Methods of Predicting the Post-Operative Position of an IOL and Uses of Such Methods

Abstract

The invention relates to the field of ophthalmic systems and procedures. In particular, the invention relates to the determination of the post-operative position of an intraocular lens (termed “IOL”) in an eye of a patient undergoing lens replacement surgery, which involves determining the position of the existing crystalline lens in the pre-operative eye of the patient and using that information and a single numerical constant to predict the post-operative intraocular lens position. Related methods, and computer programs for performing the methods of the invention, are also disclosed.

Claims

1. A method for predicting the post-operative position of a replacement intraocular lens in an eye of a patient, the method comprising the steps of: (i) measuring the position of the existing crystalline lens in the pre-operative eye of the patient; (ii) measuring the thickness of the crystalline lens in the pre-operative eye of the patient; and (iii) calculating the post-operative position of the intraocular lens relative to the position of the crystalline lens in the pre-operative eye of the patient, as a proportion of the thickness of the crystalline lens in the pre-operative eye of the patient, wherein the proportion is defined by a single numerical constant (C) which is determined by the intraocular lens type.

2. The method according to claim 1 wherein step (i) comprises measuring the axial position of the crystalline lens in the pre-operative eye of the patient.

3. The method according to claim 1 wherein the numerical constant (C) is further determined by the patient type.

4. The method according to claim 1 wherein the numerical constant (C) is further determined by the approach used to implant the intraocular lens in the eye.

5. The method according to claim 1 wherein the numerical constant (C) defines the relationship between the post-operative position of the intraocular lens in the eye of one or more eye-operated individuals, relative to the position and thickness of the crystalline lens in the pre-operative eye of the one or more eye-operated individuals.

6. The method according to claim 1 wherein the numerical constant (C) is calculated using data obtained from the two or more eye-operated individual to whom that intraocular lens type has been implanted into the eye using that implantation approach.

7. The method according to claim 1 wherein the numerical constant (C) defines a fraction of the thickness of the crystalline lens in the pre-operative eye of the two or more eye-operated individuals.

8. The method according to claim 1 wherein the intraocular lens type is adapted for implantation into the capsular bag in the eye.

9. The method according to claim 1 wherein the implantation approach is implantation of the intraocular lens into the capsular bag in the eye.

10. The method according to claim 1 wherein the numerical constant (C) is calculated from data obtained from the two or more eye-operated individuals using the following formula:
C=(IOL.sub.measured−ACD.sub.pre)/LT wherein: IOL.sub.measured is the measured position of the intraocular lens in the eye-operated individual after surgery; ACD.sub.pre is the position of the crystalline lens in the eye of the eye-operated individual before surgery; and LT is the thickness of the crystalline lens in the eye of the eye-operated individual before surgery.

11. The method according to claim 10 wherein IOL.sub.measured is determined by measuring the Anterior Chamber Depth in the eye of the eye-operated individual after surgery.

12. The method according to claim 10 wherein ACD.sub.pre is determined by measuring the Anterior Chamber Depth in the eye of the eye-operated individual before surgery.

13. The method according to claim 10 wherein the numerical constant (C) is an average value obtained from the two or more eye-operated individuals.

14. The method according to claim 1 wherein the numerical constant (C) is between about 0.0 and about 1.0.

15. The method according to claim 1 wherein the numerical constant (C) is about 0.4.

16. The method according to claim 1 wherein step (i) comprises measuring the Anterior Chamber Depth of the pre-operative eye of the patient.

17. The method according to claim 16 wherein measuring the Anterior Chamber Depth of the pre-operative eye of the patient comprises performing an ultrasound technique.

18. The method according to claim 16 wherein measuring the Anterior Chamber Depth of the pre-operative eye of the patient comprises performing an optical technique selected from the group consisting of: visible depth measurement; interferometry; partial interferometry; low coherence interferometry; Scheimpflug imaging; laser interferometry; and laser biometry.

19. The method according to claim 1 wherein measuring the thickness of the crystalline lens in the pre-operative eye of the patient in step (ii) comprises performing an ultrasound technique.

20. The method according to claim 1 wherein measuring the thickness of the crystalline lens in the pre-operative eye of the patient in step (ii) comprises performing laser interferometry or laser biometry.

21. The method according to claim 1 wherein calculating the post-operative position of the intraocular lens in step (iii) comprises executing the formula:
IOL.sub.predicted=ACD.sub.pre+C×LT wherein: IOL.sub.predicted is the predicted post-operative position of the intraocular lens in the eye of the patient; ACD.sub.pre is the pre-operative Anterior Chamber Depth of the eye of the patient; C is a numerical constant, as discussed above; and LT is the thickness of the crystalline lens in the pre-operative eye of the patient.

