**Purpose**:
According to Helmholtz, accommodation is based on the flexibility of the crystalline lens, which decreases with age, causing presbyopia. With femtosecond (fs)-lentotomy treatment, it is possible to restore the flexibility of presbyopic lenses. The efficiency of the treatment can be systematically evaluated using the finite element method based on experimental data. The purpose of this study was to quantify the shape change of ex vivo lenses in different accommodation states according to the fs-lentotomy treatment.

**Methods**:
Five lenses with ciliary body excised from ex vivo porcine eyes (age: approximately 6 months, exact age unknown) were stretched in an accommodation device before and after laser treatment. Depending on the accommodation state, the lens shape, reconstructed from lens thickness, diameter, and anterior and posterior curvature, was measured using optical coherence tomography (OCT). The complete lens shape was parameterized and each measured parameter was compared to the results of a control group (*n* = 5, age: approximately 6 months, exact age unknown) without treatment.

**Results**:
The amplitudes of the parameters thickness (+140%), diameter (+54%), and anterior radius of curvature (+57%) significantly increased after treatment (*P* < 0.05), and showed no significant change for the control group. By contrast, the amplitude of the posterior radius of curvature showed no change after treatment (*P* > 0.05).

**Conclusions**:
Measurement of the lens shape in different accommodation states was successful and showed significant changes after the treatment. The resulting data will be utilized as input for a finite element model to systematically evaluate the effect of fs-lentotomy treatment in future work.

^{1}The lens grows throughout its lifetime

^{2,3}and the lens fibers become more and more compact,

^{4}while the ciliary muscle stays active.

^{5}The commonly accepted major cause for the development of presbyopia is the hardening of the crystalline lens with age, which leads to a loss of accommodation. Investigations on this hardening of the lens with age deviate strongly with the measurement method.

^{6–10}

^{11}PresbyLASIK,

^{12}insertion of intracorneal inlays

^{13}or intraocular lenses,

^{14–16}and lens refilling.

^{17,18}Based on the idea of Krueger et al.,

^{19}we developed a femtosecond (fs)-laser treatment method, called fs-lentotomy,

^{20,21}to increase lens flexibility leading to a partial regain of accommodation ability. In fs-lentotomy, ultrashort laser pulses are used to make three-dimensional (3-D) microcuts in the lens tissue without inducing cataract formation or retina damage.

^{22,23}The fs-lentotomy treatment causes a clearly measurable static and dynamic change in thickness in ex vivo human lenses.

^{24}Ackermann et al. have also shown an increase of lens flexibility caused by fs-laser treatment on ex vivo porcine lenses (Ackermann R, et al.

*IOVS*2009;50:ARVO E-Abstract 6134).

^{6}where the crystalline lens is located on a platform and rotated around its polar axis. The resulting centrifugal forces flatten the lens, and the degree of flattening can be used to determine the lens flexibility. The curvatures are measured using a camera during rotation. Due to the mass gradient inside the lens and the dependency of these forces from the distance to the rotation axis, the resulting flattened lens shape does not correspond to the in vivo situation, where the contact points of the stretching forces are located on the outside of the lens. To simulate accommodation in accordance with the classical Helmholtz theory, it is necessary to deform the lens by placing forces on the lens capsule via zonules.

^{25}For this purpose, a lens stretching device can be used, as reported by several authors for human lenses,

^{26–30}monkey lenses,

^{26,30–32}and porcine lenses.

^{33}In this manner, it is possible to maintain the lens with ciliary body in medium during the simulation of accommodation, to keep it from drying, and to minimize its weight and also enhance accuracy of measuring lens curvature when using optical coherence tomography (OCT).

^{34–38}

^{21}In order to evaluate cutting patterns before experimental testing, a computer simulation of the continuum mechanics is appropriate, which describes the lens accommodation and the tissue cuts of fs-lentotomy using finite element (FE) methods.

^{39}The geometrical changes observed and quantified in this study will serve as input parameters (native unstretched lens) and ground truth for the evaluation of the calculated geometries (native stretched, treated unstretched, and treated stretched) of such a simulation.

