Optimizing deep bone ablation by means of a microsecond Er:YAG laser and a novel water microjet irrigation system

: The microsecond Er:YAG pulsed laser with a wavelength of λ = 2.94 µ m has been widely used in the medical field, particularly for ablating dental tissues. Since bone and dental tissues have similar compositions, consisting of mineralized and rigid structures, the Er:YAG laser represents a promising tool for laserosteotomy applications. In this study, we explored the use of the Er:YAG laser for deep bone ablation, in an attempt to optimize its performance and identify its limitations. Tissue irrigation and the laser settings were optimized independently. We propose an automated irrigation feedback system capable of recognizing the temperature of the tissue and delivering water accordingly. The irrigation system used consists of a thin 50 µ m diameter water jet. The water jet was able to penetrate deep into the crater during ablation, with a laminar flow length of 15 cm, ensuring the irrigation of deeper layers unreachable by conventional spray systems. Once the irrigation was optimized, ablation was considered independently of the irrigation water. In this way, we could better understand and adjust the laser parameters to suit our needs. We obtained line cuts as deep as 21 mm without causing any visible thermal damage to the surrounding tissue. The automated experimental setup proposed here has the potential to support deeper and faster ablation in laserosteotomy applications.


Introduction
As in ancient times, present-day bone surgery still depends mainly on mechanical tools, such as different types of oscillating saws or burs [1,2]. The main drawback of using such tools is the extent of mechanical stress they cause, leading to collateral (sometimes irreversible) damage in patients; as a result, the healing process can be delayed or the patient's life may change drastically [3]. Likewise, the bio-compatibility and degree of contamination of conventional tools pose a high risk of infection to patients. Because conventional tools are still made of metal, corrosion and wear resistance have to be evaluated and minimized. Conventional tool use also limits the surgeon's ability to achieve functional cutting shapes. Several studies have shown the value of using lasers to ablate bone, instead of mechanical tools [4][5][6][7][8][9][10]. Lasers can make contactless cuts, thereby negating any problems arising from mechanical stress. Furthermore, the laser's contact-free interaction with tissues offers greater safety during surgical procedures. Only the cover structure of the laser needs to be evaluated for bio-compatibility and various materials exist Bone ablation implies heating effects, such as carbonization, when the tissue temperature is above 100 • C. Therefore, the tissue surface may be irrigated to avoid damage to the tissues surrounding the ablated area. However, continuous irrigation of the tissue can reduce the amount of material removed as laser energy is absorbed by the water. In dentistry, the solution is to use a continuous spray to disperse the water over the ablated area [17]. This way, the lasers can make superficial cuts, < 2 mm deep. Water cooling has been studied and found to influence the ablation process, depending on the amount of water applied and the type of irrigation system used [4,17,26]. To optimize the ablation rate of the laser system, one must optimize the laser parameters and the irrigation system used. The optimization process is usually not required for superficial cuts (e.g. caries removal). For deeper cuts (in the order of centimeters), however, it is necessary to optimize all parameters, especially if the laser system is to be adapted to real bone surgery in the future.
In this work, we show the process of optimizing the irrigation system and the Er:YAG laser parameters for deep bone ablation. We investigated the effect of constantly cleaning the laser path (irrigated water, debris produced during ablation, and focusing lens) on the ablation process. We explored the laser's limitations in terms of beam quality and settings (beam spot size, energy, repetition rate) and their influence on ablation performance. Based on the results of one-pulse ablation, we estimated the ablation evolution for more pulses. The ablation process was analyzed for both hole and line ablation. Our investigation shows that the key to harnessing and exploiting the laser's capacity for deep bone ablation can be summarized by three main factors: (1) the use of an automated system that senses the need for irrigation; (2) the use of a high-pressure, thin water jet capable of reaching deep into the crater during ablation while avoiding excess water application; and (3) cleaning the laser's path so that the beam can reach the bone surface without encountering additional absorbing material. We propose a system that fulfills all three factors, thereby ensuring optimal ablation process.