22. A method for selecting a replacement intraocular lens required to provide a desired optical property in a post-operative eye of a patient, the method comprising the steps of: (a) predicting the post-operative position of a replacement intraocular lens in the eye of the patient using a method as defined in claim 1; (b) calculating the optical properties of the post-operative eye of the patient in which an intraocular lens of known power and geometry is positioned as predicted in step (a); and (c) selecting an intraocular lens having a power and geometry required to provide the desired optical property in the post-operative eye of the patient.

23. The method according to claim 22 wherein step (b) comprises establishing an optical model of the post-operative eye of the patient.

24. The method according to claim 23 wherein establishing an optical model of the post-operative eye of the patient comprises measuring one or more property of the pre-operative eye of the eye of the patient, selected from the group consisting of: the optics of the cornea; the corneal radius; the length of the eye; the axial length; the anterior chamber depth; and the crystalline lens thickness.

25. The method according to claim 23 wherein step (b) further comprises analysing the optical properties of the optical model of the post-operative eye of the patient.

26. The method according to claim 25 wherein analysing the optical properties of the optical model of the post-operative eye of the patient comprises performing an exact ray tracing analysis.

27. The method according to claim 25 wherein analysing the optical properties of the optical model of the post-operative eye of the patient comprises performing a paraxial ray tracing analysis.

28. A method for designing a replacement intraocular lens required to provide a desired optical property in the post-operative eye of the patient, the method comprising the steps of: (a1) predicting the post-operative position of an intraocular lens in the eye of the patient using a method as defined in claim 1; (b1) calculating the optical properties of the post-operative eye of the patient in which an intraocular lens of known power and geometry is positioned as predicted in step (a); and (c1) designing an intraocular lens having a power and geometry required to provide the desired optical property in the post-operative eye of the patient.

29. The method according to claim 28 wherein step (b1) comprises establishing an optical model of the post-operative eye of the patient.

30. The method according to claim 29 wherein establishing an optical model of the post-operative eye of the patient comprises measuring one or more property of the pre-operative eye of the eye of the patient, selected from the group consisting of: the optics of the cornea; the corneal radius; the length of the eye; the axial length; the anterior chamber depth; and the crystalline lens thickness.

31. The method according to claim 29 wherein step (b1) further comprises analysing the optical properties of the optical model of the post-operative eye of the patient.

32. The method according to claim 31 wherein analysing the optical properties of the optical model of the post-operative eye of the patient comprises performing an exact ray tracing analysis.

33. The method according to claim 32 wherein analysing the optical properties of the optical model of the post-operative eye of the patient comprises performing a paraxial ray tracing analysis.

34-42. (canceled)

43. A computer program for instructing a computer to perform the method defined in claim 1.

44-48. (canceled)

Description

[0317] Preferred, non-limiting examples which embody certain aspects of the invention will now be described, with reference to the following figures:

[0318] FIG. 1—Schematic diagram of the human eye, in which the various anatomical parts and structures are indicated.

[0319] FIG. 2—Model of an eye showing the refraction of light and image formation. The refraction of light through the eye takes place in the cornea (1) and the lens (2) in order to focus light at the retina (3) at the back of the eye. If there is an imbalance between any of the ocular components, the eye will need spectacle-correction to see clearly.

[0320] FIG. 3—An example of an optical scan of a normal, phakic eye performed by the Haag-Streit Lenstar biometer. The position of the normal, crystalline lens is indicated by pointing hands.

[0321] FIG. 4—An example of a post-operative scan of the same eye shown in FIG. 3 one week after surgery with an IOL in place. The position of the IOL is indicated by pointing hands

[0322] FIG. 5—Illustration of the ocular components of the eye before and after surgery.

[0323] FIG. 6—Illustration of the Stiles-Crawford effect.

[0324] FIG. 7—An example of a ray trace of Gullstrand exact schematic eye.

[0325] FIG. 8—Distribution of the x-axis ray intersections (number of rays=1000) for the Gullstrand eye assuming a pupil of 3 mm. It is noted that all rays are brought to a focus behind the retina at 24.0 mm. The eye is therefore slightly longsighted (hyperopic).

[0326] FIG. 9—Illustration of the point spread function of the Gullstrand eye at the retina (dark columns) and at the best focus 0.194 mm behind the retina (light columns).

[0327] FIG. 10—Illustration of the effect of pupil size on the refraction predicted for a normal eye of average dimension with a spherical intraocular lens implant

[0328] FIG. 11—The measured intraocular lens position (squares) relative to position of anterior (triangles) and posterior capsule (diamonds) plotted against the axial length (x-axis).

[0329] FIG. 12—The intraocular lens position expressed as fraction of lens thickness plotted against the axial length.

[0330] FIG. 13—The intraocular lens position expressed as fraction of lens thickness plotted against the corneal power by keratometry.

[0331] FIG. 14—The observed refraction plotted against the expected (predicted) refraction for two methods using ‘ACD measured’ and ‘ACD predicted’ values for the position of the intraocular lens implant.

[0332] FIG. 15—The mean absolute error of three intraocular lens power calculation methods for the calculation of the expected refraction.

