**Purpose.**:
To create a binocular statistical eye model based on previously measured ocular biometric data.

**Methods.**:
Thirty-nine parameters were determined for a group of 127 healthy subjects (37 male, 90 female; 96.8% Caucasian) with an average age of 39.9 ± 12.2 years and spherical equivalent refraction of −0.98 ± 1.77 D. These parameters described the biometry of both eyes and the subjects' age. Missing parameters were complemented by data from a previously published study. After confirmation of the Gaussian shape of their distributions, these parameters were used to calculate their mean and covariance matrices. These matrices were then used to calculate a multivariate Gaussian distribution. From this, an amount of random biometric data could be generated, which were then randomly selected to create a realistic population of random eyes.

**Results.**:
All parameters had Gaussian distributions, with the exception of the parameters that describe total refraction (i.e., three parameters per eye). After these non-Gaussian parameters were omitted from the model, the generated data were found to be statistically indistinguishable from the original data for the remaining 33 parameters (TOST [two one-sided *t* tests]; *P* < 0.01). Parameters derived from the generated data were also significantly indistinguishable from those calculated with the original data (*P* > 0.05). The only exception to this was the lens refractive index, for which the generated data had a significantly larger SD.

**Conclusions.**:
A statistical eye model can describe the biometric variations found in a population and is a useful addition to the classic eye models.

^{ 1 }in 1909. Its layout closely approximated that of a real eye, simulating the gradient refractive index of the crystalline lens by means of a shell structure and taking accommodation into account. However, as calculations of light refraction were very time consuming in that period, this model had to be simplified to be of any practical use (Le Grand,

^{ 2 }Emsley

^{ 3 }).

^{ 4 }Kooijman,

^{ 5 }Navarro

^{ 6 }), gradient index crystalline lenses (Liou and Brennan,

^{ 7 }Siedlecki et al.,

^{ 8 }Goncharov and Dainty

^{ 9 }), chromatic dispersion (Thibos et al.,

^{ 10 }Navarro

^{ 6 }), and a consideration of peripheral imaging (Pomerantzeff et al.,

^{ 11 }Escudero-Sanz and Navarro

^{ 12 }). Furthermore, eye models were proposed by Atchison et al.

^{ 13 }that included the effects of aging and myopia.

^{ 14 }For some of these models, quantitative comparisons of optical properties, such as wavefront aberration, modulation transfer function, and Strehl ratio can be found in the literature.

^{ 15,16 }

^{ 17 }

^{ 18 }for phakic eyes and by Rosales and Marcos

^{ 19 }for pseudophakic eyes. These models incorporate clinically measured biometric data to predict the total wavefront error of an eye, which was found to work well for the pseudophakic eye models, but not always well in the phakic models. This difference in success could be explained by the lack of customized knowledge of the shape and in vivo refractive index of the crystalline lens in these individual eyes.

^{ 18 }Instead average values for these crystalline lens parameters were used that did not necessarily match physiological values in those eyes. Moreover customized crystalline lens models calculated by subtracting corneal wavefront aberrations from total wavefront aberrations cannot yet be verified independently. These limitations may be overcome in the very near future with the recent introduction of ocular wavefront tomography

^{ 20,21 }and anterior segment OCT,

^{ 22,23 }both of which provide very detailed information on the refracting surfaces in the eye and refractive index distribution.

^{ 24 }as a way to generate sets of realistic wavefronts using Zernike coefficients.

^{ 13 }for a group of 66 eyes of 66 emmetropes (32 men, 34 women; 62 Caucasian, 4 non-Caucasian) with a refraction between ±0.75 D and ages between 19 and 69.3 years. These data will henceforth be referred to as the emmetropic data.

^{ 25 }and A-scan ultrasonography was used to find the lens thickness.

*n*normally distributed parameters

*x*if the mean values of these parameters and the covariance values between these parameters are known. Then the multivariate Gaussian distribution is given by: with

*M*a (1 ×

*N*) vector describing the mean values of the parameters and

*C*a (

*N*×

*N*) matrix containing the covariance values between the parameters. As there are many known correlations between the different ocular biometric parameters,

^{ 26 –30 }this covariance matrix

*C*should contain only non-0 elements.