Laser, irrigation systems, and bone samples
A Syneron Litetouch Er:YAG laser with a wavelength of λ = 2.94 µm was used for the experiments. The pulse duration and repetition rate of this laser are 100-400 µs and 1-50 Hz, respectively. The maximum average power of the laser is 9 W; the pulse energy and peak power are 10-900 mJ and 0.1-2.25 kW, respectively. To determine the divergence of the laser beam, we focused the beam with a calcium fluoride (CaF 2 ) lens of focal length f = 75 mm. Then, we measured the beam diameter at different positions along the propagation direction (z) by applying the knife-edge method [36]. A hyperbolic function fit of the form d(x) = √ a + bx + cx 2 [37], where d(x) is the beam size, and a, b, and c are the the fitting parameters, was used to determine several geometrical properties of the laser beam, such as the beam quality factor M 2 = π 8λ √ 4ac − b 2 . We determined that M 2 = 22, meaning that the beam diverges √ M 2 = 4.7 times more than an ideal Gaussian beam (M 2 = 1). We further determined the spot size of the focused beam and its depth of focus (twice the Rayleigh length) to be d 0 = 526 µm and DoF = 6.8 mm, respectively.
Several segmented (approximate dimensions 5 x 3 x 3 cm 3 ) pig femur bones were bought at a local supermarket, where they were kept in the freezer at -18 • C post-mortem. The freshness of the bones is unknown, however, the samples were stored in the freezer at -18 • C after purchase, and used within 48 hours. We performed three measurements for each experiment, so the reported results are the corresponding mean values. Figure 1 shows the schematic of the ablation setup. The Er:YAG laser beam was sent in a horizontal z-direction and focused on the bone surface by means of a CaF 2 lens with focal length f = 75 mm. The bone sample was connected to a holder attached to an xyz-actuation mechanism. Manual yz-actuation was realized using regular micrometer stages (PT1/M -Thorlabs) mounted perpendicular to each other, while x-actuation was achieved with a motorized stage (DDSM100 -Thorlabs). All stages were kept static for hole ablation experiments; the motorized stage was activated for line ablation experiments only. An irrigation system was used to cool the tissue during ablation, while pressurized air was used to blow debris off of the bone surface. Irrigation feedback was provided by means of an infrared camera; this system will be described in detail in Section 2.3.  (1). A lens (2) was used to focus the beam on the sample (3). The sample was mounted on an xyz-actuation mechanism (4). Tubes for the water jet irrigation system (5); for air deviation (6) and for pressurized air (7) are depicted. An IR camera (8) was placed to provide feedback about the sample's superficial temperature.
We compared the performance of two different irrigation systems during the ablation process. The first system was an ESI Elveflow microfluidic system, consisting of a pneumatic pressure controller and a channel that pumps air to the water reservoir (80 ml capacity). Water is delivered through a tygon tubing coil with an inner diameter of 500 µm, a maximum pressure of 2 bar, and a laminar flow regime of 1 cm long. This system offers the possibility of controlling water delivery through ON and OFF sequences with a time resolution of 0.15 s. At faster switching sequences, the system is unable to deliver water. At constant irrigation, the water flow rate is 14 ml/min. The tygon tube was placed along the xz-plane, as close to the bone surface as possible (5 mm, forming 45 • angle with the bone surface). The second irrigation system incorporated a novel, specially designed nozzle from Synova Laser MicroJet Technology, which produces a water jet 50 µm in diameter, with 10-800 bar pressure, and a laminar flow regime of length approximately 15 cm. A pump, the Maximator Schweiz AG Pressure Unit 690 bar, ref No. MP030066, was used to deliver water through the nozzle. The pump can continuously deliver pressurized distilled water, up to 690 bar. The Maximator pressure unit has a 10 liter reservoir tank. The water flow rate at 30 bar is 4.8 ml/min. At 30 bar, the thin water jet is very gentle on the soft tissue, and poses no risk of injury. Unlike the ESI system, the Maximator does not possess automated sequence control. To block water delivery, we used air ((6) in Fig. 1) to divert the water jet just enough to keep it away from the ablation area. Here we employed the ESI system to deliver the air at 2 bar by changing its operational modality. The air was delivered whenever irrigation needed to be stopped. To do this, the ESI air tube was placed above the Synova jet so that the air crossed the Synova water jet almost perpendicularly.
We also investigated the effect of using pressurized air to clean the ablated surface and to stop the accumulation of water inside the crater. For this, we applied constant pressurized air to the ablated area at 3 bar in the xz-plane (5 mm, forming a 45 • angle with the bone surface), opposite to the irrigation system.

One pulse ablation
Fundamental models for laser ablation using only one laser pulse, such as the Blow-off model or the Steady-state model are well described by A. Vogel [28]. For the Blow-off model, four main conditions must be upheld. First, the distribution of absorbed energy in the tissue should be governed by the Lambert-Beer law T = Φ Φ i = e −µ a l , where T is the optical transmission, Φ is the fluence transmitted after the incident fluence Φ i has traveled through an optical path length l, and µ a is the absorption coefficient of the material. Second, a threshold fluence Φ th is required to start ablation of the material; fluence values below Φ th only serve to heat the material. Third, material removal starts only after a laser pulse has finished. Fourth, thermal confinement must be fulfilled, which means that the laser's pulse duration τ p must be smaller than the tissue's thermal diffusion time τ d . In this way, the energy is confined to the volume that absorbs the radiation. If the energy is distributed over a larger volume, tissue damage may occur. These conditions are fulfilled for lasers with pulse durations of τ p =100 ns or less. For the Steady-state model, three conditions must be upheld. First, a fixed energy density is required to ablate a unit mass of tissue. Second, ablation starts right after the laser pulse begins. Third, a threshold fluence is required to start ablation of the material, just as in the Blow-off model. Well above the threshold, the Steady-state model predicts a linear dependence between ablation depth and incident fluence; the model is valid for microsecond pulse durations or longer. Some studies [28,38] clearly state that the applicability of either model to a data set of removed material may not be straightforward. For instance, the model that best describes ablation might change depending on the fluence range of the data set. Also, several effects are produced by the debris generated during ablation, such as shielding. This debris affects the absorption coefficient of the material, and is known as plume absorption. In our experiments, we used pressurized air on the surface of the sample to counteract the effect of the debris on the ablation process.
Investigating ablation with one pulse is the first step to analyzing laser ablation. Both Blow-off and Steady-state models were developed based on a one-pulse ablation process. Ablation with one pulse provides an understanding of the initial stage of the ablation process. To see the effect of plume formation (debris from the ablation process) on ablation rate [28], we ablated samples both with and without applying pressurized air to the ablation spot. We did not use high-speed photography to observe plume formation, therefore, the extent to which debris was suppressed is unknown. However, we set a 3 bar pressure which allowed for bone ablation without diverting the water jet from the target position.