[0333] FIG. 16—Prediction error (observed refraction minus expected refraction) according to the SRK/T formula plotted against the anterior segment size (anterior chamber depth+lens thickness=position of posterior surface of the crystalline lens). A significant bias was observed (r=0.32, p<0.0001).

[0334] FIG. 17—Prediction error (observed refraction minus expected refraction) according to the formula of the present invention plotted against the anterior segment size (anterior chamber depth+lens thickness=position of posterior surface of the crystalline lens). A non-significant correlation was observed indicating no bias (r=0.001, p>0.5).

[0335] FIG. 18—Mean prediction error (observed refraction minus expected refraction) subdivided into females (n=274) and males (n=181) according to the SRK/T and the formula of the present invention, respectively. The mean prediction error was kept zero for the total group (n=455) including both females and males by IOL constant optimization. A significant bias with gender is seen with the SRK/T method but not with the present method (p<0.05). Bars indicate standard error (SE).

[0336] FIG. 19—Comparison of the C-constant with the A-constant

EXAMPLES

Example 1—Ray Tracing Analysis of Gullstrand Eye

[0337] The exact schematic eye of Gullstrand (Gullstrand, 1909, Gullstrand, 1924) was used as an example of the ray tracing analysis. For many years the exact schematic eye of Gullstrand has been used to simulate the optical properties of the human eye. Apart from the object plane and the image plane the structure of the schematic eye is a six surface model as shown in Table 1.

TABLE-US-00001 TABLE 1 Surfaces of the exact schematic eye of Gullstrand. Each surface is given number from left to right, a name, an axis location (x-Position), a radius of curvature (positive means anterior convex and negative means anterior concave), a conic coefficient (zero for this eye model) and a refractive index. Surface Name x-Position Radius Conic index 0 Object −30 10000 0 1 1 Cornea front 0 7.7 0 1.38 2 Cornea back 0.5 6.8 0 1.34 3 Lens front 3.6 10 0 1.39 4 Nucleus front 4.15 7.91 0 1.41 5 Nucleus back 6.57 −5.76 0 1.39 6 Lens back 7.2 −6 0 1.34 7 Retina (image) 24 −13 0 0

[0338] In the Gullstrand eye the axial length of the eye is assumed to be 24.00 mm, which is the location of the retina where the image is perceived. An example of a ray trace of this eye, the structure of which is listed in Table 1, is shown in FIG. 7 for an entrance beam width of 3 mm with a limited number of incoming parallel rays. Rays are assumed to origin at infinity and being refracted at each surface according to Snell's law of refraction until they hit the posterior surface of the eye (the retina).

[0339] When using a sufficient number of rays (>1000 or more) the distribution of the ray intersections on the x-axis can be studied to give an estimate of the effective focus along the visual axis. Likewise the distribution of the ray intersections with the retina (which can be regarded as a slightly curved y-axis) can also be studied. The latter distribution is known in optical terms as the point-spread function (‘PSF’), which is a measure of the image quality. As a measure of the spread it is common practice to calculate the root-mean-square (‘RMS’) of the distances from the axial focus.

[0340] In FIG. 8 is shown the distribution of the x-axis ray intersections (number of rays=1000) for the Gullstrand eye assuming a pupil of 3 mm. It is noted that all rays are brought to a focus behind the retina at 24.0 mm. The eye is therefore slightly longsighted (hyperopic).

[0341] The analysis of the point-spread-function in the y-direction was provided at two planes: 1) at the retina and 2) at the best focus, which was found by computer iteration to locate about 0.194 mm behind the retina. FIG. 9 illustrates the point spread function of the Gullstrand eye at the retina (dark columns) and at the best focus 0.194 mm behind the retina (light columns). The corresponding RMS was found to be 0.256 and 0.109 at the retina and at the best focus, respectively.

[0342] In conclusion, this experiment has shown that the quality of the image giving the least blur would be enhanced if the axial length of the eye had been 0.194 mm longer or, alternatively, if a small spectacle correction with a power of about +0.5 D (equivalent value of shift in axial length) had been placed in front the eye.

Example 2—Ray Tracing Analysis of Eye with IOL Implant

[0343] The following ray tracing example shows an eye of average dimension with a spherical IOL implanted to give good uncorrected vision at a negligible pupil size. The effective refraction was plotted against the diameter of the pupil with and without correction for the Stiles-Crawford effect.

[0344] FIG. 10 illustrates the effect of pupil size on the refraction predicted for a normal eye of average dimension with a spherical IOL implant. As the pupil widens, the eye becomes myopic as a result of spherical aberration. The effect is compensated for by the Stiles-Crawford effect (‘SC’).

[0345] Two observations can be drawn from FIG. 10: [0346] (1) The effective refraction is dependent on the pupil size also within the normal range (less than 3-4 mm), and [0347] (2) The Stiles-Crawford effect compensates for the spherical aberration at larger pupil sizes.

