OPTICAL AND COMPUTATIONAL MODELING OF LASER-INDUCED PROCESSES IN ENDOVENOUS LASER ABLATION: HEAT TRANSFER, FLUID DYNAMICS, AND TISSUE COAGULATION

OPTICAL AND COMPUTATIONAL MODELING OF LASER-INDUCED PROCESSES IN ENDOVENOUS LASER ABLATION: HEAT TRANSFER, FLUID DYNAMICS, AND TISSUE COAGULATION | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 11 July 2025 V1 Latest version Share on OPTICAL AND COMPUTATIONAL MODELING OF LASER-INDUCED PROCESSES IN ENDOVENOUS LASER ABLATION: HEAT TRANSFER, FLUID DYNAMICS, AND TISSUE COAGULATION Authors : Vladimir I. Yusupov 0000-0002-9438-6295 [email protected] and Alexey Konovalov Authors Info & Affiliations https://doi.org/10.22541/au.175221959.93895795/v1 Published Physica Scripta Version of record Peer review timeline 210 views 134 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This study analyzes laser treatment of veins using continuous laser radiation at λ = 0.97 μm from a 600 μm optical fiber. Fluid flow, heat transfer, and protein coagulation were investigated via video and thermography. A silicone tube with egg white simulated a vein and blood. A multiphysics model in COMSOL calculated thermal fields, hydrodynamics, and coagulation in veins of different diameters under various laser powers and pullback speeds. Results showed strong agreement between experiments and simulations. Complete coagulation of veins ≥3 mm was achieved mainly through explosive water boiling-induced mixing, while smaller veins relied on convective heat transfer. Laser power significantly affected temperature distribution and coagulation, alongside linear endovenous energy density. These findings clarify laser-tissue interactions and can help optimize medical laser procedures. 1. Introduction Laser technologies have become essential tools across various scientific and engineering fields, with medicine emerging as one of the most rapidly evolving and impactful areas. Among these applications, laser treatment of varicose veins is a particularly promising and rapidly advancing technique, attracting significant attention due to its minimally invasive nature and excellent clinical outcomes. Varicose veins, caused by pathological changes that impair normal blood flow, are a common and insidious condition often associated with long-term healthcare costs [1]. In recent decades, endovascular laser ablation (EVLA) has become a widely adopted medical procedure. EVLA involves using a laser to heat and seal diseased veins, causing them to close and be excluded from circulation [2, 3]. The procedure includes inserting a laser fiber into the affected vein, which is then gradually retracted while the laser is activated. The thermal effect induces degradation of the venous walls, leading to vessel obliteration. Despite a growing consensus among clinicians regarding the basic mechanisms and optimal laser parameters, active discussions continue on how to refine the technique and better understand the complex physical interactions involved. Thus, there are active discussions about which wavelengths are better to use [3-10]. The first group consists of lasers with λ=810 nm, 940 nm, 970 or 980 nm. Such radiation is relatively weakly absorbed by water. The second group includes lasers with λ=1.47, 1.56 or 1.94 μm, the radiation of which is very effectively absorbed by water [11]. The main advantage of EVLA using lasers from the second group is a significantly greater contribution from the effects of explosive boiling of water, which leads to periodic cleaning of the fiber tip from clots of coagulated and carbonized blood [7,8], which accumulate on it [12]. In addition, frequent acts of explosive boiling lead to mixing of the liquid in the internal volume of the vein, which reduces the heating asymmetry associated with convection [7,8]. The advantage of using lasers from the first group is their availability and relative cheapness. Clinical observations show that the EVLA technology using a diode laser with λ=980 nm in continuous mode appears to be safe and effective [13]. However, for its more detailed development, it is necessary to understand what hydrodynamic processes occur in the lumen of the vein and what temperatures are achieved. The processes occurring during EVLA can be studied using experimental or computer modeling. Experimental modeling performed with blood plasma [8] made it possible to study the features of bubble generation, jet and convective flows, and coagulant formation. In [4], it was shown on an in vivo model that the average temperature at the fiber tip during EVLA with lasers from the first group exceeds 700 °C. At the same time, it turned out that on the outer surface of the vein, the temperature during EVLA reaches only from 40-49 °C [14] to 80-90 °C [15]. In [14], it was shown using thermocouples that the temperature on the optical axis at a distance of 4 mm from the fiber tip is in the range of 40-85 °C, which may be sufficient for protein denaturation. In [16], it was shown using six point thermocouples and video recording that the carbonized layer at the fiber tip promotes mixing and equalization of the temperature field due to active boiling. To clarify the mechanism of action of laser radiation in EVLA, It is necessary to compare these values at some ”points” with the results of computer modeling. Some scientific groups are attempting to numerically simulate the processes occurring during EVLA [3, 17-19]. However, it should be noted that the problem associated with modeling the processes in EVLO is extremely complex. This is due to the fact that 1) it is first necessary to calculate the dynamics of the propagation of laser radiation emerging from the end of the fiber in an inhomogeneous medium with changing absorption and scattering coefficients; 2) then determine the dynamics of the velocity and temperature fields; and 3) finally calculate the dynamics of the coagulation and carbonization fields of protein structures. Moreover, it should be taken into account that some fields affect others. In this case, the effect of gravity, the presence of phase transitions and the movement of the optical fiber should be taken into account. It is not surprising that the problem has not yet been solved in such a general form and existing models, as a rule, do not take into account phase transitions, hydrodynamic processes and protein coagulation. Most models are based on conductive heat transfer, as well as the propagation of laser radiation from a moving source and its absorption with heat release (see, for