Method for obtaining the complete shape of the lens from in vivo measurements by optical imaging techniques and method for estimating the intraocular lens position in cataract surgery from the complete shape of the lens

Abstract

The present invention relates to a method for estimating the overall shape of a lens from measurements of the lens taken in vivo by optical imaging techniques, the measurements including a visible portion of the lens, the method comprising the steps of: receiving in vivo measurements of the lens; and determining a non-visible portion of the lens diverging from the in vivo measurements, the determining the non-visible portion of the lens comprising: a) determining the positions of a first plurality of points (3, 61) defining an initial overall shape of the lens; and b) displacing the first plurality of points (3, 61) by a plurality of lengths along a plurality of directions to positions of a second plurality of points (55), the second plurality of points (55) being estimated points of the overall shape of the lens from which the in vivo measurements were taken, the initial overall shape of the lens being obtained from the in vitro measurements and the plurality of lengths being estimated from the in vivo measurements. The present invention also relates to a method for selecting an intraocular lens to be implanted in an eye. The present invention also relates to a data processing system configured to determine the overall shape of the lens.

Description

[Technical Field]

[0001] The present invention is encompassed in the field of ophthalmology, and more particularly relates to providing accurate lens geometric measurements and accurate estimation of intraocular lens position in cataract surgery. [Background technology]

[0002] STATE OF THE ART The main optical elements of the eye are the lens and the cornea. The lens is responsible for the eye's focusing function (accommodation). Therefore, understanding the properties of the lens is important for designing and evaluating solutions for presbyopia and cataracts.

[0003] There are numerous studies, both in vitro and in vivo, on the geometry of the human lens.

[0004] In vivo measurements of the lens are typically performed using Purkinje imaging, Scheimpflug imaging, magnetic resonance imaging (MRI), optical coherence tomography (OCT), etc. These measurements include the radius of curvature of the lens, the lens tilt and angle of deviation, the internal structure and surface tomography of the lens, and their changes with age and accommodation.

[0005] However, because optical imaging only captures information seen through the pupil, it is not possible to directly estimate important parameters such as the equatorial position (EPP), volume (VOL), surface area (SA), or equatorial lens diameter (DIA).

[0006] Few studies have reported on the overall shape of the lens or related interesting parameters such as EPP, VOL, SA, and DIA in vivo. Most of these reports are based on MRI of the lens, which can capture distortion-free images of the entire lens. However, MRI techniques have significantly lower resolution (approximately 20–30 times smaller) and require significantly longer imaging times than optical imaging techniques, making them unsuitable for obtaining parameters with the required accuracy.

[0007] The conventional approach to estimating lens geometric parameters such as VOL, EPP, SA, and DIA from optical imaging techniques is to estimate such parameters by intersecting two parametric surfaces that best fit the available data within the pupil size (PS) of the anterior (AL) and posterior (PL) surfaces of the lens. However, these methods (hereafter referred to as "intersection approaches") result in overestimation of the parameters VOL, SA, and DIA, and underestimation of EPP (anterior shift).

[0008] Other approaches consider the EPP to be a constant value (relative to lens thickness), while others have suggested that the EPP is subject-dependent.

[0009] Patent document WO-A2-2011 / 026068 discloses a method for creating a geometric model of the eye's lens capsule using the radii of curvature of the anterior and posterior lens surfaces and the lens thickness previously determined by Scheimpflug imaging. This method relies on a cross-sectional approach, which suffers from the problems described above.

[0010] Also, patent document US-A-2010 / 121612 discloses a method for characterizing the entire lens surface, including the anterior and posterior hemispheres as well as the equatorial region, as a single continuous mathematical representation. The disclosed method is based on photogrammetry of the image of the ocular tissue, which provides the contour of the entire lens. This is only valid in vitro.

[0011] Therefore, there is a need for a method that provides an estimation of the complete geometry or shape of the lens, particularly in vivo, and / or lens capsule, while at the same time reducing the estimation error with respect to known methods.

[0012] Preoperative estimation of postoperative IOL position (ELP) is a fundamental step in modern IOL power calculations. This is the largest source of error in the calculation (Sources of error in intraocular lens power calculation" Norrby S., Journal of Cataract & Refractive Surgery 2008; 34:368-376). Therefore, any improvement in predicting postoperative IOL position using typical formula or ray tracing-assisted IOL power calculations could provide better IOL power selection and, therefore, refractive and visual outcomes.

[0013] Various preoperative variables have been used to design formulas to predict postoperative IOL position, the so-called estimated lens position (ELP). For example, the widely used SRK / T formula (Development of of the SRK / T intraocular lens implant power calculation formula”, Retzlaff JA, Sanders D, Kraff M, Journal of Cataract & Refractive Surgery 1990;16:333-340) used axial length and anterior angle quantification to predict IOL position and the Heigis formula ("The Haigis formula", Haigis W, In:Shammas HJ (ed). Calculation of intraocular lens power. Thorofare, NJ: Slack Inc. 2004; 5-57) uses axial length and preoperative ACD, or the Olsen formula ("Prediction of the effective postoperative (intraocular lens) anterior chamber depth”, Olsen T, Journal of Cataract & Refractive Surgery 2006; 32:419-424) used a five-variable model, with input parameters being axial length, preoperative ACD, lens thickness, mean corneal radius, and preoperative refractive index. A comprehensive review is available in (Calculation of intraocular lens power: a review”, Olsen T, Acta Ophtalmologica 2007; 85:472-485, Table 5). In most approaches, ELP is estimated from parameters that are unrelated to the shape of the lens. Reports of approaches that use some information about the lens use axial measurements (1-dimensional) or 2-dimensional models / measurements, and do not include the overall shape of the lens, which intuitively seems important for accurately estimating postoperative IOL position (because the IOL is placed within the capsular bag of the lens).

[0014] Patent application US-A1-2017 / 316571 filed by the same applicant discloses a method for estimating the overall shape of an eye lens from measurements of the lens taken in vivo by optical imaging techniques, the measurements consisting of a visible portion of the lens, the method comprising defining a non-visible portion of the lens that is separate from the in vivo measurements and using a geometric model of the lens pre-constructed from the in vitro measurements. US-A1-2017 / 316571 also discloses a method for estimating IOL position from parameters obtained from the quantification of the overall shape of the lens, such as VOL, DIA, EPP or SA.

[0015] Some embodiments of the method disclosed in US-A1-2017 / 316571 rely on estimating the overall shape of the lens by fitting in vivo measurements to a first parametric surface corresponding to the anterior surface of the lens and a second parametric surface corresponding to the posterior surface of the lens. The first and second parametric surfaces are then extrapolated to the range given by the first parameter to define the central region of the lens. Data from a portion of the central region of the lens is then used to define the equatorial region of the lens using a third parametric surface. Thus, the overall shape of the lens can be estimated using multiple parametric surfaces (each representing a different portion of the lens). Several parameters derived from quantifying the overall shape, such as VOL, DIA, SA, or EPP, are used to estimate IOL position. However, further refinements are needed to estimate the overall shape of the lens and to estimate IOL position from the actual overall shape of the lens.

[0016] US7382907B2 discloses segmentation of occluded anatomical structures in medical images. Summary of the Invention

[0017] DESCRIPTION OF THE INVENTION OF THE INVENTION) In accordance with the present invention, a method is provided for estimating the overall shape of the eye's lens, where this shape is estimated using measurements obtained by optical imaging techniques such as optical coherence tomography (OCT).

[0018] Examples of applications of this method include assisting in the design of custom intraocular lenses (IOLs), predicting the estimated lens position of an IOL to be implanted in the eye, assisting in the sizing of an accommodative IOL to be implanted in the eye, and supporting prospective surgical techniques to counteract the effects of presbyopia, such as lens refill-based surgical techniques (e.g., the Phaco-Ehrsatz technique). Another use of this method is to aid in understanding the changes the lens undergoes during infancy and childhood. Understanding these changes may provide insight into their relationship to refractive correction and their potential implications for the development of refractive errors. At the same time, this method has the advantage of being applicable to noninvasive optical imaging.

[0019] One aspect of the present invention relates to a method for estimating the overall shape of an eye lens, i.e., the shape of all of the laminae that define the contour of the eye lens. The overall shape of an eye lens is therefore the shape defined by all of the constituent parts of the laminae. The overall shape is estimated from measurements of the lens obtained in vivo using optical imaging techniques, which consist of the visible portion of the lens. The lens measurements obtained using optical imaging techniques are obtained in vivo and therefore relate only to those portions of the lens, the central anterior and central posterior, that are visible through the pupil of the eye. These in vivo measurements are advantageous for optimizing the performance of state-of-the-art cataract surgery, as they enable the construction of patient-specific eye models to predict the best IOL to be implanted in a given patient. The optical imaging techniques used in the disclosed methods can be one or more of Purkinje or Scheimpflug imaging techniques, or optical coherence tomography (OCT).