IOL Data

[0348] The assumed physical characteristics of the IOL (thickness, refractive index, front and back curvature were obtained from the ‘cutting chart’ provided by Alcon). An example of the cutting chart is given in Table 2:

TABLE-US-00002 TABLE 2 ‘Cutting’ chart provided from Alcon Laboratories showing the radii of the anterior and posterior surface of the IOL according to power. The refractive index is 1.5542 (Wavelength 550 nm) and the thickness is 0.8 mm for a normal power of about 23.0 D. (Data provided by Alcon Laboratories). SA60AT & SN60AT Diopter Range Anterior Radii Posterior Radii  6.0-9.5 D 35-81 mm 75.0 mm 10.0-15.5 D 22-52 mm 37.7 mm 16.0-25.0 D 13.4-29.9 mm 25.1 mm 25.5-30.0 D 12.6-16.9 mm 17.48 mm  31.0-40.0 D 6.9-9.8 mm 25.1 mm

[0349] By ANSI definition, the power of an IOL can be calculated as the ‘thick lens’ paraxial power:

D.sub.12=D.sub.1−(T/n)D.sub.1D.sub.2 [0350] wherein: [0351] D.sub.12=total dioptric power of the lens; [0352] D.sub.1=dioptric power of front surface; [0353] D.sub.2=dioptric power of back surface; [0354] T=thickness of lens (in meters); and [0355] n=refractive index.

[0356] D.sub.1 and D.sub.2 can be found as:

D.sub.1=(n−1.336)/r.sub.1

and

D2=(1.336−n)/r.sub.2 [0357] wherein: [0358] r.sub.1=radius of curvature of front surface (m); [0359] r.sub.2=radius of curvature of back surface (with sign convention); and [0360] n=refractive index of the lens.

[0361] In this way the exact curvatures of the IOL can be found from the labelled power according to the scheme in Table 2

Example 3—Clinical Data: Identifying the Constant, C

SUMMARY

[0362] As discussed in the accompanying description, the invention is based on the inventor's discovery that the post-operativeposition of an intraocular lens is related to certain defined anatomical and physical characteristics of the pre-operative eye—in particular, the position and the thickness of the normal, biological, crystalline lens in the pre-operative eye of the patient. Thus, in light of the inventor's discovery, the measurement of certain physical parameters in the eye of a patient prior to surgery (in particular, the crystalline lens position and thickness) can be used to predict the specific post-operative position that an implanted intraocular lens will occupy in the eye of that patient.

[0363] That discovery arose from the studies discussed below. In brief, those studies involved the following steps: [0364] (1) the statistical analysis of a plurality of patients having lens surgery; [0365] (2) measuring the following preoperative parameters of the eye of the patient: the corneal radius, the axial length, the preoperative anterior chamber depth and the crystalline lens thickness; [0366] (3) measuring the following postoperative parameters of the eye: the final refraction (spectacle correction) and the position of the IOL; [0367] (4) demonstrating that the measured position of the IOL can be used in the optical model of the pseudophakic (IOL) eye; [0368] (5) generating a surprisingly simple formula predicting the post-operative position of the IOL based on a constant fraction of the biological crystalline lens thickness, depending on the IOL model and surgical technique.

Materials and Methods

[0369] A total of 590 cases (250 males and 340 females in the age range 20-94 years, mean 70.1 years, were included in the study. They comprised a consecutive series of patients referred for cataract or clear-lens surgery at the University Eye Clinic, Aarhus Hospital with uncomplicated implantation of an IOL of similar design (Alcon Acrysof SA60AT) into the capsular bag.

[0370] Before surgery the anterior corneal radius was measured in two meridians by an auto-kerato-refracto-meter (ARK700; Nidek, Hiroishi, Japan) and the two readings averaged, which is the common procedure when dealing with spherical equivalents. The axial length was measured using optical interferometry (Zeiss IOLMaster (Zeiss Meditec, Jena, Germany). The Anterior Chamber Depth (termed “ACDpre”) and the crystalline lens thickness (termed “LT”) of the pre-operative eye of the patients were measured using optical interferometry (Haag-Streit LS900 Lenstar).

[0371] Exclusion criteria were eyes with complications during surgery, IOL implantation outside the capsular bag, dislocated lenses, previous anterior (i.e. LASIK), or posterior segment surgery, negative IOL power and pre-operative or post-operative astigmatism larger than 4 D. For the present study, only cases with a post-operative best corrected visual acuity of 20/50 or more were included in order to have a reliable estimate of the final spectacle correction (the refraction).

[0372] The post-operative follow-up time was set from 1 week to 3 months. At that time the visual acuity and the refraction were recorded. The post-operative Anterior Chamber Depth (termed “ACDpost”) was measured using optical interferometry (Haag-Streit LS900 Lenstar).

[0373] A summary of the clinical data is shown in Table 3.

