2.1.

Shadow Photography

The experimental setup for shadow photography is schematically shown in Fig. 1, and it is basically the same as described in Refs. 28, 35.

Fig. 1

Schematic overview of the shadow photography experimental setup. A SG is used to trigger the CCD camera, the excitation lasers and the illumination laser. A beam expander (BE) is used to increase the diameter of the illumination beam. Two photodiodes (PD1 and PD2) and an oscilloscope (OSC) are used to detect the output of the illumination and the excitation laser, respectively. The process is controlled via a PC.

The cavitation bubbles generated in liquid by an excitation laser were illuminated by 30 ps long frequency-doubled Nd:YAG ($\lambda =532\mathrm{nm}$) laser pulses (Ekspla, Lithuania, PL2250-SH-TH), and imaged through a microscope by a charge-coupled device (CCD) camera (Basler AG, Germany, scA1400-17fm, 1.4 Mpx). The spatial resolution of the optical system was in the range of 3.6 to $5.6\mu \mathrm{m}/\text{pixel}$. For a particular series of measurements, the spatial resolution was determined using images of a calibrating pattern. The excitation and illumination lasers as well as the camera were synchronized with a signal generator (SG; Tektronix, US, AFG 3102) connected to a personal computer (PC).

Three types of excitation laser sources were used: Er:YAG ($2.94\mu \mathrm{m}$), Er,Cr:YSGG ($2.73\mu \mathrm{m}$), and Nd:YAP ($1.34\mu \mathrm{m}$). The Er:YAG system used was a LightWalker AT (manufactured by Fotona), the Er,Cr:YSGG laser was a WaterLase iPlus (manufactured by Biolase), and the Nd:YAP laser was a modified Spectro XP (manufactured by Fotona). The erbium lasers were fitted with appropriate standard FT handpieces (Fotona Er:YAG H14 handpiece with $400\mu \mathrm{m}$ PIPS tip; Biolase Er,Cr:YSGG Gold handpiece with $415\mu \mathrm{m}$ RFT3 tip), while the Nd:YAP laser was fitted with a laboratory handpiece ending with the PIPS $400\mu \mathrm{m}$ tip. The PIPS and RFT3 tips have a conical ending resulting in a radial emission out of the FT.

The lasers were operated in the following pulse modes and durations: (a) Er:YAG laser in standard SSP ($80\mu \mathrm{s}$) mode,³⁶ (b) Er,Cr:YSGG laser in H pulse ($400\mu \mathrm{s}$),³⁶ and S pulse ($2000\mu \mathrm{s}$) duration mode, and (c) Nd:YAP laser in $90\text{-}\mu \mathrm{s}$ pulse duration mode. The above pulse durations ($t_{\mathrm{L}}$) represent times during which 90% of the cumulative laser pulse energy was delivered to the liquid, as measured with a 60-MHz InAs photodiode (PD-InAs) at laser pulse energy $E_{\mathrm{L}}\approx 100\mathrm{mJ}$.

The excitation laser pulses were delivered into a large reservoir ($100\times 100\times 70\mathrm{mm}$) filled with distilled water through a corresponding FT. The FT’s end was placed $h=10\mathrm{mm}$ below the water level, as shown schematically in the inset of Fig. 1.

Using shadow photography, we measured the vapor-bubble dynamics for different laser wavelengths, pulse duration modes, and pulse energies, $E_{\mathrm{L}}$. A sequence of images from multiple events was recorded by varying the time delay between the excitation pulse and the illumination pulse. The bubble locally changes the refractive index of the liquid. Consequently, a discontinuity appears on its wall, representing the boundary between the steam and the surrounding water. This results in the refraction of the laser beam casting a shadowgraph where the FT and cavitation bubble are visible as a black area on a bright background.³⁴

A typical sequence of images of a bubble captured at different times after the beginning of a laser pulse is shown in Fig. 2. The laser-energy deposition causes water to superheat, and its explosive boiling induces a vapor bubble. As already observed elsewhere,²⁸ a spherical bubble develops when a conical FT is used while a channel-like bubble develops when a flat FT is used. All FTs used in this shadowgraphic experiment (PIPS and RFT3) had a conical ending, and, therefore, spherical bubbles were generated. The spherical bubble’s volume ($V=4\pi R^3/3$) was calculated from the bubble’s radius ($R$) as obtained using the image processing of the shadowgraphs captured by the CCD camera.

