate for corneal deformation resulting from corneal closure after corneal lenticule removal. These two deformations represent the most common cause of treatment errors due to deformation effects, and the compensation function can address these issues. A second aspect of the present invention relates to a control device configured to carry out the method described above. This results in the advantages listed above. The control device can, for example, be configured as a control chip, control unit, or user program ("app"). The control device can preferably include a processor and / or a data storage device. A processor is understood to be a device or device component for electronic data processing. The processor can, for example, include at least one microcontroller and / or at least one microprocessor. The optional data storage device can preferably contain program code for carrying out the method according to the invention.The program code can then be designed, when executed by the processor, to cause the control unit to perform one of the embodiments of the method according to the invention described above. Furthermore, the control unit can have several control units, in particular a first control unit configured to calculate the reference table, which can be independent of the treatment device, and a second control unit configured to determine the deformation-corrected corneal value to be achieved using the reference table and to provide the control data, wherein the second control unit is preferably arranged in the treatment device. In other words, the control unit in the treatment device preferably comprises only the reference table provided by the first control unit. A third aspect of the present invention relates to a treatment device comprising at least one ophthalmic surgical laser for the removal of a lenticule with predefined interfaces from a human or animal eye by means of optical breakthroughs and / or ablation, and at least one control unit for the laser(s) configured to perform the steps of the method according to the first aspect of the invention. Preferably, the treatment device is provided with the two control units mentioned above. 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, with a pulse duration of 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 range is referred to in laser technology as "deep ultraviolet." This advantageously avoids unintentional damage to the cornea caused by these very short-wavelength and high-energy beams.Photodisruptive and / or ablative lasers of the type used here typically deliver pulsed laser radiation with a pulse duration between 1 fs and 1 ns into the corneal tissue. This allows the power density of the respective laser pulse, necessary for optical breakthrough, to be spatially tightly limited, thus enabling high cutting accuracy in the generation of interfaces. The wavelength range between 700 nm and 780 nm can also be selected. In further advantageous embodiments of the treatment device according to the invention, the control device can have at least one storage device for at least temporary storage of at least one control data set, wherein the control data set(s) comprise control data for positioning and / or focusing individual laser pulses in the 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 found in the descriptions of the first aspect of the invention, whereby advantageous embodiments of each aspect of the invention are to be regarded as advantageous embodiments of the other aspect of the invention. A fourth aspect of the invention relates to a computer program comprising commands that cause the control device according to the second aspect of the invention to perform the process 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 found in the descriptions of the first to fourth aspects of the invention, whereby advantageous embodiments of each aspect of the invention are to be regarded as advantageous embodiments of the other aspects 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, as well as those subsequently mentioned in the description of the figures and / or shown in the figures alone, are not only usable in the combinations specified, but also in other combinations without departing from the scope of the invention. Thus, embodiments that are not explicitly shown and explained in the figures, but which can be derived and generated from the explained embodiments by separate combinations of features, are also to be considered as encompassed and disclosed by the invention. Embodiments and combinations of features that do not exhibit all the features of an originally formulated independent claim are also to be considered disclosed.Furthermore, embodiments and combinations of features, in particular those set out above, are to be considered disclosed which go beyond or deviate from the combinations of features set out in the cross-references of the claims. This shows: Figure 1 shows a schematic representation of a treatment device according to an exemplary embodiment; Figure 2 shows a schematic process diagram for providing control data according to an exemplary embodiment; Figure 3a shows a schematic representation of the cornea of ​​the corneal deformation model in its undeformed state; Figure 3b shows the cornea of ​​the corneal deformation model deformed by a contact element; Figure 4a shows a schematic representation of the cornea of ​​the corneal deformation model in its undeformed state before removal of a lenticule; Figure 4b shows the