Abstract:
A system and method for simulating a corneal reconfiguration in response to laser surgery uses a computer-programmed, biomechanical generalized model. The generalized model has a plurality of elements; with each element being pre-programmed based on diagnostic corneal data obtained from images of respective individual collagen fibers in a cornea. Collectively these pre-programmed elements replicate biomechanical properties of the cornea. In use, designated biomechanical characteristics on a plurality of selected elements are minimized to simulate laser surgery in an actual cornea. A computer then measures the resultant reconfiguration of the cornea model to assess an actual cornea&#39;s response to laser surgery.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention pertains generally to computer models. More particularly, the present invention pertains to models for the cornea of an eye that can be used to predict a corneal response to a predetermined stimulus. The present invention is particularly, but not exclusively, useful as a biomechanical model for a cornea that is defined and based on data pertaining to individual collagen fibers in a cornea. 
       BACKGROUND OF THE INVENTION 
       [0002]    Computer modeling has proven to be a very helpful design tool for many technical endeavors. This is particularly so when complex structures are involved. And more so, when a response of the structure to changes in forces on the structure must be predicted with great accuracy. Such is the case with the cornea of an eye. 
         [0003]    Anatomically, the cornea of an eye is a combination of several (i.e. five) different layers of tissue. Going in a direction from the anterior surface of the cornea toward its posterior surface, these layers are: the epithelium, Bowman&#39;s membrane, stroma, Descemet&#39;s membrane and the endothelium. Importantly, Bowman&#39;s membrane and the stroma structurally constitute more than ninety percent of the cornea, and both these tissues are made of collagen. 
         [0004]    A collagen fiber is a fibrous protein that is abundantly found in the extracellular matrix, tendons and bones of animals. For purposes of modeling the cornea of an eye, they can be mathematically defined in terms of their elasticity, their viscosity, and their respective shape (i.e. length and orientation in the cornea). Further, within the cornea itself, collagen fibers can be classified by “type”. In general, this classification accounts for the fiber&#39;s length, as well as its cross linking bonds with other fibers. This classification also accounts for the density of fibers in a defined volume of tissue. Although more than one “type” of collagen fiber may be present in a given tissue (e.g. the stroma), the predominance of one “type” collagen fiber will give the tissue its basic characteristics. For example, collagen fibers in Bowman&#39;s membrane are classified as “type I” or “type III” fibers. On the other hand, collagen fibers in the stroma will be mostly “type V” and “type VI” fibers. In this example, “type III” fibers are shorter, have more cross linking bonds with other fibers, and are more densely arranged than are either “type V” or “type VI” fibers. Stated differently, with a higher number “type”, a collagen fiber will be longer, have less cross linking bonds with other fibers, and will be less densely arranged. Importantly, these differences can be quantified. 
         [0005]    It is possible to image collagen fibers in the cornea. Specifically, it is known that by using well known second harmonic generation techniques, around one thousand images of a cornea can be obtained within about one minute. These images can then be used to ascertain the length and orientation of as many individual collagen fibers as are needed (e.g. tens of thousands and, possibly, millions). Also, changes in physical properties of the collagen fibers can be observed by taking images of collagen fibers under different pressure conditions in the eye. These observations can then be compared and used to attribute elastic and viscous properties to the particular fibers. The data thus collected for all fibers can then be used as input for a computer model. 
         [0006]    As envisioned for the present invention, all of the data regarding collagen fibers that is collected as indicated above, can be used to define the constituents of a generalized model cornea. At this point it is important to note, there is no need to differentiate specific layers of the cornea (e.g. Bowman&#39;s membrane and the stroma). Instead, tissue distinctions within the cornea are accounted for by data acquired from images of individual collagen fibers, and their arrangements (i.e. their “type”). The generalized model can then be further defined with an anterior surface and a posterior surface using mathematical approximations. Thereafter, standard computer techniques can be employed to ascertain responses of the generalized model to selected stimuli. 