Fig. 2

Typical shadowgraphic images of vapor bubbles in the infinite liquid induced by an Er:YAG laser equipped with a conical FT.

After the laser-induced boiling, the high pressure of the vapor leads to the rapid expansion of the bubble’s radius ($R$), observed in images from 0 to $100\mu \mathrm{s}$ in Fig. 2. During the expansion, the bubble passes over the equilibrium state. Thus, at its maximum radius ($R_{\max }$) and maximal volume ($V_{\max }=4\pi R_{\max }^3/3$) (see Fig. 2 at $120\mu \mathrm{s}$), the internal pressure is lower than the pressure in the surrounding liquid. This difference in pressures forces the bubble to collapse (e.g., see images from 140 to $240\mu \mathrm{s}$ in Fig. 2). A shockwave is emitted at the time of the bubble’s collapse (see Fig. 2 at $260\mu \mathrm{s}$). The collapse, in turn, can initiate secondary oscillations of the bubble, as visible from 280 to $440\mu \mathrm{s}$ in Fig. 2.

When the bubble reaches its maximum volume, its radial velocity vanishes. The total energy of the bubble $E_{\mathrm{B}}$ can thus be obtained as the product of its maximum volume ($V_{\max }$) and the hydrostatic pressure ($p$) of the liquid ($p={10}^5\mathrm{Pa}$ for water):^2,28

2.2.

Measurements of Fluid Motion

This set of experiments was carried out in a simulated model of a root canal including a narrow lateral canal, designed to represent typical root canal morphology consisting of accessory canals and an apical delta.^37–39 An accessory canal is defined as a branch of the main pulp canal or chamber that has communication with the external root surface.³ Depending on their location, accessory canals can be referred to as furcation canals⁴⁰ when they are in the bifurcation or trifurcation area of the multirooted teeth,⁴¹ or as lateral canals, when being in the coronal or middle third of the root.³ Similarly, an isthmus (anastomosis) is when two or more canals existing in the same root are joined by a thin communication.^5,42–44

Figure 3 shows the acrylic model of the root canal morphology used in our experiment. The horizontal groove, visible in the bottom-right corner of the model, represents an accessory/lateral canal and was prepared by placing a piece of copper wire on a steel surface, preheated to 80°C, and pressing the precut model onto it. This method allows for flexibility in the design of the canal and produces very clear, smooth imprints resulting in desirable optical properties. The lateral canal in Fig. 3 is $\sim 13.5\mathrm{mm}$ long, with a width of $160\mu \mathrm{m}$ and a depth of $70\mu \mathrm{m}$. In all the experiments described, the root canal model was filled with and submerged in distilled water.

Fig. 3

Acrylic model of a root canal used in the experiments.

The excitation laser sources used in this part of the study were Er:YAG ($\lambda =2.94\mu \mathrm{m}$) and Nd:YAP ($\lambda =1.34\mu \mathrm{m}$). The Er:YAG system (LightWalker AT) was equipped with aH14 handpiece with a conical $600\mu \mathrm{m}$ PIPS FT or a flat ended $600\mu \mathrm{m}$ VARIAN FT (both manufactured by Fotona). The Nd:YAP system was equipped with an elongated $320\mu \mathrm{m}$ fiber with a flat ending. The excitation laser pulses were delivered into the root canal model filled with distilled water through a corresponding FT or elongated fiber. The FT’s end was placed $h=10\mathrm{mm}$ below the water level, as it is schematically shown in the inset of Fig. 3.

