1. Introduction

Laser-assisted in situ keratomileusis (LASIK) is a well-established surgical technique to correct refractive errors like hyperopia, myopia or astigmatism in the human eye, with more than 18 million operations worldwide performed to date [1–4]. Keratomileusis was introduced in the 1990s by the pioneering work of Peyman, Pallikaris, and Burrato [5–8] and later refined by Juhasz and Lubatschowski who used ultrashort laser pulses for intrastromal flap dissection instead of a microkeratome [9,10]. In 2010, small incision lenticule extraction (SMILE) was introduced [11], in which two intrastromal incisions produce a lenticule that is then removed with forceps through a small side cut. This flapless approach enhances the postoperative stability of the cornea, improves the refractive outcome, and has been shown to reduce some of the side effects [12,13]. Another advantage of SMILE is that it can be performed using only the femtosecond (fs) laser system, whereas in LASIK the fs laser flap dissection is followed by ablative reshaping of the cornea by excimer laser pulses.

Despite more than two decades of experience with LASIK and SMILE, details of the cutting process are still not well known. It remains a challenge to explore the intrastromal dissection mechanisms in order to improve efficiency, precision, and safety of the refractive procedures. Usually, intrastromal cutting is performed with infrared femtosecond laser pulses at wavelengths between 1020 nm and 1060 nm [9,14] and at numerical apertures (NA) between 0.25 and 0.50. The tight focusing produces very high intensities leading to nonlinear absorption and plasma formation [15–17]. The dissection mechanism depends mainly on the free electron density in the laser plasma. Currently, two modes of corneal dissection are employed: cleavage mode and low-density-plasma mode. The cleavage mode is used in most commercial systems. Here, fs laser pulses with pulse energies between 0.3 µJ and 1.6 µJ are applied at a repetition rate of hundreds of kHz, and focused in a raster pattern with 3 µm – 6.5 µm spot separation [14]. The high plasma density at the laser focus produces a high temperature and pressure that result in shock wave emission and a rapidly expanding cavitation bubble [15,18–21]. This disruptive process is usually termed optical breakdown. Intrastromal dissection in the cleavage mode is based on the forces exerted during shock wave emission and bubble expansion that severe and separate the stromal lamellae [9,20,22]. In the low-density plasma mode, laser pulses with much smaller pulse energies in the order of approximately 50 nJ are used at high repetition rates >5 MHz with an overlap between consecutive pulses [20,21]. Due to the lower pulse energies, the free electron density in the plasma is reduced and the temperature increase is too small to generate a cavitation bubble. Dissection in the low-density-plasma mode is therefore based on free-electron mediated tissue disintegration. The focus of the investigation in the present paper lies on exploring the mechanisms of corneal dissection in the more common cleavage mode.

Laser-induced cavitation in aqueous media has been studied by many researchers [15,23–30]. Individual laser parameters that influence optical breakdown and cavitation bubble dynamics are pulse duration, wavelength, pulse energy, beam quality, pulse shape, and focusing angle [15,16,29,31,32]. About 25 years ago, Juhasz et. al. performed the first investigations on laser induced bubble dynamics in cornea [19]. The bubble was imaged by stroboscopic flash photography onto a CCD camera, and the bubble dynamics was recorded by a sequence of single events with increasing time delay between pump and imaging pulses. This way, the dynamics could be tracked over a 1-millisecond time interval, with small time steps of a few nanoseconds in the initial expansion phase and steps in the microsecond range later. Unfortunately, no view into the bubble was possible because of the collimated laser illumination, and the image quality was compromised by speckles and other coherent image artifacts. The bubbles looked round both in cornea and water which influenced the artists and scientists view on cavitation-induced cutting in LASIK and SMILE over the last decades.

In this paper, we investigate the bubble dynamics after single laser exposures by ultra-high-speed photography with adaptable time steps. The initial bubble expansion phase is captured at 50 million frames per second and after 8 images the framing rate is reduced to 1 million frames per second to cover a total time window of almost 10 µs. White light illumination at large numerical aperture enables speckle-free imaging with good view into the bubble and on its interactions with the stromal lamellae. To cover a larger time interval of 100 ms, we used a similar approach as Juhasz et. al. and took images of different events with increasing delay time between pump pulse and illumination pulse. Measurements at fixed delay time were employed to explore the energy dependence of maximum bubble size. The bubble size was evaluated by digital image processing. Recently, Freidank et. al. showed that focus shaping by vortex beams improve the intrastromal cutting quality compared to Gaussian beams [33]. To understand the observed differences in cutting quality and efficiency, we investigate the energy dependence of bubble size both for Gaussian and vortex beams in water and corneal tissue.

Furthermore, we explore to what extent the interaction between bubble and subsequent laser pulse influences cutting in high repetition rate laser systems. The laser pulses are separated both temporally (repetition rate) and spatially (spot separation in a raster pattern) and so far previous studies have always focused on one issue only. Tinne et. al. investigated the interaction mechanisms of cavitation bubbles induced by two laser pulses that were both spatially and temporally separated [34,35]. However, there is no study with regard to multiple pulse interactions and their influence on the cutting dynamics in corneal stroma yet.

Here we present high-speed videographic investigations of multiple pulse effects during intrastromal dissection in corneal tissue. For this, a large magnification and numerical aperture is required to image sufficient details but, on the other hand, the interaction of many subsequent laser pulses should be visible within the field of view. With a scanned laser beam, this would require high-resolution imaging of a field of approximately 400 µm size. Because the field of view of a microscope objective with high numerical aperture is usually much smaller, we use a stationary laser beam focused through the microscope objective and rapidly move the corneal specimen with a translation stage. The cutting dynamics and the interplay between consecutive pulses is explored by stroboscopic high-speed videography at 1 kHz, and for a better understanding of the interaction mechanisms, the cuts are inspected histologically.

2. Materials and methods

The mechanisms of corneal intrastromal laser dissection were investigated in ex-vivo corneas obtained from fresh (<4 h postmortem) porcine eyes. After enucleation, the eyes were kept in a nutrient solution (Dulbecco's Modified Eagle's Medium, low glucose, Sigma-Aldrich, Co.) at 8°C temperature. Immediately before the experiment, the epithelial layer of the cornea was removed with a soft brush, the cornea was excised by a cut close to the corneal limbus, and an 8 mm biopsy punch (KAI Medical, BP-80F) was used to prepare a circular specimen of the cornea. Then, the corneal specimen was transferred into a custom-designed holder with exchangeable cover glasses on the front and back sides that flattened the cornea during the dissection process.

2.1 Stroboscopic photography of intrastromal bubble dynamics with Gaussian and vortex beams

A schematic drawing of the experimental setup is shown in Fig. 1. This setup is used in a modified version for the investigations in 2.2–2.4. Detailed specifications of the respective components are summarized in a table in each section. For the investigations in 2.1, we used a laser system with 1030 nm wavelength and 330 fs pulse duration (see Table 1). The laser has a very high pulse-to-pulse energy stability and a tunable repetition rate between 1 Hz and 80 kHz. The beam quality parameter is specified by the manufacturer to M² = 1.09.