TABLE-US-00003 TABLE 3 Axial Preop Preop IOL Age Keratometry Length ACD LT power Data (years) (D) (mm) (mm) (mm) (D) Mean 70.1 (+13.1) 43.6 (+1.45) 23.70 (+1.52) 3.13 (+0.42) 4.59 (+0.47) 20.81 (+4.24) (+SD) Range 20-94 39.2-47.8 20.10-29.39 2.01-4.40 2.97-5.93 4.0-34.0 Clinical data of 590 cases with a known IOL implant. The axial length, the pre-operative ACD and the crystalline lens thickness were measured by laser interferometry. Mean values (+SD, standard deviation) and ranges are shown

Results

Measurement of the Post-Operative Anterior Chamber Depth

[0374] The mean position of the (centre of the) IOL after surgery was 4.90 mm+0.35 (+SD) (range 3.30-5.78 mm). This was defined as the measured anterior chamber depth+half of the known thickness of the IOL. When plotted against the axial length and the pre-operative position of the biological crystalline lens it can be seen, that the position of the IOL was a constant fraction of the thickness of the crystalline lens (‘bag size’) (FIG. 11).

[0375] Expressed as the fraction of the crystalline lens thickness the IOL position showed small positive correlation with the axial length, which was barely significant (r=0.13, p<0.01, FIG. 12).

[0376] As shown in FIG. 13, the IOL position showed a non-significant correlation with the keratometry (r=0.04, p>0.2).

[0377] The very weak or non-significant correlation with axial length and keratometry is an important observation, as this means the prediction of the IOL position can be made independently from both the K-reading and the axial length, contrary to what is assumed in all existing formulas today.

Formula to Predict the Position of the IOL

[0378] Based on the observation that the position of the IOL is a constant fraction of the crystalline lens thickness the following formula could be established predicting the IOL position in the individual case:

IOL.sub.predicted=ACD.sub.pre+C*LT [0379] wherein: [0380] IOL.sub.predicted is the expected post-operative (central) position of the IOL; [0381] ACD.sub.pre is the pre-operative anterior chamber depth; [0382] LT is the crystalline lens thickness; [0383] C is a numerical constant (C) related to the IOL type (=38.7% in current dataset).

Results of IOL Power Calculation

[0384] To verify the hypothesis that this method can be used in the calculation of the IOL power in the individual case several experiments were performed: [0385] Experiment 1: Using the observed (measured) ACD, the expected post-operative refraction was calculated using ray tracing formula as described in the preceding sections. This experiment is to be regarded as the experiment showing the ultimate accuracy resulting from a perfect method showing no error predicting the IOL position. [0386] Experiment 2: Using the new ACD formula (i.e. IOL.sub.predicted=ACD.sub.pre+C×LT), the expected post-operative refraction was calculated using the ray tracing formula as described in the preceding sections. [0387] Experiment 3: As a reference, the IOL power was calculated using the popular SRK/T method which is one of the most popular IOL power calculation methods used today. [0388] In all these experiments, the predictions were analysed for mean numerical error, standard deviation and range of error. In case of the SRK/T formula, the predictions were optimized as recommended by the authors so that the A-constant used was accurate in the average case. As is the case when evaluating formula accuracy in the field of clinical IOL power calculation, all methods were optimized for small off-set errors adjusting the numerical mean error to zero. In doing this, it is possible to evaluate formula performance by comparing the standard deviation of the error, or alternatively—as is usually the case in the field of IOL power calculation studies—by comparing the absolute error for each method.

[0389] In Table 4 is shown the results of the three experiments. As can be seen the lowest error (lowest standard deviation, lowest mean absolute error, smallest range of errors and the highest percentage of cases within +1.0 D) was found with the method using the observed (measured) ACD post-operatively.

TABLE-US-00004 TABLE 4 Error of 3 methods to calculate the refractive outcome after IOL implantation. Method ‘ACD measured’ is based on the optical model of the pseudophakic eye using ray tracing and the actual (measured) position of the IOL. Method ‘ACD predicted’ is based on the same optical model but using a predicted (calculated) position of the IOL according to Eq 1. Method ‘SRK/T’ is based on the current Sanders-Retzlaff-Kraff (‘theoretic’) formula which is one of the most widely used formula for IOL power calculation today. The error is stated as the difference between the observed and expected refraction (spherical equivalent) in the spectacle plane expressed and Dioptres (observed minus expected). IOL calc method ACD measured ACD predicted SRK/T Mean error (D) 0.00 0.00 0.00 SD (D) 0.494 0.536 0.580 Range (D) −1.48-+1.45 −1.55-+1.58 −1.75-+1.53 Mean abs error 0.385 0.413 0.459 Error <+ 0.5 (%) 70.4 67.1 60.7 Error <+ 1.0 (%) 95.6 93.2 91.8 Error <+ 1.5 (%) 100 99.1 98.7 Error >=+ 1.5 (%) 0 0.9 1.3

Comparison of Experiments 1 and 2

[0390] These two experiments were in close agreement, at can be seen in FIG. 14 showing the observed refraction plotted against the expected (predicted) refraction for the two methods. Correlation coefficients were 0.88 and 0.82 for experiment 1 and 2 respectively (p<0.001).

