2.1.

Root Canal Model

The vapor bubble’s dynamics and cleaning efficiency were investigated in the model of the root canal shown in Fig. 1. Since we used a shadowgraphic observation technique,¹⁷ the front and the rear surfaces of the canal model were made of flat and transparent material. Thus, we built a model of a plastic plate [e.g., see Fig. 1(d)] placed between two transparent glass plates, as shown in Figs. 1(a) and 1(c). They were clamped together by an aluminum clamping plate placed into an aluminum holder, as visible in Figs. 1(a)–1(c). The thickness of the plastic plate was 1.5 mm. The pulp chamber and two canals were cut from this plate with the dimensions that are shown in Fig. 1(d). The model was submerged into water and illuminated by an illumination pulse used for shadowgraphy, as described in Sec. 2.2.

Fig. 1

An in vitro model of the root canal: (a) the top view explaining the canal model components, (b) the front view, (c) the isometric view, and (d) a plastic cutout of the root canal with dimensions; the thickness of a plastic plate equals 1.5 mm.

2.2.

Experimental Setup for Shadowgraphic Observations

The experimental setup is shown in Fig. 2. The holder with the model of the root canal, described in Sec. 2.1, was submerged into a vessel with distilled water 10 mm under the water level to ensure that the canal is filled with water during the entire series of the experiments. A free-running Er:YAG laser, designed for laser dentistry ($\lambda =2.940\mu \mathrm{m}$, Fotona d.d., Slovenia, LightWalker), was used as the excitation source. We used pulses with durations of $100\mu \mathrm{s}$ and pulse energies (at the output of the fiber tip) of 54 mJ. The pulse repetition rate was 15 Hz. Typical excitation pulse power as a function of time for the laser used in our experiments can be found elsewhere.¹⁷

Fig. 2

Schematic view of the experimental setup.

The delivery of the laser pulse into the pulp chamber of the canal model was performed by using a fiber tip. The fiber tip was placed into the center of the pulp chamber, 1.6 mm below the top of the model, as visible from Fig. 3(a1). For our experiments, we used a Fotona Xpulse 400/14 fiber tip, schematically shown on the right-hand side of Fig. 2. The fiber tip was 14 mm long with a diameter of $470\mu \mathrm{m}$ and tapered at an angle of 27 deg.

Fig. 3

A series of typical images (Video 1) of a vapor bubble induced by the Er:YAG laser in the model of the root canal. The scale is shown in the upper-left corner of (a1). The time after the pulse initiation is shown on the bottom-right side of each image. (Video 1, MPEG, 10.1 MB) [URL: http://dx.doi.org/10.1117/1.JBO.21.1.015008.1].

The vapor bubble’s dynamics and the cleaning efficiency were studied by using shadowgraphy. We used the same system for shadowgraphy as described in detail in Ref. 17. As the illuminating source we used a frequency-doubled Nd:YAG laser (Ekspla, Lithuania, PL2250-SH-TH) emitting green ($\lambda =532\mathrm{nm}$) pulses with durations of 30 ps. A beam expander was used to expand the illuminating beam so that the whole area of the root canal model was illuminated. Images were captured through a microscope equipped with a charge-coupled device (CCD) camera (Basler AG, Germany, scA1400-17fm, 1.4 Mpx). Since the illuminating beam diameter was smaller than the field of view of the optical system, a bright circular area appears in the captured shadowgraphs [e.g., see Fig. 3(a1)].

2.3.

Measurements of the Bubble’s Dynamics

For the measurements of the vapor bubble’s dynamics in the root canal, we used clean and transparent glass plates. The excitation laser, illumination laser, and CCD camera were synchronized with a signal generator (Tektronix, US, AFG 3102) connected to a PC. The experimental setup was automatically controlled with custom-developed software, written in MATLAB^®, which also enables the setting of the excitation laser’s parameters, image acquisition, and image processing.

The bubble’s dynamics were measured by capturing a series of shadowgraphic images. Each image was captured at a different delay between the excitation and the illumination pulse. For each image, a new event was needed, and thus, repeatable conditions had to be ensured.

2.4.

Measurements of Cleaning Efficiency

In the experiments devoted to the study of cleaning efficiency, we applied the artificial smear layer in the front glass surface of the canal. As an artificial smear layer we used a black paint that does not dissolve in water and can be mechanically removed. In these experiments, we measured the transmittance of the illumination pulse versus the total pulse energy applied into the canal as follows.