 

Fig. 1. Experimental setup for the investigation of laser induced intrastromal bubble dynamics. Specifications of the components (pump laser, focusing objective, light source, collimator, condenser, magnification objective, and camera) for investigations in 2.1–2.4 are presented in each respective section.

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Table 1. Detailed specifications of the components for stroboscopic photography of intrastromal bubble dynamics.

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It was shown recently that cutting with a vortex beam producing a focus with larger lateral ring shape but same axial length as the focus of the Gaussian beam enables more precise intrastromal dissection in SMILE and LASIK with less mechanical side effects than the commonly used Gaussian beam [33]. To compare the different cutting mechanisms, we here investigate intrastromal bubble dynamics for both Gaussian and Laguerre-Gaussian vortex beams. The vortex beam is produced by a fused-silica spiral phase plate with maximum phase shift Δφ = 2 π (VL-209-I-Y-A, vortex grade A, HOLO/OR Ltd., Ness Ziona, Israel) that was inserted into the beam path. The phase plate converts the linear polarized Gaussian beam into a helically phased Laguerre-Gaussian vortex beam of order m = 1.

Laser pulses were focused through a microscope objective into the corneal specimen. The numerical aperture (NA) of the objective was reduced to NA = 0.38 by an aperture in the rear entrance pupil to mimic focusing conditions in clinical corneal dissection. The pulse energy at the laser focus was measured by deflecting a part of the laser beam on an Ophir PD 10 energy meter. It was pre-calibrated by measuring the pulse energy without microscope objective behind the aperture. The transmittance T of the Zeiss objective at 1030 nm was considered using manufacturer data (T = 40%). Individual cavitation bubbles were produced by single lasers pulses that were selected out of the 10 Hz fs pulse train by a mechanical shutter. The cutting plane was imaged through a combination of the focusing objective and a tube lens (Zeiss tube lens 452960). To achieve higher magnification, the intermediate image was further enlarged with a macro photo objective onto a digital camera (Nikon D5100, 4928 x 3264 pixel), providing a total magnification M = 110. The microscope objective (NA = 0.38) together with illumination at NA = 0.5 provides a diffraction-limited resolution of 0.7 µm, which is maintained in the second magnification step. The large total magnification results in significant oversampling at the camera chips such that the diffraction-limited resolution was maintained even with microchannel plates in the imaging path (section 2.3).

First, we investigated intrastromal bubble dynamics by stroboscopic photography of single bubble events at constant laser pulse energy. For illumination, we used the incoherent flash of a “Nanolite” plasma discharge lamp with about 20 ns duration. Because the Nanolite pulses exhibit a timing jitter of up to 500 ns, the actual delay between the pulse producing the cavitation bubble and the illumination pulse was measured for each event. Alternatively, one could use a laser-diode-based light source emitting pulses of 3 – 16 ns duration with less triggering jitter [36–38]. A homogeneous illumination of the dissection zone was achieved by using a photo objective in front of the flash lamp as collimator and a microscope objective below the corneal specimen as condenser (Köhler illumination). Incoherent illumination at NA = 0.5 enabled speckle-free imaging with good visualization of the bubble's structure and of its interaction with the corneal lamellae. To investigate the entire bubble dynamics, the delay between the fs laser pulse and the illuminating flash was adjusted between 10 ns and 100 ms. The corneal specimen was moved after each shot by means of a three-dimensional translation stage in a way that laser pulses were focused at 30 µm spot separation in 150 µm depth. The individual photographs of the laser induced bubble size were analyzed to determine the radius versus time curve R(t) for Gaussian and vortex beams.

2.2 Determination of bubble size as a function of pulse energy

Determination of the bubble size as a function of laser pulse energy in corneal tissue is much more difficult than in water, where the maximum bubble radius R_max can be determined from the bubble oscillation time T_osc [31]. As a reference, we first determined the bubble threshold in water and its dependence of maximum bubble size on pulse energy at NA = 0.4 using a pump-probe-scattering technique described previously [16,31,32]. In tissue, the R_max(T_osc) relation is not known and the bubble size has to be obtained by flash photography. Because the bubble size in cornea is strongly influenced by tissue parameters, it varies from shot to shot even when the laser pulse energy remains constant. To account for these statistical variations, we used a high-speed camera (Photron SA-Z) to image a large number of single bubbles at high repetition rate. The Photron camera chip has a large pixel size of 20 µm. With the large magnification factor of M = 110 used for stroboscopic photography in 2.1 and 2.2, one pixel of the Photron chip is equivalent to 180 nm in object space, which corresponds to two times oversampling the diffraction-limited resolution of 0.7 µm. The high-speed camera enabled us to photograph a sequence of 200 single bubble events at 100 frames per second for each laser pulse energy. For this purpose, bubbles were produced at 100 Hz laser pulse repetition rate in 150 µm depth in a raster pattern over a circular dissection area of 5 mm diameter. The foci of the laser pulses were separated by translating the corneal specimen at 3 mm/s in 200 lines within the dissection area. This corresponds to a spot separation of 30 x 20 µm, sufficient to guarantee that individual events do not influence each other. The complete dissection process takes about 264 s, which provides enough time for a stepwise adjustment of laser pulse energy during the procedure from bubble threshold to maximum pulse energy. As we will later see in section 3.1, the bubble in the corneal tissue rapidly expands during the first µs and then the radius decreases very slowly. Because the bubble radius remains approximately constant for a period of ≥ 10 µs after the initial expansion phase, we investigated the dependence of the intrastromal bubble size on laser pulse energy at a fixed time delay of 3.5 µs. The high-speed series were digitally analyzed to determine the bubble size as a function of pulse energy for Gaussian and vortex beams (section 2.6).

2.3 Ultra-high-speed photography of bubble dynamics in corneal stroma with up to 50 million frames per second

The experimental setup for the ultra-high-speed photography of bubble dynamics in corneal stroma is similar to the setup shown in Fig. 1, changes are summarized in Table 2. The size of the laser-induced plasma in the cornea was minimized by using 560-ps pulses from a laser with ultraviolet (UV) wavelength (355 nm). The UV wavelength reduces the focal diameter and the focal length by a factor of 3, so that the laser-induced plasma is much more compact. The UV laser system can be controlled externally in single shot mode, and after each laser pulse, the corneal specimen was moved 50 µm by the translation stage to a fresh position to avoid interaction with previously generated bubbles or corneal tissue that was changed in its optical properties by the laser irradiation. Pulse energies were selected such that bubbles with similar size as in previous experiments with IR fs pulses were produced [19].

Table 2. Detailed specifications of the components for ultra-high-speed photography of bubble dynamics in corneal stroma.