The Overall Error of the 3 Experiments

[0391] In FIG. 15 is the graphic comparison of the mean absolute error of the 3 methods. There was a statistically significant difference in accuracy between all 3 methods (p<0.05).

Further Results Showing Improvement Over Current Methods

[0392] Bias with Anterior Segment Size

[0393] As described in the foregoing sections, one of the advantages of the present invention is that it uses the pre-operative anterior chamber depth and the lens thickness as predictors for the position of the IOL. This is in contrast to other IOL power calculation formulas which use the K-reading and the axial length for all calculations including both the optical calculations and the prediction of the IOL position.

[0394] The fact that the IOL position is depending on the preoperative anterior chamber depth and the lens thickness as shown in the present invention leads to the hypothesis that other IOL power calculation formulas like the most popular SRK/T formula may show a bias with the anterior segment size (Anterior segment size=anterior chamber depth+lens thickness).

[0395] As shown in FIG. 16, this was actually the case in a series of 455 cases when the prediction error of the SRK/T formula was plotted against the pre-operative anterior segment size (r=0.32, p<0.001). The bias, which is undesirable, was not seen with the present approach (FIG. 17).

Bias with Gender

[0396] Another improvement is found with gender bias. It is well known from population studies that female and male eyes differ slightly in many ways. Examples are the corneal radius, the anterior chamber depth and the axial length which are smaller in females than in males. Also the average IOL position differs slightly, as can be demonstrated in a sufficiently large sample (unpublished observations by the author). This would pose a problem if one would like to use the same IOL constants for both females and males.

[0397] However, due to concept of the ‘C’ constant in the present invention which predicts the IOL position relative to the individual anatomy of the crystalline lens, it may be hypothesized that this method is not as prone to gender bias as the A-constant method of the SRK method which is based on the average IOL power valid for a case mix of both females and males.

[0398] As shown in FIG. 18 this was actually found to be the case when the total series was subdivided according to gender. The total series comprised 455 individuals (274 females and 181 males) where the refractive predictions have been corrected for average off-set errors by optimizing the IOL constant for the group as a whole. With the SRK/T formula, an average prediction error of −0.10 D and +0.15 D was found in the females and males, respectively, which was significantly different from zero (p<0.05). With the present method the average prediction error was found to be −0.04 D and +0.05 D in females and males, respectively, which was not significantly different from zero (p>0.05). The present method therefore shows no bias with gender.

CONCLUSIONS

[0399] 1. The current invention predicts the position of the IOL implanted in the capsular bag according to accurate measurements of the position and thickness of the natural crystalline lens [0400] 2. The formula predicts the centre of the IOL to be a constant fraction ‘C’ of the crystalline lens thickness (tag size′), depending on the IOL style and the surgical technique. Once the average position of the IOL has been determined in a sufficient number of cases, the ‘C’ value can be derived for the particular IOL. [0401] 3. The prediction of the IOL position is made independently of the measurements of the corneal power (‘K-reading’) and the axial length, which traditionally have been used in other formulas. [0402] 4. The optical model of the eye used in the present approach can utilize the information from measurements of the IOL position (as well as predicted values) to make accurate predictions [0403] 5. The resulting accuracy of the IOL power calculation is higher than with current methods like the SRK/T formula and the predictions show no bias with axial length, anterior segment size and gender. [0404] 6. Because the method relates specifically to the anatomy of the lens to be operated on, the method should work in any type of eye, including eyes that have undergone changes of the corneal anatomy, like post-refractive surgery (LASIK, LASEK, PRK, RK etc) patients having had corneal surgery for refractive errors.

Example 4—Variation in the C Constant

[0405] The position of the IOL within post-operative eye (and hence the numerical constant, C) may be influenced by the geometry of the IOL that is implanted, particularly because the diameter, shape and mechanical properties of the haptics may influence how the IOL will be pushed forward or backward as a result of the gradual contraction of the capsule after surgery.

[0406] However, as discussed below, the variation in the C value obtained using two different IOL types is surprisingly small.

[0407] Table 5 shows data obtained from two different IOLs which have different geometry and design. As can be seen the C-constant differs by only 0.06 between the two IOLs, corresponding to only 0.29 mm assuming average eye data.

TABLE-US-00005 No. of Mean Min Max IOL individuals C value SD C value C value Alcon SA60AT 100 0.38 0.04 0.31 0.58 AMO ZCB00 24 0.44 0.05 0.33 0.57

Example 5—Comparison of the C Constant with the A-Constant

[0408] The method of the present invention is performed using the numerical constant, C, which defines the relationship between the post-operative position of the IOL in the eye of two or more eye-operated individuals, relative to the thickness of the crystalline lens in the pre-operative eye of the two or more eye-operated individuals.