[0020] The method comprises the following steps:

[0021] - receiving, by a data processing system, in vivo measurements of the crystalline lens.

[0022] - determining, by the data processing system, from the in vivo measurements, the non-visible portion of the lens. The non-visible portion is the portion of the lens that is not visible through the pupil of the eye because the iris blocks light. That is, the non-visible portion of the lens is comprised of the portion of the lens that interfaces the measured central anterior portion of the lens with the measured central posterior portion of the lens. This interface is achieved by direct contact between the non-visible portion and the measured central anterior portion of the lens, and also by direct contact between the non-visible portion and the measured central posterior portion of the lens. Thus, the non-visible portion of the lens constitutes the equator of the lens.

[0023] The step of determining the non-visible portion of the crystalline lens comprises:

[0024] a) determining the location of a first plurality of points defining an initial overall shape of the eye's lens;

[0025] b) displacing the first plurality of points by a plurality of lengths along a plurality of directions to the positions of a second plurality of points, the second plurality of points being estimates of the overall shape of the lens for which the in vivo measurements were taken. The initial overall shape of the lens is obtained from the in vitro measurements, and the plurality of lengths are estimated from the in vivo measurements. In this manner, to estimate the overall shape of a particular lens of the eye, it is not necessary to match the first plurality of points to the in vivo measurements; only the plurality of displacement lengths need to be matched to the in vivo measurements. In some of these embodiments, the plurality of directions along which the plurality of lengths are located are constructed from the in vitro measurements and therefore do not need to be matched to the in vivo measurements. This is advantageous because processing resources are not consumed to match the plurality of directions to a particular in vivo measurement.

[0026] In this way, the global shape of the eye lens is estimated by displacing a first plurality of points that define the initial global shape of the eye lens. Thus, the method does not require assigning different geometric functions to different regions of the estimated global shape, and is able to describe the global shape of any lens with a very small number of variables.

[0027] Since the first plurality of points is constructed from in vitro measurements, the initial overall shape of the lens is preferably constructed before taking in vivo measurements.

[0028] In some embodiments, the estimated overall shape and / or in vivo measurements of the lens are in spherical coordinates, which allows for a more accurate reproduction of the natural growth of the lens.

[0029] In some embodiments, the step of displacing the first plurality of points to the positions of the second plurality of points by multiple lengths along multiple directions includes displacing the first plurality of points according to at least one lens deformation pattern, the at least one lens deformation pattern being obtained from in vitro measurements. The overall shape of the lens is thereby estimated by deforming the initial overall shape of the lens. Each lens deformation pattern is a deformation pattern of the overall shape of the lens. That is, each lens deformation pattern is not limited to deforming a specific reduced portion of the overall shape of the lens; different lens deformation patterns can specify details of the same portion of the overall shape. Therefore, the lens deformation patterns can be viewed as functions, and each function represents the overall shape of the lens. Furthermore, since the at least one lens deformation pattern is constructed from in vitro measurements, the at least one lens deformation pattern is suitable for construction prior to in vivo measurements.

[0030] In some embodiments, the at least one deformation pattern comprises a lens deformation pattern that generates an expansion of all points of the overall shape of the lens or a contraction of all points of the overall shape of the lens, which is particularly advantageous for increasing accuracy in estimating the overall shape of the lens.

[0031] In some embodiments, the at least one deformation pattern includes a lens deformation pattern that flattens the anterior and posterior portions of the overall shape of the lens, simultaneously increasing the equatorial diameter of the overall shape of the lens and decreasing the central lens thickness. This deformation pattern can describe the lens's accommodation, in other words, its ability to dynamically change shape to achieve near and far focus. This deformation pattern is particularly advantageous for improving the accuracy of the estimation of the overall shape of the lens.

[0032] In some embodiments, each lens deformation pattern defines a ratio for each pair of points displaced according to the lens deformation pattern, where each ratio is the ratio between the length of displacement of one point of the pair of points and the length of displacement of the other point of the pair of points. In this way, each lens deformation pattern defines a particular relative displacement between each point of the overall shape of the lens, and these relative displacements can be scaled proportionally. Each lens deformation pattern itself can be expressed in terms of the overall shape of the lens.

[0033] In some embodiments, the multiple lengths in step b) are obtained by applying a weighting factor to each of at least one lens deformation pattern. The weighting factor(s) are estimated from in vivo measurements. Thereby, the displacement length of each point of the initial overall shape of the lens is obtained by applying the weighting factor obtained from in vivo measurements to each of at least one lens deformation pattern obtained from in vitro measurements. While in other embodiments, multiple factors may be applied to each lens deformation pattern, the advantage of applying only one factor to each deformation pattern is that the estimation method is simpler and requires fewer processing resources.

[0034] In some embodiments, the step of displacing the first plurality of points is performed according to the following equation, which constitutes a linear combination of at least one lens deformation pattern:

[0035]

number

[0036] where: l is a matrix containing the coordinates of the second plurality of points resulting from the displacement of the first plurality of points.

[0037] l0 is a matrix containing the coordinates of the first plurality of points.

[0038] e k is a matrix defining at least one lens deformation pattern, and e k The matrix defines the displacement of a first plurality of points.

[0039] a k is a k scalar weighting factor for at least one weighting factor.

[0040] K is the total number of lens deformation patterns used to estimate the overall shape of the lens.

[0041] In other embodiments, the step of displacing the first plurality of points is performed according to an equation consisting of a non-linear combination of at least one lens deformation pattern, although an equation consisting of a linear combination of at least one lens deformation pattern rather than a non-linear combination is preferred due to its greater simplicity and ability to obtain an accurate estimate of the overall shape of the lens.

[0042] In certain embodiments, each lens deformation pattern is an eigenvector of the covariance matrix of the residual data, where the residual data is the difference between the overall shape of each lens in the set of in vitro lenses and the mean overall shape of the set of in vitro lenses. In this way, because each lens deformation pattern is an eigenvector, it is possible to determine which lens deformation pattern explains more of the variance in the overall shape of the lenses.

[0043] In some embodiments, each weighting coefficient applied to each lens deformation pattern is estimated from at least one quadratic coefficient, each of which is a coefficient applied to a deformation pattern of a central anterior and a central posterior portion of the overall shape of the eye's lens. The at least one quadratic coefficient, when applied to at least one of the central anterior and central posterior deformation patterns, results in a deformation of the central anterior and central posterior portions that allows for the estimation of the shapes of the central anterior and central posterior portions of the in vivo measured lens. In these embodiments, the method includes calculating at least one quadratic coefficient to be applied to the deformation pattern of the central anterior and central posterior portions of the overall shape of the lens. The at least one deformation pattern of the central anterior and central posterior portions is obtained from in vitro measurements, and the at least one quadratic coefficient is calculated from in vivo measurements. This method of estimating the overall shape of the lens can be viewed as estimating the overall shape of the lens from estimates of the central anterior and central posterior portions of the lens that are visible through the pupil.

[0044] In this disclosure, the expression "weighting factor" refers to the weighting factor of the deformation pattern of the lens, unless it is explicitly stated that it is the weighting factor of the deformation pattern of the anterior and posterior parts of the overall shape of the lens. For simplicity, in this disclosure, the weighting factor of the deformation pattern of the anterior and posterior parts of the overall shape of the lens is referred to as the "second order factor."

[0045] In some embodiments, the method further includes estimating at least one weighting factor of the lens deformation pattern as a function of estimated geometric parameters of the lens measured in vivo. The estimated geometric parameters are estimated from the in vivo measurements. Furthermore, the geometric parameters are characteristic geometric parameters of the lens shape, such as the lens thickness, the radius of curvature of the anterior surface of the lens, the radius of curvature of the posterior surface of the lens, or Zernike coefficients describing the surface of the lens. This allows an estimate of the overall shape of the lens to be obtained from the characteristic geometric parameters of the lens shape.

[0046] For example, the relationship between the at least one weighting coefficient and the geometric parameters can be obtained by applying multiple linear regression using the least squares method with the at least one weighting coefficient as a dependent variable and the geometric parameters as independent variables.

[0047]

number

[0048] where: RAL is the radius of curvature of the anterior surface of the lens.

[0049] RPL is the radius of curvature of the posterior surface of the lens.

[0050] In this way, the overall shape of the lens can be estimated from at least one weighting factor, which is obtained from commonly measured parameters of the lens, such as RAL, RPL and lens thickness.

[0051] In some embodiments, the at least one weighting factor comprises three or more weighting factors, in this way, a higher accuracy in estimating the overall shape of the lens can be achieved using only a few weighting factors.