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The ultra-high-speed camera (Specialized Imaging SIMD16) enabled us to capture the dynamics and interaction of individual cavitation bubbles with the corneal lamellae at up to 50 million frames per second. The camera has 8 gated high-resolution multichannel plates (MCPs) with a dynamic range of 12 bits on the CCD image sensor (ICX285AL, 1360 x 1024 pixel). The 18-mm high-resolution MCP features a variable gain up to a factor of 10 000. The camera is able to record up to 16 images in two sequences of 8 frames with 20 ns interframing time and 10 ns exposure time. This corresponds to a maximum frame rate of up to 50 million images per second. The image separation can be changed after the first sequence of 8 frames, so that longer observation times can be covered by the second sequence. The magnification factor M = 140 was selected such that the maximally expanded intrastromal cavitation bubble largely filled the size of the image sensors. This way, the influence of MCP inherent noise was minimized.

The short exposure time of 10 ns puts high demands on the light source for imaging. We used a plasma discharge lamp with a pulse duration of 20 – 50 µs (sufficient for the illumination of the entire high-speed series) and 200 J pulse energy. The 10-ns exposure time of the individual images is provided by the electronic gate of the MCPs. Köhler illumination by a combination of a photo objective (F = 1.2) as collimator and a microscope condenser (Leica, NA 0.55) was used to illuminate the 61 x 45 µm large object field with sufficiently bright light. The diffraction limited resolution for illumination at NA = 0.55 and imaging at NA = 0.75 is < 0.5 µm.

2.4 High-speed videography of cutting dynamics

The experimental setup is again similar to the setup in Fig. 1 with small modifications listed in Table 3. UV laser pulses (355 nm, 560 ps) emitted at 1 kHz were focused in 150 µm depth into the corneal stroma. The numerical aperture of the objective was reduced to NA = 0.38 to mimic focusing conditions used in clinical systems. The corneal specimen was moved by the translational stage at 6 mm/s and a flap of 4 mm diameter was cut with 6 x 6 µm spot separation. The dissection zone was imaged through the focusing objective combined with a tube lens and further magnified by a photo objective onto a high speed video camera (Basler 503k). The total magnification was M = 110 and the field of view 133 x 87 µm. The camera had a gate time of 829 µs, and stroboscopic illumination was realized by synchronizing the “Nanolite” plasma discharge lamp with 20 ns flash duration to the gate opening time. The delay of the flash lamp was adjusted to 2 µs and 24 µs after the laser pulse. At 1 kHz repetition rate, the flash lamp should not emit more than 100 pulses in one sequence to avoid damage due to thermal overload. Therefore, we restricted the length of the video sequences to 60 – 65 images. The laser pulse repetition rate in investigations with a stationary laser beam is limited by the possible speed of the translation stage moving the specimen and is, thus, lower than in clinical systems.

Table 3. Detailed specifications of the components for high-speed videography of cutting dynamics.

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2.5 Histology of corneal specimens

Histology was performed on corneal specimens dissected with pulse energies (0.7 µJ to 1.2 µJ) and spot separations (4 µm to 6 µm) that are often used in clinical settings. The flap was not lifted after dissection, but the entire corneal specimen was fixated for 48 hours following the protocol of Grazadei et. al. [39]. After this, the specimen was dehydrated in propyleneoxide (1,2-epoxy propane), embedded in epoxy (Epon 812, Araldite 502, Sigma Aldrich) and stained with Toluidine blue. Series of semi thin sections (0.7 µm) were cut for light microscopic analysis. In addition, classical Paraffin sections stained with Hematoxylin and Eosin (H&E) were prepared for overviews of the dissected regions.

2.6 Digital image processing

Manual evaluation of the bubble size from the high-speed photographic image series is not manageable due to the large amount of data (4000 images were recorded in the measurement series described in section 2.2). Therefore, determination of the bubble size was automated using digital image processing based on Matlab software (MathWorks, Inc). The algorithm starts with a regularized gradient-based edge detection in which the derivation in one direction and smoothing in the other direction is used to find the boundary of the bubble wall. The filter is based on the imaginary part of the Gabor transformation (Gabor filter edge detection) and a threshold relative to the maximum of the gradient amount is used to determine the contour of the bubble. In addition, if there is a gap in the bubble edge, the contour is closed by the software. The closed contour is then reduced to a line with a width of one pixel.

The sequence from the original image through gradient formation, contour determination and thinning of the contour line to the finally determined bubble edge is shown in Fig. 2. To determine the bubble size, the number of pixels within the bubble contour is converted into an area which is then transformed to an area-equivalent spherical bubble radius R. The large image magnification (M = 110) provides a high precision of the digital analysis. The accuracy of the determination of the position of the contour line is in the order of one pixel and, hence, better than 0.18 µm in object space. Systematic errors in the determination of the bubble wall position owing to the diffraction ring around the bubble would influence the absolute radius value but not affect the parameter dependence of bubble radius on time or laser pulse energy.

 

Fig. 2. Sequence of digital imaging processing for the determination of the bubble size from (a) original image, (b) gradient based Gabor filter detection, (c) thinning of the contour to a line with one pixel width, (d) final outcome of the bubble wall detection (red line). The reference bar in the images corresponds to 10 µm.

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3. Results

3.1 Time evolution of intrastromal bubble dynamics over 100 ms

Figure 3 summarizes intrastromal bubble dynamics induced by single laser pulses with Gaussian and vortex beam profiles as determined by stroboscopic photography. The energy of the laser pulses was adjusted for both beam profiles (Gauss: 162.5 nJ, Vortex: 329.9 nJ) such that the maximum bubble radius R_max is in the range between 10 µm and 12 µm, which will certainly suffice for refractive surgery at 6 x 6 µm spot separation. The investigation at equal maximum radius allows a direct comparison of the bubble dynamics for Gaussian and vortex beams. To achieve the same maximum bubble size, we had to use laser pulse energies that are 3x (Gauss) and 1.9x (Vortex) above the cutting threshold (E_cut,Gauss = 54 nJ and E_cut,Vortex = 173 nJ).

 

Fig. 3. Intrastromal bubble dynamics 20 ns to 100 ms after focusing laser pulses with Gaussian (red dots) and vortex (red circles) beam profile at NA 0.38 into the corneal stroma.

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Figure 3 clearly shows that the intrastromal bubble dynamics is similar for both beam profiles. The bubble radius increases very rapidly within the first 200 - 300 ns. After the maximum bubble size has been reached, the radius collapses to about 80% of R_max within 1 µs after which it slowly decreases between 2 µs and 100 ms from about R ≈ 7 µm to R ≈ 6 µm. The long time interval of almost constant bubble size allows us to investigate the dependence of intrastromal bubble size on laser pulse energy at a fixed time delay of 3.5 µs.