example, [20]). Additionally, some authors take into account the increase in heat transfer during boiling due to a significant increase in the thermal conductivity coefficient at a temperature of T≥95 °C [21, 22] or take into account blackbody radiation from a carbonized layer on the tip of an optical fiber [23]. In a few works [24] the hydrodynamic processes occurring in the lumen of the vein are taken into account. However, this work uses the point source approximation, which does not correspond to the real diagram of light propagation from the fiber tip. In addition, the problem was solved using the COMSOL platform for the vertical configuration of the vein, which significantly simplifies the calculation, but does not correspond to the real picture in the clinic. It should be noted that numerical modeling that takes into account the coagulation of protein structures and the occurrence of fluid flows in the lumen of the vein is still lacking. Additional important information about the processes occurring during EVLA can be provided by optical registration methods. However, this requires using transparent media instead of opaque blood. Thus, in [7] water was used as a medium for modeling processes during EVLA, and in [8] blood plasma was used. Such experimental data are also necessary for selecting the parameters used in numerical modeling, which significantly increases the reliability of the results obtained during modeling. The aim of the work was to obtain new knowledge about the processes occurring in the EVLA with λ=0.98 μm, through experimental modeling and numerical calculations taking into account the coagulation of protein structures and the occurrence of fluid flows in the lumen of the vein. 2. Experimental setup, materials and methods As a rule, water [7] and blood plasma [81-03314-0] are used for experimental modeling of the processes occurring during EVLA. The use of water is justified by the fact that blood contains more than 80% water in its composition. Blood plasma is used as the next approximation in modeling blood. Such a medium is already close in composition to blood and allows modeling the coagulation of proteins contained in plasma. A significant disadvantage of using blood plasma for modeling processes during EVLA is its low viscosity compared to the viscosity of blood: 1.8-2.5 mPa s and 5 mPa s, respectively. In our opinion, egg white is quite close in composition to blood plasma: water in egg white is 88%; protein content is about 10% (more than half of the proteins are albumin). Egg white is the most accessible and cheapest material, unlike blood plasma. It has a viscosity comparable to blood – (6.5 mPa s) [25]. In this regard, we used egg white for experimental and numerical modeling of the processes occurring during EVLA. A schematic representation of the experimental setups used in the studies is shown in Fig. 1. An LS-0.97 continuous wave fiber laser (IRE-Polyus, Russia) with a wavelength of λ = 0.97 μm and a power of up to 10 W, connected to an optical fiber of 600 μm in diameter, was used in the experiments. To control the laser radiation power, a FieldMaster power meter with an LM-10HTD measuring head (Coherent, USA) was used. Initially, calibration experiment №1 was conducted with a stationary fiber and control of the developed thermal fields using a thermal imager (Fig. 1a). Then, experiment №2 was performed, simulating the EVLA procedure with a vein model and a moving fiber (Fig. 1b). In both experiments, the dynamics of protein coagulation during laser exposure was observed using a digital camera. To prevent strong illumination of the camera by scattered laser radiation, we used an IR filter that cuts off radiation at a wavelength of 0.98 μm. Fig. 1. Schematic representation of the experimental setups. a - experiment №1 with a minicuvette, stationary optical fiber and thermograph. Inset: assembly drawing of the minicuvette with fiber. b - experiment №2 with a vein model and moving optical fiber. 1 - fiber tip, 2 - laser, 3 - minicuvette, 4 - egg white, 5 - digital camera, 6 - thermograph, 7 - PC, 8 - vein model, 9 - cuvette, 10 - horizontal shifter, 11 - illumination, 12 - capillary through which the fiber passes into the minicuvette. 2.1 Experiment №1 in a minicuvette with a fixed fiber and a thermograph This experiment is a calibration experiment. It is necessary to adjust the coefficients for numerical calculations so that the simulation results match the experimental data as much as possible. In this experiment, the laser fiber was installed horizontally inside a plastic minicuvette with a 1 mm thick glass window at the bottom (insert in Fig. 1a). A thin glass plate with a thickness of 200 μm was located on top of the minicuvette. The design was such that the fiber was located closer to the thin plate (the distance from the center of the fiber to the plate was 400 μm) in order to minimize the temperature difference on the surface of the plate and in the center of the laser spot. Egg white was poured into the cell cavity (1 mm x 15 mm x 25 mm). This design allowed us to simultaneously observe the dynamics of the temperature field formed on the surface of the thin glass plate and the dynamics of protein coagulation in transmitted light. The radiation power at the output of the optical fiber was P=5 W. The experiment was conducted at room temperature. Two separate experiments were conducted. First, the dynamics of temperature fields were measured in the case of an empty microcuvette, when the temperature on the surface of the cover glass increases due to the absorption of laser radiation directly in the glass. Then, an investigation was performed using a microcuvette filled with egg white. In this case, the glass surface was heated both due to the absorption of radiation in the glass and through thermal conductivity due to the absorption of laser radiation by the egg white. 2.2 Experiment #2 with a Vein Model and a Moving Fiber This experiment simulated the conditions of endovenous laser coagulation. The fiber was fed horizontally into the cavity of a transparent silicone tube with an internal and external diameter of 3.75 mm and 6 mm, respectively. The tube itself was located in a transparent cuvette with glass side windows. The cavity of the tube was filled with liquid egg white, and the cuvette was filled with water. The fiber was mounted on a horizontal slider to ensure that the fiber moved at a given speed during laser radiation. In this experiment, the laser radiation power at the fiber output was P = 8 W. During the experiment, the fiber moved horizontally from right to left (see Fig. 1 b) at a speed of V = 0.5 or 1 mm/s. The process of laser-induced protein coagulation was observed through the side windows of the cuvette with frontal illumination and recorded using a digital camera, which was positioned horizontally. The experiment was conducted at room temperature. 