Patent Publication Number: US-2019183636-A1

Title: Intraocular lenses having an anterior-biased optical design

Description:
FIELD 
     The present disclosure relates generally ophthalmic lenses and, more particularly, to intraocular lenses having an anterior-biased optical design. 
     BACKGROUND 
     The human eye in its simplest terms functions to provide vision by transmitting light through a clear outer portion called the cornea, and focusing the image by way of a lens onto a retina. The quality of the focused image depends on many factors including the size and shape of the eye, and the transparency of the cornea and lens. When age or disease causes the lens to become less transparent, vision deteriorates because of the diminished light which can be transmitted to the retina. This deficiency in the lens of the eye is medically known as a cataract. An accepted treatment for this condition is surgical removal of the lens and replacement of the lens with an intraocular lens (IOL) 
     An IOL typically includes (1) an optic that corrects the patient&#39;s vision (e.g., typically via refraction or diffraction), and (2) haptics that constitute support structures that hold the optic in place within the patient&#39;s eye (e.g., within capsular bag). In general, a physician selects an IOL for which the optic has the appropriate corrective characteristics for the patient. During the surgical procedure, the surgeon may implant the selected IOL by making an incision in the capsular bag of the patient&#39;s eye (a capsulorhexis) and inserting the IOL through the incision. Typically, the IOL is folded for insertion into the capsular bag via a corneal incision and unfolded once in place within the capsular bag. During unfolding, the haptics may expand such that a portion of each contacts the capsular bag, retaining the IOL in place. 
     Although existing IOLs may function acceptably well in many patients, they also have certain shortcomings. For example, existing IOL may have bi-convex optical designs and may be formed of a material having a refractive index that necessitates anterior surface curvatures in a range known to cause reflections. This phenomenon is sometimes referred to a “glint” or “scary eye.” 
     Accordingly, what is needed is an IOL having an optical design that anterior surface curvatures that reduce the incidence of glint across a large range of powers. 
     SUMMARY 
     In certain embodiments, an ophthalmic lens includes an optic having an anterior surface with an anterior surface radius of curvature (R 1 ) and a posterior surface with a posterior surface radius of curvature (R 2 ). The anterior surface radius of curvature (R 1 ) and the posterior surface radius of curvature (R 2 ) define a shape factor (X) (where X=(R 2 −R 1 )/(R 2 +R 1 )) that is greater than zero. The shape factor (X) corresponds to a curve defining shape factor (X) as a function of lens power (P), the curve monotonically decreasing with increased lens power (P). 
     In certain embodiments, the present disclosure may provide one or more technical advantages. As one example, IOLs having the above-described anterior-biased optical design may reduce the prevalence of “glint,” a phenomenon in which an external observer sees a reflection from an IOL implanted in a patient&#39;s eye. Human eye model simulations have shown that the intensity of the reflection depends on the anterior surface radius of curvature of the IOL, the intensity of the reflection being strongest in a certain range of radii of curvature that more closely match the curvature of the wavefront incident on the IOL (e.g., radii of curvature in the range of 18-40 mm). IOLs having the above-described anterior-biased optical design may result in anterior surface radii of curvature across a broad range of IOL powers that are outside the range known to cause the highest intensity reflections, thereby reducing the prevalence of glint. 
     As another example, IOLs having the above-described anterior-biased optical design may result in a stable effective lens position (ELP) across a broad range of IOL powers due to the fact that the distance between the IOL principal plane and the IOL haptic plane remains substantially constant across the power range. This stability of ELP across the IOL power range may minimize A-constant variation, which may result in better and/or more predictable refractive outcomes. 
     As yet another example, IOLs having the above-described anterior-biased optical design may be less sensitive to misalignment (e.g., decentration and tilt). More particularly, the above described IOLs have a positive shape factor, meaning they have a relatively high anterior surface curvature. The relatively high anterior surface curvature means that light rays incident on and outgoing from the anterior surface have a small average angle from normal directions such that the Gaussian optics formula deviates from Snell&#39;s law by a small amount, decreasing sensitivity to decentration. As a result, IOLs having the above-described anterior-biased optical design may result in better refractive outcomes. 
     As a final example, IOLs having the above-described anterior-biased optical design may reduce the incidence of negative dysphotopsia post-implantation. One reason for the reduction in the incidence of negative dysphotopsia is that the amount of posterior shift of the iris after cataract surgery may be reduced for IOLs having the above-described anterior-biased optical design. Because it is hypothesized that posterior iris shift may result in the patient experiencing negative dysphotopsia due to light hitting or missing different parts of the retina, reducing such shift may reduce the incidence of negative dysphotopsia. Another reason for the reduction in the incidence of negative dysphotopsia is that peripheral rays (rays entering the patient eye at a high incidence angle) that hit an IOL having the above-described anterior-biased optical design may be spread more evenly as compared to IOLs having an equi-convex design (i.e., same anterior and posterior curvatures). This even spreading of peripheral rays may reduce the perception of negative dysphotopsia. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings in which like reference numerals indicate like features and wherein: 
         FIG. 1  illustrates a top view of an exemplary ophthalmic lens, according to certain embodiments of the present disclosure; 
         FIG. 2  illustrates a cross-sectional view of the optic of the exemplary ophthalmic lens depicted in  FIG. 1  (along line A-A of  FIG. 1 ); 
         FIG. 3  illustrates a plot of shape factor (X) versus lens power (P) for an exemplary ophthalmic lens; 
         FIG. 4  illustrates a plot of anterior surface radius of curvature (R 1 ) and posterior surface radius of curvature (R 2 ) versus lens power (P) for an exemplary ophthalmic lens; 
         FIG. 5  illustrates a plot of anterior surface power (P 1 ) and posterior surface power (P 2 ) versus lens power (P) for an exemplary ophthalmic lens; 
         FIG. 6  illustrates a plot of the distance between lens haptic plane and lens principle plane versus lens power (P) for an exemplary ophthalmic lens; and 
         FIG. 7  illustrates a plot of lens power shift versus lens power (P) for an exemplary ophthalmic lens. 
     