3.2 Dependence of bubble size on pulse energy

Figure 4(a) shows a representative video with a sequence of 200 photographs of laser induced intrastromal bubbles at one pulse energy that were imaged 3.5 µs after the laser pulses. For better visibility, the photographs were converted into a video with 10 images per second. The bubbles in the video were generated by focusing single laser pulses with a vortex beam profile and 270 nJ pulse energy into the corneal stroma. It is clearly visible that the bubble size strongly fluctuates from shot to shot even though the laser pulse energy is almost constant. Furthermore, the bubbles within the corneal stroma are not spherical, rather, the bubble shape is partially elongated and the shape fluctuates from shot to shot. Therefore, the bubble size was evaluated by digital image processing and the red line in the video represents the bubble wall automatically determined by the algorithm presented in 2.6. To compensate for the shape fluctuations, the cross sectional area within the closed red line was calculated and converted into an equivalent spherical radius.

 

Fig. 4. (a) Representative video of 200 individual intrastromal bubbles generated by laser pulses (1030 nm wavelength, 330 fs pulse duration) at 100 Hz repetition rate (see Visualization 1). Laser pulses with 270 nJ single pulse energy and a vortex profile were focused through NA 0.38 into 150 µm corneal depth. Photographs were taken 3.5 µs after each laser pulse. The size of the bubble was evaluated by digital image processing and the automatically detected bubble wall is visible as red line in each image. The reference bar is 10 µm. (b) Bubble size (radius) in dependence on pulse energy for Gaussian and vortex beam profile. The black arrow at 270 nJ marks the data shown in (a).

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Figure 4(b) summarizes the dependence of bubble size on laser pulse energy for Gaussian and vortex beams. The threshold for photographically detectable bubble formation was 46.8 nJ (Gauss) and 148.6 nJ (Vortex). Above threshold, the bubble size increases rapidly with increasing laser pulse energy to R = 5.0 µm (Gauss) and R = 6.3 µm (Vortex) at 2 times bubble threshold. The increase in bubble size with laser pulse energy is, thus, steeper for the vortex beam than for the Gaussian beam.

For an even better comparison, the photographically determined bubble radius in porcine cornea is shown together with the maximum bubble radius in water in dependence on the laser pulse energy in Fig. 5 on a double logarithmic scale. Additionally, the energy required for successful flap dissection is marked both for Gaussian and vortex beams. The threshold for flap dissection was determined as described in Ref. [33]. We performed flap cuts with different pulse energies and afterwards the flap was lifted using a hockey knife. The quality of the dissection was judged subjectively and classified into one of the three categories: (1) no flap lifting, (2) hard flap lifting, or (3) easy flap lifting. Depending on this classification, the laser pulse energy was then either increased or decreased to determine the minimum value required for easy flap lifting. This procedure was repeated in 10 different corneas for both the Gaussian and the vortex beam. The transition from “hard” to “easy” flap lifting required an energy increase of less than 10%, so that the uncertainty of the respective threshold values is in the range ± 5%.

 

Fig. 5. Photographically determined bubble size in cornea (red) and maximum bubble size in water (blue) in dependence on laser pulse energy for Gaussian (dots) and vortex (circles) beams at NA 0.38 (1030 nm wavelength, 330 fs pulse duration). The threshold energy required for smooth flap cutting at 6 x 6 µm spot distance is marked in the graphs and amounts to 54 nJ (Gauss) and 173 nJ (Vortex). For these pulse energies, the bubble radius for individual intrastromal bubbles amounts to 1 µm and 0.7 µm, respectively.

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Figure 5 shows that bubbles in cornea are generated already at pulse energies below the threshold for bubble formation in water (63.2 nJ Gauss, 172.1 nJ Vortex). The bubble formation threshold in cornea could be even lower, because very small bubbles in cornea may have already disappeared in the photographs taken 3.5 µs after the laser pulse. Hence, for equal energies in the threshold range, bubbles in water are smaller than in cornea. Well above threshold, the picture then changes and the bubble radius in water is 4x larger than in cornea.

At the flap cutting threshold the bubbles are significantly smaller with the vortex beam. The bubble radius at the energy required for flap cutting at 6 x 6 µm spot distance is R = 1 µm for the Gaussian beam and R = 0.7 µm for the vortex beam, which corresponds to a 3 x reduced bubble volume.

3.3 Ultra-high-speed photography of the interaction between individual bubbles and corneal lamellae

Figure 6 shows an ultra-high-speed photography series of intrastromal bubble dynamics induced by a single laser pulse with 2 µJ pulse energy. The laser pulse energy is 3 times above the energy required for successful flap dissection that was determined in [33] and amounts to 0.67 µJ at 6 x 6 µm spot separation. The relatively high laser pulse energy enables a more detailed investigation of the interaction of the cavitation bubble with the surrounding corneal lamellae and a comparison with the results obtained previously by Juhasz et al. [19].

 

Fig. 6. High-speed photography of intrastromal bubble dynamics. A single laser pulse (355 nm wavelength, 560 ps pulse duration) with 2 µJ pulse energy was focused through NA 0.75 in 150 µm depth into the porcine cornea. The view is from the top, along the axis of the laser beam producing the bubble. The first 8 pictures are taken at 50 million frames/s, the following 8 pictures at 1 million frames/s. Imaging times are shown in each photograph. They refer to the center of the time windows set by the 10-ns camera exposure time.

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The first eight photographs in Fig. 6 show the initial bubble expansion within the first 125 ns after the laser pulse. These pictures are taken with extremely high temporal resolution (10 ns exposure time) and spatial resolution (below 0.5 µm) at 50 million frames per second. Due to the high pressure and temperature during optical breakdown, the bubble grows very fast and already after 125 ns, the bubble has a radius of more than 10 µm. However, it can also be seen from the images that the bubble does not look spherical; rather, multiple bubble lobes are formed during the expansion that are vertically connected by a channel formed by the elongated laser plasma. The different layers of bubbles expand along the lamellae of the cornea. This results in multiple layers of stacked bubble lobes that are most likely oriented along the structure of the corneal lamellae.

The following eight photographs in the ultra-high-speed series in Fig. 6 are taken with 1 million frames per second and show the initial collapse phase of the bubble during the first eight microseconds. The maximum bubble radius in the image photographed 545 ns after the laser pulse is approximately 20 µm, and four lobes lying on top of each other are identifiable. The bubble then slightly decreases in size during the following first micro second but remains almost constant in size and shape during the next 7 frames covering a time interval of 7 micro seconds.

 

Fig. 7. High-speed photography of the collapse phase during intrastromal bubble dynamics. A single laser pulse (355 nm wavelength, 560 ps pulse duration) with 1.2 µJ pulse energy was focused through NA 0.75 in 150 µm depth into the porcine cornea. The view is from the top, along the axis of the laser beam producing the bubble. The first 5 pictures are taken at 1 million frames/s and the last 3 pictures at 150000 frames/s. Imaging times are shown in each photograph.

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Fig. 8. High-speed photography of intrastromal bubble dynamics. A single laser pulse (355 nm wavelength, 560 ps pulse duration) with 3 µJ pulse energy was focused at NA 0.75 in 150 µm depth into the porcine cornea. The view is from the top, along the axis of the laser beam producing the bubble. Imaging times are shown in each photograph.