*Ref*

_{M},

*Ref*

_{J0},

*Ref*

_{J45}) written in the form of Thibos' Fourier power vectors,

^{ 31 }the anterior keratometry (

*K*

_{A,M},

*K*

_{A,J0},

*K*

_{A,J45}), the anterior corneal eccentricity

*Ecc*

_{A}, the posterior keratometry (

*K*

_{P,M},

*K*

_{P,J0},

*K*

_{P,J45}) and eccentricity

*Ecc*

_{P}, the central corneal thickness

*Pachy*, the anterior chamber depth

*ACD*, the anterior and posterior curvature of the crystalline lens (

*R*

_{LA},

*R*

_{LP}), the crystalline lens thickness

*T*, the crystalline lens power

*P*

_{L}, the ocular axial length

*L*, and the scotopic pupil size

*S*

_{P}.

^{ 32 }Instead the lens power was estimated using the T2 formula,

^{ 33 }an updated version of the SRK/T formula.

^{ 34 }However, rather than the phakic lens power, this procedure provides an estimate of the pseudophakic lens power required to obtain a certain preset refraction after cataract surgery.

*P*

_{Bennett}), as well as the pseudophakic lens power using the T2 formula (

*P*

_{T2}). Through reduced major axis regression we found the following relationship:

*P*

_{Bennett}= 1.133

*P*

_{T2}− 1.386 (

*r*= 0.922). Inserting

^{2}*P*

_{T2}into this formula allows an estimate of the real crystalline lens power to be made. Even though in individual cases the calculated crystalline lens power may deviate from the actual crystalline lens power, the calculated average and covariance values of the population would be correct.

*C*. Although the use of a linear mixed-effects model would account for such correlations, a different approach was chosen here. By including the biometry of right and left eyes into

*M*and

*C*separately, one has the opportunity to create a binocular eye model that leaves the correlation between both eyes intact for these parameters. Including this binocular aspect would introduce several interesting options, such as the study of aniseikonia and anisometropia.

*R*

_{LA},

*R*

_{LP}) and the crystalline lens thickness

*T*were taken from the emmetropic data set. With the exception of the scotopic pupil size

*S*

_{P}, the emmetropic data set contained all the model parameters included in the covariance matrix

*C*. Hence most of the covariances between the lens parameters (

*R*

_{LA},

*R*

_{LP},

*T*) and the other parameters could be inserted. However, the emmetropic data set did not include binocular information, so the covariance values between the lens parameters and the other parameters had to be used for both left and right eyes. Covariance values that could not be determined were given the default value of 10

^{−5}.

*K*

_{A,M},

*P*

_{L}, and

*L*parameters for both eyes, to obtain a more realistic correlation between the eyes. Example of the

*M*and

*C*matrices used in this work are given in the Appendix for the monocular version of the model (right eyes only).

*K*

_{A,M},

*P*

_{L}, and

*L*) would not add up to the value of

*Ref*

_{M}that was randomly generated by the model. In a healthy real eye on the other hand the refraction calculated from the biometry and the measured refraction would match very closely. This problem can be solved by using ray tracing,

^{ 35 }to calculate the refraction along the meridians of maximum and minimum corneal curvature, from which the resultant spherical and cylindrical refraction may be derived.

*Ref*

_{M},

*Ref*

_{J0},

*Ref*

_{J45}for each eye), 33 parameters were included in the following calculations.

*C*, the refraction and the keratometry of the original data were transformed into Fourier power vectors, as proposed by Thibos et al.

^{ 31 }The notation (

*Ref*

_{M},

*Ref*

_{J0},

*Ref*

_{J45}), (

*K*

_{A,M},

*K*

_{A,J0},

*K*

_{A,J45}), and (

*K*

_{P,M},

*K*

_{P,J0},

*K*

_{P,J45}) was chosen rather than the more commonly used sphere, cylinder, and axis components, because they form orthogonal sets of additive vector components. The required conversion formulas between both components were published by Thibos et al.

^{ 31 }

*R*

_{LA},

*R*

_{LP}), the thickness

*T*, and the power of the crystalline lens

*P*

_{L}are all randomly generated by the multivariate model. Therefore, if

*P*

_{L}is calculated from

*R*

_{LA},

*R*

_{LP}, and

*T*, and a fixed value for the crystalline lens refractive index

*n*

_{L}is assumed, the calculated value will not necessarily correspond with the generated value for

*P*

_{L}. This mismatch can be eliminated by calculating a value for the refractive index

*n*

_{L}that balances out all these lens parameters by means of the following equation, which was derived from the thick-lens formula

^{ 36 }: with

*n*=

*n*

_{A}=

*n*

_{V}= 1.336, respectively, the refractive indices of the aqueous (

*n*

_{A}) and vitreous (

*n*

_{V}) and

*A*=

*T*−

*R*

_{LA}+

*R*

_{LP}.