*n*= 5 treatment group and

*n*= 5 control group, approximately 6 months, exact age unknown) used in this study were obtained from a local slaughterhouse (Schlachthof Hannover GmbH, Hanover, Germany). All lenses were stored in Roswell Park Memorial Institute medium (RPMI) (RPMI 1640 without phenol red; Biochrom GmbH, Berlin, Germany) at room temperature immediately after the dissection, as established by Augusteyn et al.

^{40}Postmortem time was approximately 5 hours. For preparation, the posterior half of the globe, the cornea, and the iris were removed with a scalpel. Special care was taken not to destroy the zonules or the lens capsule during preparation. The anterior half of the eyeball including zonules, ciliary body, and sclera was mounted in a custom-made lens stretching device (see “Lens Stretcher” section) and fixated with brackets. The lenses were immersed in RPMI solution during the whole process.

**Figure 1**

**Figure 1**

^{41}was used. In brief, the light of a broadband superluminescent diode (SLD) (Superlum Diodes, Ltd., Carrigtwohill, Ireland) is transmitted through a single mode fiber into a Michelson interferometer with an 80:20 nonpolarizing beam splitter (NPBS). Here the light is split into a reference and a sample arm, which contains an

*xy*galvanometer scanner (XY) (6210H; Cambridge Technology, Inc., Bedford, MA, USA), a dichroic mirror (M2), and a Hastings-triplet-lens (HT2), which is used as scanning lens. The interferometer and scanner are mounted as compound units on a translation stage for shifting (

*Δz*) the OCT focus in

_{Samp}*z*-direction (depth) into the sample. The dispersion of the scanning lens is compensated by a second Hastings-triplet-lens (HT1) in the reference arm. The increase in the optical path length caused by the medium used was compensated by lengthening the reference arm (

*Δz*

_{Ref}) with a motorized mirror (M1). The reference signal is analyzed using an OCT spectrometer with a line camera (runner; Basler AG, Ahrensburg, Germany).

**Figure 2**

**Figure 2**

^{3}in air), composed of 800 B-mode (brightness mode) images along the

*y*-direction. To measure anterior and posterior curvature of the lens directly without distortions due to the spherical lens contour or the internal refractive index gradient, the inlay of the stretching device can be turned around to measure both (anterior and posterior) surfaces. In addition to anterior and posterior curvature determination in the fixed unstretched and stretched state, lens thickness and equatorial diameter were also measured using OCT by shifting the image region, which means shifting the OCT focus in

*z*-direction and adjusting the reference arm length. Next, the inlay of the stretching device was placed under the laser system in the stretched state. The OCT measurement protocol was performed before and after fs-lentotomy for the treatment group. The control group underwent the same protocol including OCT measurement, applanation of the lens without laser treatment, and again OCT measurement.

*λ*= 1041 nm; pulse duration: 306 fs; further details have been described by Schumacher et al.

^{22}). The 3-D cutting pattern used in this study was a modified steering wheel pattern described by Ripken et al.

^{21}with 12 triangular planes without top or bottom. The cuts are made at a depth of 0.8 mm. It was realized using a scanner (Intelliscan 20; Scanlab AG, Puchheim, Germany) with a pair of galvanometer scanners (Dynaxis L; Scanlab AG) in the

*x*- and

*y*-plane and a linear translation stage in the

*z*-direction (depth). Every lens was applanated under a glass plate during the laser process, which took approximately 30 seconds. The pulse energy applied to the lenses was around 1.4 μJ.

*t*

_{Iso}and the thickness of the anterior half

*z*

_{Iso}of every isolated lens were determined using photographs (see Fig. 3). A glass bead (SiLiBeads Type P; Sigmund Lindner GmbH, Warmensteinach, Germany) with the diameter

*t*

_{Ref}= 7.00 ± 0.01 mm was used to scale the lens dimensions in a glass cuvette filled with RPMI. The ratio

**Figure 3**

**Figure 3**

*n*= 1.5197 given for young porcine lenses.