    
    
     The skilled person in the art will understand that the drawings, described below, are for illustration purposes only. The drawings are not intended to limit the scope of the applicant&#39;s disclosure in any way. 
     DETAILED DESCRIPTION 
     In general, the present disclosure relates to an IOL having an anterior-biased optical design, the IOL including an optic having an anterior surface with an anterior surface radius of curvature (R 1 ) and a posterior surface with a posterior surface radius of curvature (R 2 ). The anterior surface radius of curvature (R 1 ) and the posterior surface radius of curvature (R 2 ) define a shape factor (X) (where X=(R 2 −R 1 )/(R 2 +R 1 )) that is greater than zero. The shape factor (X) corresponds to a curve defining shape factor (X) as a function of lens power (P), the curve monotonically decreasing with increased lens power (P). 
     An IOL having the above-described anterior-biased optical design may reduce the prevalence of glint by maintaining anterior curvatures across a broad range of IOL powers that are outside a range of curvatures known to cause reflections. Additionally, an IOL having the above-described anterior-biased optical design may result in better and/or more predictable refractive outcomes by (1) providing a substantially constant distance between the IOL principal plane and IOL haptic plane across a broad range of IOL powers, thereby providing stable ELP and reduced A-constant variation across the power range, and (2) reducing sensitivity to misalignment (e.g., decentration and tilt). 
       FIGS. 1-2  illustrate an exemplary ophthalmic lens  100  (referred to below as IOL  100 ) having an optic  102  and a plurality of haptics  104 . In particular,  FIG. 1  illustrates a top view of IOL  100  and  FIG. 2  illustrates a cross-sectional view of the optic  102  of the IOL  100  (along line A-A of  FIG. 1 ). 
     A variety of techniques and materials can be employed to fabricate the IOL  100 . For example, the optic  102  of an IOL  100  can be formed of a variety of biocompatible polymeric materials. Some suitable biocompatible materials include, without limitation, soft acrylic polymeric materials, hydrogel materials, polymethymethacrylate, or polysulfone, or polystyrene-containing copolymeric materials, or other biocompatible materials. By way of example, in one embodiment, the optic  102  may be formed of a soft acrylic hydrophobic copolymer such as those described in U.S. Pat. No. 5,290,892; 5,693,095; 8,449,610; or 8,969,429. The haptics  104  of the IOL  100  can also be formed of suitable biocompatible materials, such as those discussed above. While in some cases, the optic  102  and haptics  104  of an IOL can be fabricated as an integral unit, in other cases they can be formed separately and joined together utilizing techniques known in the art. 
     Optic  102  may include an anterior surface  106 , a posterior surface  108 , an optical axis  110 , and an optic edge  112 . Anterior surface  106  and/or posterior surface  108  may include any suitable surface profiles for correcting a patient&#39;s vision. For example, anterior surface  106  and/or posterior surface  108  may be spheric, aspheric, toric, refractive, diffractive, or any suitable combination thereof. In other words, optic  102  may be one or more of a spheric lens, an aspheric lens, a toric lens, a multifocal lens (refractive or diffractive), an extended depth of focus lens, any suitable combination of the foregoing, or any other suitable type of lens. 
