## 3 Results and Discussion
### Optical and Acoustic Tests
It is easy to calculate that in cases when the fiber diameter is 600 \(\upmu\)m, the intensity of laser radiation in the pulse at the end of the fiber will be 1.8\(\cdot\)10\({}^{5}\) W/cm\({}^{2}\), in other words, \(<<\)10\({}^{8}\) W/cm\({}^{2}\), which is necessary for the realization of the mechanism of photomechanical ablation. The depth of laser radiation penetration in the stone material is \(\delta\) = 1/\(\upmu_{\text{eff}}\)\(\approx\)0.1 mm. This distance is covered within \(\approx\)50 ns by a sound wave that spreads at a velocity of \(\approx\)1500 m/s. Thus, another condition for the realization of the mechanism of photomechanical ablation by the laser pulse duration (\(\tau<\delta/c\)) is not fulfilled, too. When it comes to photothermal ablation, the main criterion for its realization, shorter pulse duration (\(\tau\) = 0.4 ms) in comparison with \(\delta^{2}/4\alpha\approx\)10\({}^{-8}\) (and the coefficient of thermal conductivity of water \(\alpha\) = 0.143 m\({}^{2}\)/s), was not fulfilled, too. Taking into account the above-described facts, we suggested that in the present study, the destruction of the stone phantom under laser radiation was performed primarily due to thermal cavitation in the water-filled pore space of the phantom [21; 31; 32]. From the point of view of further physical processes, it is important to note that thermal cavitation occurs in a closed microscopic space [33]. The jump of pressure that is observed in this volume during fast water heating (1.6 MPa at \(T\)= 200 \({}^{\circ}\)C and 4 MPa at 250 \({}^{\circ}\)C) can lead to the disintegration of the phantom. Such laser-induced shock processes during the explosive boiling of water near the fiber end were studied using optoacoustic methods [33; 34]. It is important to mention that the effect of pulse pressure, which is observed during the explosive boiling of water in the micropores of the phantom, occurs in the conditions of heated phantom. The degree of the destruction of the material \(\Omega\)(t) under laser exposure is well-described by the Arrhenius integral [35]:  
\[\Omega(t)=\varsigma\int_{0}^{Time}\exp[-E_{a}/RT(t)]dt \tag{1}\]  
where \(\zeta\) (s\({}^{-1}\))--the frequency factor, _Time_--the full time of heating, \(E_{a}\) (J/mol)--the energy of activation; \(R\) (8.32 J/K mol)--the universal gas constant, and \(T(t)\) (K)--the absolute temperature of the material. The degree of destruction \(\Omega(t)\) exponentially depends on temperature and linearly on the time of heating. It should be noted that at \(\Omega(t)\) = 1, 63% of the material gets destroyed. During the time of laser pulse exposure, the temperature in the water-filled stone tissue (in a contact regime when the fiber end firmly touches its surface) increases by the value calculated by the formula:  
\[\Delta T=\frac{C\mu_{a}F}{\rho c_{p}}\exp(-\mu_{a}z) \tag{2}\]  
where C--the pore water content, \(\mu_{a}\)--the coefficient of absorption (cm\({}^{-1}\)), \(\rho\)--density (kg/m\({}^{3}\)), \(c_{p}\)--heat capacity at constant pressure (J/kgK), \(F\) = P\({}_{\text{p}}\)\(\tau\)--fluence or density of energy (J/cm\({}^{2}\)), and z--depth from the fiber end into the material. Depending on certain physicochemical characteristics of the stone, its heating can lead to the weakening of its structure and destruction. Note that the stone is heated exclusively through the water in the pore space (the stone itself does not absorb laser radiation). If the temperature does not exceed critical values (\(T_{crit}\)) during heating, the speed of the material destruction \(\Delta\Omega/\Delta t=\zeta\exp(-E_{a}/RT_{crit})\) is insignificantly low. On the contrary, at \(T>T_{crit}\), the speed of destruction increases exponentially. The critical temperature depends on the certain composition of the stone and its structure. For magnesium ammonium phosphate, it is 100 \({}^{\circ}\)C, for calcium oxalate monohydrate, it is 206 \({}^{\circ}\)C, for cystine, it is 264 \({}^{\circ}\)C, and for uric acid, it is 360 \({}^{\circ}\)C [36].