[0052] In some embodiments, the in vivo measured lens volume and / or lens surface area and / or lens diameter and / or lens equatorial position are estimated as a function of at least one weighting factor. The methods of the present invention can be advantageously used to obtain a preoperative estimate of lens volume (VOL), which is of great value in novel treatments for presbyopia. In particular, knowledge of lens volume is crucial in lens refilling techniques, where the degree of capsule filling is crucial to achieving proper refraction and the appropriate amplitude of accommodation. Furthermore, lens volume (VOL) is crucial in the selection of some accommodative intraocular lenses (A-IOLs), and prior knowledge of DIA and VOL enhances refraction predictability and is believed to be crucial for the correct mechanism of action of A-IOLs.

[0053] Another aspect of the present invention relates to a method for selecting an intraocular lens to be implanted in an eye, comprising predicting an estimated lens position of the intraocular lens to be implanted in the eye, the estimated lens position being obtained from an in vivo measured overall shape of the lens, the in vivo measured overall shape of the lens being estimated using the method according to the first aspect of the present invention. This is advantageous in that the estimated lens position can be predicted preoperatively, i.e., the estimated lens position can be predicted from a preoperatively estimated overall shape of the lens. Having an accurate estimate of the overall shape of the lens leads to a better selection of the IOL (intraocular lens) power of the lens to be implanted in cataract surgery. The IOL power can be calculated based on ray tracing or an IOL power calculation formula.

[0054] In some embodiments, the estimated lens position of the eye implantable lens is obtained using the following formula:

[0055]

number

[0056] where ELP is the estimated lens position.

[0057] a k is the k scalar weighting factor for at least one weighting factor.

[0058] C k is the weighting coefficient a k is the k positioning weighting factor multiplied by

[0059] C0 is the bias term.

[0060] In this way, an estimate of the position of the lens that has not yet been implanted in the eye can be obtained from at least one weighting factor.

[0061] For example, the positioning weight coefficient C kand the bias term C0 can be obtained by applying multiple linear regression with the least squares method, where ELP is the dependent variable and a k is the independent variable. In this way, the ELP can be directly estimated from at least one weighting coefficient that compactly and accurately describes the overall shape of the lens. This could potentially improve the outcome of cataract surgery in which this method of estimating intraocular lens position is used.

[0062] Another aspect of the invention relates to a method for estimating the overall shape of the eye's lens from measurements of the lens obtained by optical imaging techniques, the method comprising:

[0063] a) estimating at least one weighting factor from the measurements;

[0064] b) applying (e.g., multiplying) the lens deformation pattern by a respective at least one weighting factor to obtain a plurality of displacement lengths, where the at least one lens deformation pattern is obtained from an in vitro measurement;

[0065] c) displacing the first plurality of points to the positions of a second plurality of estimated points of the overall shape of the lens by the plurality of displacement lengths obtained in step b).

[0066] The present invention also relates to a data processing system configured to determine the overall shape of a lens of an eye by displacing a first plurality of points to a position of a second plurality of points by a plurality of lengths along a plurality of directions, wherein: The first plurality of points defines an initial overall shape of the eye's lens. The initial overall shape is obtained from in vitro measurements, and The multiple lengths are obtained by applying a weighting factor to each of the at least one lens deformation pattern.

[0067] In this way, the data processing system can be used to generate the overall shape of the lens.

[0068] Using this data processing system, it is possible to simulate various shapes of lenses and evaluate their performance under defined conditions. These simulations can be used to refine the biomechanical model of the lens. This refinement directly aids in the computational modeling of the accommodation process and the design of customized intraocular lenses. Furthermore, this simulation can be used to select a more appropriate intraocular lens to be implanted in the eye. Furthermore, this simulation can be used to more accurately determine the volume of fluid required for a particular lens filling procedure.

[0069] In some embodiments, the data processing system is configured to determine the overall shape of the lens by varying at least one weighting factor while keeping at least one lens deformation pattern constant and while keeping the initial overall shape of the lens constant, which is advantageous because only a few parameters (weighting factors) need to be varied to generate meaningful overall shape changes.

[0070] A further aspect of the present invention relates to a data processing system comprising processing means for carrying out one or more of the methods according to any of the aspects of the invention defined above.

[0071] In some embodiments, the data processing system comprises a processing means for generating a realistic overall shape of the lens, the realistic overall shape of the lens being defined by assigning a value to at least one weighting factor, the value of each of the at least one weighting factor being within a range defined by a minimum and a maximum value obtained from in vitro measurements. Constraining the value of the at least one weighting factor to a specific range obtained from in vitro measurements is advantageous because it makes it possible to ensure that the generated lens is more realistic. In some of these embodiments, the value of each of the at least one factor is within a range defined by a maximum and a minimum value of said weighting factor for a set of in vitro lenses for which in vitro measurements were obtained. These maximum and minimum values ​​are advantageous because they are easily determined when compared to other maximum and minimum values. Other maximum and / or minimum values ​​can generally be obtained, for example, by testing whether higher maximum and lower minimum values ​​result in a realistic overall shape of the lens.

[0072] In some embodiments, the data processing system is used to generate a random overall shape of the eye lens in the aforementioned simulation. The random overall shape of the lens can be defined by assigning a value to at least one weighting factor, the value being randomly taken from a probability distribution selected from a number of predetermined probability distributions. The random values ​​can be further constrained to generate a more realistic overall shape of the lens.

[0073] In some embodiments, the value assigned to at least one weighting factor is randomly taken from a probability distribution selected from a number of predetermined probability distributions, each probability distribution from the number of predetermined probability distributions being for a particular age range. The overall shape of the eye's lens changes as the lens ages, and the specific effects of aging on lens shape, and therefore lens performance, can be assessed by evaluating multiple lenses for particular ages. This allows the probability that a patient has a lens with a particular defect to be determined, thus facilitating an ophthalmologist to determine the lens defect and therefore the most appropriate treatment for treating the defect.

[0074] Another aspect of the invention relates to an optical imaging device comprising a data processing system as defined above.

[0075] It will be apparent to those skilled in the art that the obtained second plurality of points (i.e., the estimated overall shape of the lens) may be represented in an image that can be used for many purposes, such as for display on a screen, for processing the image to obtain relevant measurements of the overall shape of the first lens, for monitoring lens volume to assess the progression of a particular ocular condition (i.e., diabetes, myopia), for selecting an appropriate lens or IOL lens from a database, and / or for manufacturing an IOL lens, etc.

[0076] The different aspects and embodiments of the invention defined above may be combined with each other if they are compatible with each other.

[0077] Additional advantages and features of the present invention will become apparent from the following detailed description and will be particularly pointed out in the appended claims. [Brief explanation of the drawings]