     Anterior surface  106  may have an anterior surface diameter  114  between 4.5 mm and 7.0 mm. In one specific embodiment, anterior surface diameter  114  may be approximately 6 mm. Additionally, anterior surface  106  may comprise a full surface optic, meaning that the optic portion of anterior surface  106  extends to the optic edge  112 . Alternatively, anterior surface  106  may include one or more transition regions (not depicted) between an edge of the optic region of anterior surface  106  and the optic edge  112 . 
     Posterior surface  108  may have a posterior surface diameter  116  between 4.5 mm and 7.0 mm. In one specific embodiment, posterior surface diameter  116  may be approximately 6.15 mm (or may vary, depending on lens power, within a range including 6.15 mm). Additionally, posterior surface  108  may comprise a full surface optic, meaning that the optic portion of posterior surface  108  extends to the optic edge  112 . Alternatively, posterior surface  108  may include one or more transition regions (not depicted) between an edge of the optic region of posterior surface  108  and the optic edge  112 . 
     Optic edge  112  may extend between anterior surface  106  and posterior surface  108  and may comprise one or more curved surfaces, one or more flat surfaces, or any suitable combination thereof. In one specific embodiment, optic edge  112  may comprise a continuously curved surface extending between anterior surface  106  and posterior surface  108 . In such embodiments, the continuously curved surface may not include any tangents parallel to optical axis  110 , which may advantageously reduce the incidence of positive dysphotopsia results, at least in part, from edge glare. 
     In certain embodiments, the thickness at optic edge  112  may be constant across the entire IOL power range (e.g., 6-35 diopters). As a result, a center thickness of IOL  100  (i.e., the thickness along optical axis  110 ) may vary across the IOL power range. As one example, the thickness at optic edge  112  may be approximately 0.25 mm across the entire IOL power range. 
     Haptics  104  may each include a gusset region  118 , an elbow region  120 , and a distal region  122 . Gusset region  118  may extend from the periphery of the optic  102  and may span an angle of the periphery of optic  102  (e.g. an angle greater than or equal to 50 degrees). Elbow region  120  may couple gusset region  118  and distal region  122  and may comprise a portion of the haptic  104  having the minimum width (e.g., between 0.40 mm and 0.65 mm. As a result, elbow region  128  may create a hinge allowing haptic  104  to flex while minimizing buckling and vaulting of optic  102 . Distal region  130  may extend from elbow region  128  and may have a length in the range of 6 mm to 7.5 mm. Although a particular number of haptics  104  having a particular configuration are depicted and described, the present disclosure contemplates that IOL  100  may include any suitable number of haptics  104  having any suitable configuration. 
     In certain embodiments, anterior surface  106  of optic  102  has an anterior surface radius of curvature (R 1 ) and posterior surface  108  of optic  102  has a posterior surface radius of curvature (R 2 ). Additionally, the anterior surface radius of curvature (R 1 ) and the posterior surface radius of curvature (R 2 ) may collectively define a shape factor (X) for the optic  102  as follows: 
     