^{ 38 }

*t*-test. However, as the lack of a statistically significant difference does not necessarily mean the equivalence of both populations, the TOST procedure

^{ 39,40 }(two one-sided

*t*tests) was also performed. This procedure defines a certain range of acceptance (−Θ, +Θ) around the difference between the means of both populations and compares this with a 99% confidence interval. In case of equivalence of both populations this 99% confidence interval should completely fall within the range of acceptance. Note that this range of acceptance is not equivalent to what would be clinically acceptable (all calculations performed with MatLab 6; The MathWorks, Natick, MA, and Excel 2003, Microsoft Corp., Redmond, WA).

^{ 14 }(44 men, 73 women; 99 Caucasian, 18 non-Caucasian; refraction range, −12.38 to 0.75 D; age range (18–36 years). Comparing the crystalline lens power, calculated with the Bennett formula, with lens power obtained from the conversion of the T2 formula, generated a high correlation coefficient (

*r*= 0.806). We therefore felt it safe to use the conversion in the following.

Parameter | Unit | n | Right Eye | Left Eye | Pearson r | |||
---|---|---|---|---|---|---|---|---|

Mean (SD) | KS* | Mean (SD) | KS* | |||||

Age | Age | y | 127 | 39.88 (12.20) | 0.177 | — | — | — |

Refraction | Ref _{M} | D | 127 | −0.98 (2.00) | 0.002 | −0.98 (2.14) | 0.004 | 0.931 |

Ref _{10} | D | 127 | 0.04 (0.28) | 0.433 | 0.09 (0.37) | 0.008 | 0.688 | |

R _{145} | D | 127 | −0.04 (0.19) | 0.246 | −0.02 (0.18) | 0.103 | −0.310 | |

Anterior keratometry | K _{A,M} | D | 127 | 43.29 (1.36) | 0.936 | 43.32 (1.40) | 0.478 | 0.973 |

K _{A,J0} | D | 127 | 0.30 (0.28) | 0.811 | 0.31 (0.31) | 0.214 | 0.654 | |

K _{A,J45} | D | 127 | 0.06 (0.23) | 0.268 | −0.13 (0.24) | 0.439 | −0.515 | |

Anterior corneal eccentricity | Ecc _{A} | 127 | 0.403 (0.175) | 0.070 | 0.36 (0.20) | 0.280 | 0.694 | |

Posterior keratometry | K _{P,M} | D | 127 | −6.26 (0.22) | 0.851 | −6.28 (0.23) | 0.601 | 0.957 |

K _{P,J0} | D | 127 | −0.17 (0.07) | 0.587 | −0.15 (0.07) | 0.670 | 0.577 | |

K _{P,J45} | D | 127 | 0.00 (0.06) | 0.102 | 0.02 (0.05) | 0.602 | −0.278 | |

Posterior corneal eccentricity | Ecc _{P} | 127 | 0.15 (0.28) | 0.491 | 0.09 (0.32) | 0.225 | 0.660 | |

Anterior lens curvature† | R _{LA} | mm | 66 | 10.43 (1.400 | 0.925 | 10.43 (1.40) | 0.925 | — |

Posterior lens curvature† | R _{LA} | mm | 66 | −6.86 (0.85) | 0.525 | −6.86 (0.85) | 0.525 | — |

Lens thickness† | T | mm | 66 | 4.07 (0.35) | 0.232 | 4.07 (0.35) | 0.232 | — |

Lens power | P _{L} | D | 127 | 22.99 (2.14) | 0.247 | 23.04 (2.26) | 0.117 | 0.953 |

Pachymetry | Pachy | mm | 127 | 0.0545 (0.032) | 0.726 | 0.55 (0.03) | 0.960 | 0.945 |

Anterior chamber depth | ACD | mm | 127 | 2.87 (0.38) | 0.964 | 2.88 (0.38) | 0.984 | 0.989 |

Axial length | L | mm | 127 | 23.67 (1.12) | 0.745 | 23.64 (1.16) | 0.772 | 0.965 |

Scotopic pupil size | S _{P} | mm | 127 | 6.51 (1.12) | 0.805 | 6.43 (1.13) | 0.949 | 0.924 |

*Ref*

_{M}, OD;

*Ref*

_{M}, OS;

*Ref*

_{J0}, OS). Note that a significance level of

*P*< 0.01 was used instead of the customary

*P*< 0.05 to avoid the effects of α inflation caused by the large number of KS tests performed (Bonferroni correction).