[0409] The constant C can be determined using data obtained from a relatively small number of eye-operated patients, rendering it advantageous over previous methods (such as those using the A-constant) which require data from larger data sets.

[0410] The minimum number of eye-operated patients needed can be derived from the statistical analysis of data that has already been obtained using the present invention. For example, a typical finding is a mean value of C=39% with a standard deviation of only 4%. The small standard deviation means that very few cases are required to obtain a statistically-meaningful estimate of the constant, C.

[0411] This is in contrast to (all) other formulas using “fudged” constants (i.e. the A-constant) derived from the observed final spectacle correction.

[0412] FIG. 16 provides a numerical example illustrating the favourable benefit of the C-constant as compared to the A-constant in the analysis of aggregated data. FIG. 16 has been constructed from a random sample of clinical data by calculating the observed mean value of the new C-constant as compared to the old A-constant, and transforming the deviation from the final mean into error in the spectacle correction (Rx). As can be seen, the C-constant rapidly reaches a reasonable accuracy within 0.1 D whereas the curve for the A-constant takes at least 25 cases to do so.

[0413] FIG. 19 provides a numerical example illustrating the favourable benefit of the C-constant as compared to the A-constant in the analysis of aggregated data. FIG. 16 has been constructed from a random sample of clinical data by calculating the observed mean value of the new C-constant as compared to the old A-constant, and transforming the deviation from the final mean into error in the spectacle correction (Rx). As can be seen, the C-constant rapidly reaches a reasonable accuracy (within 0.1 D) within the first 25 cases whereas the curve for the A-constant takes at least 50 to 100 cases to stabilize.

