Abstract:
A system and method are provided for simulating a Laser Induced Optical Breakdown (LIOB) protocol to establish a surgical LIOB treatment for a patient. In the system, a library of finite element models characterizing various visual defects in corneas are programmed into a computer. Further, a library of nomograms indicating specific LIOB protocols for correcting respective visual defects are programmed into the computer. As a result, a model and a corresponding nomogram may be selected in view of a patient&#39;s diagnostic information. Further, the selected model may be individualized with the diagnostic information to more precisely characterize the patient&#39;s visual defects. Thereafter, the computer simulates the indicated LIOB protocol on the individualized model in order to achieve a desired corneal configuration. When the desired corneal configuration is achieved, the final treatment plan may be determined.

Description:
[0001]    This application is a continuation-in-part of application Ser. No. 12,016,857, filed Jan. 18, 2008, which is currently pending. The contents of application Ser. No. 12,016,857 are incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention pertains generally to computer simulations. More particularly, the present invention pertains to computer simulations that use a finite element model to predict the reshaping of a cornea in response to Laser Induced Optical Breakdown (LIOB). The present invention is particularly, but not exclusively useful as a system or method for modifying a corneal configuration defined by a finite element model with an LIOB protocol indicated by a nomogram to determine a final LIOB treatment plan for correcting a visual defect. 
       BACKGROUND OF THE INVENTION 
       [0003]    Basically, refractive surgery involves a reshaping of the cornea to correct for optical aberrations. Although such reshaping can be accomplished in several ways, for purposes of the present invention it is envisioned that refractive surgery will be accomplished in accordance with protocols disclosed in the co-pending application for an invention entitled “Method for Intrastromal Refractive Surgery,” which is assigned to the same assignee as the present invention. The contents of this co-pending application are incorporated herein by reference. 
         [0004]    In any surgical procedure, a preliminary diagnostic evaluation of the patient is essential. Moreover, for extremely complicated surgeries such as ophthalmic laser surgery, an accurate evaluation is essential for determining how the surgery should be accomplished. Further, and particularly with ophthalmic surgery, an evaluation helps determine the scope and extent of the surgery that is required. With so many variables involved, however, the ability to predict a surgical outcome with a high level of assurance can be extremely helpful. 
         [0005]    As disclosed in the parent application, from which the present invention is a continuation, the use of a finite element model can be very helpful for predicting the outcome of an ophthalmic laser surgery procedure. Specifically, the finite element model disclosed in this parent application simulates a cornea and its response to a predetermined protocol for Laser Induced Optical Breakdown (LIOB) of stromal tissue in the cornea. 
         [0006]    Every eye is unique and, accordingly, each eye has its own particular anatomical characteristics. Nevertheless, it happens that patients having similar vision defects will also have many similar anatomical characteristics in their respective corneas. Thus, in general, a finite element model may represent a corneal structure that exhibits a particular visual defect. Individualizing the model for a particular patient is then primarily a matter of scaling. 
         [0007]    Further, a history of surgical treatments for a particular visual defect may produce a nomogram that indicates a particular LIOB protocol. Specifically, after performing LIOB on patients having essentially the same visual defect, the LIOB protocols and results may be analyzed and compiled to create a nomogram for future surgeries. The LIOB protocol indicated by this nomogram can be applied with a high degree of reliability for patients outside the group who have the same vision defect. This will be so, even though exact measures of corresponding values may be unknown. The consequence here is that a diagnostic nomogram which is characteristic of a surgical correction for a particular vision defect can be representative of a successful LIOB procedure for each member in an extended group of patients. 
         [0008]    Zernike polynomials that mathematically model corneas having visual defects are given in the general form as: 
         [0000]        W (ρ,θ)=Σ c   nm   Z   nm (ρ,θ,α nm ) 
         [0009]    In the above expression, “n” pertains to the order of the polynomial (i.e. 2 nd  or 3 rd  order aberration) and “m” pertains to frequency (i.e. θ, 2θ, and 3θ). Further, c nm  is a coefficient that pertains to magnitude; and Z nm (ρ,θ,α nm ) depends on radial and azimuthal considerations as they relate to a particular axis (α nm ). 