*Ref*

_{M},

*Ref*

_{J0}) are low (i.e., around or below

*P*= 0.01), we decided not to include the refraction parameters in the model. With this in mind, we will assume in the following that a multivariate Gaussian function will provide an adequate base for our model.

*r*> 0.5). The only exceptions to this are parameters

*Ref*

_{J45}and

*K*

_{P,J45}, for which no strong correlation was expected.

*M*and

*C*into formula,

^{ 1 }we generated a random data set, which we then used to calculate the refraction of each generated eye by means of the SRK/T formula. As shown in Figure 1, this process results in a Gaussian distribution, which does not match the distribution of the original data. After the data of the right eyes are filtered, both distributions are identical (Fig. 1).

*t*tests, no statistically significant differences were found for any of the 33 parameters (Table 2). This finding was confirmed by the TOST procedure, which demonstrated that for all parameters, the original and generated data are equivalent, using a 99% confidence interval (Table 2).

Parameter | Unit | Right Eye | Left Eye | ||||
---|---|---|---|---|---|---|---|

P * | RoA, −Θ, +Θ | 99% CI | P * | RoA, [−Θ, +Θ] | 99% CI | ||

Age | y | 0.254 | −9.73, 9.73 | −5.27 to 2.05 | — | — | — |

K _{A,M} | D | 0.898 | −1.08, 1.08 | −0.40 to 0.45 | 0.524 | −1.12, 1.12 | −0.33 to 0.55 |

K _{A,J0} | D | 0.527 | −0.22, 0.22 | −0.07 to 0.12 | 0.804 | −0.25, 0.25 | −0.12 to 0.10 |

K _{A,J45} | D | 0.833 | −0.18, 0.18 | −0.08 to 0.07 | 0.567 | −0.18, 0.18 | −0.09 to 0.06 |

Ecc _{A} | 0.503 | −0.14, 0.14 | −0.04 to 0.07 | 0.731 | −0.16, 0.16 | −0.06 to 0.07 | |

K _{P,M} | D | 0.786 | −0.18, 0.18 | −0.06 to 0.08 | 0.768 | −0.19, 0.19 | −0.07 to 0.08 |

K _{P,J0} | D | 0.829 | −0.06, 0.06 | −0.03 to 0.02 | 0.915 | −0.05, 0.05 | −0.02 to 0.02 |

K _{P,J45} | D | 0.493 | −0.05, 0.05 | −0.03 to 0.02 | 0.309 | −0.04, 0.04 | −0.01 to 0.03 |

Ecc _{P} | 0.363 | −0.22, 0.22 | −0.13 to 0.06 | 0.872 | −0.25, 0.25 | −0.10 to 0.11 | |

R _{LA} | mm | 0.889 | −1.12, 1.12 | −0.48 to 0.42 | 0.728 | −1.12, 1.12 | −0.50 to 0.36 |

R _{LP} | mm | 0.824 | −0.68, 0.68 | −0.30 to 0.24 | 0.352 | −0.68, 0.68 | −0.15 to 0.39 |

T | mm | 0.065 | −0.28, 0.28 | −0.26 to 0.07 | 0.125 | −0.28, 0.28 | −0.22 to 0.09 |

P _{L} | D | 0.642 | −2.09, 2.09 | 0.14 to 1.83 | 0.654 | −2.20, 2.20 | 0.12 to 1.88 |

Patchy | mm | 0.961 | −0.03, 0.03 | −0.01 to 0.01 | 0.639 | −0.03, 0.03 | −0.01 to 0.01 |

ACD | mm | 0.863 | −0.30, 0.30 | −0.12 to 0.14 | 0.638 | −0.30, 0.30 | −0.10 to 0.14 |

L | mm | 0.294 | −0.89, 0.89 | −0.48 to 0.21 | 0.249 | −0.92, 0.92 | −0.51 to 0.20 |

S _{P} | mm | 0.093 | −0.89, 0.89 | −0.13 to 0.61 | 0.145 | −0.90, 0.90 | −0.16 to 0.58 |