deformed cornea of ​​the corneal deformation model after closure of the lenticule; Figure 5a shows an exemplary representation of a first varied corneal parameter; Figure 5b shows an exemplary representation of a second varied corneal parameter. In the figures, identical or functionally equivalent elements are provided with the same reference symbols. Figure 1 shows a schematic representation of a treatment device 10 with an ophthalmic surgical laser 18 for the separation of a lenticule 12, defined by control data, from a cornea 26 by means of photodisruption and / or ablation. The cornea 26 is bounded along an optical axis by an anterior corneal surface 30 and a posterior corneal surface 32. For the separation of the lenticule 12, a posterior interface 14 and an anterior interface 16 of the lenticule 12 are specified in the control data. A cavitation bubble path can be generated on these interfaces to separate the lenticule 12 from the cornea 26. It can be seen that a control unit 20 for the laser 18 can be provided alongside the laser 18, enabling it to emit pulsed laser pulses, for example, in a predefined pattern to generate the interfaces 14 and 16.Alternatively, the control unit 20 can be an external control unit 20 with respect to the treatment device 10. Furthermore, Fig. 1 shows that the laser beam 24 generated by the laser 18 is deflected towards the cornea 26 by means of a beam deflection device 22, namely a beam deflection device, such as a rotary scanner. The beam deflection device 22 is also controlled by the control unit 20 to generate the interfaces 14, 16, preferably also incisions or sections, along predetermined incision paths. The laser 18 shown is preferably a photodisruptive and / or ablative laser configured to emit laser pulses in a wavelength range between 300 nm and 1400 nm, preferably between 700 nm and 1200 nm, with a 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 includes a storage device (not shown) for at least temporarily storing at least one control data set, wherein the control data set(s) 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, the lenticule geometry of the lenticule 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 produced. To determine the refractive error data, which can specify a value in diopters, for example, suitable examination data for describing the refractive error can be received from a data server by the control unit 20, or the examination data can be entered directly into the control unit 20. Furthermore, a contact element 28 may be provided, which can be part of the treatment device 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 plano-concave lens that is adapted to the cornea 26 for fixation. However, fixation by means of the contact element 28 can cause the cornea 26 to deform, and thus the geometry of the lenticule 12 no longer has the originally planned dimensions. Therefore, it can happen that, for example, a planned or corrected refractive power value differs from a refractive power value achieved after treatment with the treatment device 10. Figure 2 shows a schematic process diagram for providing control data for the laser 18 of the treatment device 10, which can be carried out, for example, by the control unit 20. In step S10, the effect of a corneal deformation on predetermined corneal parameters can first be determined using a corneal deformation model, wherein the corneal deformation model can describe the cornea 26 as a volume and is preferably based on the Euler-Bernoulli beam theory. Thus, the cornea 26 can be modeled in a deformed and undeformed state, wherein, to determine the effect of the deformation, a value of at least one corneal parameter is varied in the undeformed state of the cornea, and the effect of this variation on the values ​​of the other corneal parameters in the deformed state is determined. To illustrate the corneal deformation model, the deformation of the corneal volume 26 is shown in Fig. 3a and Fig. 3b for the deformation caused by the contact element 28 and in Fig. 4a and Fig. 4b for the deformation that occurs when the cornea 26 closes after removal of the lenticule 12. Figure 3a shows, for example, the corneal volume 26 in a free state before deformation by the contact element 28, which is not shown in this figure. The volume can be bounded along the optical axis by the anterior corneal surface 30 and the posterior corneal surface 32, and radially (laterally) by lateral interfaces 38. The anterior corneal surface 30 and the posterior corneal surface 32 can be provided as ellipsoids. For illustrative purposes, a two-dimensional cross-section through the volume is shown in this figure, and the volume can be in a three-dimensional shape, in particular rotationally symmetric.In addition to the anterior and posterior corneal surfaces 30, 32, central corneal surfaces 34, 36 of the volume are also shown, whereby a central corneal surface can be provided for each position in the z-direction (direction of the optical axis) within the volume, which is not shown here for the sake 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 area before and after deformation, which is taken into account when modeling the cornea 26 based on the corneal deformation model. Preferably, each central corneal surface 34 can be described in relation to this neutral corneal surface in the corneal deformation model. Preferably, the radius of curvature of a respective central corneal surface 34 can be described using the corneal deformation