         [0010]    When considering the human eye as a genuine optical system, aberrations can be generally categorized as being either symmetric or asymmetric with respect to the optical axis of the eye. For this categorization, symmetrical aberrations are radially symmetrical with respect to the optical axis, while the asymmetrical aberrations are not. As indicated by the Zernike polynomials, in addition to their symmetry or lack thereof, the various optical aberrations of the eye can be categorized by their order. Insofar as imaging is concerned, it happens that the so-called lower order aberrations (i.e. 2 nd , 3 rd  and 4 th  order) can be significantly detrimental. These lower order aberrations include both symmetrical and asymmetrical aberrations. 
         [0011]    For purposes of the present invention, an appreciation for the interactive use of a particular model with Zernike polynomials for a finite element model is important. Specifically, it is known that a model can be created which will be representative of the cornea in all patients exhibiting a substantially same vision defect (e.g. presbyopia). Further, it is known that Zernike polynomials can be used to create the model. Using specific measurement values from a particular cornea, the Zernike polynomials can then be scaled to mathematically represent the optical condition of the particular cornea. Importantly, a model having this mathematical representation can then be used with a nomogram in a subsequent LIOB simulation. Further, the continuing modification of the model through LIOB simulation can lead to a desired corneal configuration. As a result, the necessary LIOB protocol to achieve the desired corneal configuration may be identified. 
         [0012]    In light of the above, it is an object of the present invention to create a system and method for simulating a Laser Induced Optical Breakdown (LIOB) protocol to establish a surgical LIOB treatment for a patient. Another object of the present invention is provide a library of various nomograms and associated finite element models corresponding to respective visual defects for selected use in simulating LIOB procedures. Still another object of the present invention is to provide a system and method for simulating an LIOB procedure that is simple to use, easy to implement and cost effective. 
       SUMMARY OF THE INVENTION 
       [0013]    In accordance with the present invention, a system and method are provided for establishing a Laser Induced Optical Breakdown (LIOB) treatment plan for a patient. Specifically, it is envisioned that the system and method will utilize a library that includes a plurality of finite element models and a plurality of nomograms. For optimal performance, the library is installed on a computer to provide for a quick determination of the final treatment plan. 
         [0014]    In the system, each finite element model in the library will characterize a cornea that exhibits a particular vision defect. Typically, the finite element models utilize Zernike polynomials, although other orthogonal polynomials or statistical models may be used. Specifically, a patient&#39;s corneal configuration may be mathematically represented by Zernike polynomials. More particularly, selected Zernike polynomials can be used with selected corneal configurations. For instance: myopia (Z 4 ); hyperopia (Z 4 ); presbyopia (Z 4 ); astigmatism (Z 3  and Z 5 : 2 nd  order); coma (Z 7  and Z 8 : 3 rd  order); trefoil (Z 6  and Z 9 : 3 rd  order) and spherical aberrations (Z 12 : 4 th  order). It will be appreciated by the skilled artisan that other mathematical representations can be used for this same purpose (e.g. Taylor polynomials or Fourier functions). Also, the present invention envisions the possibility that models other than a finite element model may be used. For instance, a multi-layered, thin shell model, or a model employing analytical estimations of viscoelastic changes may be used. Preferably, however, the present invention envisions a finite element model using Zernike polynomials. 
         [0015]    For purposes of the present invention, the finite element model is preferably of a type disclosed and claimed in the parent application of the present invention. Essentially, the finite element model has a first plurality of elements for simulating biomechanical characteristics for a Bowman&#39;s capsule of a cornea. And, it also has a second plurality of elements for simulating biomechanical characteristics for a stroma of the cornea. As envisioned for the present invention, these various elements will be programmed to replicate the patient&#39;s corneal configuration. 
         [0016]    For the system, each nomogram in the library will specify an LIOB treatment protocol for a particular visual defect. For instance, the library will include separate nomograms for respectively correcting myopia, hyperopia, presbyopia, astigmatism, coma, trefoil, or various common combinations of such visual defects. Typically, each nomogram is compiled by the collection of diagnostic information and surgical plans from many patients (e.g. more than one hundred patients). Specifically, this information is taken from patients having the substantially same vision defect. For example, conditions such as myopia, hyperopia, presbyopia, astigmatism, coma, trefoil, and spherical aberrations will each have a different nomogram. Most importantly, each nomogram is considered representative of a treatment for a corneal configuration for all patients with the particular vision defect. With time, each nomogram can be continuously updated by the subsequent inclusion of additional similar information. 