Surface | Diameter (mm) | Radius (mm) | Coni Constant | Thickness (mm) | Refractive Index | |||||
---|---|---|---|---|---|---|---|---|---|---|

Data | Model | Data | Model | Data | Model | Data | Model | Data | Model | |

Right eyes | ||||||||||

Anterior cornea | 7.81 (0.25) | 7.82 (0.24) | 0.807 (0.125) | 0.813 (0.144) | 0.545 (0.032) | 0.546 (0.035) | 1.376* | 1.376* | ||

Posterior cornea | 6.44 (0.23) | 6.45 (0.22) | 0.900 (0.138) | 0.887 (0.145) | 2.87 (0.38) | 2.85 (0.39) | 1.336* | 1.336* | ||

Pupil (stop) | 6.51 (1.12) | 6.47 (1.07) | ||||||||

Anterior lens | 10.43† (1.40) | 10.37 (1.40) | 4.07† (0.35) | 4.14 (0.57) | 1.431† (0.010) | 1.432 (0.013) | ||||

Posterior lens | −6.86† (0.85) | −6.85 (0.90) | 16.15‡ (1.15) | 16.21 (1.03) | 1.336* | 1.336* | ||||

Retina | −12 | −12 | ||||||||

Left eyes | ||||||||||

Anterior cornea | 7.80 (0.26) | 7.82 (0.25) | 0.833 (0.127) | 0.829 (0.148) | 0.549 (0.032) | 0.551 (0.034) | 1.378* | 1.378* | ||

Posterior cornea | 6.43 (0.24) | 6.44 (0.24) | 0.892 (0.155) | 0.883 (0.160) | 2.88 (0.38) | 2.87 (0.39) | ||||

Pupil (stop) | 6.43 (1.09) | 6.40 (1.06) | ||||||||

Anterior lens | 10.43† (1.40) | 10.39 (1.34) | 4.07† (0.35) | 4.10 (0.57) | 1.431† (0.010) | 1.432 (0.014) | ||||

Posterior lens | −6.86† (0.85) | −6.87 (0.89) | 16.12‡ (1.16) | 16.21 (1.05) | 1.336* | 1.336* | ||||

Retina | −12 | −12 |

*n*

_{L}for the generated data was 1.432 ± 0.013 (1000 right eyes), and that of the emmetropic data was 1.431 ± 0.010 (66 eyes). The mean values of both data sets were not significantly different (unpaired

*t*-test:

*P*= 0.760); however, the SD of the generated data were significantly larger than that of the original data (Levene test,

*P*= 0.007; Fig. 4).

*P*< 0.001), whereas the aniseikonia was normally distributed (

*P*= 0.147). However, both distributions of the generated data appear to roughly match that of the original data (Fig. 5).

*M*and

*C*for other population studies and to compare these directly with the current data.

*N*× 33 matrix containing the original data is reduced to the 33 × 1 vector

*M*, the 33 × 33 matrix

*C*, and the mean refraction distribution. For larger original data sets (i.e., a large

*N*), this advantage becomes more apparent. However, it is valid only if all parameters included are normally distributed.

^{ 13,29,41 }some of the parameters generated by the model may have slightly different values than if a balanced male:female population had been used. Another example is the average spherical equivalent refraction of −0.98 D in the original data, which is more myopic than the emmetropia or slight hyperopia that other studies reported in the literature.

^{ 29,41 }This discrepancy may be the result of a difference in demographics of the various study populations and will cause the model to generate slightly longer eyes than when more hyperopic eyes are included.

*R*

_{LA},

*R*

_{LP}, and

*T*). The absence of such data was remedied by including the mean and covariance values from the age-related biometry data of the emmetropic data set.

^{ 13 }As this process involved combining two separate data sets, one of which contained only emmetropes, we may have introduced an error into the model. However, as the emmetropic set contained almost all the parameters used in this work, we believe the error due to combining these two data sets is negligible. Any error due to using phakometric data from a group of emmetropes to represent the phakometry of a group containing both emmetropes and ametropes is probably also negligible, as the correlation between the lens thickness

*T*and refraction has been shown to be either nonsignificant

^{ 14,42 }or very weak.

^{ 27,43 }For this reason we also assumed that

*R*

_{LA}and

*R*

_{LP}would not show any significant changes as a function of refraction. However, this conclusion remains to be confirmed.

