**Purpose**:
Measurement of crystalline lens geometry in vivo is critical to optimize performance of state-of-the-art cataract surgery. We used custom-developed quantitative anterior segment optical coherence tomography (OCT) and developed dedicated algorithms to estimate lens volume (VOL), equatorial diameter (DIA), and equatorial plane position (EPP).

**Methods**:
The method was validated ex vivo in 27 human donor (19–71 years of age) lenses, which were imaged in three-dimensions by OCT. In vivo conditions were simulated assuming that only the information within a given pupil size (PS) was available. A parametric model was used to estimate the whole lens shape from PS-limited data. The accuracy of the estimated lens VOL, DIA, and EPP was evaluated by comparing estimates from the whole lens data and PS-limited data ex vivo. The method was demonstrated in vivo using 2 young eyes during accommodation and 2 cataract eyes.

**Results**:
Crystalline lens VOL was estimated within 96% accuracy (average estimation error across lenses ± standard deviation: 9.30 ± 7.49 mm^{3}). Average estimation errors in EPP were below 40 ± 32 μm, and below 0.26 ± 0.22 mm in DIA. Changes in lens VOL with accommodation were not statistically significant (2-way ANOVA, *P* = 0.35). In young eyes, DIA decreased and EPP increased statistically significantly with accommodation (*P* < 0.001) by 0.14 mm and 0.13 mm, respectively, on average across subjects. In cataract eyes, VOL = 205.5 mm^{3}, DIA = 9.57 mm, and EPP = 2.15 mm on average.

**Conclusions**:
Quantitative OCT with dedicated image processing algorithms allows estimation of human crystalline lens volume, diameter, and equatorial lens position, as validated from ex vivo measurements, where entire lens images are available.

^{1–10}and in vivo.

^{11–28}In vivo measurements of the crystalline lens typically come from Purkinje,

^{22–24}Scheimpflug,

^{12–15,18,19,24}magnetic resonance imaging,

^{11,17,26,28}and optical coherence tomography (OCT).

^{16,25,27}To obtain accurate anterior and posterior lens shape estimates, optical imaging methods must be corrected from optical distortion produced by refraction by the cornea and anterior lens surfaces.

^{18,29}In addition, optical imaging in the eye only allows the retrieval of information visible through the pupil, preventing direct calculation of some important parameters such as the equatorial plane position (EPP), the volume (VOL), or the diameter of the lens at the equatorial plane (DIA).

^{30}(typically axial length and corneal power

^{31,32}and, in some cases, lens thickness

^{33,34}) and statistical regression formulae obtained from a large population.

^{30,35–39}In previous reports we demonstrated the accurate construction of OCT-based patient-specific computer eye models.

^{40,41}Selection of an IOL based on ray tracing computation on patient-specific eye models, together with a more accurate estimation of the ELP will undoubtedly result in better refractive, optical and visual outcomes.

^{42}

^{43–45}It is also fundamental in the selection of several accommodative IOLs (A-IOLs), where prior knowledge of the DIA and VOL could enhance refractive predictability and be critical for the correct mechanism of action of the A-IOL.

^{46,47}Finally, estimation of the shape of the entire lens can be useful to be used in patient-dependent mathematical models and finite element modeling of the eye.

^{48–50}

^{11,17,26,28}of the lens, which is able to capture nondistorted images of the entire lens, although with significantly lower resolutions and much higher acquisition times than optical techniques. Previous approaches to estimate lens VOL, EPP, and DIA from optical techniques do not attempt to model the equatorial region of the lenses, but rather estimate those parameters from the intersection of the two parametric surfaces that best fit the data within the pupil (available data) of the anterior lens (AL) and the posterior lens (PL) surfaces

^{13,43}(Hwang K-Y, et al.

*IOVS*2015;56: ARVO E-Abstract 1356). This method, which will be referred throughout the paper as the intersection approach, results in an overestimation of VOL and DIA and underestimation (anterior shift) of EPP. Other methods consider a constant value for the EPP

^{48}(relative to the lens thickness), although some reports suggest that EPP is subject-dependent.