In each step, we applied seven pulses with frequency of 15 Hz into the canal. This was repeated until the canal was completely cleaned. After each step of seven pulses, we waited for 5 s so that the vapor bubble and the remaining gas bubbles were not present and visible any more. Then we illuminated the canal by an illumination pulse and captured an image.

To confirm repeatability, the entire procedure of cleaning the canal, described in the above paragraph, was repeated 10 times. Before each iteration, the canal model was completely mechanically cleaned and then painted with a fresh coat of paint before performing a new series of experiments.

The acquired images were processed by the custom-developed software to calculate transmittance. The total pixel intensity $I$ of each image was calculated as

The transmittance $T_N$ after the $N$th pulse, therefore, equals

The total pulse energy $E$ was measured as

3.1.

Bubble’s Dynamics in the Root Canal

In the first series of our experiments, we captured the bubble’s dynamics in the canal. Thus, both the front and the rear glass plates were kept clean during these experiments. A typical series of images of the bubble, captured at different times after the beginning of the Er:YAG laser pulse, is shown in Fig. 3.

The Er:YAG pulse, having a wavelength of $\lambda =2.940\mu \mathrm{m}$, is completely absorbed right beside the fiber tip due to the very high absorption coefficient, ${\mu }_{\mathrm{a}}=1.247\times {10}^6{\mathrm{m}}^{-1}$.¹⁵ This results in the laser energy deposition causing an explosive boiling, and the spherical bubble develops at the end of the conical fiber tip¹⁷ [e.g., see Fig. 3(b1)]. The spherical geometry of the bubble is deformed during the bubble’s expansion due to the influence of the confined geometry of the canal, as visible from Figs. 3(a2), 3(c1), and 3(d1). For the parameters used in our experiments, the bubble reaches its maximum volume around $260\mu \mathrm{s}$ after the pulse initiation [Fig. 3(a2)]. Then it starts to collapse due to the pressure of the surrounding liquid. During the collapse, it decays into two bubbles, as visible from Figs. 3(d2) and 3(a3). These bubbles oscillate several times in the top part of the canal until they disappear due to mechanical-energy dissipation. This happens around 1 ms after the pulse initiation [e.g., see Fig. 3(d3)].

As we have already shown in Ref. 17, the acoustic transient, or shock wave, is not emitted during the first bubble’s expansion, since the Er:YAG laser energy is deposited into water within a time that is three orders of magnitude longer^17,20 than the characteristic time for the propagation of stress waves across the irradiated volume.^21–23 Although in an infinite liquid shock waves are emitted during the vapor bubble’s collapses,¹⁷ this is not the case for the bubble oscillating within our canal model. In this case, the canal’s boundaries decelerate the bubble’s collapse,²⁴ and therefore, the shock waves are not emitted even during the bubble’s collapses. This finding is important, since it leads to the conclusion that shock waves do not explain the cleaning mechanism of the Er:YAG laser irrigation, as suggested in Refs. 1, 2, and 11.

It should be noted here that in the case when the dimensions of the pulp chamber would be several times larger than the maximum diameter of the vapor bubble, shock waves could be induced during the bubble’s collapses as is the case for the infinite liquid. However, we have chosen smaller dimensions of the pulp chamber to eliminate the influence of the secondary shock waves. Since the shock waves are not induced in our case, while the canal is still cleaned, we believe that they do not represent the main cleaning mechanism.

A series of typical images of a vapor bubble in the root canal reveals that the laser-induced vapor bubble oscillates only in the pulp chamber and in the top part of both canals. Thus, this bubble does not reach the bottom part of the canal (e.g., see Fig. 3). This leads to the conclusion that the laser-induced vapor bubble itself cannot be the direct canal-cleaning mechanism. However, many small gas bubbles appear within the whole canal during the vapor bubble expansion and collapse and are clearly visible in Video 1. We believe that they appear due to the shear stress on the canal walls caused by dynamic viscosity of the fluid streaming that is induced by the main vapor bubble’s oscillations. These small, submillimeter, or even submicrometer gas bubbles may also significantly contribute to the cleaning of the smear layer from the canal walls,^25–27 especially when they appear in the close vicinity of the smeared surface.²⁸

3.2.

Ability of Shadowgraphy to Detect the Shock Waves

In Sec 3.1, we have shown that the shock waves are not presented during the bubble’s oscillations within the root canal. To confirm that this finding is not affected by the potential inability of the shadowgraphy to detect the shock waves, we made additional verification experiments in an infinite liquid. We chose the nonconfined geometry, since it has been already shown¹⁷ that in an infinite liquid, the shock waves are induced by the bubble’s rebound. For verification reasons, we used the same fiber tip and the same laser pulse parameters as in the case of bubble dynamics measurements within the canal. The verification experiments confirmed that the shock waves can be easily observed by our method, as is clearly seen from Fig. 4.