*n*

_{L}was significantly higher than that of the emmetropic data set. This may be the result of the compounding of the standard deviations of the

*R*

_{LA},

*R*

_{LP}, and

*T*parameters used to calculate

*n*

_{L}. This discrepancy between both distributions could be resolved by adding a second filtering of the generated eyes using

*n*

_{L}as the filtering parameter.

^{ 44 }for randomized signs of Zernike coefficients). Moreover, if the binocular model described above is expanded, care must be taken that parameters are included only if they have a high correlation between left and right eyes, which would exclude parameters such as (e.g., the Stiles Crawford effect

^{ 45 }) or transverse chromatic aberrations.

^{ 46,47 }

*M*and

*C*required for generating monocular data for right eyes are given in Tables A1 and A2. These are to be inserted into equation 1. Note that the generated data

*f*(

_{X}*x*) may have complex values, because

*C*is composed of contributions from two separate data sets. In that case sign{re[

*f*(

_{X}*x*)]}·

*f*(

_{X}*x*) may be used instead without any significant difference in the result.

Age | K _{A,M} | K _{A,J0} | K _{A,J45} | Ecc _{A} | K _{P,M} | K _{P,J0} | K _{P,J45} | Ecc _{P} | R _{LA} | R _{LP} | T | Pachy | ACD | L | S _{P} | P _{L} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Means | 39.878 | 43.294 | 0.297 | 0.060 | 0.403 | −6.265 | −0.166 | −0.003 | 0.151 | 10.427 | −6.864 | 4.070 | 0.545 | 2.870 | 23.667 | 6.505 | 22.994 |

Age | K _{A,M} | K _{A,J0} | K _{A,J45} | Ecc _{A} | K _{P,M} | K _{P,J0} | K _{P,J45} | Ecc _{P} | R _{LA} | R _{LP} | T | Pachy | ACD | L | S _{P} | P _{L} | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Age | y | 147.821 | −0.322 | −0.281 | −0.324 | −0.825 | −0.181 | −0.069 | −0.139 | 1.271 | −8.971 | 1.555 | 5.067 | 0.017 | −2.554 | −4.691 | −6.375 | 2.174 |

Anterior keratometry | K _{A,M} | −0.322 | 1.836 | 0.127 | −0.017 | 0.010 | −0.273 | −0.036 | 0.006 | −0.108 | −0.072 | 0.089 | −0.043 | −0.002 | 0.031 | −0.581 | −0.289 | 0.065 |

K _{A,J0} | −0.281 | 0.127 | 0.077 | 0.004 | 0.014 | −0.021 | −0.012 | 0.002 | 0.000 | −0.033 | −0.021 | 0.024 | −0.001 | −0.016 | −0.065 | −0.056 | 0.060 | |

K _{A,J45} | −0.324 | −0.017 | 0.004 | 0.051 | 0.001 | 0.004 | −0.001 | −0.004 | −0.009 | 0.066 | 0.009 | −0.022 | −0.001 | 0.005 | −0.019 | 0.038 | 0.101 | |

Ecc _{A} | −0.825 | 0.010 | 0.014 | 0.001 | 0.030 | −0.001 | −0.001 | 0.000 | 0.003 | 0.033 | −0.021 | −0.031 | 0.000 | 0.004 | 0.035 | 0.022 | 0.010 | |

Posterior keratometry | K _{P,M} | −0.181 | −0.273 | −0.021 | 0.004 | −0.001 | 0.050 | 0.007 | −0.002 | 0.008 | 0.030 | −0.030 | 0.008 | −0.001 | 0.006 | 0.107 | 0.080 | −0.026 |

K _{P,J0} | −0.069 | −0.036 | −0.012 | −0.001 | −0.001 | 0.007 | 0.005 | 0.000 | −0.00 | 0.000 | −0.003 | 0.002 | 0.000 | 0.004 | 0.021 | 0.017 | −0.020 | |

K _{P,J45} | −0.139 | 0.006 | 0.002 | −0.004 | 0.000 | −0.002 | 0.000 | 0.003 | 0.000 | −0.009 | 0.003 | −0.002 | 0.000 | −0.001 | −0.005 | −0.004 | −0.010 | |

Ecc _{P} | 1.271 | −0.108 | 0.000 | −0.009 | 0.003 | 0.008 | −0.001 | 0.000 | 0.077 | −0.196 | 0.068 | 0.063 | 0.000 | −0.041 | −0.033 | −0.075 | 0.113 | |