       
         
           
             
               
                 
                   X 
                   = 
                   
                     
                       
                         R 
                         2 
                       
                       - 
                       
                         R 
                         1 
                       
                     
                     
                       
                         R 
                         2 
                       
                       + 
                       
                         R 
                         1 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     In addition, anterior surface  106  has an anterior surface power (P 1 ) and posterior surface  108  has a posterior surface power (P 2 ), the anterior and posterior surface powers defined as follows: 
     
       
         
           
             
               
                 
                   
                     P 
                     1 
                   
                   = 
                   
                     
                       
                         n 
                         2 
                       
                       - 
                       
                         n 
                         1 
                       
                     
                     
                       R 
                       1 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     2 
                   
                   = 
                   
                     
                       
                         n 
                         1 
                       
                       - 
                       
                         n 
                         2 
                       
                     
                     
                       R 
                       2 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein, 
     n 1  is a refractive index of aqueous humor or a patient&#39;s eye (approximately 1.336); 
     n 2  is a refractive index of the optic  102 ; 
     The refractive index of the optic (n 2 ) may be in a range of 1.42 to 1.7. In certain embodiments, the refractive index of the optic (n 2 ) may be in a range of 1.42 to 1.56. In certain embodiments, the refractive index of the optic (n 2 ) may be approximately 1.498. 
     The shape factor (X) of the optic  102  is greater than zero, meaning that the posterior surface radius of curvature (R 2 ) is greater than the anterior surface radius of curvature (R 2 ) (i.e., the anterior surface curvature is greater than the posterior surface curvature). In certain embodiments, the shape factor (X) falls in the range of 0.20 to 1.0 for IOLs  100  having lens powers (P) in the range of 6 to 35 diopters. 
     In certain embodiments, the shape factor (X) corresponds to a curve defining shape factor (X) as a function of lens power (P), the curve monotonically decreasing with increased lens power (P). Due to manufacturing constraints or other manufacturing considerations, the shape factor (X) may not be equal to the value defined by the curve for a given lens power (P). The shape factor (X), however, may nevertheless be selected to correspond to the curve. For example, the shape factor (X) may correspond to the curve in that, for any given lens power (P), the shape factor (X) does not deviate from the curve by more than 0.2. 
     In certain embodiments, the above-described curve to which the shape factor (X) corresponds in non-linear. For example, the curve may be defined by the following cubic equation: 
         X=X   0   +X   1   P+X   2   P   2   +X   3   P   3   Eq. (4)
 
     wherein X 0 , X 1 , X 2 , and X 3  are constants having values that are real numbers. 
     In certain embodiments, X 0  is in the range of 0.75 to 1.5, X 1  is a negative value in the range of −0.11 to −0.05, X 2  is in the range of 0.0017 to 0.0035, and X 3  is in the range of −0.0.000042 to 0.00002. In certain embodiments, X 0  is approximately 1.068, X 1  is approximately −0.075, X 2  is approximately 0.0025, and X 3  is approximately −0.00003. 
     Given equations (1)-(4), the anterior surface radius of curvature (R 1 ), the posterior surface radius of curvature (R 2 ), the anterior surface power (P 1 ), and the posterior surface power (P 2 ) may be defined as follows: 
     