Fig. 4

A series of shock waves, observed during the first bubble rebound ($\sim 500\mu \mathrm{s}$ after the pulse initiation) in the verification experiment, where the Er:YAG pulse was delivered into a nonconfined liquid.

The results of our verification experiment in an infinite liquid show that our experimental system is able to observe the shock waves. This confirms our result—presented in Sec 3.1—that shock waves do not appear within our root canal due to the confined geometry.

3.3.

Cleaning Efficiency

For the study of cleaning efficiency, we applied an artificial smear layer (i.e., the black paint described in Sec. 2.4) to the front glass surface of the canal, and we measured how this smear layer was removed during the Er:YAG pulses application. A typical series of images showing the smear layer removal by laser-induced streaming is presented in Fig. 5. Each subsequent image was captured after the additional seven Er:YAG pulses were delivered into the canal. The total pulse energy already delivered into the canal was calculated using Eq. (3) and is shown on the bottom-right side of each image in Fig. 5.

Fig. 5

A series of typical images (Video 2) showing the cleaning efficiency as a function of the total pulse energy applied into the canal. Here, the total pulse energy is calculated from the number of pulses by using Eq. (3). The scale is shown in the upper-left corner of (a1). (Video 2, MPEG, 3.62 MB) [URL: http://dx.doi.org/10.1117/1.JBO.21.1.015008.2].

From Fig. 5, we can see that in this particular case, the canal was almost cleaned ($>85\%$) when the total pulse energy of $\sim 5.4\mathrm{J}$ was applied into the water. It should be noted here that small black areas in the bottom of both canals in Fig. 5(d3) do not correspond to the smear layer. Instead, they appear due to small gas bubbles that are formed because of the main vapor bubble’s oscillations as explained in Sec. 3.1. They can be clearly recognized from Video 2.

From the results presented in Fig. 5, it can be concluded that the cleaning effects appear along the entire canal, that is, also significantly below the regions that are reached by the laser-induced vapor bubble (e.g., compare Figs. 3 and 5). Therefore, we believe that (1) water flow, induced by the dynamics of a laser-induced vapor bubble, and (2) gas bubbles appearing along the whole canal are responsible for the cleaning. The water-flow cleaning and the gas bubbles’ appearance probably happen through the shear stress caused by the dynamic viscosity.

From the images acquired during the study of cleaning efficiency (e.g., presented in Fig. 5), we calculated the transmittance by using Eq. (2). The average transmittance as a function of the total pulse energy, defined by Eq. (3), is shown in Fig. 6. Each point corresponds to the average of 10 independent measurements, and the vertical bars show standard deviations. From the results in Fig. 6, it can be seen that, on average, up to 25 J (i.e., $\sim 460\text{pulses}$) are needed to completely clean our in vitro model of the root canal.

Fig. 6

The transmittance [defined by Eq. (2)] as a function of the total energy [defined by Eq. (3)]. When the transmittance reaches unity, the canal is totally cleaned. The dots show an average value of 10 independent measurements, while the standard deviations are presented by vertical lines. The fit of the theoretical model [Eq. (8)] is shown by the black curve.

The cleaning efficiency can be modeled as follows. The small area of the smear layer $dA$ that is removed by the delivery of a small amount of the laser pulse energy $dE$ is proportional to the area $A$ that is still smeared:

Combining Eqs. (4) and (5), after integration, one can obtain the dependence of the still-smeared area $A_S$ as a function of the total pulse energy $E$:

If one assumes that the cleaning efficiency coefficient stays constant during the entire cleaning procedure, that is, in the case of the limit conditions of $\beta \to 0$, Eq. (6) is simplified to $A_S(E)=A_0{e}^{-{\alpha }_{0}E}$. In this case, a more intuitive characteristic coefficient of the cleaning efficiency, the half-energy $E_{1/2}$, can be defined as the total energy required for the cleaning of one half of the initial smear layer area:

The transmittance $T$, defined by Eq. (2), is equal to the ratio between the cleaned area $A_C=A_0-A_S$ and the area $A_0$ of the smear layer before the first pulse application: $T=(A_0-A_S)/A_0=1-(A_S/A_0)$. Thus, by using Eq. (6), the transmittance as a function of the total pulse energy $E$ can be modeled as