The dynamics of the cavitation bubble generated inside the root canal are in many aspects more complex than in the infinite liquid and may depend not only on the depth of the cavity but also on the diameter and shape of the main root canal and its side canals, and as well on the position of the side canals, diameter and shape of the delivery fiber, on the distance of the fiber end from the liquid–air interface, relative depth inside the canal, and other factors. We have studied these dependences extensively with some results already recently published.³³ The volume of the cavitation bubble decreases with the relative depth of the fiber tip inside the root canal; however, the oscillation times of the bubbles remain roughly the same. Similarly, the dimensions of the cavitation bubbles are affected by the particular shape and size of the root canal, while the oscillation period is largely unaffected by different root canal morphologies. This was tested on cylindrical models of varying radii as well as the different model root canals presented in this paper and Ref. 33. Furthermore, absolute depth (distance, in the range of 5 to 15 mm, of the fiber tip end from the water’s surface) has no significant effect on the bubbles’ volumes or oscillation periods if the relative depth of the fiber tip inside the root canal model is kept constant. Figure 4 shows a typical cavitation bubble generated with a 25-mJ Er:YAG laser pulse delivered through a conical fiber tip positioned 3 mm deep inside the model root canal. As it has already been established,³³ the oscillation period of the bubble is $\sim 200\%$ to 250% longer than in an infinite liquid. Due to various factors including friction on the root canal walls, increased volume of water to be displaced from the root canal, and so on, the volume of the vapor bubble inside the model root canal is smaller than the volume of the bubble in an infinite liquid. For reasons mentioned above, the model root canal morphology, the depth of the fiber tip inside the root canal, and the absolute depth of the fiber tip below water surface were all kept constant during the experiments. Further study is required to fully characterize vapor bubbles’ dynamics inside different root canal morphologies.

Fig. 4

A sequence of images of a typical cavitation bubble inside the model root canal, generated by an 25-mJ Er:YAG laser pulse delivered through a conical fiber tip. The images were recorded with a high-speed camera (Photron FASTCAM SA-Z) at 120,000 fps. The length of the oscillation is $\sim 550\mu \mathrm{s}$, which is roughly twice as long as in an infinite liquid (see Fig. 2). The collapse, which initiates at $\sim 280\mu \mathrm{s}$ after the beginning of the laser pulse, is less symmetrical than is the case in an infinite liquid and rebounds are less pronounced or not present at all.

Various approaches were proposed and tested to facilitate the visible detection of water flow. The introduction of ink into the root canal prior to laser agitation proved to serve as a poor indicator of the flow of water, not providing a clear-enough contrast between the colored water entering the lateral canal and the water already present in the lateral canal, and rapidly becoming more diluted with each subsequent laser pulse.

An assortment of small particles ranging from a diameter of under $1\mu \mathrm{m}$ (polishing powder) to hollow glass spheres with a mean diameter of $10\mu \mathrm{m}$ used as seeding particles specifically for the purpose of investigating gas flow were also tested and found to be inadequate. While the magnification was not sufficient to make out single particles, they provided good contrast in high-enough concentrations. But their abundance also altered the dynamics of the fluid to such an extent as to be considered incomparable to water. Furthermore, due to the relatively large variability in the size of the glass spheres, a large-enough particle would invariably get pushed into the lateral canal, clogging it and forcing the experimenter to disassemble, clean, and reassemble the model root canal, altering it to such a degree as to make subsequent measurements incomparable to earlier ones.

For monitoring the speed of water flow we utilized, instead of the previously employed methods, gas bubbles that naturally form in a water-filled root canal as a result of laser agitation. While most of the bubbles quickly dissipate, some of them get pushed into the lateral canal and can serve as an indicator of water flow. A high-speed, high-resolution camera (Velociraptor HS by OptoMotive, Mechatronics Ltd., $2048\times 1088\text{pixels}$, 340 FPS) was used to capture the motion of air bubbles through the lateral canal.