Automated feedback system using an IR camera
As a testing method and proof of concept, we monitored the superficial temperature of the sample by means of an IR camera, FLIR A655sc. The camera provides up to 50 fps at full frame 640 x 480 resolution, a spectral range of 7.5 to 14 µm, and an operating temperature range of -40 to 150 • C. The camera was placed above the setup forming an angle of approximately 45 • to not interfere with other components on the laser ablation path. We used the camera to register temperatures at 50 fps during the ablation process to determine whether the tissue needed irrigation or not. For both hole-and line-ablated shapes, the imaging depth of the camera was very limited, because the size of the craters (<1 mm diameter or width) and due to the position of the camera with respect to the ablation area. Thus, feedback was based on the superficial temperatures measured by the camera, mainly from the tissue surrounding the ablation spot.
While running the Er:YAG laser, the Maximator-Synova system, and the pressurized air (at 3 bar) mechanism on the sample during the experiments, we used LabView to control and synchronize the laser's optical beam shutter (SH1/M -Thorlabs), the ESI pump, the camera recording, and the translation stage movement in x-direction when ablating line shapes.
As a first step in the optimization process, we implemented a mechanism to detect the tissue's superficial temperature and to use this information to control tissue irrigation. To increase the ablation depth, the optimization process was done only in order to avoiding early carbonization. Nevertheless, other important heat effects, like the denaturation of proteins and collagen, occur above 60 • C. Those effects also depend on the exposure time. For instance, in the case of denaturation above 60 • C, the damage becomes irreversible if the exposure time is higher than 6 s [27]. During ablation with a pulsed laser, the tissue undergoes dramatic changes in temperature when irrigation is used in combination with the laser. The heat effects of ablation with pulsed lasers plus irrigation on the tissues are not currently well known and depend on the specific conditions of each experiment [8,39], where, most of the time, damage is detected through histology or scanning electron microscopy (SEM) images. To increase the ablation rate without creating carbonization on the surrounding tissue, we performed several experiments while setting a temperature threshold on the camera. Whenever the tissue temperature reached the threshold value, the irrigation system was activated.
In order to evaluate the automated feedback system and comparing it to other systems, the parameters of the Er:YAG laser were kept constant for all experiments in this section. The energy per pulse was 830 mJ and the repetition rate was 10 Hz. We performed different experiments as follows: (a) Automated feedback with jet φ = 50 µm and pressurized air: we used the Maximator-Synova irrigation system (nozzle diameter ϕ = 50 µm, at pressure P = 30 bar) as an automated feedback system with the IR camera. We applied constant pressurized air to the sample at 3 bar to clean debris and to blow off the remaining water. An additional air pump of 2 bar was used to divert the jet when irrigation was not needed.
(b) Automated feedback with jet φ = 50 µm and without pressurized air: we used the same system as (c) but we did not apply pressurized air to the sample target.
(c) ON/OFF sequence with jet φ = 50 µm and pressurized air: we used the ESI irrigation system with the condition (ON and OFF sequence) that we found to be the best in our previous study [26]. The water cycle sequence had a water ON duration of 0.25 s and a water OFF duration of 0.9 s, giving a total period of 1.15 s. For this experiment, we used the Maximator pump and the Synova nozzle with diameter ϕ = 50 µm. Since the water pump could not be controlled by ON and OFF sequences, we used 2 bar air from the ESI pump to divert the thin water jet when it had to be OFF. Additionally, we applied constant pressurized air to the sample at 3 bar to clean debris and to blow off the remaining water.
(d) ON/OFF sequence with jet φ = 50 µm and without pressurized air: we used the same system as (c) but we did not apply pressurized air to the sample target.
(e) ON/OFF sequence with ESI jet φ = 500 µm and without pressurized air: we used the ESI irrigation system with tube diameter ϕ = 500 µm at pressure P = 2 bar and using the best ON and OFF sequence we identified in [26].
For the ON/OFF sequence with the ESI irrigation system we did not apply pressurized air to the sample surface. Compared to the ESI system's pressure capacity of 2 bar, the available pressurized air was either insufficient for blowing off excess water and debris or too high to divert the entire jet, and therefore exposed the target area to carbonization.
We investigated the performance of the irrigation systems and conditions described above while ablating bone. Line ablation was performed using an optimized lateral speed for ablation according to the results of our previous study [40]. Hence, the motorized stage ran at 8 mm/s along the x-direction during ablation. We made up to 800 iterative line cuts at several y-positions.

Optical coherence tomography (OCT)
To obtain cross-section images of the ablated holes and lines, we used an optical coherence tomography (OCT) system built in our laboratory. The OCT system has an Axsun swept laser source with central wavelength λ 0 = 1060 nm, bandwidth ∆λ = 100 nm, and swept rate 100 kHz. The acquired volume size is 7 x 3.56 x 7 mm 3 , and the volume rate is 0.37 volumes s . The axial and lateral resolution of the OCT are 11 and 40 µm, respectively. We acquired B-scans with a field of view of 7 mm and imaging depth of 3.56 mm in air. For image analysis, ablation depths and widths were measured by manual segmentation using ImageJ. The measured depth was the distance from the deepest point of the cut to the surface of the sample, and the diameter (width) was the full width at half maximum (FWHM) of the cut. Due to range of depth limitations of the OCT (max. 3.56 mm), the cut profile of deeper craters appears folded in the OCT image. To measure the entire depth of such cuts, we moved the sample in the vertical direction using the translation stage as often as needed until reaching the deepest point of the cut within the image axial range. This procedure did not affect the final depth measurement because the medium was still air inside the crater. Figure 2 shows an example of manual depth measurement of the crater. Figure 3 shows the depth values obtained with only one laser pulse as a function of incident peak fluence. The continuous and the dashed linear fits refer to ablation with constant pressurized air and without air, respectively. The graph shows the results obtained after averaging over 10 measurements for each incident peak fluence, the error bars correspond to the standard deviation for each data point. In Fig. 3 the ablation was deeper when pressurized air was applied, meaning that the debris were at least partially blown off. The fitting parameters for the ablated depth l using pressurized air gives the following equation for linear fit:

One pulse ablation
where Φ 0 is the incident peak fluence and c is the intersection value on the vertical axis. The linear dependence shows a constant ablation efficiency regime (dl/dΦ 0 ). Based on the experimental data, the fitting parameters are dl/dΦ 0 = 0.0316 mm 3 /J and c = 0.02 mm. Equation (1) and its fitting parameters are valid only for the fluence range used. Whenever the fluence range changes, probably other model will describe the phenomena better. Because our measurements are in the high fluence regime and ablation efficiency is constant (linear fit) for one pulse ablation, a Steady-state model [28] would predict the ablation evolution when more pulses are applied in the specified fluence regime. Additionally, to estimate the maximum obtainable depth not only in the middle of the cut (as shown in fitting Eq. (1)), but also along the crater at each depth (in the xy-plane, r in cylindrical coordinates), the fluence applied to the entire xy-plane should be estimated. A detailed analysis is presented in Section 3.2.1.

Automated irrigation feedback system using an IR camera
To automate the irrigation on the ablated tissue, we set a threshold value for which the camera would register the temperature; this was done in a LabView program. To establish a temperature threshold that both provides a high ablation rate and also prevents tissue carbonization, we tested different values in the temperature range of 30-150 • C. The deepest ablation without any visible sign of carbonization was obtained at 104 • C, just above the vaporization temperature of water. At slightly higher threshold temperatures, we observed yellow tones in the areas surrounding the ablated spot, and the ablation was also deeper. For threshold temperatures above 110 • C, the tissue was carbonized (brown and black tones) and the ablation depth decreased as well. The yellowish marks on the tissue indicated an early carbonization stage [26]. Hence, we considered temperatures above 104 • C unsafe for the tissue and set T th = 104 • C as the temperature threshold for the experiments (a) and (b), where we utilized an IR camera for feedback (Section 2.3).

Hole ablation
For the experiments (a)-(e), we used different irrigation systems and conditions as described in Section 2.3. The ablation times were in the range of 5-300 s (50-3000 laser pulses). For experiments (c) to (e), we used the sequence of water ON = 0.25 s and OFF = 0.9 s. The Predicted ablation as given in Fig. 4(a) was calculated for hole ablation based on the initial depth in fitting Eq. (1), and extended in time according to the number of pulses used. Figure 4(b) shows a comparison of ablation depths from the automated system (experiment (a)) and the calculated cases where the beam quality is improved by lowering its M 2 value. The M 2 values used were 15, 10, 5 and 1, the latter being the ideal Gaussian beam. The beam shape of the Er:YAG laser we used is unknown. Therefore, to calculate the propagation of the beam in z-direction, we used the fundamental Gaussian mode TEM 00 but included the divergence of our beam through its M 2 value, M 2 = 22. The fluence distribution Φ(r, z) along the beam (r-direction on the xy-plane) is where Φ 0 is the peak fluence of the beam, w 0 is the beam waist radius at the focal plane, in our case w 0 = d 0 /2 = 263 µm, E p is the pulse energy and is the beam waist radius of the beam with wavelength λ = 2.94 µm along its propagation direction z. After applying the fitting Eq. (1), we obtained an ablated depth for the first pulse with pressurized air at 830 mJ (peak fluence 764 J/cm 2 ). When replacing Eqs. (4) and (3) in (2), and then in (1), and adding the depth obtained by the first pulse, we obtained the ablated depth for the second pulse, and so on. Hence, the Predicted ablation in Fig. 4(a) shows calculations for bone ablation with up to 3000 laser pulses (300 s), based on the first pulse ablation. Registered depth is that of the middle of the cut (the deepest one). Likewise, the ablation evolution shown in Fig. 4(b) was estimated by replacing the different M 2 values in Eq. (4). Hence, the ablation calculation is also based on the first pulse ablation. In Fig. 4(b), the ablation evolution is shown for several M 2 values and compared to the ablation evolution obtained in our experiment using the ON/OFF sequence system for irrigation and pressurized air on the target sample (experiment (c)).
In Fig. 4(a), the Predicted ablation overlaps the ablation using the automated feedback system (experiment (a)), up to 30 s ablation, giving a depth of almost 13 mm ± 1 mm. Among the experiments, the automated feedback with air (experiment (a)) yielded the best performance, with up to 13 mm depth. After 50 s, the best performance was achieved by the ON/OFF sequence using the Synova 50 µm diameter nozzle (experiment (c)), the depth at 50 s was 13 mm. The diameter as the FWHM of the cut was approximately constant over time for each experiment. The diameters were greater when pressurized air was used. The smallest one was obtained with experiment (d) as 490 µm ± 30 µm, and the greatest one with experiment (a) as 890 µm ± 20 µm. Figure 4(b) shows an important improvement in ablation depth when beam quality is improved, i.e for M 2 as low as possible. For instance, for a cut 50 mm deep (gray dashed horizontal line), the ideal laser (M 2 = 1) would take only 25 s to ablate it, while a laser with M 2 = 5 would take 123 s, and a laser with M 2 =10 would take 300 s. Our current laser (M 2 =22) would never reach a deep cut of 50 mm.