       
         
           
             
               
                 
                   
                     R 
                     1 
                   
                   = 
                   
                     1 
                     
                       
                         1 
                         
                           R 
                           2 
                         
                       
                       + 
                       
                         P 
                         
                           
                             n 
                             2 
                           
                           - 
                           
                             n 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     R 
                     2 
                   
                   = 
                   
                     
                       2 
                        
                       
                         ( 
                         
                           
                             n 
                             2 
                           
                           - 
                           
                             n 
                             1 
                           
                         
                         ) 
                       
                     
                     
                       P 
                        
                       
                         ( 
                         
                           X 
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     1 
                   
                   = 
                   
                     
                       
                         
                           n 
                           2 
                         
                         - 
                         
                           n 
                           1 
                         
                       
                       
                         R 
                         1 
                       
                     
                     = 
                     
                       
                         P 
                          
                         
                           ( 
                           
                             X 
                             + 
                             1 
                           
                           ) 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     2 
                   
                   = 
                   
                     
                       
                         
                           n 
                           1 
                         
                         - 
                         
                           n 
                           2 
                         
                       
                       
                         R 
                         2 
                       
                     
                     = 
                     
                       
                         
                           P 
                            
                           
                             ( 
                             
                               1 
                               - 
                               X 
                             
                             ) 
                           
                         
                         2 
                       
                       = 
                       
                         P 
                         - 
                         
                           P 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     In embodiments in which the shape factor (X) corresponds to a curve defined by Eq. (4) and X 0  is approximately 1.068, X 1  is approximately −0.075, X 2  is approximately 0.0025, and X 3  is approximately −0.00003, the curve to which the shape factor (X) corresponds is depicted in  FIG. 3 . As noted above, due to manufacturing constraints or other manufacturing considerations, the shape factor (X) may not be equal to the value defined by the depicted curve for all lens powers (P) but may nevertheless be selected to correspond to the curve (e.g., the shape factor (X) may not deviate from the curve by more than 0.2). 
     In embodiments in which optic  102  of IOL  100  has a refractive index of approximately 1.498 and the shape factor (X) corresponds to the curve depicted in  FIG. 3 , the radius of curvature of the anterior surface (R 1 ) and the radius of curvature of the posterior surface (R 2 ) may correspond to the curves depicted in  FIG. 4 . In such embodiments, the anterior surface power (P 1 ) and the posterior surface power (P 2 ) may correspond to the curves depicted in  FIG. 5 . Like the variation in shape factor (X) relative to the desired curve discussed above with regard to  FIG. 3 , manufacturing constraints or other manufacturing considerations may necessitate that, for a given lens power (P), the surface radii and/or powers may not be equal to the curves depicted in  FIGS. 4-5 . The surface radii and/or powers, like the shape factor (X), may nevertheless correspond to the curves in that they do not deviate from the curves by more than a certain amount (e.g., the anterior surface radius of curvature (R 1 ) may not deviate from the curve by more than 2 mm). 
     In certain embodiments, one or both of the anterior surface  106  and the posterior surface may be aspheric. For example, anterior surface  106  may be aspheric, with the deviation from the base curvature (i.e., the above-described curvature of anterior surface  106 ) defined as follows: 
     
       
         
           
             
               
                 
                   sag 
                   = 
                   
                     
                       
                         cr 
                         2 
                       
                       
                         1 
                         + 
                         
                           
                             1 
                             - 
                             
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   k 
                                 
                                 ) 
                               
                                
                               
                                 c 
                                 2 
                               
                                
                               
                                 r 
                                 2 
                               
                             
                           
                         
                       
                     
                     + 
                     
                       
                         a 
                         4 
                       
                        
                       
                         r 
                         4 
                       
                     
                     + 
                     
                       
                         a 
                         6 
                       
                        
                       