[0078] To complete the description and to provide a better understanding of the invention, a set of drawings are provided. The drawings form an integral part of this specification, illustrate embodiments of the invention, and should not be construed as limiting the scope of the invention, but merely as examples of how the invention can be practiced. The drawings consist of the following figures: [Figure 1A] This is the first example of a B-scan of the crystalline lens. [Figure 1B] A second example of a B-scan of the crystalline lens. [Figure 2] 1 illustrates a schematic diagram of an exemplary method for obtaining a three-dimensional digital model of the overall shape of a lens from a B-scan of the lens. [Figure 3] 1 is an example of the average overall shape of a crystalline lens. [Figure 4] FIG. 1 illustrates the overall shape of a particular lens minus the average overall shape. [Figure 5A1] FIG. 10 illustrates a first embodiment of a first lens deformation pattern. [Figure 5A2] FIG. 10 illustrates a second embodiment of a first lens deformation pattern. [Figure 5B1] FIG. 10 illustrates a first embodiment of a second lens deformation pattern. [Figure 5B2] FIG. 10 illustrates a second embodiment of a second lens deformation pattern. [Figure 5C1] FIG. 10 illustrates a first embodiment of a third lens deformation pattern. [Figure 5C2] FIG. 10 illustrates a second embodiment of a third lens deformation pattern. [Figure 5D1] FIG. 10 illustrates a first embodiment of a fourth lens deformation pattern. [Figure 5D2] FIG. 10 illustrates a second embodiment of a fourth lens deformation pattern. [Figure 5E1] FIG. 10 illustrates a first embodiment of a fifth lens deformation pattern. [Figure 5E2] FIG. 10 illustrates a second embodiment of a fifth lens deformation pattern. [Figure 6A1]1A-1C are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, a first perspective view of three overall shapes of the lens. [Figure 6A2] 1A-1C are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, a second perspective view of three overall shapes of the lens. [Figure 6A3] 1A and 1B are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, front views of lenses with three overall shapes. [Figure 6A4] 1A and 1B are diagrams showing how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, plan views of lenses with three overall shapes. [Figure 6A5] 1A-1C are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, bottom views of lenses with three overall shapes. [Figure 6A6] 1A-1C are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, and more specifically, rear views of lenses with three overall shapes. [Figure 6A7] 1A and 1B are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, more specifically, right side views of lenses with three overall shapes. [Figure 6A8] 1A and 1B are diagrams illustrating how a first lens deformation pattern deforms the overall shape of the lens, more specifically, left side views of lenses with three overall shapes. [Figure 6B1] FIG. 10 is a diagram illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, a first perspective view of the overall shape of three lenses. [Figure 6B2] FIG. 10 is a diagram illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, a second perspective view of the overall shape of the three lenses. [Figure 6B3] 10A-10C are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, front views of lenses with three overall shapes. [Figure 6B4] 10A and 10B are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, and more specifically, plan views of lenses with three overall shapes. [Figure 6B5] 10A-10C are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, bottom views of the lens in three overall shapes. [Figure 6B6] 10A-10C are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, rear views of the lens in three overall shapes. [Figure 6B7] 10A-10C are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, right side views of the lens in three overall shapes. [Figure 6B8] 10A and 10B are diagrams illustrating how a second lens deformation pattern deforms the overall shape of the lens, more specifically, left side views of lenses with three overall shapes. [Figure 6C1] 10A and 10B are diagrams illustrating how a third lens deformation pattern deforms the overall shape of the lens, more specifically, first perspective views of three overall shapes of the lens. [Figure 6C2] 10A and 10B are diagrams illustrating how a third lens deformation pattern deforms the overall shape of the lens, and more specifically, second perspective views of the three overall shapes of the lens. [Figure 6C3] 10A-10C are diagrams illustrating how a third lens deformation pattern deforms the overall shape of the lens, more specifically, side views of three overall shapes of the lens. [Figure 6D1] 10A and 10B are diagrams illustrating how a fourth lens deformation pattern deforms the overall shape of the lens, and more specifically, first perspective views of three overall shapes of the lens. [Figure 6D2] 10A and 10B are diagrams illustrating how a fourth lens deformation pattern deforms the overall shape of the lens, and more specifically, second perspective views of three overall shapes of the lens. [Figure 6E1] 10A-10C are diagrams illustrating how a fifth lens deformation pattern deforms the overall shape of the lens, more specifically, a first perspective view of the lens in three overall shapes. [Figure 6E2] 10A and 10B are diagrams illustrating how a fifth lens deformation pattern deforms the overall shape of the lens, and more specifically, second perspective views of the three overall shapes of the lens. [Figure 6E3] 10A and 10B are diagrams illustrating how a fifth lens deformation pattern deforms the overall shape of the lens, more specifically, side views of the lens in three overall shapes. [Figure 6F1] FIG. 10 is a diagram illustrating how a sixth lens deformation pattern deforms the overall shape of the lens, more specifically, a first perspective view of three overall shapes of the lens. [Figure 6F2] FIG. 10 is a diagram illustrating how the fifth lens deformation pattern deforms the overall shape of the lens, more specifically, a second perspective view of the three overall shapes of the lens. [Figure 6F3] 10A-10C are diagrams illustrating how a fifth lens deformation pattern deforms the overall shape of the lens, more specifically, side views of three overall shapes of the lens. [Figure 7] 1 is a graph showing the arithmetic mean and standard deviation values ​​of the root mean square error (RMSE) in the overall shape estimation of the lens and the arithmetic mean and standard deviation values ​​of PVar, each value corresponding to a selection of a specific number of lens deformation patterns. [Figure 8] 1 is a graph showing the arithmetic mean and standard deviation values ​​of the root mean square error (RMSE) for global lens shape estimation, where each value corresponds to a specific method for estimating global lens shape, some of which constitute the state of the art. [Figure 9] This image shows a cross section of the anterior segment of the eye, measured in vivo using OCT (optical coherence tomography) technology. [Figure 10A] FIG. 10 is a diagram showing a schematic diagram of obtaining a parameter formula for estimating a weighting coefficient of a deformation pattern of the entire shape of the crystalline lens from the weighting coefficients of the deformation patterns of the anterior and posterior parts of the entire shape of the crystalline lens. [Figure 10B] FIG. 10 is a diagram illustrating the estimation of the overall shape of the crystalline lens from the estimation of the anterior and posterior parts of the overall shape of the crystalline lens. [Figure 11A]Three types of two-dimensional probability distributions of two weighting factors for the lens deformation pattern are shown, each of which is conditional on the lens being a specific age. [Figure 11B] 11B shows the overall shape of a lens randomly generated by sampling the probability distribution shown in FIG. 11A. DETAILED DESCRIPTION OF THE INVENTION

[0079] The following description is not to be taken in a limiting sense, but is made merely for the purpose of illustrating the broad principles of the invention. Embodiments of the invention will now be described, by way of example only, with reference to the above-mentioned drawings.

[0080] In the following, an embodiment of the method for estimating the overall shape of the eye lens according to the present invention is described. This embodiment adheres to the tenets of the Declaration of Helsinki and has been approved by the Institutional Review Boards of CSIC, BST, and LVPEI. This work is part of a series of studies approved by the National Institute of Standards and Technology (NIS) and the National Institutes of Health (NIH).

[0081] A three-dimensional digital model of the overall shape of each of 133 isolated lenses was constructed. The 133 lenses were obtained from 112 human donors. 28 lenses from 24 donors were "Banc" lenses. de Sang i Teixits" commonly known as "BST" (Barcelona, The remaining 105 lenses were isolated from eyes obtained from the BST Eye Bank (Spain). The donor age range was 19-71 years (i.e., y / o), with an arithmetic mean of 48 y / o and a standard deviation of 13 y / o. The remaining 105 lenses were obtained from 88 donors and were classified as "Ramayamma". International Eye Bank at LVPrasad Eye Institute, commonly known as The cells were isolated from eyes obtained from "LVPEI" (Hyderabad, India). The age range of donors at the LVPEI eye bank was 0-56 years, with an arithmetic mean of 26 years and a standard deviation of 14 years.

[0082] The following procedure was performed to separate the lens from the eyeball: After enucleation, the surgeon carefully separated the lens from the eyeball and immediately placed it in a custom-made lens holder on nylon sutures in a cuvette containing a preservative solution. The lens preservative solution at the "BST" eye bank was "DMEM / F-12 The lens preservation solution used at the LVPEI eye bank was BSS, Alcon. The lens holder was advantageous because it prevented contact between the lens and the bottom of the cuvette.

[0083] Initially, 157 lenses were measured, but lenses containing capsular detachments and lenses showing any obvious damage were excluded from further study, leaving 133 lenses.

[0084] The "BST" eye bank's lenses were measured using a custom-developed spectral-domain optical coherence tomography (SD-OCT) system using a superluminescent diode light source with a central wavelength of 840 nm and a full width at half maximum (FWHM) of 50 nm. The axial range was 7 mm in air, with an axial pixel size of 3.4 μm and an axial optical resolution of 6.9 μm in tissue. The acquisition rate was 25,000 A-scans / s, and a 3D digital model of the entire lens shape was constructed from 60 B-scans and 1,668 A-scans per B-scan in a 12x12 mm lateral area of ​​the lens.

[0085] The lenses of the "LVPEI" eye bank were imaged using the commercially available imaging system ENVISU, which uses a superluminescent diode with a central wavelength of 880 nm and a half-width of 40 nm as a light source. Measurements were taken with another SD-OCT system using the R4400 (Bioptigen Inc.). The axial range was 15.18 mm in air, with a pixel size of 7.4 μm in the axial dimension, resulting in an optical resolution of 6.4 μm in tissue in the axial dimension. The acquisition rate was 32,000 A-scans / s, and the 3D digital model of the entire lens shape consisted of 100 B-scans in a 15 x 15 mm lateral area and 600 A-scans per B-scan.

[0086] The lens was aligned with the corresponding OCT system to collect B-scans of the lens's overall shape, with each B-scan encompassing a cross-section of the lens, parallel to a plane containing the anterior and posterior vertices of the lens. The lens was first scanned with its anterior portion facing the OCT system's light beam. Multiple B-scans were taken with the lens in this position relative to the OCT system. Figure 1A shows an example of B-scan A during scanning of a lens with the OCT system, with the anterior portion A1 facing the OCT system's light beam. The light beam emitted from the OCT device's light source approaches the lens from above, as shown in Figure 1A, and enters the lens through the anterior portion A1 of the lens.

[0087] Each lens was then flipped over and scanned with its posterior portion facing the OCT beam. Multiple B-scans were taken with the lens in this position relative to the OCT system. Figure 1B shows an example B-scan P of a lens with its posterior portion P1 facing the OCT system light source while being scanned by the OCT system. The OCT system light source emits a beam of light approaching the lens from the top of Figure 1B, passing through the posterior portion P1 of the lens and entering the lens.

[0088] In addition, each of FIGS. 1A and 1B shows the equatorial plane A4 of the crystalline lens.

