Graefe's Archive for Clinical and Experimental Ophthalmology

, Volume 246, Issue 6, pp 897–906

fs-Laser induced elasticity changes to improve presbyopic lens accommodation

Authors

    • Laser Zentrum Hannover e.V.
  • Uwe Oberheide
    • laserforum koeln e.V.
  • Michael Fromm
    • Laser Zentrum Hannover e.V.
  • Silvia Schumacher
    • Laser Zentrum Hannover e.V.
  • Georg Gerten
    • laserforum koeln e.V.
  • Holger Lubatschowski
    • Laser Zentrum Hannover e.V.
Medical Ophtalmology

DOI: 10.1007/s00417-007-0699-x

Cite this article as:
Ripken, T., Oberheide, U., Fromm, M. et al. Graefes Arch Clin Exp Ophthalmol (2008) 246: 897. doi:10.1007/s00417-007-0699-x

Abstract

Background

According to the Helmholtz theory of accommodation, one of the major reasons for the development of presbyopia is the progressive sclerosis of the crystalline lens. However, both the ciliary muscle and the lens capsule stay active and elastic. Thus, the concept for regaining the deformation-ability of the crystalline lens is to create microincisions inside lens tissue to achieve gliding planes.

Methods

For the preparation of the microincisions, near-infrared femtosecond laser pulses are used, generating laser-induced optical breakdowns. Different cutting patterns were performed, and the elasticity regain of the lenses were measured with Fisher’s spinning test for thickness determination.

Results

The creation of gliding planes inside lens tissue shows very good results in terms of increasing the deformation-ability. The optimization of laser parameters leads to a minimally invasive surgery with no remarkable side effects like residual gas bubbles. Furthermore, ex vivo elasticity measurements of untreated and treated pig lenses show an improvement in the flexibility of the lens. The deformation-ability increases up to 26% with a very low standard deviation (1.6%) and a high significance (p < 0.05).

Conclusion

Generating particular cutting patterns inside lens tissue can increase the deformation-ability of the crystalline lens. Thus, it might be one possible way to treat presbyopia.

Keywords

Ultrashort laserPresbyopiaAccommodationLentotomyFemtosecond laser

Introduction

Laser surgery in ophthalmology has become a wide and successful field. Nevertheless, while the average age of the population is increasing, a non-invasive treatment of presbyopia which preserves the natural crystalline lens is still missing. Up until now, only lens implants or monovision surgeries offer solutions for the lack of accommodation ability with age. Reading glasses and contact lenses are the common ‘treatment’.

Presbyopia is recognized at the age of about 40, and leads usually to a complete loss of the accommodation ability within 15 years. According to the Helmholtz [13] theory of accommodation, it is nowadays accepted that one main part of the accommodating system is moulding of the lens due to the reset force of the lens capsule. This reset force allows the lens to become thicker, with a stronger curvature of the surface. This leads to a stronger refractive power of the lens. Therefore, one of the major reasons for the development of presbyopia is the increasing sclerosis of the lens and a consequent loss of its flexibility [6]. The deformation-ability of the whole lens decreases, while ciliary muscle, zonular fibers and lens capsule stay active almost the whole life [1, 10].

More precisely, the loss of lens flexibility develops steadily over the whole life, and is measurable from the early childhood years [9].

It seems clear that while the lens thickens with age, its fibers become more compact, and thus make not only the nucleus but also the cortex denser, harder and less flexible [8, 21]. The lens becomes more and more inelastic through the years, and since the restoring forces of the lens capsule can not thicken the lens for an accommodation of more than 2 diopters, it becomes less possible to achieve near vision, regardless of whether the surrounding muscles contract and release the zonular fibers. Finally, a full loss of accommodation ability takes place.

To regain elasticity and deformation-ability respectively, Krueger and Myers [18] suggested creating small cuts inside the crystalline lens. They call the process photophaco modulation (if the laser has to change the elasticity modules of the lens) or photophaco reduction (if the lens volume is reduced in certain places to change the optical power of the lens). First experiments with nanosecond laser pulses showed the possibility of increasing the deformation-ability of the lens after laser treatment [15]. However, the lenses showed strong undesirable side effects such as residual gas bubbles that alter volume and density of the lens. Last but not least, these bubbles may stay and cause unacceptable light scattering.