^{33}With the corrected lens thickness

*t*and the ratio

*σ*taken from photographs of the isolated lens, the distance

*z*

_{apex}from the anterior lens apex to the position of the equator plane (assumed at

*z*= 0) could be estimated to be

*z*

_{apex}=

*tσ*. A substack (

*Δy*= 80.375 μm) of 10 B-scans around the lens apex was extracted from the OCT volume data. This substack was projected using the median in order to find the position of the lens apex, represented by the height maximum of the resulting curved line. After rescaling the

*z*-axis by a factor found through calibration measurements with OCT on the glass bead with 7.00 ± 0.01 mm in diameter in the same medium (RPMI), the central curvatures were extracted from the projected layer. The peripheral portion was in part shadowed by the lens stretching device, and also partly insufficiently contrasted in OCT because of the drop of backscattering at higher angles of incidence of the probe beam on the lens surface (see grayscale inverted B-mode image stack median projections in Fig. 4).

**Figure 4**

**Figure 4**

*x*, the distance from the apex to apex axis, which is defined as

*z*-axis with zero at the lens equator (see Fig. 4). Therefore, the curvature can be described by the following equation

^{42}:

*c*was determined using a manual circle fit at the lens apex with the radius of curvature

*c*

^{−1}; the asphericity

*k*refers to a point

*P*located on the lens shape, and

*z*

_{apex}is the

*z*-position of the apex. The asphericity can be calculated using

*x*

_{p}and

*z*

_{p}of point

*P*with the formula

*c*

_{eq}and asphericity

*k*

_{eq}(beyond

*P*

_{ant/post}) can then be calculated by inserting the following inverse formula

^{42}in Equation 1 by use of continuity conditions at point

*P*and parameter

*x*

_{eq}, which is half of the lens diameter:

*P*. The distance of

*P*to the optical axis was set to

*x*

_{P,ant}= 2.5 mm for the anterior half, and to

*x*

_{P,post}= 2.0 mm for the posterior half. These maximum

*x*values for point

*P*refer to the maximum reflecting angle of 45° for the OCT beam. For the anterior image, a much smaller value was chosen in order not to place point

*P*outside the high-contrast imaging range.

*BFD*), given by the distance from the posterior surface to the focal point, was determined using ray tracing software (ZEMAX-EE 2011; Radiant ZEMAX LLC, Kirkland, WA, USA). First, the central lens part was modeled on the measured parameters thickness

*t*, anterior curvature

*c*

_{ant}, and posterior curvature

*c*

_{post}, with the corresponding asphericities

*k*

_{ant}and

*k*

_{post}for each state. Then the quick focus function was used to find the focal point with the minimum spot diameter for apertures from near 0 to 5 mm in diameter.

^{43}for the lenses was unknown, due to their individual inner structure, an equivalent refractive index of

*n*

_{eq}= 1.4955 for the lens

^{44}was used. The outer medium is supposed to be aqueous and vitreous humor

^{45}each with

*n*

_{h}= 1.336.

*t*-test (paired) was conducted to evaluate these 11 hypotheses.

*P*< 0.05 means statistical significance;

*P*< 0.001 means extreme statistical significance; and

*P*> 0.05 means no statistical significance throughout this article.

*BFD*, are shown with standard deviation for the porcine lenses (

*n*= 5) before laser treatment for the unstretched and stretched state. The curvature is given in form of the radius of curvature (reciprocal value). Furthermore, the mean values of the change of all parameters, due to the stretching process, are quoted with the standard deviations.

**Table 1**

*n*= 4 lenses (lens 3 excepted). Consequently the

*t*-tests were also conducted with

*n*= 4 lenses.

**Figure 5**

**Figure 5**

*P*< 0.001, Table 2). The mean amplitude of the lens diameter increased by 54% from 0.396 ± 0.096 to 0.610 ± 0.093 mm (

*P*< 0.05), and the mean amplitude of the anterior radius of curvature increased by 57% from 0.778 ± 0.372 to 1.220 ± 0.458 mm (

*P*< 0.05). The mean amplitude of the posterior radius of curvature and the absolute mean amplitude of the calculated optical power did not change significantly (

*P*> 0.05) after the laser treatment.