[0089] Figure 2 shows a schematic of the main steps for obtaining a 3D digital model of the entire lens shape from B-scans. The main steps for obtaining a 3D digital model are B-scan segmentation (51), distortion correction (52), and deskew and registration (53). B-scan segmentation automatically segmented the entire lens shape in each B-scan using thresholding, a Canny edge detector, morphological operations, and prior knowledge of the measurements. The 3D data consisting of the segmentation of all B-scans was then fitted with Zernike polynomials up to the fourth order, and the segmentation was iteratively refined using the smooth surface defined by the resulting Zernike polynomials. This process was repeated by applying the segmentation to B-scans in three different orientations.

[0090] The fan distortions present on the surface segmented from each B-scan were Fan distortion is caused by the scanning structure and optical system of the SD-OCT system.

[0091] As previously described, the 3D digital model of the entire shape of the lens was constructed by segmenting the B-scans of the entire lens shape measured with the anterior surface A1 facing the OCT beam and the B-scans measured with the posterior surface P1 facing the OCT beam, as shown in Figures 1A and 1B. Specifically, when constructing the 3D digital model of the entire lens shape, measurements of the anterior surface A1 of the entire lens, measured with the anterior surface A1 facing the OCT beam, and measurements of the posterior surface P1 of the entire lens, measured with the posterior surface P1 facing the OCT beam, were integrated. This has the advantage of minimizing changes to the measurements of the anterior surface A1 and posterior surface P1 due to previous optical surface refraction or the lens's gradient refractive index (GRIN).

[0092] Distortion of the 3D digital model of the entire lens due to the presence of the storage solution was corrected by dividing the geometric sagging of the surface by the group refractive index of the storage solution. HEPES no phenol red, GIBCO" and 880nm "BSS, Alcon Laboratories' was 1.345.

[0093] The tilt of the corrected anterior and posterior surfaces of the 3D digital model of the overall shape of the lens was removed, and both surfaces were combined to generate the overall shape of the lens. The anterior and posterior surfaces were then aligned in the same Cartesian coordinate system so that the equatorial centers of the anterior and posterior surfaces of the 3D model coincided on the XY plane. This combination of the anterior and posterior surfaces is shown diagrammatically in step 53 of Figure 2. Next, taking into account the rotation that may occur when the lens is inverted, one surface was rotated relative to the other to maximize their overlap. Z-axis registration was performed by matching the central lens thickness (LT), which was calculated independently using the optical thickness obtained from the OCT scan, the refractive index of the storage medium, and the deformation of the cuvette image. The central lens thickness here is understood to be the thickness from the apex of the anterior lens surface to the apex of the posterior lens surface.

[0094] This resulted in a three-dimensional digital model of the overall shape of each of the 133 lenses. From these models, the positions of a first plurality of points defined by the average value of the overall shapes of the 133 lenses were obtained. To facilitate mathematical operations using the three-dimensional digital models, each model was defined in spherical coordinates using the following procedure.

[0095] Step 1: The origin 0 of the spherical coordinate system of the 3D digital model was located in the lateral direction, i.e., with respect to axes X and Y, at the center of the equator of the 3D digital model of the overall shape of the lens. The origin 0 of the coordinate system was located in the axial direction, i.e., with respect to axis Z, at the midpoint of the central thickness LT of the lens calculated previously.

[0096] Step 2: The location of each segmentation point in the 3D digital model. The segmentation points obtained by segmenting the previous B-scan are defined in spherical coordinates (r, θ, φ) with respect to the origin 0 obtained in the previous step 1, where r is the distance from the segmented point to the origin of coordinate 0, θ is the elevation angle, and φ is the azimuth angle. These coordinates are shown in Figure 3.

[0097] Step 3: The 3D digital model is sampled at 10,000 points, Q = 100 azimuth angles φ j Each is defined as P=100 and the elevation angle θ i Q=100 azimuth angle φ j are uniformly spaced in the interval [-π,π], and P=100 with an elevation angle θ i were uniformly spaced in the interval [-π / 2,π / 2].

[0098] Although this sampling method does not provide evenly spaced points on the spherical surface, it was chosen because it is simpler and the lens deformation patterns obtained with different high-density samplings were observed to be very similar.

[0099] Step 4: For all pairs (θ i ,φ j ),i ∈ [1,…,P],j ∈ [1,…Q], the distance r from the coordinate origin 0 to the surface of the entire shape of the lens θi,φj The positions of the 10,000 sampling points mentioned above were calculated by cubic interpolation from the segment points obtained as a result of the previous B-scan segmentation. This resulted in the following PxQ vector, where each element specifies the position of a point on the 3D model.

[0100]

number

[0101] where l n is a three-dimensional digital model of the overall shape of lens "n" of 133 lenses.

[0102] Step 5: The average lens l (l bar) is calculated by the vector l of the 133 lenses n The average value was calculated.

[0103]

number

[0104] In this manner, an average value of the overall shapes of 133 lenses (hereinafter referred to as the "average lens") was obtained from the in vitro measurements. This average lens established the locations of a first plurality of points defining the initial overall shape of the eye's lens. An exemplary average 3 of the overall shapes of 133 lenses is shown in FIG. 3.

[0105] Then, the residual data Δ of each of the 133 3D digital models of the lens was n The deformation pattern of the lens was obtained from the residual data Δ n As shown in Figure 4, is obtained as the deviation between the 3D digital models of the 133 lenses and the average lens.

[0106]

number

[0107] Figure 4 shows the residual data Δ n This residual data is composed of the distance between point 21 of the three-dimensional digital model of the overall shape 2 of the crystalline lens and point 31 of the average crystalline lens 3. Point 21 of the three-dimensional digital model of the overall shape 2 of the crystalline lens and point 31 of the average crystalline lens 3 are determined by the elevation angle θ i , the intersection of a straight line 4 having an azimuthal angle φi and including the origin 0 of the coordinates with the three-dimensional digital model of the overall shape 2 and the mean lens 3.

[0108] Step 6: The covariance matrix C of the residual data of the 133 3D digital models was calculated and subjected to principal component analysis.

[0109]

number

[0110] The principal components were obtained by solving the following diagonalization problem:

[0111]

number

[0112] where e k is the k principal component, and λ k is the eigenvalue of the k principal component. e k As the k deformation pattern, more specifically as the k lens deformation pattern, the overall shape of the lens is the average lens 3 plus the lens deformation pattern e k can be expressed as a linear combination of

[0113]

number

[0114] where K is the overall shape representation of the lens. i The number of lens deformation patterns used in a lens deformation pattern is at least one, and k is the lens deformation pattern e k This means that a lens must have at least one coefficient a k (k=1,...,K). Therefore, the scalar weighting coefficient a k is sufficient to characterize the overall shape of the crystalline lens, the advantage is that the overall shape of the crystalline lens can be expressed with a smaller amount of data.

[0115] Equation (6) is a second plurality of points l, which are estimates of the overall shape of the lens. iis obtained by displacing a first plurality of points l along a plurality of directions and a plurality of lengths in the plurality of directions, where the plurality of directions and the plurality of lengths are the lens deformation pattern e k a scalar weighting coefficient a k In combination with at least one lens deformation pattern e k The advantage is therefore that, unlike other methods that estimate the overall shape of the lens from measurements made in vivo by optical imaging techniques, the present method estimates the lens deformation pattern e k Once we have obtained, we can finally obtain a smooth and very compact model. This model is compact because it has a small number of weighting coefficients a k The overall shape of the represented lens is smooth because the lens deformation pattern is added to the average lens 3, which is itself smooth, to obtain a lens with a smooth overall shape.

[0116] Furthermore, each lens deformation pattern e k comprises a set of ratios between the length of displacement of the points of the mean lens 3 and the length of displacement of the remaining points of the mean lens 3.

[0117] In addition, this lens deformation pattern e k The estimation of the overall shape of the lens based on the above makes it possible to easily create a three-dimensional digital model of the overall shape of the lens. k is the principal component, and therefore each other lens deformation pattern e k Since the 3D digital model of the overall shape of the lens is perpendicular to the lens, the variations in the lens shape are limited to a small number of lens deformation patterns e k Furthermore, lens deformation patterns are easy to interpret and represent congruent changes in the overall lens shape (e.g., anterior surface, posterior surface, lens thickness), facilitating the interpretation of lens geometric changes due to, for example, age, accommodation, or refraction.

[0118] The principal component with the highest eigenvalue (i.e., the lens deformation pattern e k ) represent the primary ways or modes of variation that the points of the lens's overall shape tend to move together (i.e., how the overall shape changes) across the lens's overall shape relative to the average lens 3. Thus, the principal components can be thought of as the deformation patterns of the lens.