         [0007]    In light of the above, it is an object of the present invention to provide a generalized biomechanical model of a cornea that is based on the physical characteristics of individual collagen fibers. Another object of the present invention is to provide a generalized biomechanical model of a cornea that comprises a substantially uninterrupted, essentially continuous, data presentation of corneal tissue attributes. Yet another object of the present invention is to provide a generalized model of a cornea that is easy to use and comparatively cost effective. 
       SUMMARY OF THE INVENTION 
       [0008]    In accordance with the present invention, a system and method for simulating the reshaping of a cornea requires a generalized model of a cornea and a computer that is electronically connected to the model. Specifically, the computer is connected with the model to selectively stimulate the model and to measure its response to the input stimulus. For the present invention, the model is based on diagnostic data obtained from collagen fibers in the cornea that is being modeled. Both the anterior surface of the model cornea and the posterior surface of the model cornea are based on mathematical approximations. 
         [0009]    In detail, the diagnostic data that is used to create the generalized model cornea is taken from different images of the cornea, and is used to establish biomechanical characteristics for the model. As envisioned for the present invention, these images can be taken by any means known in the pertinent art, such as by second harmonic generation imaging. Further, these images are preferably generated under different pressure conditions. Consequently, individual collagen fibers in these images can be identified, classified and characterized under the influence of a pressure differential. Thus, not only can the length and orientation of individual collagen fibers be determined, their individual responses to the pressure differential can also be observed. This information is then collectively used, along with general characteristics that are attributed to the “type” of fiber, to establish elastic and viscous properties for specific elements in the model. Each element so established corresponds to an individual collagen fiber in the images. 
         [0010]    As indicated above, mathematical approximations are used to define the surfaces for the model cornea. In particular, the anterior surface and the posterior surface for the cornea are modeled by considering an axis perpendicular to the surfaces and passing through respective apexes. The surfaces are further considered as having curvatures that are approximated by a respective conic section. In this case, the conic section for each surface is expressed as: 
         [0000]    
       
         
           
             
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         [0011]    For the above expression, “R” is the radius of curvature of a respective corneal surface, and “e” is the eccentricity of the cornea. 
         [0012]    In its operation, the present invention requires use of a generalized model cornea that is programmed as described above. Specifically, the model cornea has its plurality of elements pre-programmed to respectively simulate biomechanical characteristics of individual collagen fibers in the cornea. The computer can then be used to stimulate the model. For this stimulation, the biomechanical characteristics on selected elements are minimized. Then, the cornea which is reshaped in response to the minimization, is measured and evaluated. Several iterations of this minimization, measuring and evaluation can be accomplished until the response is considered an indication of an accurate and precise outcome. An actual, surgical operation can then be performed, accordingly. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which: 
           [0014]      FIG. 1  is a schematic representation of the interactive components of the present invention; 
           [0015]      FIG. 2  is a perspective view of a cornea (model cornea); 
           [0016]      FIG. 3  is a perspective representation of a plurality of lamellae of collagen fibers; 
           [0017]      FIG. 4  is a representation of a plurality of individual (“type I, III”) collagen fibers, typical of tissue in Bowman&#39;s membrane of a cornea; 
           [0018]      FIG. 5  is a representation of a plurality of individual (“type V, VI”) collagen fibers, typical of tissue in the stroma of a cornea; 
           [0019]      FIG. 6  is a cross section view of a cornea as seen along the line  6 - 6  in  FIG. 2  under different pressure conditions; 
           [0020]      FIG. 7A  shows a collagen fiber with a shape and orientation under a first pressure condition; and 
           [0021]      FIG. 7B  shows the collagen fiber of  FIG. 7A  under a second pressure condition. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0022]    Referring initially to  FIG. 1  a system in accordance with the present invention is shown schematically and is generally designated  10 . In  FIG. 1  it will be seen that the system  10  includes a computer  12  electronically connected to a model  14 . Further,  FIG. 1  indicates that diagnostic data  16  and mathematical approximations  18  are provided as input to the computer  12 . The computer  12  will then use the diagnostic data  16  and the mathematical approximations  18  for the creation of the model  14 . Thereafter, the computer  12  can use the model  14  for purposes of evaluating physical changes to a cornea  20  that may result in response to selected stimuli. 