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The collapse phase becomes even more interesting when looking at a longer time period, as presented in Fig. 7. Here, the bubble dynamics is captured at smaller laser pulse energy (1.2 µJ) than in Fig. 6 (2 µJ). The first five photographs are taken at 1 million frames per second and the following three photographs at 150 000 frames per second, which allows a longer observation time of 17.6 µs. Due to the lower pulse energy, the laser-induced plasma is shorter and only two overlapping bubble lobes are formed. The high speed images of the collapse phase show that the small lobe collapses first and pushes its content into the bigger bubble. The vertically in the image plane oriented, elongated bubble part (marked by blue arrows) collapses from the sides, not from the ends as it would occur in water. The collapse is, therefore, probably driven by the elastic force exerted by the collagen fibrils which are elongated along the bubble axis.

Figure 8 shows an ultra-high-speed series of intrastromal bubble dynamics at even higher pulse energy (3 µJ). The first eight photographs show the initial, fast bubble expansion during the first 150 ns. The bubble dynamics is very similar to the dynamics shown in Fig. 6, even at the higher pulse energy when the entire bubble gets larger. The next five photographs in Fig. 8 are taken at 1 million frames per second followed by 3 photographs at 150 000 frames per second, which allows an entire observation period of 17.6 µs. Again, multiple overlapping bubble lobes are formed within the corneal stroma that collapse slowly from their sides, where the collagen fibers are elongated. We evaluated the size of the bubbles in Fig. 8 to obtain insights on the bubble dynamics during initial and collapse phase. Figure 9 shows the temporal evolution of the equivalent spherical diameter on a logarithmic time scale between 5 ns and 17.6 µs.

 

Fig. 9. Evaluation of the bubble dynamics from single-shot ultra-high-speed photography of intrastromal bubble formation (Fig. 8). A single laser pulse (355 nm wavelength, 560 ps pulse duration) with 3 µJ pulse energy was focused through NA 0.75 in 150 µm depth into the porcine cornea.

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3.4 High-speed videography of cutting dynamics

Figure 10 shows high speed videography of intrastromal cutting dynamics with (a) 1.2 µJ and (b) 2.3 µJ laser pulse energy at 1 kHz repetition rate. These energies are 1.8 and 3.4 times larger than the energies required for successful flap dissection, respectively. The time delay between laser pulses and flash illumination was 2 µs. The corneal specimen was moved below the stationary focus at constant velocity (6 mm/s) so that the laser foci were separated by 6 µm. The corneal specimen in the videographs in Fig. 10 was moved from right to left and the videos show the interaction of 65 consecutive laser pulses. The upper part of the specimen shows already separated tissue in which a homogeneous bubble layer appears.

 

Fig. 10. High-speed videography of intrastromal dissection at 1 kHz with (a) 1.2 µJ (see Visualization 2) and (b) 2.3 µJ laser pulse energy (see Visualization 3). The view is from the top, along the axis of the laser beam producing the dissection. The video shows the interaction of 65 consecutive laser pulses (355 nm wavelength, 560 ps pulse duration) that were focused at NA 0.38 into 150 µm depth in porcine cornea. Time delay between laser pulse and flash illumination was 2 µs

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On the videos, the interaction of the laser pulses with residual bubbles from previous laser pulses as well as the interaction of the bubble with the surrounding corneal lamellae can be observed. In some cases, the laser pulses are focused into the already existing bubble layer, so that hardly any energy is deposited. However, as soon as the laser pulse reaches corneal tissue again, a cavitation bubble is formed, which then spreads along the corneal lamellae. As a result, partially pointed bubble lobes are formed. Overall, this results in a progressive dissection of the tissue along the pre-existing bubble layer, with the cavitation bubble always separating a new section of the tissue in the direction along the cutting movement.

 

Fig. 11. High-speed videography of intrastromal dissection at 1 kHz with (a) 0.64 µJ (see Visualization 4) and (b) 1.2 µJ laser pulse energy (see Visualization 5). The view is from the top, along the axis of the laser beam producing the dissection. The video shows the interaction of 65 consecutive laser pulses (355 nm wavelength, 560 ps pulse duration) that were focused at NA 0.38 into 150 µm depth in porcine cornea. Time delay between laser pulse and flash illumination was 24 µs.

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Figure 11 shows high speed videographs of intrastromal cutting dynamics with lower pulse energy (a) at threshold for flap cutting (0.64 µJ) [33] and (b) 1.8 times above threshold (1.2 µJ). The time delay between laser pulses and flash illumination was 24 µs. Although the delay time is longer than in Fig. 10, the cutting mechanics is very similar, which is due to the slow collapse phase of the intrastromally generated cavitation bubbles, as already shown in the previous sections.

3.5 Histology of corneal specimens

Figure 12 shows a histology image of a corneal specimen stained with H&E after intrastromal dissection. The laser pulse energy was 0.69 µJ, slightly above threshold for successful flap dissection at 4 µm spot separation. The flap has a thickness of 200 µm and the intrastromal cut is hardly visible in the histology. Some large residual bubbles within the dissection area are visible, but neither the bubble size nor the number of bubbles are correlated to the initial laser spot separation. Instead, the cut has closed again and the residual gas has collected in isolated large bubbles along the cutting plane.

 

Fig. 12. Overview of an intrastromal dissection in 200 µm depth using laser pulses with 355 nm wavelength, 560 ps pulse duration, and 0.69 µJ pulse energy focused at NA 0.38 into porcine cornea. Spot separation 4 x 4 µm, Paraffin embedding, H&E staining. Residual bubble are formed within the dissection plane

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For more details, Fig. 13 shows semi-thin histological sections of corneal specimens after dissection stained with Toluidine blue at larger magnification. Large cavities with diameters between 5 µm and 30 µm are formed within the dissection plane as seen in Fig. 13(a). The cuts have closed through surface tension. The layer thickness influenced by intrastromal cutting is below 10 µm thickness, especially in the reclosed regions. However, the thickness of material removal in the dissection plane is much smaller than 10 µm because the stroma was cleaved along the lamellar structure. Figure 13(b) shows that local tissue bridges can arise, when lamellae cross the cutting plane. These tissue bridges lead to difficulties in flap lifting.

 

Fig. 13. Semi-thin histological cross section of an intrastromal dissection using laser pulses with 355 nm wavelength, 560 ps pulse duration, and 0.85 µJ pulse energy focused at (a) NA 0.38 and (b) NA 0.28 into porcine cornea, spot separation 4 x 4 µm. Araldite embedding, Toluidine blue staining. The laser beam was incident from the top of the images. The dissection plane is marked by the arrows. In (b), a tissue bridge remains across the dissected plane.

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Figure 14 shows semi-thin histological sections of corneal specimens after dissection stained with Toluidine blue at even higher magnification. The dissection zone can be identified by a slightly modified shape of the lamellar structure, with a thickness of less than 4 µm. Cutting is apparently due to crack formation between the lamellae. Figure 14(a) shows a smooth intrastromal cut with interspersed gas bubbles. These bubbles have an elongated shape along the horizontally oriented corneal tissue lamellae. The crack between the bubbles is closed through surface tension. In contrast, the cut shown in Fig. 14(b) seems to involve a region with lamellae crossing the dissection plane in the central part of the image. This crossing reduces crack formation along the lamellar structure. Figure 14(c) shows besides the main dissection cleavage also a subsidiary crack oriented in 60° upward direction along the lamellar structure, which will lead to tissue bridges that make it difficult to detach the flap.