^{26}

^{29,51}has shown to be an excellent technique to image the anterior segment of the eye, due to its high resolution and high speed.

^{52–56}In this study, the shape of the entire lens and, therefore, VOL, DIA, and EPP were estimated from in vivo OCT measurements. The method was validated using 27 ex vivo lenses (in which the information of the whole lens was available). In vivo conditions were simulated for three-dimensional (3D) OCT volumes, assuming that only the information within a given pupil size (PS) was available. The entire lens geometry was estimated from the limited pupil information using a parametric model, and the lens VOL, DIA, and EPP compared to those computed from the whole lens. Finally, these models were applied to in vivo measurements in 2 young eyes during accommodation and 2 cataract eyes.

^{3,57,58}Eyes were shipped in sealed vials at 4°C and wrapped in gauze soaked in preservation medium (Dulbecco modified Eagle medium/F-12 medium [DMEM/F-12], HEPES, no phenol red; Gibco, Carlsbad, CA, USA). The lens was carefully extracted from the eye and immersed in the same preservation medium at room temperature. During the measurements, the lens was placed horizontally on a ring in a DMEM-filled cuvette. Damage, incomplete (not whole lens information available), or excessively tilted lenses were identified from OCT images and excluded from the study, therefore leaving 27 useful lenses (9 lenses <45 and 18 lenses >45 years of age). The handling and experimental protocols had been previously approved by the Institutional Review Boards of Transplant Service Foundation and CSIC. Methods for securing human tissue were in compliance with the Declaration of Helsinki.

^{59}Briefly, the set up was based on a fiberoptic Michelson interferometer configuration with a superluminescent diode (λ

_{0}= 840 nm; Δλ = 50 nm) as a light source and a spectrometer consisting of a volume diffraction grating and a complementary metal-oxide semiconductor camera as a detector. The effective acquisition speed was 25,000 A‐scan/s. The axial range was 7 mm in depth in air, resulting in a theoretical pixel resolution of 3.4 μm. The nominal axial resolution was 6.9 μm in tissue.

^{58}

^{27}For cataract measurements, one 3D volume was composed of 360 A‐scans and 50 B‐scans on a 7 × 15 mm lateral area, acquired in 0.72 second. Five repeated measurements were taken under natural conditions for relaxed accommodation. More details can be found in Marcos et al.

^{60}The specifications of the spectrometer and light source did not allowed sufficient axial range to capture all anterior segment surfaces in a single acquisition. To solve that, three sets of 3D images were captured sequentially at 5 seconds after blinking: (1) cornea, (2) anterior lens, and (3) posterior lens, shifting axially the plane of focus; all 3D sets of data contained the iris.

^{61}(anterior surface in “anterior-up” images, posterior surface in “posterior-up” images) and then registering both anterior and posterior surfaces. B‐scans were processed with semiautomatic surface segmentation algorithms and fan and optical distortion correction algorithms (group refractive index of the solution was taken as 1.345 at 825 nm).

^{62}Registration was achieved by identifying, for both AL and PL, the lens cross-section parallel to

*x*-

*y*plane (i.e., normal to the optical axis of the lens,

*z*) exhibiting maximum area (i.e., the equatorial plane, where curvature changes from AL to PL) and by finding the 3D displacement that maximized the intersection area between both (AL and PL) cross-sectional planes. Figure 1 shows raw OCT images (“anterior-up” [left] and “posterior-up” [middle] measurements) and reconstructed volumes (right) for 38-year-old (Fig. 1A) and 67-year-old (Fig. 1B) donor lenses.

^{27,63}Three-dimensional segmented corneal, AL, and PL surfaces were registered using the pupil center (obtained from the automatically identified iris volume in every of the three captured images in different depths) as a reference.

^{27}Registered volumes were corrected for fan and optical distortion using 3D ray tracing routines.

^{29,51}The corneal group refractive index was taken as 1.385,

^{64}the aqueous humor group refractive index as 1.345, and the crystalline lens refractive index was obtained from the age dependent average group refractive index expression derived by Uhlhorn et al.