         [0023]    For purposes of the present invention, a cornea  20  as shown in  FIG. 2  will have an anterior surface  22 , a posterior surface  24  and a periphery  26  that interconnects the surfaces  22  and  24 . Mathematically, the anterior surface  22  and the posterior surface  24  are both considered as being conic sections. For the generalized model  14 , an axis  28  is defined that is perpendicular to the surfaces  22  and  24 , and it passes through respective apexes  30  and  32  of the surfaces  22  and  24 . Thus, as shown in  FIG. 2 , the curvatures of the anterior surface  22  and the posterior surface  24  are approximated by a respective conic section expressed as: 
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         [0024]    In the above expression, the radius of curvature “R” for the anterior surface  22  is approximately 7.86 mm; the radius of curvature “R” for the posterior surface  24  is approximately 6.76 mm; and “e” for the eccentricity of the cornea  20  is 0.32. Collectively, this information is input to the computer  12  as mathematical approximations  18 . 
         [0025]    Corneal tissue between the anterior surface  22  and the posterior surface  24  consists of a plurality of collagen lamellae, such as the exemplary collagen lamellae  34   a  and  34   b  shown in  FIG. 3 . Within each lamella  34  there are a plurality of collagen fibers  36 . And, the collagen fibers  36  will differ from each other, according to the nature of tissue that is involved. For example, with reference to  FIG. 2 , consider a lamella  34  located in Bowman&#39;s membrane of cornea  20 . Also consider a lamella  34 ′ that is located in the stroma of cornea  20 . In this example, the collagen fibers  36  of the lamella  34  (in Bowman&#39;s membrane) will be generally arranged as represented in  FIG. 4 . On the other hand, collagen fibers  36 ′ of the lamella  34 ′ (in the stroma) will be generally arranged as represented in  FIG. 5 . When comparing  FIG. 4  with  FIG. 5  it is to be appreciated that the collagen fibers  36  of lamella  34  shown in  FIG. 4  are shorter, and have more linking bonds with other fibers  36 . Further, they are more densely arranged than are the fibers  36 ′ in the lamella  34 ′ of the stroma shown in  FIG. 5 . In an accepted classification scheme, the fibers  36  in Bowman&#39;s membrane ( FIG. 4 ) are classified as “type I or III.” On the other hand, fibers  36 ′ in the stroma ( FIG. 5 ) are classified as either “type V” or “type VI”. Stated differently, with a higher number “type”, a collagen fiber  36  will be longer, have less cross linking bonds with other fibers  36 , and will be less densely arranged. Importantly, these differences can be quantified. 
         [0026]    Referring now to  FIG. 6 , a representative cross section of the cornea  20  is shown with a superposed cornea  20 ′ to demonstrate a change in configuration of the cornea  20  caused by a pressure differential (represented by the arrow  38 ). More specifically, the cornea  20  is shown responding to normal intraocular pressure in the eye. On the other hand, the cornea  20 ′ shows a response due to an increased pressure (i.e. pressure differential  38 ). The actual pressure differential  38  can be measured and imposed in accordance with known techniques. For purposes of the present invention, this pressure differential  38  affords the opportunity to obtain and evaluate additional information (i.e. mathematical characteristics) pertaining to collagen fibers  36  in the cornea  20 . To do this, images of both the cornea  20  and the cornea  20 ′ are taken from the patient as disclosed above. 