When measuring the dependence of the fluid motion in a lateral canal on Er:YAG laser energy ($E_{\mathrm{L}}$), and in order to eliminate any influence of slight changes in the pulse duration with laser system output energy, these measurements were made with the Er:YAG laser system operating at a fixed SSP pulse duration mode and at a fixed system output energy of 130 mJ, resulting in a fixed laser pulse duration of $t_{\mathrm{L}}=85\mu \mathrm{s}$. The laser energy ($E_{\mathrm{L}}$) at the exit of an FT was then varied by inserting apertures of different diameters into the laser handpiece.

On the other hand, when measuring the dependence of the fluid motion on Er:YAG laser pulse duration ($t_{\mathrm{L}}$), the system output energy was fixed, and the pulse duration was measured with the InAs photodiode and was varied by changing the pulse duration mode.

Figure 5 shows an example of a pair of air bubbles that are visible in the lateral canal, after each laser pulse. By tracking the position of these bubbles, it was possible to evaluate the dynamics of the flow of water through the lateral canal as a result of PIPS.

Fig. 5

Movement of a pair of gas bubbles inside the lateral canal.

By examining light intensities along the length of the lateral canal in individual frames of the recorded video and applying appropriate filters, it is possible to detect and track the position of individual bubbles. Figure 6 shows the intermediate results of the analysis for two typical paths of bubbles at laser frequencies 3 and 4 Hz. The $y$-axis represents the position along the length of the canal (in pixels) and the $x$-axis represents individual frames in the video. The angle of travel depends on the frequency of laser pulses, while the per-pulse speed of the bubble can be determined by examining the movement of the bubbles along the $y$-axis.

Fig. 6

Bubbles’ position versus time at laser frequencies of 3 and 4 Hz.

Figure 7 shows the results of a typical diagram created by applying a peak detection algorithm. The spatial resolution of the system was determined by using images of a calibration pattern. The speed of fluid motion ($v_{\mathrm{f}}$), measured in mm/pulse from the distance traveled by an individual bubble following each laser pulse, was extracted for further analysis.

Fig. 7

Peak detection was used to determine bubbles’ positions after each laser pulse. $T_{\mathrm{p}}$ stands for the period corresponding to the frequency of the laser pulses and $\mathrm{\Delta }x$ is the distance traveled by the bubble (in pixels).

3.1.

Analysis of Shadowgraphic Data

Figure 8 shows the measured maximal radii ($R_{\max }$) of cavitation bubbles as obtained for different laser wavelengths, pulse duration modes, and FTs.

Fig. 8

Measured maximal bubble radii $R_{\max }$ as a function of laser energy ($E_{\mathrm{L}}$) for (i) Er:YAG laser pulse with $t_{\mathrm{L}}=80\mu \mathrm{s}$ (SSP mode) delivered through the $400\mu \mathrm{m}$ PIPS FT (circles); (ii) Er,Cr:YSGG laser pulse with duration of $t_{\mathrm{L}}=400\mu \mathrm{s}$ delivered through the $415\text{-}\mu \mathrm{m}$ RFT3 FT (H mode; diamonds) or $t_{\mathrm{L}}=1800\mu \mathrm{s}$ (S mode; triangles); and (iii) Nd:YAP laser with $t_{\mathrm{L}}=90\mu \mathrm{s}$ delivered through the $400\text{-}\mu \mathrm{m}$ PIPS FT (squares).

The mechanical energies of the bubbles ($E_{\mathrm{B}}$) are calculated from bubble’s radii (shown in Fig. 8) using Eq. (1) and shown in Fig. 9.