2.3 Modeling of processes in COMSOL The modeling was carried out in COMSOL Muliphysics 6.1 as a problem with time dynamics in 3D geometry. The calculation was carried out for two geometries (two problems) corresponding to two experiments (Fig. 2). Fig. 2. Geometry and computational grid for modeling processes in experiments No. 1 and No. 2. a - stationary fiber in a minicuvette. b - moving fiber in the cavity of a cylinder simulating a vein. 1 - base of a minicuvette or cylinder; 2 - cavity filled with protein; 3 - optical fiber. In problem №1, the optical fiber was located inside a rectangular flat cell. A thin plate simulating a cover glass was located on top of the cell. In problem №2, the optical fiber was located in the center of the cylinder cavity. The fiber moved at a speed of V. The cylinder cavity simulated a vein. This model does not take into account the vein wall as a separate element of geometry, since its thermophysical parameters are not so different from the surrounding tissue as to significantly affect the heat transfer pattern. The cylindrical cavity in Fig. 2b is not through. This is necessary to simulate the compression of the vein before surgery. The calculation was performed for 3 areas, in each of which the material and its properties were set. In Fig. 2, these areas are designated by numbers 1, 2 and 3. Calculation areas for problem №1: 1 – cell walls and a thin plate on top. The material of this area is glass; 2 – cell cavity filled with egg white; 3 – optical fiber. The material of this area is quartz glass. Calculation areas for problem №2: 1 – cylinder with an internal cavity. The material of this area is the biological tissue “Muscle” from the COMSOL database; 2 – cylindrical cavity filled with egg white; 3 – optical fiber. The material of this area is quartz glass. The modeling was performed as a strongly coupled multiphysics problem. We took into account the following processes: 1. Absorption and scattering of laser radiation; 2. Thermal conductivity; 3. Hydrodynamic flows that occur in the liquid medium during fiber movement, as well as convective flows caused by non-uniform heating; 4. Coagulation, which is accompanied by a sharp increase in the absorption and extinction coefficients, as well as protein viscosity. During coagulation, absorption and scattering change due to protein folding. This is well known from studies that investigated the optical properties of tissues during their coagulation [26, 27]. We described the absorption and scattering of laser radiation in protein as a decrease in radiation intensity with some effective extinction coefficient μ eff ( C ). Absorption was described by some effective absorption coefficient μ a ( C ). Both of these parameters in our model are a linear function of the coagulation parameter C, which corresponds to the proportion of native (non-coagulated) protein (For more details, see the Supplementary Materials (SM) to this article.). This approach allows us to describe, in the first approximation, the sharp changes in the optical parameters of protein during its coagulation. The heating process was described by us using the “Heat Transfer in Solids and Fluids” node in a multiphysics link with the “Laminar Flow” node. In this case, when modeling flows using the “Laminar Flow” node, it was taken into account that viscosity changes during the heating of the protein. We took the form of the dependence of the dynamic viscosity of the protein on temperature from [25]. Using this dependence and the data on the viscosity for room temperature of the specific protein that we used in our experiments, we proposed a model for describing the dynamic viscosity of the protein as the sum of two components: \(\eta=\eta_{0}(T)+\text{δη}\left(1-С\right)^{2}\) (1) The first term in (1) is related to the slow decrease in viscosity with increasing temperature, as is usually occurs in liquids. The second term describes the rapid increase in viscosity during coagulation according to the square law from the degree of coagulation 1-C, which shows the proportion of coagulated protein. The quadratic dependence was chosen to better match the data provided in [25] (for more details, see the SM). The coagulation process model was based on the Arrhenius integral approach. Unlike the standard approach using the Arrhenius integral, we used the differential form, taking into account that the liquid protein moves at a speed \(\overrightarrow{u}\): \(\frac{\partial C}{\partial t}+\overrightarrow{u}\bullet\nabla C=-\text{CA}e^{-E_{p}/\text{RT}}\), (2) where C is the fraction of uncoagulated protein, A and E p are the known constants of the Arrhenius integral. At the beginning, we calculated the thermal field and coagulation for problem №1 with a stationary fiber. This experiment with a flat mini-cell and its modeling were necessary to find the corresponding parameters describing the optical properties of the protein μ eff ( C ) and μ a ( C ), at which the calculated temperature field on the cover glass coincides well with the experimental data. Then the obtained optical parameters for the protein were used to model the EVLA process in problem №2 A more detailed description of the model, including the values of all parameters used in the calculations, is given in the Supplementary materials. 