         [0027]    By cross referencing  FIG. 6  with  FIGS. 7A and 7B , the effect that a pressure differential  38  will have on individual collagen fibers  36  in the cornea  20  can be appreciated. For this comparison, the fiber  36  shown in  FIG. 7A  corresponds to the condition for cornea  20  shown in  FIG. 6  (i.e. no pressure differential has yet been imposed on the cornea  20 ). In  FIG. 7B , the fiber  36 ′ (i.e. the same fiber  36  as is shown in  FIG. 7A ) is shown after a pressure differential  38  has been imposed. As indicated above, the configuration of fiber  36  ( FIG. 7A ) and the configuration of fiber  36 ′ ( FIG. 7B ) can each be imaged. These images are then compared and the configuration changes of the fiber  36 / 36 ′ are measured. More specifically, the end coordinates (x 1 y 1 z 1  and x 2 y 2 z 2 ) of fiber  36  can be compared with the end coordinates (x′ 1 y′ 1 z′ 1  and x′ 2 y′ 2 z′ 2 ) of fiber  36 ′. This then provides information needed for calculating the mathematical characteristics that will identify the elasticity and viscosity of the fiber  36 . Additionally, generally known information about the “type” of the fiber  36  (e.g. “type I or III”) can be used to further refine the mathematical characteristics of the fiber  36 . Also, to facilitate programming the computer  12 , it can happen that a group  40  of aligned fibers  36  can be identified (see  FIG. 5 ). If so, each fiber  36  in the group  40  can be given the same mathematical characteristics. This may particularly be possible in the case of fibers  36  in the stroma where the fibers  36  are less dense and more likely to be aligned with other fibers  36 . 
         [0028]    As will be appreciated by the skilled artisan, the mathematical characteristics considered above can be ascertained for tens or hundreds of thousands of different fibers  36 . Collectively, these mathematical characteristics are used to create the diagnostic data  16  that is input to the computer  12 . This diagnostic data  16 , together with the mathematical approximations  18  mentioned above that are used for configuring the anterior surface  22  and the posterior surface  24  of the cornea  20  establish and define the generalized model  14  for the system  10  of the present invention. Further, use of the diagnostic data  16  and the mathematical approximation  18  recognize that the resultant generalized model  14  is axisymmetric and is based on a nonlinearly elastic, slightly compressible, transversely isotropic formulation with an isotropic exponential Lagrangian strain-energy function based on: 
         [0000]        W =½ C ( e   Q −1)+ C   compr ( I   3   InI   3   −I   3 +1) 
         [0000]      and 
         [0000]        Q=b   ff   E   2   ff   +b   xx ( E   2   cc   +E   2   ss   +E   2   cs   +E   2   sc )+ b   fx ( E   2   fc   +E   2   cf   +E   2   fs   +E   2   sf ) 
       Where: 
       [0029]    I are invariants, 
         [0030]    W is the strain potential (strain-energy function), 
         [0031]    C is stress-scaling coefficient, 
         [0032]    C compr  is bulk modulus (kPa), 
         [0033]    E is strain, 
         [0034]    b ff  is fiber strain exponent, 
         [0035]    b xx  is transverse strain component, and 
         [0036]    b fx  is fiber-transverse shear exponent. 
         [0037]    For an operation of the system  10  of the present invention, the computer  12  is programmed to create the generalized model  14 . To do this, the diagnostic data  16  and the mathematical approximations  18  are provided as input to the computer  12 . Once the generalized model  14  has been created, selected elements in the model  14  can then be minimized to stimulate a surgical procedure. In effect, such a minimization of elements mimics a proposed cut, or a number of cuts in the cornea  20  (preferably the stroma). The response of the generalized model  14  can then be evaluated. And, based on the response, additional iterations of the process can be made if needed. In any event, the information obtained from operation of the generalized model  14  can be used for the preparation and conduct of an actual surgical procedure. 
         [0038]    While the particular Generalized Modeling of the Cornea as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.