                         r 
                         6 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein, 
     r denotes a radial distance from the optical axis  110 ; 
     c denotes a base curvature of the anterior surface  106 ; 
     k denotes a conic constant; 
     a 4  is a fourth order deformation constant; 
     a 6  is a sixth order deformation constant. 
     In certain embodiments, the constants of Eq. (9) (k, a 4 , and a 6 ) may be selected such that a target spherical aberration for IOL  100  is achieved. As one example, the constants of Eq. (9) (k, a 4 , and a 6 ) to achieve a target spherical aberration of 0.2 μm. 
     An IOL  100  having the above-described anterior-biased optical design (e.g., an IOL  100  having shape factors as depicted in  FIG. 3  and anterior and posterior radii of curvature as depicted in  FIG. 4 ) may reduce the prevalence of “glint,” a phenomenon in which an external observer sees a reflection from an IOL implanted in a patient&#39;s eye. Human eye model simulations have shown that the intensity of the reflection depends on the anterior surface radius of curvature of the IOL, the intensity of the reflection being strongest in a certain range of radii of curvature that more closely match the curvature of the wavefront incident on the IOL (e.g., 18-40 mm). An IOL  100  having the above-described anterior-biased optical design may result in anterior surface radii of curvature across a broad range of lens powers (P) (e.g., lens powers (P) in the range of 12 to 35 diopters) that are outside the range known to cause the highest intensity reflections, thereby reducing the prevalence of glint. 
     Additionally, an IOL  100  having the above-described anterior-biased optical design (e.g., an IOL  100  having shape factors (X) corresponding to the curve depicted in  FIG. 3  and anterior/posterior radii of curvature (R 1 /R 2 ) corresponding to the curves depicted in  FIG. 4 ) may result in a stable effective lens position (ELP) across a broad range of IOL powers due to the fact that the distance between the IOL principal plane and the IOL haptic plane (Δ PP , described below) remains substantially constant across the power range. This stability of ELP across the IOL power range may minimize A-constant variation, which may result in better and/or more predictable refractive outcomes 
     The above-described IOL haptic plane may be defined as a distance (IOL HP ) from an apex of the posterior surface as follows: 
     
       
         
           
             
               
                 
                   
                     IOL 
                     HP 
                   
                   = 
                   
                     
                       Sag 
                       OE 
                     
                     + 
                     
                       ET 
                       2 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein, 
     Sag OE  represents a distance between a posterior surface height at the apex of posterior surface  108  and a posterior surface height at the optic edge  112 ; and 
     ET represented the thickness at optic edge  112 . 
     The above-described IOL principal plane may be defined as a distance (IOL PP ) from an apex of the posterior surface as follows: 
     
       
         
           
             
               
                 
                   
                     IOL 
                     PP 
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             n 
                             1 
                           
                            
                           
                             ( 
                             
                               IOL 
                               CT 
                             
                             ) 
                           
                         
                       
                        
                       
                         ( 
                         
                           P 
                           1 
                         
                         ) 
                       
                     
                     
                       
                         n 
                         2 
                       
                        
                       
                         ( 
                         P 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     11 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein, 
     n 1  is a refractive index of aqueous humor or a patient&#39;s eye (approximately 1.336); 
     n 2  is a refractive index of the optic  102 ; 
     IOL CT  is the center thickness of IOL  100 ; 
     P 1  is the anterior surface power; and 
     P is the IOL lens power. 
     Given Eq. (10) and Eq. (11), the distance between the IOL principal plane and the IOL haptic plane (Δ PP ) can be defined as follows: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     PP 
                   
                   = 
                   
                     
                       
                         IOL 
                         HP 
                       
                       + 
                       
                         IOL 
                         PP 
                       
                     
                     = 
                     
                       
                         Sag 
                         OE 
                       
                       + 
                       
                         ET 
                         2 
                       
                       - 
                       
                         
                           
                             
                               n 
                               1 
                             
                              
                             