Line ablation
In real surgeries, surgeons desire flexible cut shapes (instead of deep holes) that meet the specific requirements of each type of surgery. Hence, experiments with line ablation provide a more realistic situation. To simplify the experiments, we ablated line shapes with a fixed length of 10 mm. We chose the four best performing experiments from the hole ablation investigation; those were (a), (b), (c) and (d). The deepest line ablation achieved was 21 mm ± 2 mm, and it was achieved with the automated feedback system with additional pressurized air on the target sample (experiment (a)). This experiment performed best along the entire range of # lines made on the bone. It is followed by the ON/OFF sequence, using the Synova 50 µm diameter nozzle and pressurized air as well (experiment (c)). As in hole ablation, the greatest width was obtained when using pressurized air (experiment (a)) as 900 µm ± 100 µm, and the smallest one when pressurized air was not used (experiment (e)) as 610 µm ± 30 µm. The ablation rate was calculated as the ablated volume over the total pulses applied in each number of line cuts (12.5 pulses per line). Since no OCT volumes were acquired, the volume used here is an approximation calculated from the line width as the FWHM of the cut, the total length of the lines (10 mm for all), and the achieved depths for the respective number of line cuts. As seen in Figs. 5(d) and 5(e), the experiments performed without applying pressurized air to the sample show poor ablation performance, while the experiments using the thin Synova nozzle show the best performance.
No fracture or cracks were observed either by eye, OCT, nor microscope, examples can be observed in Figs. 5 and 6.

Optimal laser settings for bone ablation
Alongside studying beam quality, irrigation system, and conditions for ablating bone, laser parameters, such as pulse energy and average power, should also be optimized. The relation between average power P mean , energy per pulse E p , and the repetition rate R r is The beam radius w 0 = 263 µm remained constant, the incident peak fluence Φ 0 was estimated using Eq. (3), and the average intensity I mean is in our experiments, the maximum average intensity was 3.82 kW/cm 2 , achieved at pulse energy 830 mJ and repetition rate 10 Hz.
Using the automated feedback system that performed best at fixed laser parameters up to 13 mm depth, we adopted the same temperature threshold determined in Section 3.2 (T th = 104 • C). We performed two sets of experiments in this section. First, the number of pulses was fixed at 100. Second, ablation duration was fixed at 20 seconds. For both sets, the laser energy varied in the range of 100-800 mJ (Peak Fluence range 92-736 J/cm 2 ) at repetition rates of 5, 10 and 20 Hz. These line ablation experiments provide a broader view for understanding the influence of laser parameters, like energy, power, and beam size, on the ablation process. Figure  Some energy and repetition rate combinations were not possible due to the limitations of the laser, as mentioned in Section 2.1. The maximum average power of the laser is ca. 9 W. The maximum obtainable energy after the optics used is 830 mJ at 10 Hz. For 100 pulses, the minimum ablation depth was 3.2 mm ± 0.4 mm at 100 mJ, and the maximum 7.1 mm ± 0.3 mm at 800 mJ, both at any repetition rate ( Fig. 7(a)). For 20 s, the minimum ablation depth was 3.8 mm ± 0.5 mm at 1 W, and the maximum 11.5 mm ± 0.5 mm at 8 W, both at any repetition rate (Fig. 7(d)).
As did the ablation depth, the measured diameters as the FWHM of the cut increased with the energy and average power. The diameter increased from 320 µm ± 10 µm at 100 mJ to 840 µm ± 30 µm at 800 mJ, and from 340 µm ± 40 µm at 1 W to 1000 µm ± 90 µm at 8 W.

One pulse ablation
The results from one-pulse ablation experiments can be used to estimate how the ablation will evolve as more pulses are delivered to the tissue. Nevertheless, any prediction must also consider several effects that might affect ablation performance. For instance, during one-pulse ablation, the temperature increase was not considered, though it may affect the absorption characteristics of the tissue. This is part of an accumulative process, where more pulses interact with the tissue. We attempted to compensate for this effect by adding a temperature-based feedback system to properly irrigate the ablated area with water. Another effect that could not be considered during one-pulse ablation was the shielding produced by the debris generated from the ablation process. The shield forms in front of the ablation area, and also absorbs laser energy, thereby disturbing the ablation process. One-pulse ablation was performed both with constant pressurized air at 3 bar and without. As shown in Fig. 3, the air removed at least a portion of the debris, as higher ablation rates were obtained when the pressurized air was applied. Moreover, due to the weakness of the peak fluence as the beam propagates in depth, linear ablation cannot be assumed from the first pulse. Summing up the initial depth several times to calculate the final depth after a certain number of pulses is not accurate. To make the calculation more accurate, we included beam propagation (Eq. (2)) in the z-direction and beam size evolution (Eq. (4)), considering the divergence of the beam through its M 2 value and the pressurized air case. Still, more can be done to further improve the accuracy of the propagation calculation. For instance, the real intensity distribution of the beam is unknown, and was not considered, so we assumed the fundamental TEM 00 Gaussian mode in Eq. (2).
The ablation efficiency found from Fig. 3 was obtained for the peak fluence range specified in our experiments. Note that this value can change depending on the fluence range the measurements are, as stated in [28]. Examples of different fluence regimes where other ablation efficiencies are reported are in [42,43]. Additionally, most studies report the measurements calculated using the average fluence, we did it with the peak fluence.