**Table 2**

*P*< 0.05, Table 3). The lens diameter did not change significantly in the state of near vision (

*P*> 0.05). The anterior radius of curvature decreased significantly by 0.560 ± 0.290 mm from 6.988 ± 0.542 to 6.428 ± 0.448 mm (

*P*< 0.05). The posterior radius of curvature and the calculated optical power did not change significantly (

*P*> 0.05) in the unstretched state.

**Table 3**

*P*< 0.05) after treatment. The increasing diameter of 0.102 ± 0.044 mm from 9.254 ± 0.563 to 9.356 ± 0.605 mm shows statistical significance (

*P*< 0.05) after the laser treatment in the disaccommodated state. The change of anterior and posterior radius of curvature and calculated optical power was not statistically significant in the state of distance vision (

*P*> 0.05).

*BFD*for the four states of lens 1, referenced to their equatorial planes with an aperture of 3 mm in diameter.

**Figure 6**

**Figure 6**

*BFD*with different apertures (near 0–5 mm in diameter) of lenses 1, 2, 4, and 5 in all four states are shown in Figure 7. The

*BFD*of all lenses decreased with increasing aperture in the unstretched and stretched native state. This indicates a monotone shift of focus to shorter

*BFD*for higher apertures, which points to a positive spherical aberration for the unstretched and stretched native state. Therefore the spherical aberration remained positive in both stretching states after the laser treatment.

**Figure 7**

**Figure 7**

*Δ*) between the native and treated state for lenses 1, 2, 4, and 5 of the simulated

*BFD*are shown for the unstretched and stretched state.

**Figure 8**

**Figure 8**

**Figure 9**

**Figure 9**

^{3}(from 198.224 ± 48.479 to 198.021 ± 50.559 mm

^{3}) in the unstretched state (0.3%) and by 3.753 ± 3.688 mm

^{3}(from 222.141 ± 54.278 to 218.387 ± 57.753 mm

^{3}) in the stretched state (2.0%), which was not statistically significant. This means that no measurable inflation of the lenses takes place due to the fs-laser pulses, but a real increase of deformability of the tissue. Furthermore, potential compression of the lenses during the applanation process can be eliminated.

^{33,46}The protein content and distribution in porcine lenses are comparable to those in human lenses,

^{47,48}and porcine lenses are easily obtainable. Domestic pigs show a relatively small body weight until the age of 50 days, after which body weight increases.

^{49}This could imply that the hardening of the lens proceeds in a similar way from the age of 50 days on, which would mean that lenses from older pigs (late puberty reached with 180 days)

^{50}should be a good model for presbyopia studies.

^{33}Kammel et al.

^{33}showed that the change of optical power with stretching is approximately five times higher for young porcine lenses (150–180 days) than for sows (270–720 days), but without knowing the individual ages. Unfortunately, there was (and is) no possibility to obtain individual ages of the pigs from our local slaughterhouse. We only could assume that lenses of different sizes were from animals of different ages, but so far there has been no possibility to do a comparative study with lenses from pigs of a known older age.

*n*= 5) for native, unstretched porcine lens thickness (5.432 ± 0.515 mm), diameter (8.858 ± 0.608 mm), and anterior (6.988 ± 0.542 mm) and posterior radius of curvature (3.516 ± 0.151 mm) are below those measured by Kammel et al.

^{33}(7.7 ± 0.2 mm thickness, 10.0 ± 0.3 mm diameter) and Wong et al.

^{51}(lens thickness: 7.4 ± 0.1 mm, anterior radius of curvature: 7.08 ± 0.35 mm, posterior radius of curvature: 5.08 ± 0.14 mm) at zero stretching. The smaller dimensions in our study might be attributed to a younger average age of the pigs. The high standard deviation could indicate a higher variance in age, due to some older animals among the young pigs.