As shown by, for example, Juhasz [17] or Heisterkamp et al. [11], photodisruption with ultrashort laser pulses offers an excellent and reliable tool for ophthalmic surgery. It is well known that cuts created by femtosecond lasers show fewer side effects than those of nanosecond pulses, such as stresswaves, shockwaves, cavitation bubble size and increase of tissue temperature [12, 23]. Thus, ultrashort laser pulses can give the necessary precision for this recommended surgery.

If a laser wavelength in the near-infrared is used, both the cornea and the lens are transparent for the laser radiation. Thus, it is possible to focus a femtosecond laser inside the lens without opening the eyeball and to create a laser-induced optical breakdown (LIOB) at the very focal point. The shortness of the pulses results in very high peak-powers, and thus very high intensities resulting from the focus. These very high intensities lead to high field intensities at the focus, initialize nonlinear absorption processes and result in the generation and acceleration of free electrons, and finally an optical breakdown. The heated plasma expands explosively, driving a shockwave and, if the LIOB takes place in a fluid-like medium, a cavitation bubble develops. After the collapse of this cavitation bubble, a resistant gas bubble may stay in place for a few seconds or longer before it dissolves [19, 24].

While scanning the laser spot inside the lens and positioning one spot close to the other, it is possible to disrupt tissue in a one-, two- or three-dimensional pattern. Hence, cutting in the micrometer range is possible, limited in precision only by the spot size and the resolution of the scanner.

It is thus possible to create defined planes inside lens tissue. In a previous study, we have shown with Krueger et al. [7, 16] that after cutting inside rabbit crystalline lens tissue in vivo the lens stays clear for at least 3 months. In six treated eyes, no cataract due to the laser procedure occurred, and the 3-month post-op showed good transparency for all eyes. In an ultrastructure analysis with transmission electron microscopy (TEM), the number of laser-induced changes at the border layer of the cuts was determined to be less then 0.5 μm.

The aim of this work is to show the potential of increasing the lens deformation-ability after laser treatment with near-infrared ultrashort laser pulses. This procedure will be called Lentotomy.

Methods and materials

To regain crystalline lens elasticity and to increase crystalline lens deformation-ability respectively, we create gliding planes inside the lens tissue while leaving the lens capsule unaffected.

These planes were generated by scanning the focus of the laser pulses by means of a conventional galvanometer-scanner with a resolution of about 1 micron in a defined pattern inside the crystalline lens.

Laser system

For the experiments a Bright Laser from Thales (Paris, France) was used. The applied average output power was between 2.5 mW and 10 mW at a repetition rate of 5 kHz and 780 nm wavelength. The minimum pulse duration is 125 fs and was controlled by a single-shot autocorrelator. In the experiments, only energy in the range of 1 microjoule was used.

Scanning and eye-fixating unit

To create cuts inside the crystalline lens, the focus of the laser beam has to be scanned inside the lens tissue. The beam can be addressed to each desired position by a two-mirror galvano-scanner in the x-y-plane with an operating range of 9 mm in diameter and a resolution of better than 1 micron. To achieve a translation in the direction of propagation, a micro-translation stage can control the distance between scanner and focusing optics on the one side and the fixation unit on the other side, by shifting the treated eye or just the lens within a sub-micron resolution. This fixation unit consists of a glass plate that applanates the cornea surface, surrounded by a suction ring that fits to the curvature of the treated eye. For experiments with extracted lenses, only a much smaller fixation unit optimized in size was used. With respect to the experiment, the cuts were performed in extracted crystalline lenses or inside lens tissue using the whole eyeballs.

The focusing optic is a f-theta-optic with 75 mm focal length optimized for 780 nm wavelength and pulses of a duration of 125 femtoseconds. The laser can be focused to a minimal spot size of about 5 μm proved with the knife-edge method [14].

Figure 1 shows a schematic drawing of the used scanner and fixating system.
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Fig. 1

Schematic drawing of scanning, focusing and fixation system

The eyes

The ex vivo pig eyes were used within a few hours after enucleation. They were kept in saline solution to preserve the transparency of the cornea as well as the crystalline lens. If whole eyeballs were used, they were attached below the scanner by the suction unit. If extracted crystalline lenses were used, they were enucleated just before the surgery and placed in a small vat below an applanation glassplate. Thus, distortion of the beam and refraction errors due to steps in the refractive index can be avoided.

