## 3 Thermophysical Simulation of Endovasal Laser Treatment of a Vein with TOTFC
The dependences shown in Figure 3 allows choosing a \(T_{TOTFC}\) acceptable (at a constant traction speed and a constant internal diameter of the vein, which in this case, equal to 5 mm) to achieve the \(T_{vw}\) value of 80 \({}^{\circ}\)C required for the coagulation of the vein wall (\(T_{TOTFC\_80}\)). For example, at the traction speed \(v=2\) mm/s, in order for \(T_{vw}\) to be equal to or above 80 \({}^{\circ}\)C, the temperature \(T_{TOTFC\_80}\) has to be \(\geq\)500 \({}^{\circ}\)C, which is consistent with the results presented in [16]. In the EVLT process, changing the average laser power and the traction speed to ensure that the temperature on the vein wall reached 80 \({}^{\circ}\)C required for its coagulation is crucial for the success. In this regard, it should be expected that for the coagulation of the vein wall in the EVLT process, when the traction speed changes, it is necessary to change the temperature of the TOTFC, and therefore the laser radiation power be adjusted for the vein wall to have the temperature of 80 \({}^{\circ}\)C. Thus, as a result of computer simulation, for each traction speed, it is necessary to determine the average laser radiation power (\(P_{\_80}\)) and the temperature TOTFC (\(T_{TOTFC\_80}\)) so that the vein wall temperature reaches 80 \({}^{\circ}\)C. The dependence of these values on the varied traction speeds is shown in Figure 4.  
Figure 4: The dependences of the average laser radiation power \(P_{\_80}\) (**a**) and the temperature of the TOTFC required for the vein wall temperature to reach 80 \({}^{\circ}\)C \(T_{TOTFC\_80}\) (**b**) on the traction speed (\(v\)) of the TOTFC (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). Figure 3: The dependence of \(T_{vw}\) on \(T_{TOTFC}\) at varied traction speeds (\(v\)) (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). It can be seen that with an increase in the traction speed, the average power of the laser radiation \(P_{\_80}\) and the temperature \(T_{\_TOTTFC\_80}\) is increased. As a result of an analysis of the data represented above, the dependence of \(T_{\_TOTTFC\_80}\) on \(P_{\_80}\) was plotted at varied traction speeds in the range of 1-7 mm/s (Figure 5). This dependence shows what would be the temperature \(T_{\_TOTTFC\_80}\) for a given \(P_{\_80}\). If this temperature is not reached, then we would have to either change the average power of the laser radiation at a constant traction speed until the temperature of the TOTFC reaches the required value, or to change the traction speed at a constant average power of the laser radiation until the temperature of the TOTFC reaches the required value. A change in the traction speed \(\
u\) by a certain amount \(\Delta\
u\) would lead to a change in the temperature TOTFC by the mount \(\Delta T_{\_TOTTFC\_80}\) and can be compensated by a change in the average power of the laser radiation \(\Delta P_{\_80}\). The dependences demonstrating how much the average laser radiation power and the temperature of TOTFC would have to change compared to the current value in order for the temperature of the \(T_{\_}{vw}\) vein wall to remain equal to 80 \({}^{\circ}\)C when changing \(\
u\) by the value of \(\Delta\
u\) are shown on Figure 6.  
Figure 5: The dependence of \(T_{\_}{TOTTFC\_80}\) on \(P_{\_80}\) at varied traction speed (\(\
u\)) (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). Figure 6: The dependences of \(\Delta P_{\_80}\) (**a**) and \(\Delta T_{\_}{TOTTFC\_80}\) (**b**) on the step of change in the traction speed TOTFC \(\Delta\
u\), provided that the temperature of the vein wall is 80 \({}^{\circ}\)C (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). It can be seen that with \(\Delta\
u\) increasing, the average laser radiation power \(\Delta P\_80\) and the temperature \(\Delta T_{TOTFC\_80}\) is increased.