[0119] eigenvalue λ k High lens deformation pattern e k (i.e., the principal component) has a lower eigenvalue for the lens deformation pattern e k Therefore, the eigenvalue λ k The most common lens deformation pattern is e k is the most important mode of change in the overall shape of the lens. The advantage of this is that there are fewer lens deformation patterns e k For example, a very accurate representation can be obtained with a number of 5 or 6 lens deformation patterns e k It allows for very accurate representation and only two lens deformation patterns e k Furthermore, accurate representation can be obtained even with the lens deformation pattern e k Other lens deformation patterns k , and the orthogonality allows different lens deformation patterns to be easily separated, so This is a feature that is suitable for representation.

[0120] Each of FIGS. 6A1 to 6F2 represents a particular lens deformation pattern e according to the following formula: k a scalar weighting coefficient a k 1 shows the change in the average lens 61 produced by two values ​​of σ, namely positive and negative.

[0121]

number

[0122] Two values ​​of each scalar weighting factor are ak =-3σ k and a k =3σ k where σ k is the standard deviation of the coefficients in all lenses of the specific lens k. Since equation (7) is used in FIGS. 6A1 to 6F2, the values ​​a k =0 corresponds to an average lens of 61.

[0123] Lens deformation patterns e of FIGS. 6A1 to 6A8 k is for all lens deformation patterns e k The highest eigenvalue λ k Therefore, the most important and most common lens deformation pattern of the overall shape of the lens across all lenses is e k As shown in FIGS. 6A1 to 6A8, this lens deformation pattern e k changes the size of the overall shape 61 of the crystalline lens. More specifically, the crystalline lens deformation patterns e k causes the expansion of all points of the overall shape of the lens or the contraction of all points of the overall shape of the lens. Also, the weighting coefficient a k By changing the sign of the weighting coefficient a, the type of deformation (i.e., contraction of all points of the overall shape of the lens or expansion of all points of the overall shape of the lens) can be changed, and in the cases shown in FIGS. 6A1 to 6A8, the weighting coefficient a has a positive value. k The contraction is generated by applying

[0124] a k =-3σ k The scalar weighting factor of =-48.5 is used for the lens deformation patterns e of FIGS. k and adding the result to the average lens 61 produces an exemplary overall shape 612 of the lens. k =3σ k The scalar weighting factor of 48.5 is used for the lens deformation patterns e of FIGS. k and adding the result to the average lens 61 produces an exemplary overall shape 611 of the lens.

[0125] Lens deformation patterns e of FIGS. 6A1 to 6A8 k is depicted in FIGS. 5A1 and 5A2 alone, that is, without being attached to any mean lens 3.

[0126] Lens deformation patterns e of FIGS. 6B1 to 6B8 k is the second highest eigenvalue λ among all the lens deformation patterns of FIGS. 6A1 to 6F2. k As shown in Figures 6B1 to 6B8, this lens deformation pattern changes the aspect ratio of the overall shape 61 of the lens, i.e., flattens the anterior and posterior portions of the overall shape of the lens, while increasing the equatorial diameter of the overall shape of the lens and decreasing the central thickness of the lens.

[0127] a k =-3σ k The scalar weighting factor of =-33.1 is used for the lens deformation patterns e of FIGS. k produces an exemplary flattened overall shape 622 of the lens. k =-3σ k The scalar weighting factor of 33.1 is used for the lens deformation patterns e k , produces an exemplary less flattened overall shape 621 of the lens.

[0128] Lens deformation patterns e of FIGS. 6B1 to 6B8 k is depicted in FIGS. 5B1 and 5B2 alone, that is, without being attached to any mean lens 3.

[0129] Lens deformation patterns e of FIGS. 6C1 to 6C3 k The lens deformation patterns of Figs. 6D1 and 6D2 are e k are the third and fourth highest eigenvalues, λ, respectively. k As shown in FIGS. 6C1 to 6C3 and 6D1 to 6D2, these lens deformation patterns e k Each of these asymmetrically changes the overall shape 61 of the average lens.

[0130] Lens deformation patterns e of FIGS. 6C1 to 6C3 k is depicted alone in Figs. 5C1 and 5C2, i.e., without being attached to any mean lens 3. k is depicted in FIGS. 5D1 and 5D2 alone, that is, without being attached to any mean lens 3.

[0131] Lens deformation patterns e of FIGS. 6E1 to 6E3 k and the lens deformation pattern e of Figs. 6F1 to 6F3. k are the fifth and sixth highest eigenvalues, λ, respectively. k As shown in FIGS. 6E1 to 6E3 and 6F1 to 6F3, these lens deformation patterns e k Each of these slightly changes the overall shape of the average lens 61. These changes are related to the asphericity of the cone (conicoid) or the rotationally symmetric Zernike polynomials.

[0132] Lens deformation patterns e of FIGS. 6E1 to 6E3 k is depicted in FIGS. 5E1 and 5E2 alone, that is, without being attached to any mean lens 3.

[0133] Therefore, several lens deformation patterns e k The overall shape of the lens can be accurately defined by the highest eigenvalue λ k Lens deformation pattern with k and, in addition, the average lens 61. The scalar weighting coefficient a k The larger the number of vertices, the higher the precision and accuracy of the estimated overall shape, but the more computation and data memory required, and the less compact the representation.

[0134] Furthermore, each lens deformation pattern e k Other lens deformation patterns k Since it is perpendicular to each lens deformation pattern e kAny other lens deformation pattern e k and therefore a set of scalar weighting coefficients {a k Any lens estimated from} is realistic. That is, it is advantageous to obtain a realistic lens, and each scalar weighting coefficient a k The value of is a maximum value, which is the highest value of the scalar weighting coefficient for any of the 133 lenses, and a k As explained above, 133 lenses were measured ex vivo, and from these measurements, the overall shape and lens deformation pattern of the average lens 3,61 were determined. k is obtained following steps 1 to 6 above.

[0135] Lens deformation pattern e k To evaluate the accuracy of the overall shape estimated from the average lens, 3,61 and therefore the ability to represent the overall shape of lenses different from the 133 lenses, a 10-fold cross-validation was performed, i.e., a training set consisting of N = 120 of the 133 lenses and a test set consisting of the remaining 13 of the 133 lenses, with the test set shifted once each time. In the test step of the 10-fold cross-validation, a scalar weighting coefficient a for each specific lens in the test set was used. k is subtracted from the 3D digital model of the overall shape of a specific lens, resulting in the residual data Δ n Then, the residual data Δ n is the deformation pattern e of the lens obtained in the training set. k (i.e., projected onto the principal components).

[0136] We repeated 100 times the 10-fold cross-validation and averaged the error on the test set to estimate the root mean square error (RMSE). This error is calculated by comparing the overall shape of the actual lens in the test set with the deformation patterns of multiple K lenses.k This is the difference from the estimate using

[0137] Lens deformation patterns in the representation of the overall shape of the lens k To understand the impact of variability in the number K, we analyzed two metrics: the percentage of variance explained by the set of the first K eigenlenses (PVar), and the root mean square error (RMSE) obtained by applying the 10-fold cross-validation described above. We also calculated the standard deviation (STD) of RMSE (across lenses and folds) and PVar (across folds). Note that when PVar=100 or RMSE=0, the overall shape of all test lenses can be represented without error.

[0138] Figure 7 shows the STD, the arithmetic mean of PVar and STD, and the arithmetic mean of RMSE as a function of the number of lens deformation patterns k used to represent the overall shape of the lens. The arithmetic mean of RMSE is represented by points 910-919, and the STD of RMSE is represented by error bars centered on the arithmetic mean of RMSE, where the total length of each error bar is 2 STD. The arithmetic mean of PVAR is represented by dashed line 920, and the STD of PVAR is represented by error bars centered on the arithmetic mean of PVAR, where the total length of each error bar is 2 STD.

[0139] In light of the average RMSE and the average Pvar, the lens deformation pattern e k The method for estimating the overall shape of the lens using the average overall shape of the lens is considered to be accurate. Furthermore, in light of the graph shown in Figure 7, as can be seen from the graph, the RMSE does not decrease significantly (or the PVar does not increase significantly) even when the value of K increases, so we recommend using K=6 as the lens deformation pattern e k can be thought of as the optimal number of

[0140] State-of-the-art representation of the overall shape of the crystalline lens To assess whether the accuracy achieved by the SoA (art:SoA) method was significantly different from the estimation of the overall shape of the lens using K = 6 lens deformation patterns (statistical significance was defined as a p-value less than 0.05), we compared the average RMSE across the test lenses by applying a multiple comparison test with Bonferroni correction. The arithmetic mean and standard deviation were estimated.

[0141] The global shape of the lens is estimated by finding the best spherical fit of the anterior global shape, the posterior global shape, the lens thickness, and the vertex position of the posterior global shape, with the vertex position being given by two parameters, for a total of five parameters.

[0142] The overall shape of the lens was estimated by obtaining the best conicoid fit using a total of seven parameters: the same parameters as in the previous best spherical fit of the SoA method (anterior overall shape, posterior overall shape, lens thickness, and posterior overall shape apex position) plus the asphericity values ​​of the anterior overall shape and posterior overall shape.