Cutting patterns

To create gliding planes inside lens tissue, three main geometrical cuts were used and, moreover, a combination of all three was realized.

First, an annular pattern (Fig. 2left) with any desired number of rings is possible. The cutting is located in one frontal plane without any sagittal movement. For this, the laser is scanned in an annular part of a spiral pattern. Inner and outer diameter can be chosen freely, as well as the spot separation between subsequent laser pulses.
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Fig. 2

Schematic drawing of the cutting patterns inside the lens; left: annular pattern; middle: sagittal or star-like pattern; right: cylindrical pattern

Perpendicular to the frontal cut, a star-like sagittal pattern (Fig. 2middle) can be attained while leaving the innermost region untreated. In this case, inner and outer starting and ending points can be chosen, as well as the number of stripes and their depth in direction of the optical axis. Due to shielding effects by previous optical breakdowns, this pattern starts at the rearmost (posterior) spot, at about the middle of the lens. Subsequently, the distance between the crystalline lens within the eye and the scanner with the focussing optic is increased, and the focal plane moves upwards (anterior) to perform the cut in height.

The third basic cutting pattern is a cylinder (Fig. 2right) with programmable diameter and depth in sagittal direction. Similar to the star-like case, the cut starts in the posterior segment of the lens and creates a cut in the anterior direction.

A peculiarity of the annular and the cylindrical pattern is a doubled instantaneous spot separation: as outlined before, a gas-filled residual bubble remains for a few seconds following the optical breakdown. This could influence the next optical breakdown. To prevent this, the laser is allowed to run the spiral—or rather the circle of a cylindrical pattern—twice and double the spot separation. On the first pattern, the bubble distance is large enough to suppress interaction of adjacent bubbles. During the second pattern, all the tissue bridges remaining from the first run were cut. In this way, a smoother cut with smaller bubbles and a higher precision can be obtained, as shown in previous experiments [11].

In addition to these three patterns a combined, steering-wheel-like cutting pattern (Fig. 3) is performed. For this, a star-like cut (Fig. 3a) is surrounded by two cylindrical patterns (Fig. 3c) 500 microns from the inner and the outer ending points from the eight cuts. The typical average procedure time for a steering-wheel pattern is about 4 minutes, limited by the repetition rate of the laser.
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Fig. 3

Schematic drawing of the combined, steering-wheel pattern (left). a Sagittal-starlike cuts. b Frontal-annular cuts. c Cylindrical cuts; right: steering-wheel pattern inside the crystalline lens in a pig eyeball

At the posterior and anterior plane inside the crystalline lens, an annular pattern (Fig. 3b) is processed from the inner to the outer cylinder. If not described otherwise, the spot separation was 5 μm in all crystalline lenses. A peculiarity of the cuts in direction of the optical axis is an increased gas-bubble size. To suppress intra-lens bubbles and improve cutting quality, two strategies are used. First, the cylindrical cuts are generated with a certain off-axis angle (Fig. 4).
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Fig. 4

Scheme of the cylindrical and conical cuts with off-axis angle variation of 0° (a), 30° (b) and 45° (c)

Second, in all sagittal cuts the spot separation in z direction was varied. It was increased from 5 μm to 40 μm (Fig. 5). This leads to a smoother cut, but the deformation-ability is not affected at all.
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Fig. 5

Schematic drawing of the z-axis spot separation variation; 5-, 10-, 20- and 40-μm spot separation were applied

Some of the experiments to improve the cutting quality were performed in polyacrylamid (PAA) samples, because of the higher reproducibility and ease of recording the results. The PAA samples have a water content between 65 and 70%, which is seemingly comparable to that of crystalline lens tissue [4].

To maximize deformation-ability, the number of star-like cuts (Fig. 3a) was altered from eight to four and 12 respectively. The top and bottom annular cuts (Fig. 3b) were also changed and cut under a specific angle (Fig. 4). This angle fits the direction of the main force component which appears during accommodation.

It should be similar to the effective angle of the summation of centrifugal and gravitational force during the rotational experiments described later on. Considering Fisher [3] and the used rotational speed, this is an off-axis angle of about α = 25° to the equatorial plane. In the steering-wheel pattern, the number of cylindrical cuts is varied as well.