3. Results and Discussions 3.1 Experiment №1 with a fixed fiber and a thermograph The presented frames (Fig. 3) show that the laser action leads to the gradual formation of a clot of coagulated egg white near the tip of the laser fiber. With frontal illumination (the source shines directly on the camera through a transparent minicuvette) and the time from the moment the laser is turned on 0.5 s < t < 7.5 s, the formed clot stands out as an object with a horizontal cross-section in the form of an ellipse, which is darker than the background. The size of this clot gradually increases over time. At a time t in the interval between 4.7 and 4.8 s, rapid explosive changes in the shape of the clot are observed. In this case, a bubble of ~ 0.8 mm in size located at some distance from the fiber tip disintegrates into several smaller ones. With further exposure, the size of the protein clot continues to increase. In scattered light, the formed clot also stands out clearly, but as a light spot on a darker background field ( t = 7.5 s). Fig. 3. Sequential frames illustrating the formation of a clot of coagulated egg white near the tip of a laser fiber during laser heating. The time t from the moment the laser was turned on is shown. The shooting was carried out from above with frontal illumination ( t <7.5 s) and in diffused light ( t =7.5 с) Figure 4 shows some thermograms reflecting the temperature distribution on the surface of the minicuvette cover glass at different moments in time. Already at t =0.3 s, a heated section is distinguished on the thermogram in the area in front of the projection of the laser fiber. Over time, the maximum heating temperatures T max gradually increase, and the shape of the temperature isolines is transformed from elongated along the optical axis to slightly oblong ellipses. It can be seen that at t =4.7 s, T max on the glass surface already reaches 100 °C. Note that it was at this time that the observed explosive changes in the shape of the clot occurred ( t =4.8 s, Fig. 3). Fig. 4. Thermograms reflecting the temperature distribution on the surface of the minicuvette cover glass at different moments in time. The projection of the laser fiber on the surface of the cover glass is shown as an elongated white quadrangle, the dashed line shows the projection of the optical axis. The time t from the moment the laser is turned on is shown. The features of the spatio-temporal temperature distribution on the surface of the minicuvette cover glass under laser irradiation are shown in Fig. 5. It is evident that when egg white is added to the minicuvette, the growth rate of T max increases significantly with time (Fig. 4a). In this case of an empty cuvette, a monotonous dynamics is observed, while when the cuvette is filled with protein at t ~4.7 s, a sudden decrease in temperature by ~14 °C is observed. Note that it is at t ~4.7 s that explosive changes in the shape of the protein clot occur (Fig. 3). The dynamics of T max in a minicuvette filled with egg white can be more clearly traced by the derivative of this temperature (∂T/∂ t ). In the case of an empty minicuvette, the slope of the curve after turning on the laser radiation monotonously decreases with time. However, in the case of a cuvette with protein, a more complex picture is observed for the derivative ∂T/∂ t . ∂T/∂ t first increases and gradually reaches a plateau, then at t ~0.8 s a kink is observed and the slope of the derivative becomes negative. We believe that this kink corresponds to the onset of protein coagulation. In the range t =2-4.7 s, the T( t ) dependence becomes almost linear. The temperature distribution at t =4.75 s immediately before its abrupt decrease is shown in Fig. 5b. Here, for clarity, to show the possible contour of the coagulated protein, the temperature range up to the temperature of its active coagulation (~60 °C) is shown. According to the presented temperature profiles (Fig. 5c), it can be seen that up to t =4.7 s, the maximum temperature value gradually increases, and the position of the maximum also gradually approaches in the projection of the tip of the laser fiber. It should be noted that simultaneously with the explosive change in the shape of the protein clot described above, the surface temperature values decrease in a relatively small region of the maximum of 0-3 mm (Fig. 5 d). Fig. 5. Features of the spatio-temporal temperature distribution on the surface of the minicuvette cover glass under laser irradiation. a – T max dynamics in the case of an empty cuvette (without egg white) and a cuvette with egg white. The dotted line in arbitrary units shows the value of ∂T/∂t for temperature T , when the cuvette is filled with egg white. Time t =0 corresponds to the moment of laser switching on. b – temperature distribution at t =4.75 s to the temperature of active protein coagulation (~60 °C). c , d – temperature distributions along the projection of the optical axis at different moments in time: t ≤4.7 s (s) and t ≥4.7 s (d). 3.2 Simulation with a fixed fiber The experiments conducted in a minicuvette with a fixed fiber allowed us to calibrate and select egg white parameters (absorption, scattering, viscosity, see supplemental materials), which is necessary for the maximum approximation of the results of numerical simulation performed on the Comsol platform to the results of physical simulation. Fig. 6 shows the calculated spatial distribution of temperature and degree of coagulation of protein 1-C at different moments in time. It is evident that laser heating leads to both gradual heating of the liquid and gradual formation of a clot with coagulated egg white at the fiber tip. In this case, by the time t =4.7 s the maximum temperature T max , which exceeds 140 °C, is achieved in the volume of liquid at a small distance from the fiber tip. In pictures showing the distribution of protein coagulation on a logarithmic scale, it can be seen that at t = 0.5 s, an area with coagulated protein is formed in the region near the fiber tip. In this case, the degree of coagulation does not exceed 10%. Note that in the frames of optical shooting, a similar area is also quite clearly visible ( t =0.5 s in Fig. 2). By t =4.7 s, the area with coagulated protein with a degree of coagulation of more than 50% is an elongated ellipsoid, 1.7 mm long, ~1.3 mm in diameter, limited from above by the cover glass of the minicuvette. (Fig. 6). By the same time, a similar area 1.9 mm long with a maximum diameter of ~1.4 mm is recorded in the optical images ( t =4.7 s in Fig. 3). Thus, the dimensions of the coagulated region obtained experimentally and by numerical modeling correlate quite well. Fig. 6. Dynamics of temperature and degree of coagulation of protein 1-C in a minicuvette with a fixed fiber (1) based on the results of modeling in Comsol. The time from the moment the laser is turned on is shown. The top view and the side view are presented. The coagulation distribution is presented in normal and logarithmic scales. Fig. 7 shows the features of the spatio-temporal temperature distribution in the minicuvette with egg white based on the results of modeling in COMSOL. From Fig. 7a it can be seen that the calculated curve for T max on the surface of the minicuvette coincides quite well with the curve obtained experimentally. The curves illustrating