         [0017]    From the above, it may be understood that each nomogram is associated with a particular visual defect, and each visual defect is associated with a specific corneal configuration. As a result, each model characterizing a particular corneal configuration will correspond to a particular nomogram. Therefore, for Zernike polynomial-based models, both the model and the corresponding nomogram are associated with a same Zernike polynomial. 
         [0018]    In operation, the patient is initially evaluated to identify the visual defect(s) present in the patient&#39;s eye. Further, specific diagnostic information, such as the tensors at predetermined locations in the patient&#39;s cornea, are measured. After the patient is evaluated, a final desired corneal configuration resulting from surgery is determined. Further, a nomogram is selected to obtain the desired corneal configuration. Specifically, the selected nomogram will indicate an LIOB treatment protocol for correcting the visual defect noted by the patient evaluation. Also, a finite element model will be selected in conjunction with the nomogram. Mathematically, the finite element model will establish an initial corneal configuration that characterizes the patient&#39;s cornea. In order to more precisely model the patient&#39;s cornea, the diagnostic information obtained during patient evaluation may be input into the selected model. As a result, the model will define an individualized corneal configuration that more accurately represents the patient&#39;s cornea. 
         [0019]    For the LIOB simulation, the computer has an electronic means for modifying the individualized corneal configuration. Specifically, the individualized corneal configuration is modified in accordance with the LIOB treatment protocol indicated by the selected nomogram. This modification is done to simulate the reshaping of a cornea in response to the indicated LIOB protocol. The computer also includes a means for determining the modified corneal configuration from the finite element model, after simulation of the LIOB protocol has been completed. The computer can then compare the modified corneal configuration with the desired corneal configuration to identify any difference therebetween that may serve as an error signal. If an error signal is present, the LIOB protocol can be appropriately modified in a fractionated process, and a subsequent simulation can be performed. If it is determined that further reduction in the error signal is not attainable, the computer can choose a new finite element model to characterize the modified corneal configuration. Thereafter, further simulation may be performed until the desired corneal configuration is obtained. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0020]    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: 
           [0021]      FIG. 1  is a schematic view of a system for determining a treatment plan for ophthalmic surgery in accordance with the present invention; 
           [0022]      FIG. 2  is a perspective view of a layer of a finite element model in accordance with the present invention; 
           [0023]      FIG. 3  is a cross-sectional view of a plurality of element lines, in a plurality of layers, in the finite element model as seen along the line  3 - 3  in  FIG. 2 ; and 
           [0024]      FIG. 4  is a presentation of patterns in accordance with Zernike polynomials for use with the present invention. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0025]    Referring initially to  FIG. 1 , a system for determining a final treatment plan for ophthalmic surgery is shown and generally designated  10 . As shown in  FIG. 1 , the system  10  includes a library  12  that stores a plurality of finite element models  14  and a plurality of nomograms  16 . For the system  10 , the library  12  may be installed or temporarily input into a computer  18 . 
         [0026]    Mathematically, the models  14  approximate shapes and fractions of shapes that correspond to the structure of a cornea. For purposes of the present invention, the models  14  may use Zernike polynomials, other orthogonal polynomials, or functions resulting from statistical analysis. For each finite element model  14 , a unique number of elements observed in a cornea may be required. Further, each finite element model  14  may have a unique mathematical structure. As a result, any given cornea structure may be represented by a plurality of models  14  that provide varying accuracy in simulating the corneal structure. In any event, the models  14  may approximate aberrations in a cornea. 
         [0027]    In the system  10 , each nomogram  16  indicates an LIOB protocol that is used in ophthalmic surgery to correct a particular visual defect, or a particular group of visual defects. Typically, a nomogram  16  is created after analyzing the results of multiple surgical treatments of an optical condition found in successive patients. For instance, a surgeon may perform ophthalmic surgery on one hundred patients who exhibit a similar optical aberration like astigmatism. Upon analyzing the treatment plans and surgical results for these one hundred patients, the surgeon creates a nomogram  16 . An exemplary nomogram  16  may require a cylindrical cut in the cornea at a specified distance from the optical axis. This nomogram  16  may then be followed during surgery on subsequent patients exhibiting a similar visual defect. 