 

Fig. 14. Semi-thin histological section of an intrastromal dissection using laser pulses with 355 nm wavelength, 560 ps pulse duration, and 1.2 µJ pulse energy focused at NA 0.38, spot separation 6 x 6 µm. Araldite embedding, Toluidine blue staining. The laser beam was incident from the top of the images. The dissection plane in (a) and tissue bridges in (b) are clearly visible. Formation of a subsidiary crack oriented in 60° upward direction away from the dissection plane with the main cleavage can be identified in (c).

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4. Discussion

Understanding intrastromal bubble dynamics und the mechanisms of corneal laser dissection requires knowledge about the anatomical structure of the cornea. Intrastromal dissection is usually performed in the corneal stroma in the anterior part 100–200 µm below the front surface. The corneal stroma amounts to 90% of the entire corneal thickness. The major structural element of the stroma is fibrillar type I and V collagen, which has approximately 70% of the corneal total dry weight [40–42]. The collagen in the human cornea forms long fibrils with a diameter of 31 to 34 nm [43]. Size, spacing and stability of the fibrils are regulated by nonfibrillar collagen (type VI) and proteoglycans in the interfibrillar matrix [40]. The organization of collagen fibrils into independent bundles leads to collagen fibers of approximately 1 to 2 µm thickness and up to 100 µm width, also known as corneal lamellae [22]. The lamellae are oriented in-plane across the cornea and are stacked vertically in 2 -3 µm thick layers. Thereby, the lamellae in the central cornea are aligned predominantly along the horizontal or vertical axis of the cornea, and each layer has a preferential orientation rotated by 90° relative to its neighbors [44]. At the posterior end, near Descement´s membrane, the fibers run in parallel almost entirely uninterrupted for several millimeters [45]. In contrast, the collagen organization in the anterior part of the cornea relevant for intrastromal dissection is much more complex. Within the first 150 – 200 µm of the cornea, fibers can change direction and interact with adjacent fibers. It was shown in studies by two-photon generated second harmonic signals that sutural fibers can run upward and insert into Bowman's layer collagen [46,47]. Winkler et. al. showed that collagen fibers in the anterior stroma tend to branch into multiple distinct fibers that then fuse with each other or even with unrelated fibers originating from a different layer [48]. Furthermore, they identified new collagen fiber types named bow spring and anchor like fibers. Bow spring like fibers originate from the intertwined layers beneath the Bowman's layer, and arc up and backward through the underlying layers in a near-parabolic shape, whereas anchor like fibers originate near the limbus and extend for several millimeters through different layers across the cornea [49]. Transmission electron microscopy images also showed a larger degree of interconnectivity between fibrils in the anterior stroma in comparison to the posterior stroma [22,50]. The densly intertwined meshwork and the connection between Bowman's layer and anterior stroma by sutural or bow spring fibers increases the effective elastic modulus in the anterior corneal stroma [49]. The axial heterogeneity in fiber intertwining and mechanical rigidity has important implications for understanding the effects of refractive surgery [49], and will strongly influence intrastromal bubble dynamics and dissection. Although the present study was performed in porcine cornea, it was recently shown that the structure is very similar to human cornea [51].

In the following sections, we will step by step discuss laser-induced bubble formation in water and corneal tissue, followed by the interpretation of single-pulse effects on intrastromal bubble dynamics, and finally the consequences for multiple-pulse effects during intrastromal dissection.

4.1 Bubble size in water and corneal tissue

The study of laser-induced bubble sizes in water and corneal tissue requires knowledge about the underlying processes that finally lead to bubble formation. Water and corneal tissue are largely transparent in the wavelength range between 350 nm and 1050 nm [52,53]. Hence, energy deposition relies on nonlinear absorption at very high intensities that can be achieved by strong focusing of ultrashort laser pulses [15]. Above the optical breakdown threshold, a high-density free electron plasma is generated that leads to a high temperature and pressure increase and to shock wave emission and a rapidly expanding cavitation bubble [15,18–21]. In water, the rapid vaporization of the liquid leads to such a fast expansion of the bubble that it expands far above its equilibrium radius and collapses again after reaching its maximum radius, often exhibiting several re-oscillations. In this process, the initial bubble oscillation is almost undamped and bubble expansion and collapse take about the same amount of time. The maximum radius of the laser induced cavitation bubble is closely linked to the bubble oscillation time [54,55]. The situation in corneal tissue is very different. Here, the laser-induced bubble must work against the restoring forces of the lamellar structure during expansion, and lamellar rupture results in a loss of bubble energy. This means that no symmetrical bubble oscillation as in water is observed; rather, after an initial small overshoot of the radius, the bubble gets stuck and the collapse progresses very slowly. The observed bubble dynamics in porcine cornea in Fig. 3 shows the rapid expansion of the bubble (the maximum radius is reached already after 300 ns) and the very slow bubble collapse lasting for milliseconds. The different dynamics of cavitation bubbles in corneal stroma and water was already investigated by Vogel et. al. for nanosecond and picosecond laser pulses [18], and by Juhasz et. al. for femtosecond laser pulses [19] but the study in this paper was performed at a much higher temporal and spatial resolution. The image sequence from stroboscopic photography in Fig. 4(a) shows that the bubble size in cornea fluctuates from shot to shot and many of the bubbles have distinct lobes along the lamellar structure. Therefore, the study of the energy dependence of bubble size requires averaging over several events to obtain more accurate conclusions.

The comparison of bubble sizes in water and corneal tissue in Fig. 5 shows that the bubble formation threshold in cornea is lower than in water. If we estimate the bubble thresholds for cornea from the bubble size dependence on laser pulse energy, they are approximately 45 nJ for Gaussian and 140 nJ for vortex beams. This is about 20%−30% below the thresholds for water at 63.2 nJ and 172.1 nJ, respectively. Probably, the biomolecules in cornea provide intermediate energy levels within the bandgap of water leading to more efficient multiphoton ionization, so that the threshold for optical breakdown is slightly reduced compared to water. In previous investigations, researchers stated that the threshold for laser-induced bubble formation is similar for water and ocular media [34,56], but this result may be due to lower temporal and spatial resolution when determining the thresholds.