the spatial distribution of T max along the projection of the optical axis on the surface of the minicuvette also coincide satisfactorily ( t =4.7 s in Fig. 7b). This indicates that the modeling adequately describes the occurring processes. Note that during the heating process, at t =4.7 s, the T max on the surface reaches 100 °C, while in the depth of the liquid near the fiber tip T max ~144 °C. In this case, the change in the spatial distribution of T max over time in the volume of the liquid is described by the curves shown in Fig. 7c. Fig. 7. Features of the spatio-temporal temperature distribution in a minicuvette with egg white under laser action based on the results of modeling in COMSOL. a – dynamics of the maximum temperature T max on the surface of the cover glass and in the volume of liquid. The green dotted line shows the change in temperature on the surface based on the results of experiment №1. Time t =0 corresponds to the moment the laser is turned on. b – temperature distribution on the surface of the minicuvette at different times. The black dotted line shows a similar curve for t =4.7 s from the experiment. c – distributions of T max in the volume of liquid at different moments in time. 3.3 Experiment №2 with a vein model and a moving fiber Fig. 8 shows individual frames from experiment №2 with a vein model filled with egg white and an optical fiber moving in it. In the case where the filter cutting off 980 nm radiation is missing, existing micro-inhomogeneities and structures formed during protein coagulation are additionally illuminated by this radiation (Fig. 8a). It can be seen that the existing weak glow of the area near the fiber end (t = 0.2 s in Fig. 8a), associated with scattering of radiation λ = 980 nm, by t = 0.4 s due to protein coagulation, is significantly enhanced. Subsequently, the size of the glowing region gradually increases. However, during laser heating for t ~7.1 s, an explosive change in the shape of this region occurs, in which brightly glowing fragments fill almost the entire internal space of the tube by t =7.2. In the presence of an IR filter, the area with coagulated protein appears darker compared to the background (Fig. 8b, c). If the fiber is located not in the center of the tube simulating a vein, but near its side wall, a strongly elongated area of coagulated protein with a high aspect ratio of ~13 to t = 10 s is formed. This can be explained by the effect of coagulant adhesion to the wall surface and the peculiarities of the thermal field formation. In the frame obtained at t = 10 s (Fig. 8b), it is clearly seen that during the advancement of the fiber, two events occurred associated with explosive boiling of water, which led to the disruption of the smooth shape of the coagulant. The centers of the areas with these disrupted structures are located at a distance of 1.7 and 4.3 mm from the fiber tip. As the fiber moves along the central part of the tube simulating a vein, the formation of the protein coagulant begins at t =0.4 s (Fig. 8c). The shape of the coagulant near the fiber tip, gradually increasing in size, resembles an ellipsoid ( t =3.2 s in Fig. 8c). The almost ideal shape is abruptly disrupted as a result of explosive boiling of water ( t =3.6 s in Fig. 8c). Fig. 8. Video frames of the processes in experiment No. 2 with a vein model and a moving optical fiber. a – there is no IR filter, so the structures formed during protein coagulation are illuminated by laser radiation. b and c – recording of processes during protein coagulation using an IR filter, in the case of fiber movement near the side (front) wall ( b ) and in the case when the fiber is far from the tube walls ( c ). 3.4 Simulation with a vein and a moving fiber Fig. 9 shows the results of numerical simulation in COMSOL of laser-induced processes occurring in a tube (vein model) during fiber movement. By the time t =0.4 s, an elongated region of heated egg white is visible ahead of the tip of the optical fiber. In the immediate vicinity of the side and tip surfaces of the optical fiber, the liquid velocity approximately coincides with the fiber velocity. Gradually, as the distance from the fiber tip increases, an upward component of the liquid egg white velocity appears, which is associated with the occurrence of thermogravitational convection. A small elliptical region of coagulant appears near the optical fiber tip, similar to what was observed in the experiment (Fig. 8c). Over time, the volume of the heated liquid and the maximum temperature values increase. The egg white region near the fiber tip also increases, moving together with the fiber ( t =10 s in Fig. 9b) as a single entity. As the size of the coagulant increases, the effect of liquid protein flows flowing around this coagulant is observed. Also, over time, an increase in the asymmetry in the velocity field and the shape of the coagulant is observed. This is seen in Fig. 9b for the time moment of 10 s, at which the coagulant has a slightly upward elongated shape. This is due to the action of convective flows directed upward in the presence of gravity. Such an effect was not observed in the experiment, since before the coagulant was stretched and directed upward, it was ruptured by a microexplosion (Fig. 8c, time moments of 3.6 s and 4.6 s) as the result of the water in the egg white was overheated. Fig. 9. Changes in temperature, flow rate and area of coagulated egg white near the tip of the laser fiber (1) with a vein model and a moving fiber based on the results of modeling in COMSOL. The time from the moment the laser was turned on is shown. A side view is shown. The inner diameter of the tube is D=3.75 mm, the radiation power is P=8 W, the fiber movement speed is V=1 mm/s. See attached video files: to fig9a_ temperature; to fig9b_flow rate; to fig9c_coagulation. For a more detailed analysis of the processes occurring in the capillary with a moving fiber, we performed similar calculations for capillary diameters of 1.5 mm, 2.0 mm and 3 mm and for different fiber speeds and different laser radiation powers. Fig. 10 shows the features of the spatial distribution of temperature and coagulation of egg white in a tube with a diameter of D = 2 mm in the region of the optical axis (coinciding with the tube axis) by the time t = 10 for laser radiation powers of 8 W, 12 W and 16 W and fiber speeds of 0.5 mm/s and 1.0 mm/s. It is evident that at P = 8 W, a twofold decrease in the fiber speed (from 1 mm/s to 0.5 mm) does not lead to a significant