Rotation stage

To induce a force on the crystalline lens, it is placed on the central axis of a rotation stage according to Fisher’s apparatus [5]. The rotational frequency can continuously be chosen up to 1900 rounds per minute. The applied centrifugal forces simulate the tension as it usually appears when driven by the relaxed ciliary muscle during deaccommodation [3]. As a first approximation, the resulting force can be calculated from the centrifugal force Fz = −mω2r with mass m = 0.78 g [22] in one point with distance r = 2.75 mm from the rotational axis. With the rotation frequency ω = 1900 rpm = 31.67 Hz
$${\text{F}}_{{\text{z}}} = - 0.78{\text{g}} \times 4\pi ^{2} \times {\left( {31.67} \right)}^{2} {\text{s}}^{{ - 2}} \times 2.75\,{\text{mm}} = - 84.9\,{\text{mN}}$$
can be obtained. This value is close to the ones used by Burd [2] and Weeber [25] (F = 0.1 mN) but larger than Fisher’s [5] (F = 0.01 mN).
The platform, upon which the crystalline lens lies, has a small vat matched in radius for the posterior lens radius. The crystalline lens was observed by a CCD-camera, and images of the side-view of the rotating lens were taken at different rotational frequencies. Figure 6 illustrates this setup. To make a comparison between the deformation changes of lenses of different sizes, the factor ηnorm = drot / d0 as a standardisation is established. d0 and drot are the thickness of the unrotated and rotated crystalline lens respectively.
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Fig. 6

Schematic drawing of the setup of the rotation stage experiment to induce centrifugal forces to the crystalline lens

Treating procedure

To test crystalline lens deformation-ability changes, it is necessary to compare cut and uncut lenses. An occurring problem is that the lenses become less elastic in air very rapidly. Thus, a direct comparison is difficult to achieve and is afflicted by large errors. Therefore a statistical method is used. Thirty-six fresh enucleated pig crystalline lenses were rotated. From these lenses, a native relative deformation-ability ηnative was obtained.

For the lenses which were treated, the entire cutting process was performed in the unopened eyeballs. Afterwards, the crystalline lenses were extracted and rotated the same way. Fifteen to 20 lenses of the original 36 native lenses were analyzed for every cutting pattern (beside the 36 native lenses). After rotating the lenses, the thickness was measured again and compared to their initial values.

Comparison of flexibility changes

To compare the deformation-abilities of the different cutting patterns to each other, the dependence of the average of the normalized lens thicknesses from the rotational frequency ω was fitted using a squared function: \(\eta _{{{\text{fi}}t}} = 1 - {\text{c}}_{{\text{i}}} \omega ^{2} \) with i the label of different cutting patterns. Then the coefficients of the squared terms ci were set in relation. The flexibility change is defined as \(\Phi = {1 - {\text{c}}_{{\text{i}}} } \mathord{\left/ {\vphantom {{1 - {\text{c}}_{{\text{i}}} } {\text{c}}}} \right. \kern-\nulldelimiterspace} {\text{c}}_{{{\text{native}}}} \) in percent.

Additionally, to get statistical information, the normalized lens thicknesses for each cutting pattern for a rotational frequency of 1800 rpm are compared to the average of the native lens thicknesses. Afterwards single t-tests are performed for every pattern and the native lenses.

Results

Cutting crystalline lens tissue without influencing the surrounded lens capsule is possible for all cutting patterns and the main planes (frontal, sagittal and horizontal).

Cutting quality

Figure 7 shows a steering-wheel pattern inside an enucleated lens directly after treatment. As one can see, in the frontal (annular) cutting pattern the bubble size is much smaller than in the sagittal star-like cuts and the cylinders. It is a homogeneous plane, without any noticeable big bubbles.
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Fig. 7

Steering-wheel pattern cut inside an enucleated pig crystalline lens; in the frontal cut are no big bubbles (black circles), whereas the sagittal and cylindrical cuts show strong scattering at bigger residual gas bubbles (black arrows)

In Fig. 8, the spot separation in direction of beam propagation was altered from 5 μm to 10 μm, 20 μm and 40 μm. The amount and size of residual gas bubbles decreases with increased spot separation. Despite this the cut was still complete, as was proven by separating two pieces of PAA after this cutting procedure.
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Fig. 8

Comparison of four cylindrical cuts in PAA (polyacrylamid) with different spot separation in direction of the propagation: a 5 μm, b 10 μm, c 20 μm, d 40 μm

The result of the second concept for improving cutting quality is shown in Fig. 9. The angle for the cylindrical cuts was varied from 0° to 30° and 45°.
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Fig. 9

Histological section of three conical cuts in a pig crystalline lens with different off-axis angles; a 0°, b 30°, c 45°

The histopathological section shows a pig cornea with these three cuts. Obviously, the most and biggest bubbles appear in the cut without an off-axis angle. For the 45° angle, the cut is just a thin dark line without gas bubbles. All three cutting angles enable the separation of tissue, as was proven in PAA again.