^{51}measured 49.9 ± 1.5 diopters (D) for the refractive power (6-mm aperture) of a porcine eye lens

^{51}in solution, and Vilupuru et al.

^{44}measured 25.89-mm effective focal length, which corresponds to a refractive power of 51.6 D (surrounding refractive index of

*n*= 1.336) in solution. Birkenfeld et al.

^{43}used a laser ray tracing system to measure the back focal length of porcine lenses (2-mm ring of light), corresponding to a higher optical power of 61.9 ± 2.4 D in solution, calculated by inverting the back focal length multiplied by the refractive index of the medium.

^{43}

*BFD*, based on the measured lens shape and an equivalent refractive index, without taking into account the existing GRIN of the crystalline lens. The equivalent refractive index

*n*

_{eq}= 1.4955 taken from literature might be too high, and the mean thickness of our lenses is relatively small, so that the ZEMAX simulation overestimates the refractive power of the lens.

^{33}for young lenses (3.5 D), but is in the range of Wong et al.

^{51}(11.899 D).

^{33}also worked with porcine lenses in a lens stretching device, and measured a mean optical power for young porcine lenses of 39 ± 0.8 D (unstretched) and 35.5 ± 0.9 D (2 mm stretched).

^{33}The same calculations for the optical power with an equivalent refractive index of

^{51}found by comparing measurements using scanning laser ray tracing and simulations using mathematical ray tracing on a porcine lens refilled with silicone oil, led to 54.700 ± 1.988 and 42.801 ± 2.134 D for the unstretched and stretched state, respectively.

*P*< 0.05). The laser cuts cause a higher deformation ability of the tissue, which leads to the lens forming a more spherical shape in the state of simulated near vision and a more flat shape in the state of simulated distance vision. Only the amplitude of the smaller posterior radius of curvature decreases by 10% after laser treatment, which is not statistically significant (

*P*> 0.05). The accommodation amplitude of the calculated optical power increases nonsignificantly by 1% on average (

*P*> 0.05).

*BFD*simulation shows a positive spherical aberration in all cases. In some cases, the spherical aberration increases (lenses 1 and 5 in the unstretched, lens 4 in the stretched state) due to the laser treatment, meaning a decrease of the optical power in the unstretched state for higher aperture values (lenses 1 and 5 in the unstretched state). We found no relation to a specific geometric parameter of the lens shape. The effect of laser treatment on the spherical aberration of the lens and the possibility of a beneficial influence will be investigated in more detail in our future work using a laser ray tracing setup.

^{24}due to laser treatment measured with the Fisher spinning test. For porcine lenses, we have shown an increase of deformation ability of 26.7% based on the amplitude of the normalized central lens thickness by inducing the steering wheel pattern with 12 planes plus a conical top and bottom.

^{21}All these experiments were conducted on isolated lenses without zonules and ciliary body. Compared to our former results on isolated porcine lenses obtained with the Fisher spinning test, our current study would show an even higher increase in deformation ability as calculated by Ripken et al.

^{21}Strictly speaking, such a calculation of the deformation ability cannot be performed in the same way, because in the Fisher spinning test, the entire curve of stretch versus angular velocity (and the resulting centrifugal force on the volume) was used to evaluate the deformation ability of the isolated lens, while in the case of the current study, there was a constant amplitude radial stretch of the lens together with the entire ciliary body (and the resulting tensile stress on the lens), mimicking an isometric amplitude of ciliary muscle contraction. In terms of material properties of the lens, the Fisher spinning test might be suitable, but in terms of the real anatomical situation in the eye, the stretcher experiments are more meaningful. A more general discussion of the validity of the Fisher spinning test is given by Burd et al.

^{52}

**J. Hahn**, None;

**M. Fromm**, None; ROWIAK GmbH (E);

**F. AL Halabi**, None;

**S. Besdo**, None;

**H. Lubatschowski**, ROWIAK GmbH (I, E), P;

**T. Ripken**, P;

**A. Krüger**, None

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