increase in temperature (from T = 192 °C to T = 209 °C). At the same time, аn increase in power leads to a significant change in temperature. In the case of P=12 W V=0.5 mm/s T max reaches 296 °C, and at P=16 W V=1 mm/s – already 344 °C (Fig. 10a). Fig. 10. Features of the spatial distribution of temperature (a) and coagulation of egg white (b) in the tube on the optical axis at the time t =10 s when the fiber moves at different speeds and at different laser radiation powers according to the results of modeling in COMSOL. The inner diameter of the tube is D=2 mm. The initial temperature is T=21 °C. The vertical dotted lines show the initial position of the tip of the optical fiber. As the numerical calculation shows, the maximum temperature T max in the tube initially increases rapidly, but then reaches a plateau (Fig. 11). Up to approximately t =0.5 s, T max is practically independent of the inner diameter of the tube D. It is interesting that the values of T max for a relatively long laser exposure time t >1 s increase with increasing D (see the inset in Fig. 11a). Fig. 11. Dynamics of the maximum temperature T max in tubes with different internal diameters ( a ) and with different combinations of P and V, but the same value of LEED=P V ( b ) according to the results of modeling in COMSOL. The inset in Fig. 11a shows the dependence of T max at the moment t =10 s on the internal diameter of the tube. Initial temperature T=21 °C. Regarding protein coagulation, as the capillary diameter decreases, there is a noticeable increase in the length of the coagulated area compared to a capillary diameter of 3.75 mm. At the 10th second, the area with a coagulation degree of 1% or more extends from the fiber tip to the initial position of the fiber 12 mm. If we estimate the size of the coagulant by the 50% coagulation level, then for P = 8 W and V = 1 mm/s, the length of the coagulant is 6.9 mm. For a capillary with a diameter of 3.75 mm at the same radiation power and the same speed, the length of the coagulant was 2.4 mm. In the real EVLA procedure, the initial temperature, unlike our experiment, is equal to the human body temperature. A higher initial temperature can significantly affect the size of the coagulated area. We performed calculations for the initial temperature T 0 =37 °C in a vein with an internal diameter of D=2 mm, at P=8 W, V=0.5 mm/s. Fig. 13 shows the calculation results. As a result of numerical modeling in the COMSOL program, we found that an increase in the initial temperature does indeed lead to an increase in the coagulation zone. Thus, in Fig. 12c at t =10 s the coagulation area of the vein walls is visible, whereas with the same parameters, but at T 0 =21 °C, coagulation of the vein walls did not occur. It should also be noted that with a smaller capillary’s diameter, the coagulant has a symmetrical shape throughout the entire length of the fiber movement (Fig. 12c). The asymmetry arises, as mentioned above, due to the significant influence of thermogravitational flows directed upwards. In the case of small capillary diameters, these flows are negligible, especially when the coagulant diameter is almost the same as the capillary diameter. Fig. 12. Changes in temperature, flow velocity and area of coagulated egg white near the tip of the laser fiber (1) with a vein model and a moving fiber based on the results of modeling in COMSOL. The time from the moment the laser was turned on is shown. The side view is shown. D=2 mm, P=8 W, V=0.5 mm/s. Initial temperature T=37 °C. See attached video files: to fig12c_coagulation; fig12c_coagulation_3D. Fig. 13 shows the features of the spatial distribution of temperature and coagulation of egg white in the inner upper and lower parts of the tube with D=2 mm at time t =10 s at an initial temperature T=37 °C for different values of P and V. Fig. 13. Features of the spatial distribution of temperature (a) and coagulation of egg white (b) in the inner upper and lower parts of the tube by the time t=10 s when the fiber moves at different speeds and at different laser radiation powers according to the results of modeling in COMSOL. The inner diameter of the tube is D=2 mm. The initial temperature is T=37 °C. The vertical dotted lines show the initial position of the tip of the optical fiber. 4. Discussions Optical video recording of the processes showed that under laser action, a clot of coagulated protein is formed near the fiber tip, the size of which gradually increases over time. However, with a sufficiently long exposure ( t ~4.7 s), rapid explosive changes in the shape of the coagulant and its rupture occur. Thermograms reflecting the temperature distribution on the surface of the minicuvette cover glass showed (Fig. 4, Fig. 5) that at this moment T max reaches 100 °C. And literally 100 ms later, the T max value unexpectedly and abruptly decreases by 15 °C (Fig. 5a, Fig. 5d). Such processes are the result of microexplosions in the overheated water of the egg white. It is known that in a superheated liquid in a metastable state, explosive boiling begins with the appearance of critical nuclei in it, the probability of whose appearance increases with an increase in the degree of overheating (an excess of temperature over the boiling point, which is 100 °C at normal pressure) [28]. This is confirmed by our calculations, which showed that while T max on the surface of the cover glass reaches 100 °C by t ~4.7 s during laser heating, T max in the volume of the liquid by this time already exceeds 140 °C (Fig. 7a). In this case, the volume with such strongly superheated water (overheating ΔT>40 °C) is located in the region of the optical axis directly in front of the tip of the laser fiber at some distance from it (Fig. 6). It is known that explosive boiling of a liquid leads to the formation of steam bubbles compressed to high pressure [29-31], the expansion and collapse of which leads to the generation of shock and acoustic waves [30-32], hydrodynamic processes, including submerged jets [33]. In our experiments, as a result of explosive boiling at t = 4.8, the coagulant ruptured and its shape changed abruptly (Fig. 3). At the same time, the temperature near the fiber tip decreased abruptly (Fig. 5a, d) due to a sharp expansion, energy costs for vaporization and mixing of liquid protein in the volume of the minicuvette. As a result of experimental and numerical modeling of the processes in the minicuvette, coefficients were selected that allowed us to fit the results of numerical