## 3 Thermophysical Simulation of Endovasal Laser Treatment of a Vein with TOTFC  
Within the model of the EVLT described above, a computer simulation of heating the TOTFC and the vein wall during TOTFC with the laser radiation wavelength of 980 nm was performed for varied average laser radiation powers and traction speeds. The relationship between the maximum converter temperature (_TTOTFC_), the maximum vein wall temperature (_Tvw_), and the traction speed (_v_) at a varied average laser radiation power (_P_) is shown in Figure 2.  
The maximum temperature of the TOTFC is reached inside the converter. It is localized at a negligible distance from its center in the direction of the optical quartz fiber, which is due to the influence of the heat sink along the optical quartz fiber. With an increase in the average laser radiation power, _TOTFC_ increases, and with an increase in the traction speed, _TOTFC_ slightly decreases (Figure 2a). As the heat from the _TOTFC_ diffuses to the vein wall, it causes the vein wall to heat up. With an increase in the average power of laser radiation, the temperature of the vein wall (_Tvw_) increases, and with an increase in the traction speed, the value of _Tvw_ decreases significantly (Figure 2b). The latter dependence can be attributed to the contribution of the effect of heat accumulation to _Tvw_ at a certain point of the vein wall. This contribution is greater the longer the point remains close to the heat source and, accordingly, with the speed increasing, this contribution decreases. It should also be noted that the simulation did not take into account the contribution of the phase transition when the water contained in the vein wall was boiling, and therefore _Tvw_ in Figure 2b, does not exceed 100 \({}^{\circ}\)C. It can be seen that with an average laser power of \(P\) = 8 W, the value of _Tvw_ does not reach the 80 \({}^{\circ}\)C required for the coagulation of the vein wall. With an average laser power of \(P\) = 10 W, the temperature of _Tvw_ can be higher or equal to 80 \({}^{\circ}\)C at \(\
u\leq\) 2.5 mm/s, while the temperature of _TOTFC_ reaches the value of -510 \({}^{\circ}\)C. With an average laser power of \(P\) = 12 W, the temperature of _Tvw_ can be higher or equal to 80 \({}^{\circ}\)C at \(\
u\leq\) 4.8 mm/s, while the temperature of _TOTFC_ reaches the value of -580 \({}^{\circ}\)C. With an average laser power of \(P\) = 14 W, the temperature of _Tvw_ can be higher or equal to 80 \({}^{\circ}\)C at \(\
u\leq\) 6.6 mm/s, while the temperature of _TOTFC_ reaches -640 \({}^{\circ}\)C. The dependence of _Tvw_ on the traction speed manifests pronounced non-linearity. At low traction speeds (1-2 mm/s), the value of _Tvw_ decreases less significantly with increasing traction speed than at high traction speeds (2-7 mm/s). At low traction speeds, a decrease in _Tvw_ with an increase in traction speed and the accumulation effect may also be due to the instability of thermal convection in the liquid (here--blood) at the beginning of the TOTFC movement [21]. At high traction speeds, these effects may be supplemented by the movement of uneven areas of fluid when the TOTFC is moving. Figure 2: The dependences of _TOTFC_ (**a**) and _Tvw_ (**b**) on the traction speed (_v_), at a varied average laser radiation power (_P_) (the wavelength of laser radiation is 980 nm, the inner vein diameter is 5 mm). As a result of the analysis of the data represented above, the dependence of \(T_{vw}\) on \(T_{TOTFC}\) was obtained at varied traction speeds in the range of 1-7 mm/s (Figure 3). In this case, the change in \(T_{TOTFC}\) is caused by a change in the average power of the laser radiation from 8 W to 14 W (see Figure 2a). It can be seen that \(T_{vw}\) increases with increasing \(T_{TOTFC}\) and decreases with the increasing traction speed at constant \(T_{TOTFC}\).