[0143] -Zernike approximations of the anterior and posterior surfaces of the global shape of the lens, using 6, 15, and 28 coefficients to estimate the anterior global shape, and 6, 15, and 28 coefficients to estimate the posterior global shape, respectively (total of 12, 30, and 56 coefficients, respectively).

[0144] Figure 8 shows rectangular bars with heights corresponding to the average RMSE values ​​estimated for the overall lens shape representation methods. The average RMSE 71 using the K = 6 lens deformation pattern, which uses a similar number of parameters (i.e., six parameters) compared to the spherical fitting (five parameters) and the conicoid fitting (seven parameters), and fewer parameters than the Zernike approximations Z12. and Z30., is significantly lower than the average RMSE 72 using the spherical fitting SPh., significantly lower than the average RMSE 73 using the conicoid fitting Con., significantly lower than the average RMSE 74 using the Zernike approximation Z12. with 12 coefficients, and significantly lower than the average RMSE 75 using the Zernike approximation Z30. with 30 coefficients. Only the Z56. representation was able to obtain a similar average RMSE 76, but required more parameters (56 parameters instead of six).

[0145] The average RMSE72 of the best sphere fitting Sph. was 2.23 times the average RMSE71 of the K=6 lens deformation patterns. The average RMSE73 of the best conicoid fitting Con. was 2.20 times the average RMSE71 of the K=6 lens deformation patterns. The average RMSE74 of the 12-coefficient Zernike approximation Z12. was 2.39 times the average RMSE71 of the K=6 lens deformation patterns. The average RMSE74 of the 30-coefficient Zernike approximation Z30. was 1.51 times the average RMSE71 of the K=6 lens deformation patterns.

[0146] at least one scalar weighting factor a of the estimated overall shape of the particular in vivo lens; k Measurement of the lens is necessary to obtain the "STATE OF THE ART" and "DESCRIPTION OF THE INVENTION" As described in "FOR THE INVENTION," optical imaging techniques can be used to obtain measurements. FIG. 9 shows an image of the anterior segment 40 of the eye obtained by OCT performed in vivo. FIG. 9 shows the cornea 44, the anterior surface 41 of the eye's lens, and the posterior surface 42 of the lens. Optical imaging techniques performed in vivo do not allow for measurement of the entire shape of the lens that is not visible through the pupil of the eye. These non-visible portions of the lens cannot be measured by optical imaging techniques performed in vivo because the iris 43 blocks light from the optical device used in the optical imaging techniques. Therefore, only the central portions of the anterior segment 41 and the posterior segment 42 of the lens can be measured by optical imaging techniques.

[0147] Lens deformation patterns for estimating the overall shape of the lens under the unfavorable conditions where only the anterior and posterior portions of the lens can be measured. k The suitability of the optics was evaluated by simulating in vivo measurement conditions. Thus, an experiment was conducted in which in vitro measurements of the lens were limited to the central anterior and posterior portions of the lens. Parts of this experiment are shown schematically in Figures 10A and 10B.

[0148] In the experiment, the lens measurements were limited to the anterior central and posterior central portions of the lens as seen through a 5 mm diameter pupil. The experiment was then repeated by limiting the anterior central portion of the lens as seen through a 4 mm diameter pupil and the posterior central portion of the lens. From these lens measurements, the lens deformation pattern e was determined, simulating the in vivo condition. k At least one scalar weighting factor a k To estimate , the following methodology was followed.

[0149] First, the deformation patterns of the anterior and posterior parts of the overall shape of the lens were determined from 133 lenses. These deformation patterns were called lens deformation patterns e k Unlike the above, it simply defines the deformation of the anterior and posterior portions 511 of the overall shape of the crystalline lens, but does not define the deformation of the overall shape of the crystalline lens.

[0150] The lens deformation pattern obtained in steps 1 to 6 k The deformation patterns of the front and rear of the overall shape were obtained using a similar method, but with the following differences.

[0151] In steps 1 to 4, the three-dimensional digital model is not a three-dimensional digital model of the overall shape of the crystalline lens, but a three-dimensional digital model of the anterior and posterior parts 511 of the overall shape of the crystalline lens. Therefore, in step 4, the positions of the points defining only the anterior and posterior parts 511 of the overall shape of the crystalline lens are acquired, rather than the positions of the points defining the overall shape of the crystalline lens.

[0152] In step 5, the average overall shape of the lens is 3,61 Instead of obtaining l (El bar), we obtained the average value of only the anterior and posterior parts of the overall shape of the lens. Also, we obtained the residual data Δ n Instead of acquiring residual data of the entire shape of the lens, residual data of only the anterior and posterior parts 511 of the entire shape of the lens is acquired.

[0153] In step 6, instead of calculating the covariance matrix C of the residual data of the entire lens shape, the covariance matrices of only the anterior and posterior parts 511 of the entire lens shape were calculated. Furthermore, the principal component e k Instead of calculating the principal components of the anterior and posterior parts 511 of the entire shape of the lens, the principal components of the anterior and posterior parts 511 of the entire shape of the lens were calculated. Therefore, the principal components of the anterior and posterior parts 511 of the entire shape of the lens are calculated based on the lens deformation pattern e k a scalar weighting coefficient a k Similarly, the overall shape of the lens can be defined by the scalar weighting coefficients c k can be defined by For simplicity, the scalar weighting coefficients for the anterior and posterior deformation patterns of the entire lens shape are hereinafter referred to as the lens deformation pattern e k a scalar weighting coefficient a k To distinguish it from the above, we will call it the "secondary weighting coefficient."

[0154] Then, for each lens deformation pattern e k a scalar weighting coefficient a k The quadratic coefficient c of the same overall shape of the lens k To estimate the α-value, a set of parametric equations was calculated, as shown in equation (8), which was obtained by applying multiple linear regression by least squares to 133 lenses.

[0155]

number

[0156] In this way, the overall shape of the lens can be estimated from the anterior and posterior parts of the overall shape of the lens. The reason is that the lens deformation pattern e k Weighting coefficient a k The secondary weighting coefficient c k Therefore, the quadratic weighting coefficient c can be estimated by measuring only the anterior and posterior parts 511 of the entire shape of the lens. k Therefore, the overall shape of the crystalline lens can be estimated from measurements of only the anterior and posterior parts 511 and 512 of the crystalline lens. In order to evaluate the suitability of this method for estimating the overall shape of the crystalline lens from measurements of only the anterior and posterior parts, the following experiment shown in Figures 10A and 10B was carried out.

[0157] First, the 133 lenses were divided into a training set consisting of 120 lenses and a test set consisting of 13 lenses. As shown schematically in Figure 10A, the quadratic weighting coefficient c k The lens weighting factor a as a function of k The overall shape 512 of each lens in the training set and the anterior and posterior portions 511 of each lens in the training set were measured to calculate a set of parametric equations 52 that give the quadratic weighting coefficients c k From the weighting factor a kand therefore estimate the overall shape 55 of the lens from the test set.

[0158] The difference between the estimated overall shape of the test lens and the actual overall shape of the test lens was taken to estimate the accuracy of this method of estimating the overall shape of the lens.

[0159] Table 1 shows the quality of the overall shape estimation from the center. The quality is evaluated by the secondary weighting coefficient c k From the adjusted coefficient of determination R 2 and lens deformation pattern e k a scalar weighting coefficient a k This was done by calculating the p-value for the prediction.

[0160] [Table 1]

[0161] Furthermore, the accuracy of the estimated overall shape depends on the actual overall shape of the lens and the deformation pattern of the lens e k The estimated scalar weighting coefficient a k The average RMSE was calculated between the estimated overall shape and the estimated overall shape using the MRI system. The average RMSE for the experiment simulating a 4 mm pupil was RMSE = 0.072 ± 0.023. The average RMSE for the experiment simulating a 5 mm pupil was RMSE = 0.068 ± 0.022.

[0162] This results in an estimated scalar weighting coefficient a kBy obtaining this data, the overall shape of the in vivo lens measured by optical imaging techniques can be estimated with high accuracy. Therefore, this lens shape estimation method is advantageous for customizing solutions for cataracts and presbyopia. For example, it is advantageous for estimating the position of an implantable IOL within the eye. Furthermore, it may be advantageous for promising surgical techniques to counteract the effects of presbyopia. Some examples of these techniques are surgical procedures based on lens refilling and the sizing of accommodative IOLs, whose design is highly dependent on the capsular bag volume and the equatorial diameter of the lens. This method of estimating the overall shape of the lens is advantageous for sizing these accommodative IOLs because the capsule volume and equatorial diameter can be estimated from the estimated overall shape. For example, some accommodative IOLs consist of one or two components, the axial position of which depends on the lens size. Furthermore, this method of estimating the overall shape of the lens is advantageous for some accommodative IOLs that include a shape-changing mechanism that relies on capsular bag contraction or relaxation. In these accommodating IOLs, fluid released from reservoirs located in the haptics, for example, can flow into the central portion of the lens, reshaping it. The reshaping of the central portion of the lens is influenced by the capsular bag. Methods for estimating the overall shape of the lens improve estimation of the capsule shape and, consequently, estimates of reshaping.