modeling to the experiment as closely as possible. Thus, the curves shown in Fig. 7a, reflecting the dynamics of the maximum temperatures on the surface of the minicuvette cover glass, obtained using a thermal imager (green dotted line ”T”) and numerical calculations (blue curve ”on surface”) coincide quite well. According to both of these curves, by t = 4.7 s, T max on the surface of the minicuvette reaches 100 °C. The sizes and shapes of the coagulant formed near the tip of the optical fiber according to the results of experiment № 1 (Fig. 3) and numerical calculations (Fig. 6) at different points in time are in good agreement. All this allowed us to conclude that the numerical modeling adequately reflects the processes taking place, including the formation of temperature fields and the distribution of the volume of coagulated egg white. It is worth noting that this result was achieved thanks to the precise delineation of the coagulated area boundaries using optical methods, which can be further improved [34]. In the second series, experimental studies (Fig. 1b) and numerical simulation (Fig. 2b) were carried out with a vein model and a moving fiber. The processes occurring in the tube simulating the vein in experiment №2 were qualitatively similar to those observed in experiment №1. Just as in Fig. 3, over time, a coagulant region gradually formed near the fiber tip in the form of an ellipsoid of (Fig. 8a, c). The only difference was that the coagulant adhered to the fiber tip moved along with the fiber. Just as for the experiments with the minicuvette, after some time, there was a sharp change in its coagulant, accompanied by active mixing of the liquid in the internal volume of the tube ( t =7.2 s in Fig. 8a and t =3.6 s in Fig. 8c). The occurrence of violent mixing is most clearly visible in frames with the missing IR filter, when all induced inhomogeneities of the refractive index of the medium are illuminated by laser radiation ( t =7.2 s in Fig. 8a). As has already been shown above, both the abrupt change in the shape of the coagulant and the active mixing of the liquid are caused by the explosive boiling of water due to its significant overheating. Experiments with the tube also showed that the resulting structures of coagulated protein can, as it were, ”cling” to rigid surfaces. Thus, in Fig. 8b it is evident that when the axis of the optical fiber is shifted toward the side wall of the tube during the process of pulling the fiber, a strongly elongated region of coagulant is created (t=10 s in Fig. 8b). The numerical modeling performed in COMSOL confirmed that it adequately reflects the ongoing processes of forming the volume of coagulated egg white, since the calculated spatial distributions of the coagulant at different points in time (Fig. 9c) coincided quite well with the experimental results (Fig. 8c). During the numerical simulation with a moving fiber, some regularities were revealed. In particular, a noticeable elongation of the coagulated zone with a decrease in the capillary diameter. Such a noticeable difference in the length of the coagulated area for capillaries of different diameters is not associated with a difference in temperatures for different capillaries. For a capillary with D = 2 mm, the temperature is even lower than for a diameter of D = 3.75 mm (Fig. 11 a). The elongation of the coagulant with a smaller capillary diameter is associated with the effect of its stretching during fiber movement due to viscous resistance at the capillary walls. This is consistent with the effect of coagulant stretching, which was observed experimentally when the fiber was located closer to the capillary wall (Fig. 8b). At large diameters, this resistance force is quite small, since the walls are at a sufficiently large distance from the coagulant and the coagulant moves as a single entity together with the fiber tip. The effect of fiber stretching is clearly visible from the peculiarities of the velocity field distribution in the region near the fiber tip. For a capillary with D = 3.75 mm, almost the entire coagulation region (1-C> 50%) moves with approximately the same speed. 1 mm/s (Fig. 9 b). Whereas for a capillary with D = 2 mm, a strong velocity gradient arises in the region near the fiber tip. This indicates that near the surface of the tip, the egg white moves approximately at the speed of the fiber, and at a small distance from the tip, this speed is noticeably lower, i.e. the egg white movement lags behind the fiber tip and the coagulant is stretched. This effect can be seen in Fig. 12 b, but for a fiber speed of 0.5 mm/s. Another interesting feature revealed during numerical modeling with a moving fiber in a capillary is the effect of decreasing maximum temperature near the fiber tip with decreasing capillary diameter (Fig. 11 a). In our opinion, this is also related to the above-described effect of coagulant stretching. The fact is that at large diameters, the coagulant moves together with the fiber tip as if it were a single solid object. In this case, heat removal from the local laser energy input zone is mainly determined by thermal conductivity. When the coagulant is stretched, additional heat removal occurs due to the movement of the most highly heated region of the coagulant relative to the tip. In this regard, the maximum temperature for smaller capillary diameters decreases. Our studies have shown that the calculated temperature patterns, flow rates in the tube and coagulation are in good agreement with the experimentally observed phenomena occurring in the vein model. However, it should be noted that our mathematical model did not take into account possible phase transitions. Therefore, such a model can accurately describe the processes occurring in the tube volume only up to the moment when explosive boiling of water occurs due to overheating. As has been established, such boiling leads to a violation of the coagulant shape and strong mixing of the liquid in the internal volume of the tube. An interesting result obtained by numerical modeling in COMSOL is the dependence of the spatial distribution of temperature and coagulation of egg white in the tube on various combinations of fiber speed V and laser radiation power P (Fig. 10). Thus, it turned out quite unexpectedly that at P=8 W and a two-fold decrease in fiber speed (from 1 mm/s to 0.5 mm), the expected proportional increase in the maximum temperature does not occur: T max increased not by 2 times, but only by 10%. But an increase in power