^{10}

^{65}: where

*x*and

*y*are the coordinates of the sampling points within PS (i.e., so that x

^{2}+ y

^{2}≤ (

*PS*/2)

^{2}); and vector

*θ*= (

*θ*

_{1},

*θ*

_{2},

*θ*

_{3},

*θ*

_{4},

*x*

_{0},

*y*

_{0},

*z*

_{0}) contains the parameters of the surface. Note that

*θ*

_{1}= 1/

*R*,

_{x}*θ*

_{2}= 1/

*R*,

_{y}*θ*

_{3}=

*Q*and

_{x}*θ*

_{4}=

*Q*in biconicoids;

_{y}*θ*

_{1}=

*θ*

_{2}= 1/

*R*and

*θ*

_{3}=

*θ*

_{4}=

*Q*in conicoids; and

*θ*

_{1}=

*c*/

*a*

^{2},

*θ*

_{2}=

*c*/

*b*

^{2},

*θ*

_{3}=

*a*

^{2}/

*c*

^{2}− 1, and

*θ*

_{4}=

*b*

^{2}/

*c*

^{2}− 1 in ellipsoids, with

*a*,

*b,*and

*c*the semi-axes of the ellipsoid along

*x, y,*and

*z*(axial) axes. Terms (

*x*

_{0},

*y*

_{0},

*z*

_{0}) are the coordinates of the center of the parametric surface. The fitting was performed using a nonlinear multidimensional minimization algorithm.

*α*(diameter that defines the central portion, with

*α*≥

*PS*) were extrapolated in AL and PL using the best fitted parametric surfaces (

*θ*

^{*}) from Equation 1 in the domain defined by

*α*: with

*x*

^{2}+

*y*

^{2}≤ (

*α*/2)

^{2}, as illustrated in Fig. 2C.

*ρ*of the central portion (

*z*) measured inward starting from an outermost end of

_{ext}*z*was taken to fit every lens side, that is, lens side 1: ∀

_{ext}*x*,

*y*≤ −

*α*/2 +

*ρ*; lens side 2:

*x*≥

*α*/2 −

*ρ*, ∀

*y*; lens side 3: ∀

*x*,

*y*≥

*α*/2 −

*ρ*; and lens side 4:

*x*≤ −

*α*/2 +

*ρ*, ∀

*y*.

*z*with

*x*(lens sides 2 and 4) or

*y*(lens sides 1 and 3) in order to obtain a surface oriented along the desired axis.

^{65}Figure 2D shows the data taken (blue points) to fit the lens side 1 (Fig. 2E, green surface). Figure 2F shows the final lens model after the fitting of the four surfaces (lens side 1 in green, lens side 2 in pink, lens side 3 in orange, and lens side 4 in yellow).

*α*and

*ρ*values (i.e., large

*α*values will lead to an overestimation of DIA and VOL and vice-versa; large

*ρ*will lead to smoother lens equatorial regions but lower ability of the model to adapt to fast curvature changes). The optimal

*α*depends on the lens geometry, in particular, lens DIA. As DIA is not known a priori,

*α*is chosen as a proportion (PROP) of the diameter in the intersection (ID) of the anterior and posterior fitting surfaces from Equation 1, which can be calculated for every lens (i.e.,

*α*=

*PROP**

*ID*). Figure 3 shows the definition of ID, equatorial plane position (EPP), which is given as the distance from AL apex, and other parameters of interest.

*ρ*which minimized the following function: where VOLe, DIAe, and EPPe are the mean estimation errors (absolute value of the difference between the estimation and the actual value) across lenses, normalized by subtracting their means and dividing by their standard deviations to be comparable.

*J(PROP, ρ)*(Equation 3) and the optimal parameters found in the training process, PROP

^{*}and

*ρ*

^{*}. Also, we studied the VOL (Fig. 4B), DIA (Fig. 4C), and EPP (Fig. 4D) average estimation error (with sign) as a function of (PROP,

*ρ*) pairs. For any

*ρ*, as PROP tends to 1, the model approximates to an intersection approach (Fig. 3, purple points). When PROP and

*ρ*are low, the VOL and DIA are underestimated and the EPP is overestimated.