model according to the formula, which provides the radius of curvature of the central corneal surface 34 before deformation (rcent, pre). Here, rcaden describes the radius of curvature of the anterior corneal surface 30 and rcp 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, where q can take a value between 0 and 1. Similarly, a position in the z-direction, which depends on the radial position, can also be described for the radius of curvature, with the z-direction running in the direction of the optical axis. This can be described for the respective central corneal surface 34 with the formula, where rX describes a radial position starting from the center of the cornea 26 and dcc a central thickness of the cornea 26 at the highest point or inflection point of the cornea 26. In the corneal deformation model, when the cornea 26 is deformed by the contact element 28, the radius of curvature of the anterior corneal surface 30 can be adapted to a radius of curvature of the contact element 28. This situation is illustrated, for example, in Fig. 3b, although the contact element 28 is not shown here for clarity. It can be seen that the anterior corneal surface 30 is indented, and consequently, so are the central corneal surfaces 34 and 36. However, according to the Euler-Bernoulli beam theory, the neutral corneal surface 36 retains the same area as before the deformation. During this deformation, it is assumed that the volume can deform freely and is not limited laterally. In Fig. 4a, the cornea 26 is shown in an undeformed state before the removal of the lenticule 12. Here, too, the cornea 26 can be modeled as a volume formed from the respective central corneal surfaces 34 and 36. To determine the deformed cornea in the corneal deformation model, the anterior interface 16 of the lenticule is pressed against the posterior interface 14 of the lenticule 12, thereby altering the curvatures of the overlying corneal surfaces 30 and 34. The corneal deformation model is based on the same principles and formulas as already described for Figs. 3a and 3b. During the deformation of the cornea 26 by closing the area of ​​the lenticule 12 in the corneal deformation model, it is provided that the radius of curvature of the anterior interface 16 is adapted to a radius of curvature of the anterior interface 14, so that the cornea 26 is formed according to Fig. 4b. In this process, the anterior interface 16 can move downwards onto the posterior interface 14, thereby also adapting the corneal surfaces located above the anterior interface, in particular the neutral corneal surface 34 and the anterior corneal surface 30. Figures 5a and 5b illustrate exemplary variations of corneal parameters and their effect on other corneal parameters in the deformed state of the cornea, as can be carried out in process step S10. Both figures, 5a and 5b, show the effects on corneal parameters that can be caused by deformation of the cornea 26 by the contact element 28. The x-axis of Fig. 5a shows the corneal parameter rca, which represents the radius of curvature of the anterior corneal surface 30. This corneal parameter rca is varied within a predefined range of values, which preferably comprises standard values ​​of the corneal parameter from a patient cohort, and the effect of this variation on other corneal parameters, shown on the y-axis of Fig. 5a, is determined. In this example, the other corneal parameters are a refractive power, in particular a ratio of a planned refractive correction Dplan to the refractive correction Dpast determined by the corneal deformation model, a ratio of the planned radius of the anterior interface 16 (Rcap) to that determined by the corneal deformation model, and a ratio of the planned lenticule diameter (including the transition zone TZ) to that determined by the corneal deformation model.In addition to these exemplary corneal parameters, effects on other corneal parameters can also be determined in the corneal deformation model, such as an optical distance between the anterior corneal surface and a posterior corneal surface, a corneal thickness, a radial distance from a limbus to a center of the cornea, an optical distance between the anterior corneal surface and an anterior interface of a lenticule to be separated, a lenticule thickness, a radius of curvature of the contact element, a relative corneal thickness and / or an incision angle of an incision cut. To determine the graph shown in Fig. 5a, the corneal deformation model can be used, for example, as follows: The radius of curvature of the anterior corneal surface rca can be selected as a first predefined corneal parameter, with this value initially set at 7 mm in the undeformed state. The cornea, which has a radius of curvature of 7 mm, is then deformed using the corneal deformation model, and the effect of this deformation on the other corneal parameters plotted on the y-axis is determined.The corneal parameter rca can then be varied. This means that a radius of curvature of 7.5 mm is assumed in the undeformed state, and the cornea is deformed using the corneal deformation model in the same way as previously described, and the effect on the other corneal parameters is determined. This variation can then be repeated until a sufficient number of values ​​are obtained. Once the entire range of values ​​for the radius of curvature of the anterior corneal surface rca has been determined, it is possible, given a known radius of curvature of a real cornea, to reconstruct