## 2 Characteristics of the Shock Wave and Its Sources
The entire shock wave healing process is shown in Figure 2. However, some believe that implosions of caviar bubbles may break the covalent bonds of water molecules [14]; in other words, they may promote the formation of free radicals, which in turn may have a negative impact on the health of the living organism. Each therapy requires selecting the appropriate parameters. Inadequate values can have completely different, catastrophic consequences for a living organism. Therefore, what is crucial is to consider metrics that allow us to assess and compare generated shock waves without empirical tests of the wave in vivo and with no comparison of its effects. The basic parameter describing the shock wave is the acoustic pressure amplitude (expressed in MPa) at a given point in the medium and at a given time [19]. This means that it is a value that depends on the distance from the wave source and the time that has elapsed since its generation. This will significantly influence the accuracy of measurements we made on experimental test benches, which we describe later in the paper. The tests include measurement with a piezoelectric vibration sensor and hydrophone measurement. Based on the acoustic pressure value, it is possible to determine the instantaneous acoustic intensity in the direction of the wave vector, given by the formula (2) [1,14]:  
\[I(t)=\frac{p^{2}}{\rho c}\ \ \ \ \ \ \left[\frac{\text{W}}{\text{m}^{2}}\right] \tag{3}\]  
where:  
\(p\)--sound pressure,  
\(\rho\)--medium density,  
\(c\)--speed of wave in the medium (1500 m/s for water). The denominator of formula (3) is, in fact the acoustic impedance, which is \(1.5\times 10^{6}\) kg m\({}^{-2}\) s\({}^{-1}\) for water, 1.4 \(\times\) 10\({}^{6}\) kg m\({}^{-2}\) s\({}^{-1}\) for urine, and 5 \(\times\) 10\({}^{6}\) for kidney stones 5 \(\times\) 10\({}^{6}\) kg m\({}^{-2}\) s\({}^{-1}\). The mentioned parameters (3) are important for the researcher of acoustic waves, but not for the physiotherapist, who should be able to assess the therapeutic usability of the shock wave. For this purpose, the energy flux density (expressed in mJ/mm\({}^{2}\)) was introduced. It depends on the acoustic pressure of the point \(\xi\) in the medium throughout the duration of the shock wave. The energy flux density [1,2,13,15,19] can be determined based on the formula:  
\[E(\xi)=\frac{1}{\rho c}\int_{0}^{\lambda}\ p^{2}(\xi,t)dt\ \ \ \ \ \left[\frac{\text{J}}{\text{mm}^{2}}\right] \tag{4}\]  
where:  
\(p\)--sound pressure at point \(\xi\) at time t,  
\(\rho\)--medium density,  
\(c\)--speed of wave in the medium,  
\(\lambda\)--duration of the shock wave at point \(\xi\). The value of quantity (4) is important for physiotherapists and shows them whether the generated shock wave will have a therapeutic effect by penetrating the operated tissue or focusing only on a small area of it. The literature defines some energy thresholds (energy flux density values) above which pro-therapeutic effects occur. The square of the integrand in the formula (4) allows us to consider both phases of the wave: positive and negative. Figure 2: Chain reaction initiated by a shock wave in the tissue. In practice, the value of energy flux density in the operated tissue ranges from 0.004 to 0.6 (sometimes 0.8) mJ/mm\({}^{2}\)[1]. There are many classifications of a shock wave due to its energy flux density. Generally, there are three energy classes [1]: low, medium, and high (Table 1). For the low-class energy flux, density should not exceed 0.1 mJ/mm\({}^{2}\); for the medium class 0.3 mJ/mm\({}^{2}\), and, for the high class, 0.6 mJ/mm\({}^{2}\). An alternative to the measure (4), which is rarely used, is the displacement given in the paper [13].