^{*}and

*ρ*

^{*}parameters. Figure 5, blue bars, shows the error in the estimation of VOL (Fig. 5A), DIA (Fig. 5B), and EPP (Fig. 5C) for each individual lens, using PS = 5 mm, with the proposed method. Volume, DIA, and EPP estimation errors were below 20 mm

^{3}, 0.9 mm, and 100 μm, respectively, for all lenses. On average (Fig. 6, blue bars), crystalline lens VOL (Fig. 6A) was estimated within 96% accuracy (mean errors across lenses: 9.30 ± 7.49, 8.29 ± 7.00, and 6.92 ± 6.43 mm

^{3}for PS = 4, 4.5 and 5 mm, respectively). Errors in DIA (Fig. 6B) were 0.26 ± 0.22, 0.24 ± 0.23, and 0.22 ± 0.21 mm, respectively, and EPP (Fig. 6C) was estimated with error <45 μm (errors of 40 ± 32, 39 ± 34, and 36 ± 32 μm, respectively).

^{2,12,43}(Hwang K-Y, et al.

*IOVS*2015;56: ARVO E-Abstract 1356) and EPP with the constant value (EPP/thickness = 0.41) proposed by Rosen et al.

^{2}VOL, DIA, and EPP estimation errors with the state-of-the-art approaches were below 42 mm

^{3}, 2 mm, and 300 μm, respectively, for all the lenses. Figure 6 shows the average VOL (Fig. 6A) and DIA (Fig. 6B) estimation errors across lenses with the proposed method and the intersection approach. Figure 6C shows the average EPP estimation error with the proposed method and with other methods applied: (1) intersection approach, (2) a constant value derived from our data set (EPP/thickness = 0.43), (3) the constant value from Rosen et al.,

^{2}and (4) with EPP = thickness/2. Estimates for PS = 4, 4.5 and 5 mm are shown.

*P*= 0.35), with average values across measurements of 179.8 ± 3.5 (0 D) and 180.3 ± 2.8 (6 D) mm

^{3}in S1 and of 155.2 ± 3.3 and 155.4 ± 3.3 mm

^{3}in S2. Diameter decreased with accommodation (statistically significant, 2-way ANOVA,

*P*< 0.001) from 9.46 ± 0.05 to 9.32 ± 0.06 mm in S1 and from 8.58 ± 0.07 to 8.44 ± 0.06 mm in S2, and EPP increased, that is, backward shifted (statistically significant, 2-way ANOVA,

*P*< 0.001) from 1.72 ± 0.02 to 1.82 ± 0.02 mm in S1 and from 2.02 ± 0.02 to 2.19 ± 0.03 mm in S2. Note that subject had also significant effects in DIA, EPP, and VOL and that the interaction was significant in EPP. Figure 7 shows raw OCT volumes (Fig. 7, left) and anterior segment reconstruction, including the estimation of the whole crystalline lens (Fig. 7, right), for S1 in 0 D (Fig. 7A) and 6 D (Fig. 7B).

^{3}, DIA = 9.46 ± 0.05 and 9.68 ± 0.07 mm, and EPP = 2.07 ± 0.02 and 2.23 ± 0.03 mm in both subjects, respectively. Figure 8 shows raw OCT volumes (Fig. 8, left), anterior segment reconstruction, and estimation of the whole crystalline lens (Fig. 8, right) for S1.

^{26}and Marussich et al.

^{9}However, Gerometta et al.

^{66}measured an increase of lens VOL with accommodation.

*ρ*and PROP. We simulated the effect of merging errors on the estimated VOL, DIA, and EPP, by assuming a Gaussian variability in posterior lens axial shifts (μ = 0 and σ = 0.25 mm, which is likely higher than real shifts). With these variations, optimal PROP changed from 0.7 to 0.75 and

*ρ*from 0.5 to 1.5, leading to average estimation errors of 7.23 ± 5.69 mm

^{3}in VOL, 0.12 ± 0.09 in DIA, and 42 ± 33 μm in EPP, showing that merging errors are not critical for the performance of the algorithm.