how, for example, a planned refractive correction Dplan results from corneal deformation to Dpaständer. Similarly, in addition to the radius of curvature of the anterior corneal surface rca30, other corneal parameters can also be varied, as shown, for example, in Fig. 5b. Fig. 5b is essentially the same as Fig. 5a, except that in Fig. 5b, the corneal parameter being varied is the optical distance between the anterior corneal surface 30 and the anterior interface of the lenticule 12 to be separated, which is denoted here as kcap. This means that in Fig. 5b, the corneal parameter kcap is varied, and for the respective value of kcap in the undeformed state, the effect of the corneal deformation on the other corneal parameters, which in this case are the same as in Fig. 5a, is stored. Returning to the process diagram of Fig. 2, after determining the effect of the deformation in step S10 (illustrated in Figs. 5a and 5b), step S12 can determine the most important corneal parameters for treatment and / or deformation of the cornea 26 by identifying those corneal parameters that have the greatest effect from the deformation. In this example, the corneal deformation can be caused by the contact element 28, and the treatment can be a refractive correction of the cornea 26. From the effects of the deformation determined in step S10, for example from several tables or graphs, which can be structured similarly to Fig. 5a, Fig. 5b, the most important corneal parameters can be determined.Figure 5b, where additional corneal parameters not shown here are varied, allows us to determine which initially assumed corneal parameters have the greatest effect on the refractive correction due to corneal deformation 26. In this example, the corneal parameters rca and kcap shown in Figures 5a and 5b can have the greatest effect of all corneal parameters on the refractive correction Dpost / Dplan, and it is also possible to determine more than two corneal parameters. For clarity, the example continues below with two corneal parameters (rca, kcap). After determining the most important corneal parameters for treatment and / or deformation, one or more predefined fit functions can be adapted to the values ​​of the determined most important corneal parameters in step S14 to determine a compensation function that can be provided to compensate for the deformation, in particular the refractive correction. As shown in Figs. 5a and 5b, preferably only a finite number of values ​​are determined, in this example five values ​​or support points. The respective fit functions can then be adapted to these values, whereby a polynomial function, in particular a second-order polynomial, can preferably be used as the fit function to obtain the values ​​of the entire parameter range of the respective corneal parameter. In other words, a first polynomial function can be fitted to the values ​​of Dpost / Dplander in Fig. 5a and to the corresponding values ​​of Fig.5b a second polynomial function, where the respective polynomial functions may be the same or different, or a single fit function may be fitted to both functions, in particular a mixed polynomial with two variables. In this example, a first polynomial function for the refractive power correction Dpost / Dplan may have been fitted to Fig. 5a and a second polynomial function to Fig. 5b, whereby the two polynomial functions can be combined to form a compensation function. In particular, the respective polynomial functions / fit functions can be combined as a product or sum in the compensation function, whereby the type of combination may depend on the respective corneal parameter. This compensation function can then be provided to the treatment device 10, in particular the control unit 20, to compensate for the deformation in order to perform a deformation-corrected refractive power correction. Thus, in step S16, a deformation-corrected treatment value can be calculated using the compensation function by inserting preoperative values ​​of the most important corneal parameters into the compensation function, thereby generating the deformation-corrected treatment value. In this example, the deformation-corrected treatment value is the refractive power correction to be determined by the compensation function. To correct the originally planned refractive power correction for the expected deformation, the preoperative values ​​of the most important corneal parameters, which in this example are rca and kcaps, can be determined from predetermined examination data and then inserted into the calculated compensation function.The compensation function thus allows the influence of both the corneal parameter rca and kcap on refractive correction to be compensated for corneal deformation 26, particularly simultaneously, which provides improved deformation correction since the most important corneal parameters are taken into account in the compensation function. Similarly, a compensation function can also be determined for the other corneal parameters Rcap, TZ, and others, taking into account the most important corneal parameters, whereby the deformation can then be compensated for accordingly for these corneal parameters as well. Finally, in step S18, the deformation-corrected treatment values ​​obtained in this way can be provided as control data for the treatment device 10, in particular the control unit 12. Overall, the examples show how a simple and quick compensation of deformation effects can be achieved using the compensation function.