Phakometry | R _{LA} | −8.971 | −0.072 | −0.033 | 0.066 | 0.033 | 0.030 | 0.000 | −0.009 | −0.196 | 1.924 | −0.616 | −0.376 | −0.011 | 0.316 | 0.311 | 0.000 | −1.136 |

R _{LP} | 1.555 | 0.089 | −0.021 | 0.009 | −0.021 | −0.030 | −0.003 | 0.003 | 0.068 | −0.616 | 0.712 | 0.098 | −0.001 | −0.050 | −0.172 | 0.000 | 0.924 | |

T | 5.067 | −0.043 | 0.024 | −0.022 | −0.031 | 0.008 | 0.002 | −0.002 | 0.063 | −0.376 | 0.098 | 0.191 | 0.000 | −0.091 | −0.008 | 0.000 | 0.185 | |

Biometry | Pachy | 0.017 | −0.002 | −0.001 | −0.001 | 0.000 | −0.001 | 0.000 | 0.000 | 0.000 | −0.011 | −0.001 | 0.000 | 0.001 | −0.002 | 0.001 | −0.002 | −0.012 |

ACD | −2.554 | 0.031 | −0.016 | 0.005 | 0.004 | 0.006 | 0.004 | −0.001 | −0.041 | 0.316 | −0.050 | −0.091 | −0.002 | 0.143 | 0.239 | 0.264 | −0.287 | |

L | −4.691 | −0.581 | −0.065 | −0.019 | 0.035 | 0.107 | 0.021 | −0.005 | −0.033 | 0.311 | −0.172 | −0.008 | 0.001 | 0.239 | 1.233 | 0.653 | −1.120 | |

S _{P} | −6.375 | −0.289 | −0.056 | 0.038 | 0.022 | 0.080 | 0.017 | −0.004 | −0.075 | 0.000 | 0.000 | 0.000 | −0.002 | 0.264 | 0.653 | 1.237 | −0.750 | |

Lens Power | P _{L} | 2.174 | 0.065 | 0.060 | 0.101 | 0.010 | −0.0261 | −0.020 | −0.010 | 0.113 | −1.136 | 0.924 | 0.185 | −0.012 | −0.287 | −1.120 | −0.750 | 4.561 |

*T*with age and the decreases in anterior chamber depth

*ACD*and pupil size

*S*

_{p}, all of which are well known age-related physiological changes.

^{ 13 }

Age | Sph | Cyl | Axis | K _{A,M} | K _{A,J0} | K _{A,J45} | Ecc _{A} | K _{P,M} | K _{P,J0} | K _{P,J45} | Ecc _{P} | R _{LA} | R _{LP} | T | nl | Pachy | ACD | L | S _{P} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 20.0 | −0.09 | −0.68 | 167.2 | 44.10 | −0.30 | 0.15 | 0.16 | −6.54 | −0.09 | −0.04 | 0.14 | 10.16 | −5.99 | 4.14 | 1.435 | 0.517 | 3.05 | 22.76 | 6.5 |

2 | 22.2 | 0.88 | −1.92 | 107.1 | 44.26 | 0.81 | 0.55 | 0.61 | −6.24 | −0.23 | −0.08 | 0.38 | 9.35 | −6.33 | 4.31 | 1.436 | 0.517 | 2.93 | 22.32 | 7.4 |

3 | 24.9 | 0.35 | −1.05 | 98.5 | 43.54 | 0.51 | 0.15 | 0.21 | −6.19 | −0.26 | −0.05 | −0.78 | 12.78 | −7.39 | 3.82 | 1.419 | 0.552 | 3.47 | 24.73 | 6.4 |

4 | 27.7 | 0.26 | −1.39 | 116.0 | 42.62 | 0.43 | 0.55 | 0.80 | −6.10 | −0.20 | −0.08 | 0.07 | 10.85 | −5.40 | 3.96 | 1.428 | 0.551 | 3.51 | 23.48 | 8.3 |

5 | 30.0 | 0.18 | −0.44 | 125.3 | 42.09 | 0.07 | 0.21 | 0.32 | −6.04 | −0.27 | −0.06 | −0.15 | 10.13 | −6.27 | 4.38 | 1.415 | 0.540 | 3.10 | 24.76 | 9.3 |

6 | 32.4 | 0.37 | −0.72 | 112.4 | 43.92 | 0.26 | 0.26 | 0.67 | −6.31 | −0.13 | −0.07 | 0.20 | 12.44 | −6.64 | 4.31 | 1.441 | 0.450 | 3.46 | 23.27 | 7.6 |