^{27}We estimated experimentally that the effect of the OCT lateral sampling, axial resolution and merging process produced errors of <1% in VOL, DIA, and EPP.

^{5,67}suggesting that gravity will likely have a negligible impact on our results.

^{27}if distortions are not corrected, anterior lens and posterior lens curvature radii will be highly overestimated. We compared lens parameter estimates with and without fan and optical distortion corrections in lenses in vivo and found that not correcting for these distortions resulted in an overestimation of VOL by 25%, of DIA by 15%, and an anterior shift of EPP by 8%.

^{3}to 12.28 mm

^{3}, the DIA from 0.26 mm to 0.34 mm, and the EPP from 40 μm to 61 μm, when using 2D versus 3D data sets. These errors will be larger for 2D meridians that differed from the average profile (VOL, DIA, and EPP estimation errors up to 20.31 mm

^{3}, 0.55 mm, and 133 μm, respectively) or when the 2D measurement is not obtained through the lens apex. These results are in agreement with recent studies that reveal the relevance of lens surface astigmatism

^{3,27}and errors associated to the assumption of lens rotational symmetry.

^{9}The proposed approach could be implemented in current commercial devices such as Scheimpflug-imaging based systems or clinical anterior segment OCT. Nevertheless, as demonstrated before, distortion correction is critical to obtain accurate results.

^{18,29,68}

^{9}showed that an uncertainty of ±0.01 in the refractive index produced an uncertainty on the order of ±1% in the lens VOL and suggested that ignoring the GRIN introduced a negligible error. Siedlecki et al.

^{69}showed that GRIN did not affect significantly the estimation of lens radii of curvature, although posterior lens asphericity estimates may in fact be affected by neglecting the presence of GRIN. Recent estimates of GRIN distribution profiles in human lenses

^{57,58}can be used to further refine the estimates.

^{*}and

*ρ*

^{*}) across lenses of different ages and that VOL was estimated to be constant with accommodation in vivo, suggests that the method can also be applied in vivo in young lenses. The model could be further refined using a sample with younger lenses mounted in a stretcher system.

^{9}

^{42}Therefore, improvements in the prediction of postoperative IOL position will be critical to achieve a better IOL selection.

^{26}we also found that the EPP/thickness changed across individuals (from 0.40 to 0.47 in our data set; from 0.39 to 0.46 in the study by Hermans et al.

^{26}), indicating the limitation of assuming a constant value and stressing the importance of individual anatomical measurements for proper estimation of the ELP. For example, using Rosen et al's constant,

^{2}EPP/thickness resulted in a mean EPP estimation error of 152 ± 58 μm (Fig. 6) and was close to 300 μm in 2 lenses and approximately 200 μm in 8 lenses (Fig. 5), which would result in a refractive error of approximately 0.5 to 0.6 D in the IOL power calculation in short eyes.

^{30}Estimations of the EPP by using an intersection approach

^{2,12,43}(Hwang K-Y, et al.

*IOVS*2015;56: ARVO E-Abstract 1356) or the thickness/2 leads to even higher IOL power errors.

^{33}Regression equations are generally corrected by the use of an A constant, suggested for each IOL by the manufactured and normally adjusted from clinical outcomes. In some cases the assumption that the IOL position matches the natural equatorial lens position may not hold (i.e., angulated haptics or biomechanical response of the lens). However, knowledge of the lens whole shape, and in particular lens volume, will be very valuable to estimate the deviation of the ELP from the EPP using a systematic approach. Full OCT-based 3D quantification of the anterior segment of the eye and accurate estimation of ELP in patients prior to cataract surgery will pave the way to patient-specific computer eye models and ray tracing based IOL power selection. Further studies on patients before and after cataract surgery will provide further support.

**E. Martinez-Enriquez**, None;

**M. Sun**, None;

**M. Velasco-Ocana**, None;

**J. Birkenfeld**, None;

**P. Pérez-Merino**, None;

**S. Marcos**, P

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