With regard to intrastromal dissection, the threshold value for bubble formation is less relevant because it also depends on pulse duration, wavelength, and focusing angle. Instead, the minimum bubble size that is required for successful flap dissection is crucial for the cutting mechanisms. If we look at the single pulse bubble size at the minimum energy required for successful flap dissection, it amounts to 1 µm for the Gaussian and 0.7 µm for the vortex beam which is surprisingly much smaller than the spot separation of 6 µm in our study. Intrastromal cutting at energies relevant for flap dissection must therefore be related to a dynamic multipulse interaction with a continuous cleavage propagation along the corneal lamellae as we will later discuss in section 4.3. It is also interesting to note that the bubbles at flap cutting threshold have a 3 times smaller volume with the vortex beam than with the Gaussian beam. When the bubbles are smaller at the flap cutting threshold, the cutting mechanisms must be more efficient. While cutting with the Gaussian beam is based on explosive vaporization and large bubbles, cutting with the vortex beam is more a gentle thermoelastic cleavage with less vaporization and smaller bubbles. The use of vortex beams for gentle and ultraprecise intrastromal corneal dissection and its advantage compared to Gaussian beams was already shown by our group [33] but now we were able to visualize the differences in more detail and explain the higher efficacy. To completely understand the higher efficacy of the vortex approach, it is required to investigate the interaction of cavitation bubbles with corneal tissue that underlies the cutting process. This will be discussed in the following chapters.

4.2 Cavitation bubble dynamics in the layered corneal stroma

Ultra-high-speed photography of the interaction between individual bubbles and corneal lamellae after single laser pulses enabled us to investigate the cavitation bubble dynamics in the layered corneal stroma. Figures 6–8 show image series of the intrastromal bubble dynamics with up to 50 million frames per second. Here, the incoherent illumination under a large focusing angle provides novel insights into the bubble dynamics and its interaction with the lamellar structure. For comparison, Fig. 15 shows photographs of intrastromal bubbles from (a) Juhasz et. al. [19] and (b) our work. In the present images, it is clearly visible that the intrastromal bubble is not spherical like assumed previously, rather, the bubble expands along the lamellar structure and forms multiple bubble lobes that are vertically connected by a channel formed by the elongated laser plasma. The length (l) and diameter (d) of the laser focus are given by Abbe's equations d = λ/NA and l = 4(λ/NA²) [57]. The ratio l/d is 10.5 for NA = 0.38, which is relevant for clinical systems for flap cutting and was mainly used in our study. The length/diameter ratio of more than 10 illustrates that the laser plasma is not ideally suited for cutting horizontally to the elongated axis, the laser “knife” is oriented in the wrong direction. For λ = 1030 nm and λ = 355 nm, the focal length is l = 28.5 µm and l = 9.8 µm, respectively. Thus, even though the plasma size will be somewhat smaller due to the nonlinearity of the absorption process [15], the plasma length exceeds by far the 2 – 3 µm thickness of a single corneal lamellae, especially when working above the threshold. Therefore, several overlapping bubble lobes are formed along the elongated plasma, which was now shown by our ultra-high-speed photographic technique. Interestingly, the orientation of the bubble lobes also corresponds to the preferred direction of the lamellae. On the photographs, each layer has an orientation rotated by 90° relative to its upper or lower neighbors, which reflects the structure and organization of collagen within the central corneal stroma [44].

 

Fig. 15. Laser induced cavitation bubble dynamics in corneal stroma. (a) Stroboscopic photograph of bubble formation in bovine cornea (pulse energy 3 µJ, 1 µs delay) by Juhasz et. al. [19] (copyright 1996 Wiley-Liss, Inc.) showed a dark, spherical bubble and coherent imaging artefacts; (b) Present image of bubble formation in porcine cornea (pulse energy 3 µJ, 1.6 µs delay) enables a view into the bubble revealing several bubble lobes. (c) Bubble size evolution from single-shot ultra-high-speed photographs of intrastromal bubble formation (red dots) in comparison to Juhasz data (black dots) which were obtained from flash photography of several events [19]. Reference bar in the photographs is 20 µm

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The time dependence of the bubble size in the present study in comparison to the data from Juhasz et. al. [19] is shown in Fig. 15(c) on a logarithmic scale. The fundamental sequence of bubble dynamics is similar, but the ultra-high-speed photography now allows the study of the intrastromal bubble interaction with the corneal lamellae in a single-shot technique. It revealed the interaction of the bubble with the corneal lamellae producing a lobular bubble shape. The R(t) curve from [19] exhibits a stronger overshoot at R_max than observed in the present paper, where the bubble radius decreases more slowly. A strong overshoot is typical for bubbles in water. In our investigations, all experiments were performed less than 4 h after enucleation. A R(t) curve closer to that of water may be due to a longer storage time of the eyes in saline solution. This could also explain the differences in bubble shape, which was observed to be approximately round in Ref. [19].

The results obtained in the first part of the present paper, in which the intrastromal cutting mechanisms was investigated exclusively via the interaction of single laser-induced cavitation bubbles, lead to the suggest that a homogeneous intrastromal cut would require a complete coverage of the entire dissection area with bubbles when the laser pulses are applied in a raster pattern. Due to the lobed bubble shape, large bubbles are needed to achieve a cut, and the long plasma shape then leads to a relatively thick dissection layer. However, as shown in Fig. 5, the size of individual bubbles is at the pulse energy required for intrastromal flap cutting actually much smaller than the spot separation. This is surprising, especially when considering that cutting in the anterior part of the stroma is difficult due to the intertwining lamellae which are also partially tilted with respect to the cutting plane. The interwoven stromal architecture near Bowman’s layer with suture lamellae make this even more difficult. Correspondingly, the histology of intrastromal cuts in Figs. 12 – 14 show some tissue bridges, where bubbles from neighboring plasmas do not meet, which is also known from clinical flap creation in LASIK [58]. The dissection mechanism is, therefore, much more complex than would be suggested by just looking at individual bubble dynamics.

A first attempt to solve this puzzle was made by Brujan and Vogel in 2006 [59]. They compared the individual bubble dynamics from Juhasz et. al. summarized in Fig. 15(c) with model predictions for spherical bubble dynamics in tissue-like elastic-plastic media. Their fit to the experimental data provided elastic tissue properties for the cornea, namely the elastic modulus E = 144 MPa, the shear modulus G = 48 MPa and the fracture stress Y = 74 MPa. The elastic modulus E of the human cornea under physiological conditions is much smaller, in the range of 0.2 – 0.5 MPa [60–62]. This means that under rapid deformation such as during bubble formation for intrastromal cutting, the cornea stiffens [63,64] and tearing becomes cleavage.

4.3 Multiple pulse effects during intrastromal dissection

The individual bubble dynamics and the histology in our study already explains some novel features of the dissection mechanisms. However, at sufficiently high repetition rate of the laser system, there is a transition from sequential cavitation events to crack propagation. This dynamics was explored by high-speed videography with a moving specimen. The repetition rate of 1 kHz is lower than clinical repetition rates due to the use of a translation stage but already provides valuable insights.