Claims

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, wherein the method comprises the following steps performed by at least one control device (20): - Determining (S10) an effect of a deformation of the cornea (26) on predetermined corneal parameters by means of a corneal deformation model, wherein the corneal deformation model allows the cornea (26) to be modeled in a deformed and undeformed state, wherein, to determine the effect of the deformation, values ​​of several predetermined corneal parameters are varied in the undeformed state of the cornea (26) and the effect of this variation on values ​​of the corneal parameters in the deformed state of the cornea (26) is determined;- Determining (S12) the at least two most important predefined corneal parameters for treatment and / or corneal deformation (26) depending on the magnitude of the determined effect; - Fitting (S14) one or more predefined fit functions to the values ​​of the at least two most important predefined corneal parameters, wherein the one fitted fit function provides a compensation function to compensate for the deformation or the several fitted fit functions are combined to form the compensation function; - Calculating (S16) a deformation-corrected treatment value using the compensation function and preoperative values ​​of the at least two most important predefined corneal parameters; - Providing (S18) the deformation-corrected treatment value as control data for the treatment device (10); - wherein the one or more predefined fit functions are polynomial functions of the form z(x, y) = ax² + b*xy + cy² + dx + ey + f; are, where z(x, y) is a treatment value of a corneal parameter to be deformation-corrected, x and y are values ​​of at least two key predefined corneal parameters to be used as preoperative values ​​in the compensation function, and a, b, c, d, e and f are coefficients obtained by fitting to the values ​​of the key corneal parameters from the corneal deformation model. Method according to claim 1, wherein the corneal deformation model is based on the Euler-Bernoulli beam theory. Method according to one of the preceding claims, wherein, to determine the effect of the deformation, the values ​​of the predetermined corneal parameters are varied within respective predetermined value ranges, wherein the value ranges have respective standard values ​​of the respective corneal parameter. Method according to one of the preceding claims, wherein for the compensation function the adapted fit functions of the at least two most important predetermined corneal parameters are multiplied or summed together. Method according to one of the preceding claims, wherein the compensation function adjusts a planned refractive power correction and / or a planned lenticule diameter. Method according to one of the preceding claims, wherein the compensating function compensates for a deformation of the cornea (26) which is produced by a contact element (28) and / or wherein the compensating function compensates for a deformation of the cornea (26) which is produced when the cornea (26) closes after a lenticule (12) has been removed from the cornea (26). Control device (20) which is configured to perform a method according to any one of claims 1 to 6. Treatment device (10) with at least one ophthalmic surgical laser (18) for the separation of a lenticule (12) with predefined interfaces (14, 16) from a human or animal eye by cavitation bubbles and at least one control device (20) according to claim 7. Treatment device (10) according to claim 8, characterized 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, with 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 device (10) according to claim 8 or 9, characterized in that the control device (20) comprises at least one storage device for at least temporary storage of at least one control data set, wherein the control data set(s) comprise control data for positioning and / or focusing individual laser pulses in the cornea (26); 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 of the laser (18). Computer program comprising commands that cause the control device (20) according to claim 7 to perform the method steps according to any one of claims 1 to 6. Computer-readable medium on which the computer program according to claim 11 is stored.

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