Improvement in lens deformation-ability

An explicit change in lens thickness due to different speeds of rotation is shown in Fig. 10.
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Fig. 10

Changes in pig crystalline lens thickness due to different rotational frequencies; a 0 rpm, b 1035 rpm, c 1850 rpm

In the left picture, no rotation is applied, which means no centrifugal force is generated. In the middle picture, the rotational frequency is set to 1035 rounds per minute; the lens flattens. A very obvious change is observable in the right picture with a rotational frequency of 1850 rounds per minute. The crystalline lens has decreased in height and increased in diameter. After rotation, one of all 146 lenses stayed 0.1 mm thinner. All the others returned to their initial thickness.

Figure 11 shows the differences in normalized lens thicknesses η for the variation of the number of sagittal planes related to native lenses ηnative.
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Fig. 11

Normalized lens thickness with respect to the rotational speed for steering-wheel pattern with four, eight and 12 sagittal planes; average of 36 (native), 20 (eight planes) and 15 lenses respectively, standard deviation at maximum < 2%

As one can see, the flexibility increases with the number of sagittal planes. The gain of deformation-ability Φ is 8.2%, 16.6% and 26.6% for four, eight and 12 sagittal planes respectively.

In Fig. 12, steering-wheel patterns with different numbers of cylindrical cuts were compared. No significant increase of the deformation-ability for the three and four cylindrical cuts can be noticed in relation to the ‘standard’ steering-wheel with two cylinders, 8 sagittal planes and two annular patterns.
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Fig. 12

Normalized lens thickness with respect to the rotational speed for steering-wheel pattern with two, three and four cylindrical cuts; average of 36 (native), 20 (two-cylinder) and 15 lenses respectively, standard deviation at maximum < 2%

If the steering-wheel (eight planes) is cut without top and bottom annular cuts, the overall gain of deformation-ability is decreased to just 3.2% related to native lenses. Figure 13 shows the corresponding normalized lens thicknesses η.
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Fig. 13

Normalized lens thickness with respect to the rotational speed for steering-wheel patterns with and without top and bottom annular cuts; average of 36 (native), 20 (eight planes) and 15 lenses respectively, standard deviation at maximum < 2%

Finally, the top and bottom cuts were made under a specific angle α, that fits the main force component appearing during accommodation. For lower rotational speeds up to 1400 rounds per minute, the off-axis steering-wheel pattern leads to a higher deformation-ability (Fig. 14). For maximum speeds, this advantage is lost, and both 12-plane patterns are equal. The maximum gain of deformation-ability is 26.7%.
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Fig. 14

Normalized lens thickness with respect to the rotational speed for steering-wheel patterns with the annular cuts with off-axis angle α; average of 36 (native) and 15 lenses respectively, standard deviation at maximum < 2%

The statistical results for a rotational speed of 1800 rpm are shown in Table 1. Highly significant changes (p < 0.05) are noticeable for the cutting pattern with eight planes, with 12 planes and 12 planes with conical top and bottom. A less significant change (p < 0.1) can be found for the cuts with four planes, whereas the other cutting patterns do not show any significant changes. It is obvious that the results with a large increase in deformation-ability in percent show significance in the t-test, whereas those with either a small or almost no increase in deformation-ability have no significance.
Table 1

Statistical analysis for the deformation-ability measurements in pig lenses for a rotational speed of 1800 rpm

 

0

A

B

C

D

E

F

G

No. of lenses

36

20

15

15

15

15

15

15

Φ [%]