Automated irrigation feedback system using an IR camera
For ablation optimization, irrigation should be adjusted to each laser setting, like energy or repetition rate. For example, the ON and OFF sequence using the ESI irrigation system in [40] was optimized for energies close to 900 mJ at a 10 Hz repetition rate. This sequence might not work well if it is implemented together with other laser parameters, even if they theoretically yield higher ablation rates. An automated feedback system for irrigating tissue can be easily implemented and adjusted to other laser settings or systems. By maximizing the ablation rate with the automated feedback, the ablation process can therefore be considered independent of irrigation. This process allowed us to proceed with finding the best laser settings, provided that irrigation would adapt to each change in the laser's parameters through temperature detection (see Section 4.3). We determined a temperature threshold value of T th = 104 • C; temperatures below T th were considered safe to continue the ablation process without any irrigation on the sample. Temperatures higher than T th were considered unsafe, as the tissue was at risk of carbonization. Hence, once the threshold level was reached, water was delivered to the area of interest to keep the temperature at a safe level.
For this study, the integration time of the camera is 20 ms, much larger than the pulse duration of the laser (max. 400 µs at max. energy per pulse). Therefore, the registered temperature is an average of the real temperature value. For this reason, we do not consider T th = 104 • C as a stated threshold value from now on. This threshold value must depend on the systems used. For using the automated feedback proposed here, a calibration of the system must be always performed to find a proper threshold value.

Hole ablation
When the ON/OFF configuration was used (with both jet sizes 50 and 500 µm), we noticed a yellowish tone in the surrounding areas of the ablated spot, which was also reported by [26]. The pre-carbonized condition (yellowish tone) was present for the ON/OFF sequence because the rising temperature of the bone was never controlled. Since irrigation has a constant delivery rate, it does not adapt to temperature changes of the tissue, making an automated feedback system more important. Furthermore, as mentioned in Section 3.2, for threshold values higher than 104 • C, although the ablation was deeper, the tissue had visible signs of pre-carbonization and carbonization. Therefore, ablation depths can be increased but the drawback is a pre-carbonized area that most likely suffers thermal damage. The severity of the damage is beyond the scope of this work, however, we continued to optimize ablation based on the criterion of not incurring visible damage and ablating as deeply as possible.
As seen in Fig. 4(a), the ablation was always deeper for the conditions using pressurized air, than for the conditions without. We know from Section 3.1 that pressurized air is necessary during one-pulse ablation to blow off the debris. Additionally, when ablating with more pulses, the debris and the irrigation water not only prevent ablation because of the shielding effect, but they also adhere to the lens that focuses the beam. Both phenomena become stronger as ablation progresses, because they are accumulative processes.
The effect of irrigation can be summarized in two stages: less than and more than 40 s ablation. During the first 40 s, the ablation can achieve depths up to 12 mm. As expected, ablation with the automated system (experiment (a)) was deeper than the rest and matched the predicted ablation curve. Similar depths were obtained when using the ON/OFF sequence without pressurized air and the 50 µm nozzle at 30 bar (experiment (d)), and the ESI system with the 500 µm tube at 2 bar (experiment (e)). Nevertheless, after 40 s of ablation, the ON/OFF sequence with the 50 µm nozzle and pressurized air (experiment (c)) yielded deeper holes, but the ablation was saturated. When we observed the samples ablated after 40 s, they were carbonized at the bottom of the cut. This occurred because the camera could only give feedback from the surface of the tissue. Since the irrigation water was frequently running over the surface, its temperature remained below the threshold for longer. Additionally, the pressurized air had already dehydrated the tissue at deeper layers, but there was no feedback about it. This is the main reason why the curve saturates and stops following the predicted ablation curve. In contrast, with automated feedback but no pressurized air on the sample (experiment (b)), carbonization did not occur, but water had accumulated at the bottom of the cut. Both situations describe saturated ablation, see Fig. 4(a) experiments (a) and (b). These results indicate outstanding ablation performance when using an automated feedback system for irrigation. A mechanism for blowing off debris and remaining water, like pressurized air or an extraction system, is necessary. An automated system that can monitor the bone layer by layer during ablation would improve performance further. This information could be provided, for instance, by using phase-sensitive OCT [44].
In Fig. 4(a), the predicted ablation and the ablation using the automated feedback (experiment (a)) follow the same tendency up to 30 s ablation. However, there is a discrepancy in the ablation depth. The main reason for this discrepancy is that the real shape of our beam is unknown, and we based our calculation on the ideal Gaussian beam shape. For our laser with M 2 = 22, the actual beam should be a combination of different higher order spatial modes. The result is usually a beam with several side lobes that were not considered in our calculation. The accuracy should increase by computing the real shape of the beam. Figure 4(b) shows the estimated performance of the laser in terms of ablated depth in the case of a well-optimized irrigation system (i.e. no thermal damage and no accumulation of water or debris). We are unable to lower the M 2 value of our laser at present. The best performance of the laser after 30 s (experiment (c) in Fig. 4(b)) is being compared to situations where the quality of the beam would have been improved by changing the M 2 quality factor of the beam, reducing it to M 2 = 15, M 2 = 10, M 2 = 5, and M 2 = 1. We observed a great improvement when reducing the quality factor M 2 . This information can be used in future to build a more efficient laser capable of ablating deeply and in less time.