The high-speed videography of multiple pulse effects during intrastromal dissection in Figs. 10 and 11 showed that the cutting dynamics is based on progressive fracture formation between the lamellar layers of the cornea. The interaction between the laser-induced cavitation bubble, the still existent and slowly collapsing cavitation bubble from the previous pulse, the residual bubble layer in the dissected area, and the lamellar structure of the cornea is highly complex. If the laser pulse energy is too high, the dissection process becomes less efficient, because the laser pulses are focused into already existing bubbles and almost no energy is deposited. Therefore, the energy must be in-between the bubble formation threshold and an energy, at which the subsequent laser pulses will reach corneal tissue, in which a cavitation bubble can be generated. The interaction results in a progressive dissection of the tissue starting from the pre-existing bubble layer, with the cavitation bubble always separating a new section of the tissue in the direction along the cutting movement. Each bubble expansion advances the crack propagation in the stroma along the bubble lobes. We found that the tip part of the crack closes again in the millisecond time interval between subsequent laser pulses (Figs. 10 and 11). However, we still see a continuous crack propagation in the videos taken at 1 kHz, which can be improved at higher repetition rates and then occur at lower pulse energies. At sufficiently high repetition rates, the laser spot movement can probably be matched to the propagation speed of the crack produced by the sequence of individual pulses, and the crack tip propagates continuously. That enables to lower the pulse energy, saves total cutting energy and reduces the damage range along the cut. This hypothesis is confirmed by the fact that a higher efficiency in flap cutting and reduced side effects were observed when the repetition rate of clinical devices from Intralase was increased from 15 kHz to 60 kHz, and 150 kHz, respectively [65,66]. To further understand the mechanisms of corneal dissection we will now discuss the mechanisms of crack formation in more detail.

4.4 Crack dynamics relevant for intrastromal dissection

The study of crack formation began with the pioneering work of Griffith in 1921 who experimentally and theoretically investigated cracks and rupture in fragile solids like glass [67]. Later, this model was extended by Orowan et. al. to elastic plastic materials [68], and in 1948 the work has been extended and systematized to form the science of fracture mechanics [69,70]. Often this work was performed to determine practical criteria to estimate the fracture toughness, which is the resistance of a material to the propagation of cracks [71]. In fracture mechanics, the stress field around a crack must be determined when external forces are subjected to the material. These forces induce a complicated system of stresses in its interior, but the stresses are particularly large near the end of the crack. Hence, for most purposes it is enough to know the stress field near the tip of the crack which can be described by stress intensity factors [70,72]. In the work from Eshelby, crack formation of mode I deformation was defined as a crack that opens up by tension transvers to its length. This type of deformation corresponds quite well to the behavior of a cavitation bubble created at the end of an existing crack in an intrastromal cut between corneal lamellae as schematically shown in Fig. 16.

 

Fig. 16. Schematic drawing of laser induced cavitation bubble formation that induces crack formation along the corneal lamellae as fundamental cutting mechanism in intrastromal dissection.

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The elastic field near the crack tip can be calculated to determine the threshold for crack propagation. It is reasonable that the tip of the crack is pulled apart by the underlying forces, and held together by the cohesive forces acting between the faces inside the tip [73]. Barenblatt assumed that for small loads the cohesive forces are able to compensate the external forces, but at a critical threshold value, this equilibrium is suddenly broken, so that a stress-singularity develops and the crack begins to extend [73]. This fracture or crack dynamics induced by repetitive formation of intrastromal cavitation bubbles is, in our understanding, the fundamental mechanism of intrastromal dissection.

Another view of the fracture process that is worth discussing is based on the crack extension force that leads to an energy release at the crack tip. When the crack propagates, the elastic energy of the specimen and the potential energy of the loading mechanism responsible for the applied stress change [70]. In Griffith`s theory of brittle fracture in solids, the decrease of elastic and potential energy must be equal to or exceed the surface energy of the freshly formed crack as a condition for energy release and crack propagation [67]. Can we this way estimate the energy that is required to separate the corneal tissue for intrastromal dissection? Smolek & McCarey determined the average adhesive strength in human corneas by measuring the tearing force required to separate the cornea lamellae [74]. They found a tearing force per unit tissue width of F_spec = 0.142 kp/cm which corresponds to a force for tearing a stripe of 1 cm width F_tear = 1.39 N and a tearing work for 1 cm tear length of W_tear = 1.39 10⁻² J. Therefore, the separation energy per unit area is E_sep = 1.39 10⁻² J/cm² and the required separation energy amounts to E = 5 nJ for each square at 6 x 6 µm spot separation. This corresponds to a very small fraction of the incident laser pulse energy that ranges between hundreds of nanojoules up to microjoules. Thus, the amount of deposited energy and available bubble energy should be sufficient for the separation of the lamellae, and induction of crack formation along the lamellar structure of the cornea.

Both views of the crack dynamics provide a valid explanation of the mechanisms of intrastromal corneal dissection. Nevertheless, many opportunities remain to improve intrastromal cutting dynamics for refractive surgery. A prerequisite is the optimum combination between pulse duration, wavelength, repetition rate, spot separation and pulse energy. Our work does not provide final parameters for this, but the investigation of the cutting dynamics performed in this work and the insights that we obtained already constitute an important step towards understanding and optimization of the dissection process in refractive surgery. It will be worthwhile to perform further high-speed photographic investigations at pulse repetition rates similar to those employed in clinical systems but that involves the use of scanned laser beams and solving the challenge of imaging a large field at high spatial resolution.

5. Conclusions

In this paper, we investigated the mechanisms of corneal intrastromal laser dissection for refractive surgery by ultra-high-speed photography at up to 50 million frames per second. The unprecedented spatial and temporal resolution enabled us to look inside the intrastromal bubble and to visualize the interaction with the corneal lamellae. We found that the bubble dynamics in corneal tissue is much more complex than in water. The laser-induced bubbles exist longer in tissue and the bubbles are not spherical, rather, multiple bubble lobes are formed along the elongated laser plasma within the cornea. The different layers of the bubbles expand along the corneal lamellae, which are about 2 - 3 µm thick. This results in multiple layers of bubble lobes that are each oriented overlapping along the corneal structure.

Intrastromal cutting is based on a progressive dissection of the tissue along the pre-existing bubble layer, with the cavitation bubble always separating a new section of the tissue in the direction along the cutting movement. Each bubble expansion thereby advances crack propagation in the stroma along the bubble lobes.

The optimization of crack propagation is, hence, the key for a gentle, precise and efficient intrastromal dissection. It depends on many factors like, for example, an appropriate focus shape. If the laser induced plasma is too long and the intrastromal bubble has many lobes, the propagation of many cracks must be strongly driven. With a vortex beam, which has a larger focal diameter but the same length, force distribution is more favorable for crack propagation in horizontal cutting direction along the lamellae. Fewer cracks arise and one crack will more rapidly win the competition. This way unwanted tissue bridges are reduced, as shown by Freidank et. al. [33]. In this context, a short plasma length will also help, which can be achieved by a high NA of the focusing optics and a short laser wavelength. In addition, a high repetition rate in combination with a small spot separation will likely lead to a smoother crack propagation. For these improvements, further investigations are necessary, but the approach presented in this paper opens new avenues for a deeper understanding and future optimization of the mechanisms of corneal intrastromal laser dissection for refractive surgery.