7 | 35.0 | 0.58 | −0.74 | 108.3 | 43.13 | 0.30 | 0.22 | 0.37 | −6.33 | −0.15 | 0.06 | 0.09 | 11.03 | −6.45 | 3.81 | 1.420 | 0.551 | 2.35 | 23.62 | 6.1 |

8 | 37.4 | 0.05 | −0.44 | 73.7 | 41.44 | 0.19 | −0.12 | 0.19 | −6.13 | −0.22 | −0.04 | 0.18 | 10.84 | −6.04 | 4.12 | 1.435 | 0.541 | 3.11 | 23.80 | 6.9 |

9 | 40.0 | 1.22 | −1.67 | 101.2 | 43.36 | 0.79 | 0.33 | 0.48 | −6.30 | −0.18 | 0.08 | 0.30 | 8.01 | −6.38 | 4.14 | 1.418 | 0.586 | 2.49 | 22.93 | 7.4 |

10 | 42.5 | 0.49 | −1.22 | 95.2 | 45.09 | 0.61 | 0.11 | 0.36 | −6.40 | −0.25 | −0.03 | −0.31 | 9.22 | −6.56 | 4.07 | 1.425 | 0.573 | 2.75 | 22.67 | 7.4 |

11 | 45.1 | −0.10 | −0.61 | 144.9 | 44.16 | −0.10 | 0.29 | 0.31 | −6.29 | −0.27 | −0.15 | 0.17 | 12.19 | −6.84 | 3.95 | 1.441 | 0.480 | 3.46 | 23.30 | 5.8 |

12 | 47.5 | 0.63 | −1.24 | 91.5 | 46.73 | 0.63 | 0.03 | 0.35 | −6.76 | −0.26 | −0.06 | 0.17 | 8.18 | −6.14 | 5.11 | 1.419 | 0.514 | 2.46 | 22.21 | 6.7 |

13 | 50.1 | 0.22 | −0.72 | 92.7 | 40.92 | 0.36 | 0.03 | 0.26 | −5.95 | −0.24 | −0.07 | 0.56 | 11.29 | −7.85 | 5.08 | 1.431 | 0.594 | 3.33 | 25.57 | 7.1 |

14 | 52.4 | 0.85 | −1.10 | 99.1 | 44.41 | 0.54 | 0.18 | 0.33 | −6.41 | −0.15 | −0.05 | 0.21 | 8.20 | −5.83 | 5.20 | 1.425 | 0.527 | 2.44 | 22.44 | 6.3 |

15 | 55.0 | −0.01 | −0.22 | 115.9 | 41.86 | 0.07 | 0.09 | 0.56 | −5.95 | −0.08 | −0.09 | 9.31 | −7.08 | 4.76 | 1.422 | 0.513 | 2.65 | 24.60 | 6.4 | |

16 | 57.5 | 0.17 | −0.51 | 30.7 | 43.21 | −0.12 | −0.22 | 0.22 | −6.25 | −0.14 | 0.02 | 0.28 | 9.18 | −8.02 | 4.12 | 1.436 | 0.641 | 2.37 | 23.24 | 5.2 |

17 | 60.4 | 0.13 | −0.70 | 63.9 | 44.33 | 0.22 | −0.28 | 0.54 | −6.47 | −0.22 | 0.10 | −0.14 | 10.69 | −9.16 | 4..72 | 1.446 | 0.552 | 2.82 | 23.52 | 6.1 |

18 | 61.8 | 0.26 | −0.29 | 103.1 | 42.04 | 0.13 | 0.07 | 0.45 | −6.06 | −0.13 | −0.07 | −0.02 | 8.96 | −6.40 | 5.07 | 1.435 | 0.552 | 2.91 | 23.57 | 6.8 |

19 | 67.9 | 0.43 | −0.85 | 88.7 | 44.35 | 0.43 | −0.02 | 0.29 | −6.50 | −0.23 | −0.03 | 0.17 | 6.94 | −5.75 | 5.81 | 1.409 | 0.526 | 2.50 | 23.43 | 4.7 |

20 | 69.4 | 0.35 | −0.87 | 8.5 | 43.32 | −0.42 | −0.13 | 0.10 | −6.37 | −0.13 | 0.04 | 0.31 | 9.16 | −7.17 | 4.96 | 1.442 | 0.540 | 2.25 | 22.76 | 4.9 |