         [0028]    Because each specific nomogram  16  is associated with a specific visual defect, each nomogram  16  is associated with the structure of a cornea exhibiting that defect. Further, as noted above, a plurality of models  14  approximate shapes and fractions of shapes corresponding to the structure of a specific cornea. Therefore, it may be understood that a specific nomogram  16  corresponds to a model  14  or a specific group of models  14  that may be used to simulate the cornea. 
         [0029]    With this understanding of nomograms  16  and models  14 , the method for determining an ophthalmic surgical treatment plan may be understood. As shown in  FIG. 1 , at action block  20 , a patient is initially examined and diagnostic information about the patient&#39;s visual defects is obtained. 
         [0030]    Specifically, the diagnostic information may include a diagnosis of a visual defect or defects. Further, the diagnostic information may include specified intracorneal biomechanical data, such as tensors, at certain locations in the cornea. As shown in block  22 , a doctor or the computer  18  may select the appropriate nomogram  16  from the library  12  in view of the diagnostic information. Specifically, the selected nomogram  16  indicates an LIOB protocol previously used to correct visual defects similar to those exhibited by the patient. 
         [0031]    As shown in  FIG. 1 , in conjunction with the selection of the nomograms  16 , the computer  18  chooses a model  14  from the library  12  to create an initial corneal configuration representative of the patient&#39;s cornea (block  24 ). After the model  14  is chosen, the specific diagnostic information is entered into the chosen model  14  to individualize the model  14  and form an individualized corneal configuration (block  26 ). Once the chosen model  14  is individualized, the computer  18  determines whether the individualized model  14  can be used in an LIOB simulation. Specifically, the computer  18  must determine whether the individualized model  14  converges at inquiry block  28 . If the individualized model  14  fails to converge, then the computer  18  chooses another model  14  at block  24 , and individualizes it at block  26 . After an individualized model  14  is found to converge at inquiry block  28 , the computer  18  performs an LIOB simulation (action block  30 ). This simulation is performed according to the LIOB treatment protocol indicated by the nomogram  16  selected from the library  12  at block  22 . As a result of the LIOB simulation, the computer  18  predicts the structural effect on the initial corneal configuration to establish a modified corneal configuration (action block  32 ). 
         [0032]    As shown in  FIG. 1 , a desired corneal configuration is determined in view of the patient&#39;s diagnostic information and is stored in the computer  18  (at action block  34 ). In the method of the present invention, the computer  18  compares the desired corneal configuration with the modified corneal configuration at action block  36 . As a result of the comparison at action block  36 , the computer  18  determines whether there is an error signal. Specifically, the computer  18  determines whether there is a non-negligible difference between the desired corneal configuration and the modified corneal configuration (inquiry block  38 ). 
         [0033]    In the initial iteration, or in subsequent iterations in which the error signal (the difference between the modified and final corneal configurations) is reduced, the method moves from inquiry block  38  to action block  40 . At action block  40 , the computer  18  revises the LIOB procedure. Specifically, the computer  18  revises the previously used nomogram  16  in view of the changes in the corneal configuration due to the previous LIOB simulation. For instance, the computer  18  may simply adjust the parameters of the currently used nomogram  16 . Alternatively, the computer  18  may acquire another nomogram  16  from action block  22 , and add a fractionated step or steps from the newly acquired nomogram  16  to the LIOB procedure. After the LIOB procedure is revised, the computer  18  again simulates LIOB at action block  30  to obtain a new modified corneal configuration (at action block  32 ). Thereafter, the configurations are compared at action block  36  to again determine the error signal. 
         [0034]    Still referring to  FIG. 1 , it can be seen that the presence of an error signal at inquiry block  38  leads to inquiry block  42 . At inquiry block  42 , the computer  18  determines whether the error signal is acceptable, i.e., whether the error signal indicates that the LIOB protocol may be revised to further reduce the error signal. In this determination, the limits of the model  14  in use may be identified. Specifically, if the error signal is not reduced from a previous iteration, then the model  14  may not be suitable for continuing the characterization of the modified corneal configuration. Therefore, the inquiry block  42  provides for the computer  18  to select another model  14  at action block  24  to represent the modified corneal configuration. As may be understood, the method will then progress from action block  24  as previously indicated. 