REFERENCES

[0414] Baker T Y. Ray-tracing trough non-spherical surfaces. Proc Physical Soc (UK) 1943; (24): 361-364. [0415] Binkhorst R D. The optical design of intraocular lens implants. Ophthalmic Surg 1975; (6): 17-31. [0416] Binkhorst R D. Intraocular lens power calculation. Int Ophthalmol Clin 1979; (19): 237-252. [0417] Colenbrander M C. Calculation of the power of an iris clip lens for distant vision. Br J Ophthalmol 1973; (57): 735-740. [0418] Connors R, Ill, Boseman P, Ill, Olson R J. Accuracy and reproducibility of biometry using partial coherence interferometry. J Cataract Refract Surg 2002; (28): 235-238. [0419] Drexler W, Findl O, Menapace R, Rainer G, Vass C, Hitzenberger C K, Fercher A F. Partial coherence interferometry: a novel approach to biometry in cataract surgery. Am J Ophthalmol 1998; (126): 524-534. [0420] Dubbelman M, Sicam V A, van der Heijde G L. The shape of the anterior and posterior surface of the aging human cornea. Vision Res 2006; (46): 993-1001. [0421] Dubbelman M, Weeber H A, van der Heijde R G, Volker-Dieben H J. Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography. Acta Ophthalmol Scand 2002; (80): 379-383. [0422] Dunne M C, Royston J M, Barnes D A. Normal variations of the posterior corneal surface. Acta Ophthalmol (Copenh) 1992; (70): 255-261. [0423] Findl O, Kriechbaum K, Sacu S, Kiss B, Polak K, Nepp J, Schild G, Rainer G, Maca S, Petternel V, Lackner B, Drexler W. Influence of operator experience on the performance of ultrasound biometry compared to optical biometry before cataract surgery. J Cataract Refract Surg 2003; (29): 1950-1955. [0424] Fyodorov S N, Galin M A, Linksz A. Calculation of the optical power of intraocular lenses. Invest Ophthalmol 1975; (14): 625-628. [0425] Gernet H. [Intraocular lens planning. Geometric-optical and Sanders-Retzlaff-Kraff I and II formulas]. Ophtalmologie 1990; (4): 96-101. [0426] Gullstrand A. Die Dioptrik des Auges. In: Handbuch der physiologischen Optik. (Ed. Helmholz H). Hamburg: L Voss, 1909; 3: 41-375. [0427] Gullstrand A. The dioptrics of the eye. In: Helmholtz's Treatise on Physiological Optics. (Ed. Southall JPC). Optical Society of America, 1924; 351-352. [0428] Haigis W. Pseudophakic correction factors for optical biometry. Graefes Arch Clin Exp Ophthalmol 2001; (239): 589-598. [0429] Haigis W. The Haigis formula. In: Intraocular lens power calculations. (Ed. Shammas HJ). Slack Inc, 2004; 5-57. [0430] Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000; (238): 765-773. [0431] Hoffer K J. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993b; (19): 700-712. [0432] Hoffer K J. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993a; (19): 700-712. [0433] Hoffer K J. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000; (26): 1233-1237. [0434] Holladay J T, Prager T C, Chandler T Y, Musgrove K H, Lewis J W, Ruiz R S. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988; (14): 17-24. [0435] Jansson F, Kock E. Determination of the velocity of ultrasound in the human lens and vitreous. Acta Ophthalmol (Copenh) 1962; (40): 420-433. [0436] Kiss B, Findl O, Menapace R, Wirtitsch M, Petternel V, Drexler W, Rainer G, Georgopoulos M, Hitzenberger C K, Fercher A F. Refractive outcome of cataract surgery using partial coherence interferometry and ultrasound biometry: clinical feasibility study of a commercial prototype II. J Cataract Refract Surg 2002; (28): 230-234. [0437] Olsen T. On the calculation of power from curvature of the cornea. Br J Ophthalmol 1986a; (70): 152-154. [0438] Olsen T. Prediction of intraocular lens position after cataract extraction. J Cataract Refract Surg 1986b; (12): 376-379. [0439] Olsen T. Theoretical approach to intraocular lens calculation using Gaussian optics. J Cataract Refract Surg 1987a; (13): 141-145. [0440] Olsen T. Theoretical vs empirical prediction of aphakic refraction. Arch Ophthalmol 1987b; (105): 1042-1045. [0441] Olsen T. Theoretical, computer-assisted prediction versus SRK prediction of post-operative refraction after intraocular lens implantation. J Cataract Refract Surg 1987c; (13): 146-150. [0442] Olsen T. On the Stiles-Crawford effect and ocular imagery. Acta Ophthalmol (Copenh) 1993; (71): 85-88. [0443] Olsen T. The Olsen formula. In: Intraocular lens calculations. (Ed. Shammas HJ). Thorofare, N.J.: Slack Inc, 2004; 27-40. [0444] Olsen T. Prediction of the effective post-operative (intraocular lens) anterior chamber depth. J Cataract Refract Surg 2006; (32): 419-424. [0445] Olsen T. Calculation of intraocular lens power: a review. Acta Ophthalmol Scand 2007; (85): 472-485. [0446] Olsen T, Corydon L. We don't need fudge factors in IOL power calculation. Eur J Implant Refract Surg 1993; (5): 51-54. [0447] Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995; (21): 313-319. [0448] Olsen T, Funding M. Ray-tracing analysis of intraocular lens power in situ. J Cataract Refract Surg 2012, in press. [0449] Olsen T, Gimbel H. Phacoemulsification, capsulorhexis, and intraocular lens power prediction accuracy. J Cataract Refract Surg 1993; (19): 695-699. [0450] Olsen T, Olesen H, Thim K, Corydon L. Prediction of post-operative intraocular lens chamber depth. J Cataract Refract Surg 1990a; (16): 587-590. [0451] Olsen T, Olesen H, Thim K, Corydon L. Prediction of pseudophakic anterior chamber depth with the newer IOL calculation formulas. J Cataract Refract Surg 1992; (18): 280-285. [0452] Olsen T, Thim K, Corydon L. Theoretical versus SRK I and SRK II calculation of intraocular lens power. J Cataract Refract Surg 1990b; (16): 217-225. [0453] Olsen T, Thim K, Corydon L. Accuracy of the newer generation intraocular lens power calculation formulas in long and short eyes. J Cataract Refract Surg 1991; (17): 187-193. [0454] Olsen T, Thorwest M. Calibration of axial length measurements with the Zeiss IOLMaster. J Cataract Refract Surg 2005a; (31): 1345-1350. [0455] Olsen T, Thorwest M. Calibration of axial length measurements with the Zeiss IOLMaster. J Cataract Refract Surg 2005b; (31): 1345-1350. [0456] Packer M, Fine I H, Hoffman R S, Coffman P G, Brown L K. Immersion A-scan compared with partial coherence interferometry: outcomes analysis. J Cataract Refract Surg 2002; (28): 239-242. [0457] Retzlaff J. A new intraocular lens calculation formula. J Am Intraocul Implant Soc 1980; (6): 148-152. [0458] Retzlaff J A, Sanders D R, Kraff M C. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990; (16): 333-340. [0459] Sanders D, Retzlaff J, Kraff M, Kratz R, Gills J, Levine R, Colvard M, Weisel J, Loyd T. Comparison of the accuracy of the Binkhorst, Colenbrander, and SRK implant power prediction formulas. J Am Intraocul Implant Soc 1981; (7): 337-340. [0460] Sanders D R, Retzlaff J, Kraff M C. Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg 1988; (14): 136-141. [0461] Sanders D R, Retzlaff J A, Kraff M C, Gimbel H V, Raanan M G. Comparison of the SRK/T formula and other theoretical and regression formulas. J Cataract Refract Surg 1990; (16): 341-346. [0462] Stiles W S, Crawford B H. The luminous efficiency of rays entering the eye pupil at different points. Proc Roy Soc (London) B 1933; (112): 428-450. [0463] Vogel A, Dick H B, Krummenauer F. Reproducibility of optical biometry using partial coherence interferometry: intraobserver and interobserver reliability. J Cataract Refract Surg 2001; (27): 1961-1968.