                               ( 
                               
                                 IOL 
                                 CT 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               P 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             n 
                             1 
                           
                            
                           
                             ( 
                             P 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
     The above-described stability of effective lens position (ELP) is illustrated in  FIG. 6 , which depicts the distance between the IOL haptic plane and IOL principal plane (Δ PP ) versus lens power (P) for an IOL  100  having shape factors (X) and anterior/posterior radii of curvature (R 1 /R 2 ) as depicted in  FIGS. 3 and 4  respectively. This is further illustrated by  FIG. 7 , which illustrates the power shift resulting from the distance between the IOL haptic plane and IOL principal plane (Δ PP ) plotted in  FIG. 6 . Although  FIGS. 6-7  illustrate Δ PP  and corresponding power shift for lenses having shape factors (X) and radii of curvature (R 1 /R 2 ) equal to the curves depicted in  FIGS. 3-4 , the present disclosure contemplates that, due to the above-described deviation of shape factors (X) and radii of curvature (R 1 /R 2 ) from the curves depicted in  FIGS. 3-4  resulting from manufacturing constraints or other manufacturing considerations, there may be corresponding deviation from the curves depicted in  FIGS. 6-7 . 
     In embodiments in which there is deviation from the curve depicted in  FIG. 6  for the reasons discussed above, the amount of acceptable variation in Δ PP  between any two lenses of different lens powers (P) may decrease with increased lens power (P). As just one example, the amount of acceptable variation at various lens powers (P) mat be as follows: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 IOL Power (D) 
                 Range of acceptable variation (mm) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 6 
                 0.29 
               
               
                   
                 10 
                 0.17 
               
               
                   
                 20 
                 0.08 
               
               
                   
                 30 
                 0.05 
               
               
                   
                 34 
                 0.04 
               
               
                   
                   
               
            
           
         
       
     
     Additionally, an IOL  100  having the above-described anterior-biased optical design (e.g., an IOL  100  having shape factors (X) corresponding to the curve depicted in  FIG. 3  and anterior/posterior radii of curvature (R 1 /R 2 ) corresponding to the curves depicted in  FIG. 4 ) may be less sensitive to misalignment (e.g., decentration and tilt). More particularly, the above-described IOLs  100  have a positive shape factor, meaning they have a relatively high anterior surface curvature. The relatively high anterior surface curvature means that light rays incident on and outgoing from the anterior surface have a small average angle from normal directions such that the Gaussian optics formula deviates from Snell&#39;s law by a small amount, decreasing sensitivity to decentration. As a result, IOLs  100  having the above-described anterior-biased optical design may result in better refractive outcomes. 
     Finally, an IOL  100  having the above-described anterior-biased optical design (e.g., an IOL  100  having shape factors (X) as depicted in  FIG. 3  and anterior/posterior radii of curvature (R 1 /R 2 ) as depicted in  FIG. 4 ) may reduce the incidence of negative dysphotopsia post-implantation. One reason for the reduction in the incidence of negative dysphotopsia is that the amount of posterior shift of the iris after cataract surgery may be reduced for IOLs having the above-described anterior-biased optical design. Because it is hypothesized that posterior iris shift may result in the patient experiencing negative dysphotopsia due to light hitting or missing different parts of the retina, reducing such shift may reduce the incidence of negative dysphotopsia. Another reason for the reduction in the incidence of negative dysphotopsia is that peripheral rays (rays entering the patient eye at a high incidence angle) that hit an IOL having the above-described anterior-biased optical design may be spread more evenly as compared to IOLs having an equi-convex design (i.e., same anterior and posterior curvatures). This even spreading of peripheral rays may reduce the perception of negative dysphotopsia. 
     It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems or applications. It will also be appreciated that various presently unforeseen or unanticipated alternatives, modifications, variations or improvements therein may be subsequently made by those skilled in the art which alternatives, variations and improvements are also intended to be encompassed by the following claims.