         [0035]    As shown at inquiry block  38 , when the computer  18  finds no error signal, the method causes the finalization of a treatment plan at block  44 . Specifically, the computer  18  compiles all successful procedures simulated at action block  34  to finalize the treatment plan. Further, the computer  18  optimizes the final treatment plan to eliminate redundant or unnecessary procedures during the compilation process. Thereafter, the final treatment plan is identified at action block  46 . 
         [0036]    Referring to  FIGS. 2-3 , a exemplary finite element model is discussed. In  FIG. 2 , a portion of a finite element model, generally designated  50 , is shown in accordance with the present invention. The model  50  includes at least one layer  52 , such as the one shown in  FIG. 2 . Preferably, however, it will include a plurality of layers  52 , as more fully disclosed below. As will be appreciated with reference to  FIG. 2 , the model  50  defines an axis  54 , and each layer  52  of the model  50  is, in part, defined by a plurality of lines  56  that radiate outwardly from the axis  54 . Additionally, the layer  52  is shown with an apex  58 , and the axis  54  is shown perpendicular to the layer  52  at the apex  58 . Further, a plurality of rings  60  are centered on the axis  54 , with each intersection of a line  56  with a ring  60  defining the location of an element  62 . Thus, as shown, the finite element model  50  comprises a plurality of the elements  62 . 
         [0037]      FIG. 3  shows that the model  50  includes a plurality of different layers  52  (the layers  52 ′ and  52 ″ are only exemplary) in the simulated cornea  64 .  FIG. 3  also shows a first plurality  66  of layers  52  having a first group of elements  62  that are pre-programmed to simulate biomechanical characteristics for Bowman&#39;s Capsule in the simulated cornea  64 .  FIG. 3  also shows a second plurality  68  of layers  52  having a second group of elements  62  that are pre-programmed to simulate biomechanical characteristics in the stroma in the simulated cornea  64 . 
         [0038]    By way of example, the finite element model  50  preferably has nine layers  52 . In these nine layers  52 , the first (anterior) plurality  66  of layers  52  and elements  62  comprises three layers  52  that simulate Bowman&#39;s Capsule. The second (posterior) plurality  68  of layers  52  and elements  62  comprises six layers  52  and simulates stromal tissue in the simulated cornea  64 . Additional layers  52  of elements  62 , in each plurality  66  and  68 , are, of course, possible. 
         [0039]    Within the finite element model  50 , each element  62  is three-dimensional. Mathematically, each element  62  is defined by tensors, with respective coefficients corresponding to bio-mechanical stresses and strains. In this case, coefficients for the pre-programmed elements of both the first and second groups are established according to diagnostic corneal data. Also, in line with anatomical consideration, the stress-scaling coefficient for Bowman&#39;s Capsule (C Bowman ) is approximately five times greater than the stress-scaling coefficient for the stroma (C stroma ). 
         [0040]    In greater detail, the finite element model  50  for the present invention 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   ss   +E   cs   +E   2   sc )+ b   fx ( E   2   fc   +E   2   cf   +E   2   fs   +E   2   sf ) 
         [0000]    where: 
         [0041]    I are invariants, 
         [0042]    W is the strain potential (strain-energy function), 
         [0043]    C is stress-scaling coefficient, 
         [0044]    C compr  is bulk modulus (kPa), 
         [0045]    E is strain, 
         [0046]    b ff  is fiber strain exponent, 
         [0047]    b xx  is transverse strain component, and 
         [0048]    b fx  is fiber-transverse shear exponent. 
         [0049]    Referring now to  FIG. 4 , patterns are illustrated in accordance with Zernike polynomials for use with the present invention. As stated above, for the present invention, each finite element model in the library will characterize a cornea that exhibits a particular vision defect. Typically, the finite element models utilize Zernike polynomials. More particularly, selected Zernike polynomials can be used with selected corneal configurations. In  FIG. 4 , certain Zernike polynomials are illustrated. For instance: myopia (Z 4 ); hyperopia (Z 4 ); presbyopia (Z 4 ); astigmatism (Z 3  and Z 5 : 2 nd  order); coma (Z 7  and Z 8 : 3 rd  order); trefoil (Z 6  and Z 9 : 3 rd  order); and spherical aberrations (Z 12 : 4 th  order). 
         [0050]    While the particular System and Method for Simulating an LIOB Protocol to Establish a Treatment Plan for a Patient 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.