Fig. 9

Bubble energy $E_{\mathrm{B}}$ as a function of laser energy ($E_{\mathrm{L}}$) for (i) Er:YAG laser pulse with $t_{\mathrm{L}}=80\mu \mathrm{s}$ (SSP mode) delivered through the $400\text{-}\mu \mathrm{m}$ PIPS FT (circles); (ii) Er,Cr:YSGG laser pulse of duration $t_{\mathrm{L}}=400\mu \mathrm{s}$ delivered through the $415\text{-}\mu \mathrm{m}$ RFT3 FT (H mode; diamonds) or $t_{\mathrm{L}}=1800\mu \mathrm{s}$ (S mode; triangles); and (iii) Nd:YAP laser with $t_{\mathrm{L}}=90\mu \mathrm{s}$ delivered through the $400\text{-}\mu \mathrm{m}$ PIPS FT (squares).

3.2.

Analysis of Fluid Motion Data

Figure 10 shows the measured dependence of fluid motion per pulse ($v_{\mathrm{f}}$) in the lateral canal on Er:YAG ($t_{\mathrm{L}}=85\mu \mathrm{s}$) laser energy for a conical (PIPS) and flat (VARIAN) FTs.

Fig. 10

Measured dependence of fluid motion per pulse ($v_{\mathrm{f}}$) in the lateral canal on the Er:YAG ($t_{\mathrm{L}}=85\mu \mathrm{s}$) laser pulse energy for a conical ($600\mu \mathrm{m}$ PIPS) and flat ($600\mu \mathrm{m}$ VARIAN) FT.

The measured dependence of fluid motion ($v_{\mathrm{f}}$) on laser pulse duration ($t_{\mathrm{L}}$) is shown in Figs. 11 and 12. Figure 11 shows the dependence of $v_{\mathrm{f}}$ on $t_{\mathrm{L}}$ for Er:YAG laser pulses with two different pulse energies: $E_{\mathrm{L}}=30\mathrm{mJ}$ and $E_{\mathrm{L}}=40\mathrm{mJ}$. Figure 12 shows the measured dependence of $v_{\mathrm{f}}$ on $t_{\mathrm{L}}$ for two types of FTs ($600\mu \mathrm{m}$ PIPS and $600\mu \mathrm{m}$ VARIAN) at the same laser pulse energy of $E_{\mathrm{L}}=14.5\mathrm{mJ}$.

Fig. 11

Dependence of the fluid motion per pulse ($v_{\mathrm{f}}$) on pulse duration ($t_{\mathrm{L}}$) for Er:YAG laser pulses with the following two different pulse energies: $E_{\mathrm{L}}=30\mathrm{mJ}$ and 40 mJ. A $600\text{-}\mu \mathrm{m}$ PIPS FT was used.

Fig. 12

Measured dependence of the fluid motion per pulse ($v_{\mathrm{f}}$) on pulse duration ($t_{\mathrm{L}}$) for two types of FTs ($600\mu \mathrm{m}$ PIPS and $600\mu \mathrm{m}$ VARIAN) at the same laser pulse energy of $E_{\mathrm{L}}=14.5\mathrm{mJ}$.

As can be seen from Figs. 10 and 12, the fluid motion per pulse is larger when a conical FT is used rather than a flat one (see Figs. 10 and 12). The difference is statistically significant ($P<0.0001$). This is in agreement with a previously published study,²⁸ where it was shown that the OD energy-conversion efficiency (${\eta }_{\mathrm{OD}}$) is higher for a conical FT, and that with a conical FT a spherical bubble develops, while with the flat FT a cylindrically shaped vapor channel gets formed.

Measurements were made also with the Nd:YAP wavelength. Figure 13 shows the measured $v_{\mathrm{f}}$ laser pulse energy for the Nd:YAP ($t_{\mathrm{L}}=90\mu \mathrm{s}$) laser with a flat, $320\text{-}\mu \mathrm{m}$ FT ending.

Fig. 13

Measured dependence of the fluid motion per pulse ($v_{\mathrm{f}}$) on laser pulse energy ($E_{\mathrm{L}}$) for the Nd:YAP ($t_{\mathrm{L}}=90\mu \mathrm{s}$) laser with a flat ended $320\mu \mathrm{m}$ FT. For comparison, the data from Fig. 11 for Er:YAG PIPS are also shown.