0

16.6

4.4

0.8

8.2

26.6

3.2

26.7

Average normalized lens thickness

0.916

0.904

0.917

0.919

0.910

0.893

0.916

0.893

SD

0.017

0.016

0.011

0.016

0.012

0.014

0.012

0.015

p value

-

0.0026

0.84

0.46

0.099

2.12 × 10−5

0.9

4.1 × 10−5

0.05 significance

-

Yes

no

no

no

yes

no

Yes

0: native lenses; A: eight planes; B: eight planes, three cylinders; C: eight planes, four cylinders; D: four planes; E: twelve planes; F: eight planes w/o top and bottom; G: 12 planes conical top and bottom

Discussion

All experiments show the possibility of creating defined, ultrathin cutting patterns inside crystalline lens tissue. In comparison to previous results [16], the cutting quality is improved significantly. Frontal cuts in particular are possible with almost no bubbles visible, even with slit-lamp illumination. But the cuts in the direction of beam propagation generate many more and bigger residual gas bubbles. This is due to the elongated zone of optical breakdown following the intensity of the focused laser pulse. As the Rayleigh range is much longer than the transversal dimension of the focus, the pulse overlap is much higher, and larger bubbles can be formed by accumulated pulse energy.

The concept of the off-axis angle leads to an obvious improvement in cutting quality. Since the off-axis angle concept presents not simply a sagittal or horizontal cut but a combination with a frontal pattern, the concept of increased spot separation shows very good results as well. If the spot separation in propagation direction is increased up to the Rayleigh range of about 25 μm, an additional advantage is a decrease in the operation time by the factor by which the spot separation is increased compared to the horizontal cutting part. In these experiments, a factor of four times the lateral spot separation yields the best results for sagittal cuts.

The experiments for enhancing the deformation-ability of the crystalline lens show promising results, even better than the ones presented earlier [21]. The maximum increase was about 14% for eight-plane steering-wheel patterns; now we are able to push this limit to over 26% for 12-plane cuts with frontal or conical annular cuts. In the latter case in particular, an improvement in deformation-ability for slower rotation and therefore fewer emerging forces can be shown. For this, fitting a squared function is critical and the developing of values seems to be more complicated. In this work, the square fit is used due to better comparability. In relation to the first in vitro studies of Krueger et al. [15], no residual gas bubbles and no noticeable increase of volume can be detected.

The approach to creating the gliding planes in the direction of the main force components appearing during accommodation seems to be particularly promising, and should be put under intensive investigation.

To achieve a large, homogeneous deformation, the placement of the microcuts should be expanded to the central regions of the crystalline lens. This is especially necessary in enabling the lens nucleus to deform, since the lens nucleus is thought to be harder than the lens cortex. Of course, this is critical due to scattering and thus a possible negative influence on vision.

An important topic is the probability of inducing a cataract or not. Early in vivo studies with New Zealand White rabbits have shown that there was no cataract formation within three months [16]. Additionally, no scattering or haze was observed by Krueger and Gerten et al. [7].

Nevertheless, further investigations on presbyopic lenses have to be performed. Eventually, older, more flattened lenses might reach bigger curvatures just because of the fs-laser cuts inside. Furthermore, experiments regarding the speed of accommodation and the possibility of induced wavefront errors have to be made in animal models.

Conclusion

In conclusion, the concept of Lentotomy for improving presbyopic crystalline lens flexibility is very promising. The changed conception for the sagittal cutting pattern offers better cutting quality and shorter procedure times. The advancement of the cutting patterns used in ex vivo pig crystalline lenses presented here shows two striking aspects. First, the number of cuts and gliding planes is an important factor. The more sagittal cuts were generated, the better the gain in deformation-ability. Second, the direction of gliding planes plays a significant role. When conical planes were cut in the direction of the emerging forces, the results were even better for lower rotational speeds.

Summarizing the results of ex vivo pig lenses, experiments demonstrate that the treatment of presbyopia with fs-laser-induced cuts is one reasonable approach to cure the loss of accommodation ability. A better ability of deformation after treatment through fs-laser-induced microcuts has been ascertained, while scattering due to bubble formation was suppressed and procedure time was improved. Therefore, it seems to be possible to increase the flexibility of the lens tissue of presbyopic crystalline lenses. If the lens capsule is strong and elastic enough, it will thicken the whole crystalline lens in a way that helps to reduce the loss of accommodation, and as a consequence may treat presbyopia.

Acknowledgments

Parts of this work were supported by the German Ministry of Education and Research (BMBF), FKZ 13N8712 and FKZ 13N8709.

Copyright information

© Springer-Verlag 2007