Line ablation
Investigating the ablation of shapes is important for evaluating applicability and performance in real bone surgery settings. In our study, we ablated lines using the best four irrigation systems and conditions as determined by the hole ablation experiments, Section 4.2.1. As seen in Fig. 4(a), in the case of line ablation we found that the automated system (experiment (a)) performed best over the entire time window of up to 1000 s. The second best was the ON/OFF sequence condition with pressurized air (experiment (c)). Due to the lack of pressurized air, the automated feedback and the ESI sequential system, experiments (b) and (e), respectively, did not perform as well. Unlike the hole ablation case, the different irrigation systems performed as expected for line ablation. We expected the automated feedback system to communicate with the irrigation system if the tissue was dry or not, and irrigate the bone accordingly. The imaging depth limitation of the camera was present for line ablation as well but the irrigation water was spread and distributed more homogeneously over the line cut during ablation, resulting in a more uniform temperature distribution. Hence, the temperature at the deeper layers of the ablated line was similar to that of the surface. Temperature information was then processed by the automated system, and irrigation water was delivered accordingly. As shown in Fig. 5(b), we achieved a depth of 19 mm (line length 10 mm) after 400 lines in 500 s (8.33 min). The maximum depth achieved was 21 mm after 800 lines in 1000 s. Of the experimental setups provided, no other irrigation system could improve the laser ablation to reach an equivalent depth. Additionally, as the pressurized air cleaned the laser's path, laser energy was mostly employed for ablation. Far less ablation depth was achieved with the other three irrigation conditions. Their curves achieved a state of saturation, thus, using those systems, deeper ablation could never be reached. Even with the second-best setup (experiment (c)), the laser hardly achieved 15 mm depth after 500 lines and it continued to be saturated. Experiments (b) and (e) reached saturation at 13 and 10 mm, respectively.
During line ablation, the advantages of having a thin water jet of 50 µm at 30 bar pressure instead of the 500 µm at 2 bar jet became clear. The thin jet can reach ablated tissue as deep as 15 cm without losing its compactness, making it ideal for deep ablation. Likewise, its high pressure makes it so robust that it cannot be easily diverted from the ablation area when the pressurized air hits the sample. Only the water that has already been delivered to the tissue is removed by the pressurized air. Therefore, the cooling performance of this thin water jet was exploited to great benefit in this study.
The maximum ablation depth of 21 mm of homogeneous cortical bone reported here exceeds the maximum reported in literature. An Er:YAG laser with average intensity 1.89 kW/cm 2 ablated up to 15 mm depth of combined cortical, cancellous and diseased bone in [25]. An Er:YAG laser was also used for human cadaver mandible osteotomy, reaching a maximum depth of 23 mm of combined cortical and spongy bone [45]. The deepest ablation of cortical bone achieved using a CO 2 laser in [6] was 7.7 mm, with average intensity 83.8 kW/cm 2 .
Since the beam gets weaker as it propagates inside the cut, displacing the beam towards the bone might increase the ablation depth. However, for our particular conditions, there is no space available between the pressurized air and the bone, limiting the mobility of the bone towards the beam. Despite displacing the beam can be a solution, in many systems where the displacement in the propagation direction is limited, this would not be possible to do. For instance in endoscopic applications.
A few studies on different optical methods show that carbonization can be detected during the ablation process. For instance, information about thermal expansion of the tissue, detected by phase-sensitive optical coherence tomography (OCT) [44,46], can be used to determine the temperature distribution. In the case of a plasma-generated ablation process, laser-induced breakdown spectroscopy (LIBS) could provide information about the carbonized state [47]. These methods would be potentially more precise for pre-carbonization detection as feedback from the tissue is provided layer-by-layer, not only superficially. These methods, however, demand profound investigation before they could be applied rigorously to our study. Additionally, robust systems would have to be adapted to the current ablation setup. Figure 7(a) shows the depth obtained with 100 pulses, while varying the energy of the laser at different repetition rates. At any fixed energy position, the ablation was almost the same, independent of the repetition rate of the laser. In Fig. 7(b), at first, it seems like increasing the average power by increasing the energy and decreasing the repetition rate is enough to provide deeper ablation. However, when the ablation time is fixed, i.e. 20 s, it is possible to determine how the ablation can be increased over time. In Fig. 7(c), at any fixed energy position, ablation is deeper at higher repetition rates. Figure 7(d) shows that at any fixed position of average power, ablation is the same, and only increases when increasing both the energy and the repetition rate.