[0163] Furthermore, accurate and highly precise estimation of the overall shape of the lens enables the design of an IOL that is more suited to a specific eye, improving the customizability of the IOL.

[0164] Furthermore, since the overall shape of the crystalline lens can be estimated accurately and with high precision, it is useful for investigating changes in the overall shape of the crystalline lens due to aging in the living body, particularly aging during infancy.

[0165] Another advantage is that, to achieve high accuracy, the scalar weighting factor a k The advantage is that less

[0166] Some embodiments of the method according to the present invention include a lens deformation pattern e k a scalar weighting coefficient a k By assigning random values ​​to , it can be applied to generate random realistic overall shapes of eye lenses, for example, as described below, for the random generation of realistic overall shapes of eye lenses for people of a particular age.

[0167] scalar weighting coefficient a k The conditional probability distribution of is given by K |age=A) is given, this probability distribution P(a1,...,a K |age=A) is assumed to be multivariate normal, and the probability distribution P(a1,…,a K The mean vector and covariance matrix of |age=A) were estimated.

[0168] To avoid the constraint of using data from only lenses of a particular age to estimate the mean vector and covariance matrix for a given age, we used all data (i.e., data from the entire shape of the 133 lenses) and weighted all samples with a Gaussian kernel (see below). This Gaussian kernel is a function of the age of interest, A, and each specific sample, age sample It depends on the squared difference between the age of

[0169]

number

[0170] The parameter W controls the width of the Gaussian kernel and was set to 5. The covariance matrix and mean vector were estimated from the weighted data.

[0171] If the probability distribution can be estimated, the probability distribution (a1,...,a K |age=A) and sample the typical lens shape corresponding to the mean vector of the probability distribution, or the "atypical" lens shape, i.e., the scalar weighting coefficient a kThe values ​​of are away from the mean vector, or the overall shape of the lens by randomly sampling the distribution can be obtained to create a lens of a given age A.

[0172] Figure 11A shows the relationship between the three ages P(a1, a2 | age = 60 y / o)113, P(a1,a2|age=30 y / o)112 and P(a1,a2|age=5 Two scalar weighting factors a for y / o)111 k A probability distribution P(a1,…,a K |age=A). A random vector (a1, a2) was obtained from each distribution. Figure 11B shows the overall shape of a lens generated using the obtained vectors (a1, a2). The vector (a1, a2) for the overall shape 121 of a 5-year-old lens was generated from the probability distribution P(a1, a2|age=5) 111. The vector (a1, a2) for the overall shape 122 of a 30-year-old lens was generated from the probability distribution P(a1, a2|age=30) 112. The vector (a1, a2) for the overall shape 123 of a 60-year-old lens was generated from the probability distribution P(a1, a2|age=60) 113.

[0173] This allows us to calculate the realistic overall shape of the eye lens at a specific age A using a probability distribution P(a1,...,a K |age=A). Thus, advantageously, the changes that the overall shape of the lens undergoes with age can be generated by sampling a probability distribution P(a1, ..., a K |age=A), which can be easily estimated. For example, this makes it easier to study the potential impact of changes in the shape of the lens on the development of refractive errors.

[0174] Furthermore, automated construction of realistic lenses is important for building computational models of lens accommodation that are representative of large populations and for virtually testing the effects of treatments or IOL implantation prior to in vivo (or ex vivo) studies.

[0175] In this document, the term "comprise" and its derivatives (such as "comprising") should not be understood in an exclusive sense, i.e., these terms should not be interpreted as excluding the possibility that what is described or defined may include additional elements, steps, etc.

[0176] However, the present invention is clearly not limited to the particular embodiment(s) described herein, but also encompasses all modifications (e.g., in terms of materials, dimensions, choice of components, etc.) that may occur to those skilled in the art within the general scope of the invention as defined in the claims.

Claims

1. 1. A method of estimating the overall shape of a lens from measurements of the lens obtained in vivo by optical imaging techniques, the measurements including a visible portion of the lens, the method comprising: - receiving, by a data processing system, in vivo measurements of said lens; - determining by the data processing system a non-visible portion of the lens that is separated from the in vivo measurements, the step of determining the non-visible portion of the lens comprising: a) determining the locations of a first plurality of points (3, 61) defining an initial overall shape of the lens; b) displacing the first plurality of points (3, 61) by a plurality of lengths along a plurality of directions to positions of a second plurality of points (55), the second plurality of points (55) being points of estimate of the overall shape of the lens at which the in vivo measurements were taken, the initial overall shape of the lens being obtained from in vitro measurements and the plurality of lengths being estimated from the in vivo measurements; Equipped with the step of displacing the first plurality of points (3, 61) by a plurality of lengths along a plurality of directions to the positions of the second plurality of points (55) comprises displacing according to at least one lens deformation pattern (811, 821, 831, 841, 851), the at least one lens deformation pattern (811, 821, 831, 841, 851) being obtained from in vitro measurements; A method wherein each lens deformation pattern (811, 821, 831, 841, 851) defines a ratio for each pair of points to be displaced according to said lens deformation pattern, each ratio being the ratio between the length of displacement of one point of said pair of points and the length of displacement of the other point of said pair of points.

2. 2. The method of claim 1, wherein the multiple lengths of step b) are obtained by applying a weighting factor to each of the at least one lens deformation pattern (811, 821, 831, 841, 851), and at least one weighting factor is estimated from the in-vivo measurement.

3. 3. The method of claim 2, wherein the step of displacing the first plurality of points (3, 61) is performed according to the following equation: [Equation 1] where: l is a matrix containing coordinates of the second plurality of points (55) resulting from displacing the first plurality of points (3, 61); l 0 is a matrix containing the coordinates of the first plurality of points (3, 61), e k is a matrix defining the k lens deformation patterns (811, 821, 831, 841, 851) of the at least one lens deformation pattern, and e k a matrix defining the displacements of the first plurality of points (55); a k is the k scalar weighting factor of the at least one weighting factor, The method, wherein k is the total number of lens deformation patterns (811, 821, 831, 841, 851) used to estimate the overall shape of the lens.

4. 2. The method of claim 1, wherein each lens deformation pattern (811, 821, 831, 841, 851) is an eigenvector of a covariance matrix of residual data, the residual data being the difference between the overall shape (2) of each lens of a set of ex vivo lenses and the average overall shape of the set of ex vivo lenses.

5. 3. The method according to claim 2, wherein each weighting coefficient applied to each lens deformation pattern (811, 821, 831, 841, 851) is estimated from at least one quadratic coefficient, each of which is a coefficient applied to a deformation pattern of a central anterior part (53) and a central posterior part (53) of the overall shape of the lens, said method comprising: - calculating said at least one quadratic coefficient to be applied to the deformation pattern of the central anterior and central posterior parts of the overall shape of the lens, - at least one central anterior and central posterior deformation pattern is obtained from ex vivo measurements; - a method wherein said at least one quadratic coefficient is calculated from in-vivo measurements.

6. 3. The method of claim 2, further comprising the step of estimating the at least one weighting factor as a function of an estimated geometric parameter of the crystalline lens measured in vivo, wherein the estimated geometric parameter is estimated from in vivo measurements, and the geometric parameter is a characteristic geometric parameter of the shape of the crystalline lens, such as the lens thickness, the radius of curvature of the anterior surface of the crystalline lens, the radius of curvature of the posterior surface of the crystalline lens, or a Zernike coefficient describing the surface of the crystalline lens.

7. 3. The method of claim 2, wherein the lens volume and / or lens surface area and / or lens diameter and / or equatorial position are estimated as a function of said at least one weighting factor.

8. 10. A method for selecting an intraocular lens that can be implanted in an eye, comprising predicting an estimated lens position of a lens that can be implanted in the eye, wherein the estimated lens position is obtained from the overall shape of an in vivo measured lens, and the overall shape of the in vivo measured lens is estimated using the method of claim 1.

9. 10. A method for selecting an intraocular lens implantable in an eye, comprising predicting an estimated lens position of a lens implantable in the eye, the estimated lens position being obtained from a global shape of an in vivo measured lens, the global shape of the in vivo measured lens being estimated using the method of claim 2, an estimated lens position of the implantable lens in the eye is obtained using the formula: [Equation 2] where: ELP is the estimated lens position, a k is the k scalar weighting factor of the at least one weighting factor; C k is the k positioning weight coefficient, C 0 is the bias term,method.

10. A data processing system comprising processing means for performing the method of claim 1.

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