Optimal laser settings for bone ablation
To the best of our knowledge, the optimal combination of laser parameters (beam quality, beam size, energy, and repetition rate) for deep ablation of bone, has not yet been discussed in the literature. Some authors report on the performance of lasers for superficial ablation (few mm deep) [6,17,48], and some others report on the thermal damage to tissues [8,39,49]. As suggested by the results of this work, exploring ways to achieve deeper ablation implies a more profound study of irrigation systems and the optimal combination of laser parameters. Energy and average power are often studied separately. For instance, it is well known that increasing the energy at a fixed repetition rate increases ablation. In [15], the maximum ablation depth of enamel and dentin was achieved at a maximum energy of 400 mJ and a repetition rate of 2 Hz (average power 0.8 W). Other studies show that when average power is high (13.8 W), the repetition rate is high (200 Hz) and energy is relatively low (69 mJ) [24], bone ablation depth increases as well. It is not obvious which combination of laser parameters will provide deeper ablation. One reason for this is that the same average power can be obtained by different combinations of energy and repetition rates (P mean = E p · R r ). The second reason is because of the shielding effect provoked by excess water and debris on the beam path. A slower repetition rate results in less accumulation of debris on the beam path between one pulse and another [50]. Nevertheless, we managed to evade the shielding effect up until a certain depth. Thus, it is now possible to study the ablation process dependent on the laser parameters only, when using the automated system with pressurized air up to a depth at which it is considered to work well (12 mm). Ablation now depends on which parameter has a greater impact on the ablation rate: the energy, repetition rate, or average power. According to our results (see Fig. 7), the deepest possible ablation is achieved by increasing the average intensity. Thus, the energy and repetition rate should be increased, while the beam size should be decreased (Eq. (6)). However, increasing the average intensity by decreasing the spot size will result in faster divergence (decrease in depth of focus), leading to superficial ablation only. A careful balance between spot size and depth of focus of the beam is required. The ablation depth will depend on how fast the peak fluence Φ 0 decreases along the depth until it reaches the ablation threshold value Φ th . Φ 0 approaches Φ th faster when the depth of focus (DoF) is shorter. Then, it is also important to calculate ablation depth progress using the geometric parameters of the beam, like beam quality M 2 , beam radius w 0 and even beam shape Φ(r, x) (Eqs. (1)-(4)). Additionally, thermal damage can be avoided by setting the correct repetition rate. The repetition rate of the laser must not exceed approximately (10 · T d ) −1 , where T d is the thermal diffusion time; T d = D 2 z /4α [50], where D z is the thickness of the damage zone, and α is the thermal diffusivity of the tissue. For human cortical bone, the thermal diffusivity was found to be 0.1461 mm 2 /s and for bovine cortical bone 0.2264 mm 2 /s [51]. For Er:YAG laser with typical pulse duration of hundred microseconds, the damage zone of bone reported is up to 15 µm [22,39,52]. Thus, the maximum repetition rate that can be set is approximately 260 Hz for human cortical bone and 400 Hz for bovine cortical bone.

Conclusion
The study of bone ablation using a microsecond Er:YAG laser was performed by exploring and analyzing different aspects that contribute to optimizing the ablation process. First, the result of the one-pulse ablation experiment was used to estimate the ablation process after the application of several pulses. In this estimation, we also considered the laser's characteristics, such as incident fluence, divergence, and beam spot size. Experimentally obtained ablation results, using different irrigation systems and conditions, were compared to the estimated ones. This comparison was useful for understanding the limitations of the systems used in the experiments. For instance, the ablated depth obtained with the automated system (experiment (a)) and the calculated depth followed the same path until saturation started. Saturation (see Fig. 4) occurred at the point where the bottom of the crater started to carbonize. The carbonization was due to temperatures exceeding the threshold temperature we found T th = 104 • C. At this point, the limitation of the IR camera to detect only superficial temperatures was revealed. The need for an appropriate automated system became clear, as well. With further information from experiments focused on thermal damage to the tissue, the ablation process could be easily adjusted by changing the temperature threshold in the software. However, by implementing a system that is able to detect a pre-carbonized state, layer by layer, and deeper as the ablation progresses, the feedback will be more precise and the ablation will go deeper and faster.
A thin water jet of 50 µm at 30 bar pressure was very convenient for deep ablation. The jet could deliver water deep into the ablated tissue, cooling the entire ablated area. Provided that pressurized air or a suction system is also used to blow off the debris and excess water, the ablation will be optimized. This fact was especially visible for line ablation (see Fig. 5(b)) in our study. The maximum ablation depth was obtained while using the automated feedback system with a thin water jet and applying pressurized air to the sample. The maximum depth obtained was approximately 20 mm, already considered deep ablation for bone. To optimize the laser settings for bone ablation, the automated feedback system was used to ablate within the range where it was working properly (depths below 12 mm). Besides correcting for thermal damage that can occur due to high temperatures on the tissue and other phenomena that could drop the quality of ablation, the most efficient way to optimize the laser parameters is to look at the average intensity of the beam. Increasing the average intensity may guarantee high ablation rate. As observed in Fig. 7(b), for a fixed ablation time, the ablation is the same when the average intensity remains constant and both the repetition rate and the energy of the laser change. Thus, maximizing average intensity using any combination of energy and repetition rate will maximize the ablation rate as well. In principle, the beam size should be decreased. Nevertheless, if the objective is to ablate deep in the bone, there is a trade-off between the size and the average intensity of the beam. If the beam size of the laser is fixed, as it was in our case, the optimization parameter (average intensity) is simplified as the average power of the beam (see Fig. 7(b)). The drawback of choosing very high repetition rates is that the automated irrigation feedback system must be fast enough to detect fast temperature changes on the tissue and that it might lead to thermal damage if not set correctly.

Funding
Werner Siemens Foundation through the Minimally Invasive Robot-Assisted Computer-guided LaserosteotomE (MIRACLE project).