at the same speed leads to an almost proportional increase in T max : with an increase in power from P=8 W to P=16 W, the maximum heating increases by 89% (Fig. 10a). One of the important controversial issues related to endovenous laser coagulation technology is whether it is sufficient to set only the linear endovenous energy density (LEED) value to perform the procedure [1-4, 6-9]. LEED is determined by dividing the power P by the fiber velocity V and is measured in J/cm. Fig. 11b shows the dynamics of T max in a tube with D=2 mm for one value of LEED = 160 J/cm and for different combinations of P and V. It is evident that for the same LEED, the T max values differ significantly. For P=8 W, T max reaches 208 °C in 10 s, and for P=16 W – 349 °C. At the same time, for P=16 W, the temperature of 208 °C is reached in just 0.3 s. Since the processes occurring in the tube volume are significantly affected by explosive boiling of the liquid, it is important to estimate the frequency of such events. If we assume that explosive boiling occurs when T max =200 °C is reached, then from the dependencies presented in Fig. 11b we can obtain that at P=8 W the first act will occur at t=3.5 s, while at P=16 W - at t=0.3 s. That is, at the same value of LEED=160 J/cm, a decrease in power from P=16 W to P=8 W will lead to a decrease in the frequency of explosive boiling acts by more than an order of magnitude. This, in turn, will lead to significantly less mixing of the liquid in the volume of the vein, which significantly affects the temperature field and coagulation. Thus, we can conclude that it is important for EVLA technology to set not only LEED values, but also P. The conducted studies made it possible to answer to some extent another very important question for this medical technology about symmetry during coagulation of the upper and lower walls of the vein [7, 8] [33, 35]. Numerical modeling showed that the degree of asymmetry significantly depends on the laser exposure parameters used. For example, coagulation occurs symmetrically (Fig. 12b) with parameters P=12 W, V=0.5 mm/s, whereas with other parameters P=8 W, V=1 mm/s, a pronounced asymmetry is observed in the degree of coagulation of the surfaces of the upper and lower walls of the vein. As can be seen from Fig. 13a, for these two cases the temperature on the upper and lower internal surfaces of the vein differs slightly. The appearance of asymmetry in the degree of coagulation with such a small difference in temperature can be explained by the exponential Arrhenius temperature dependence. It should be noted that the laser parameters used in the studies resulted in partial coagulation of a fairly thin layer of the inner surface of a fairly thin vein with D=2 mm (t=10 s in Fig. 12c). In the clinic, the same and smaller LEED parameters lead to more extensive destruction, and in the case of veins with a much larger diameter [2, 3]. We believe that a possible reason for the more effective vein coagulation observed in practice is associated with the fact that the model used does not take into account the influence of phase transitions accompanied by the generation of bubbles and jet streams, as well as possible exothermic reactions. Phase transitions lead to intense mixing of the liquid medium, more effectively transferring heat from the heated areas near the fiber tip to the inner wall of the vein. It should be noted that further consideration should be given to the effects of using other types of fibers employed for EVLA [4, 36, 37]. 5. Conclusions This article presents the results of experimental and numerical modeling of processes occurring during endovenous laser coagulation using continuous laser radiation with λ=0.97 μm and optical fiber with a light-conducting core diameter of 600 μm. In the experiments, the dynamic processes occurring were studied using video filming and thermography methods, with the vein being modeled by a transparent silicone tube, and the blood in the vein cavity by egg white. Numerical modeling was performed in the COMSOL Muliphysics package using the developed multiphysical model, which took into account the movement of the optical fiber in the vein, the absorption and scattering of laser radiation emerging from the fiber tip, fluid flows and protein coagulation. The studies showed good agreement between the experimental data and the calculation results. Using the proposed model, thermal fields, hydrodynamic flows and coagulation were calculated for veins of different diameters and different laser exposure conditions (radiation power, fiber speed) The simulation showed that, depending on the vein diameter and laser exposure parameters, different patterns of spatial temperature distribution, convective flows and protein coagulation are formed. With large diameters and low powers, the coagulant at the fiber tip moves as a single entity with the fiber, exhibiting pronounced asymmetry with a clear upward direction caused by convection inside the vein. For smaller diameters, the coagulant has a symmetrical shape that stretches over time as the fiber moves, influenced by the internal walls. It was also found that due to the coagulant elongation, the temperature near the fiber tip is lower in veins of smaller diameter. It is shown that laser power is a key parameter for endovenous laser ablation, largely determining the temperature distribution and the extent of coagulation on the inner surface of the vein. It has been established that, besides thermal conductivity and convective flows caused by uneven heating, processes related to explosive boiling play an important role at typical laser settings used in practice. The results can help clarify the mechanisms of action and improve medical technologies. Appendix A . Supplementary data Supplementary data to this article can be found online Highlights • Multiphysics model predicts heat, flow, and coagulation in veins accurately • Vein diameter and laser power are key in forming physical fields • Thin veins show no asymmetry in coagulation patterns Large vein coagulation depends solely on explosive boiling mixing Acknowledgment This work was carried out within the state assignment of NRC “Kurchatov institute”. Author contributions: VY: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Supervision; Validation; Visualization; Writing-draft; Writing – review and editing AK: Data curation; Formal analysis; Investigation; Methodology; Software; Validation; Visualization; Writing – review and editing Funding sources: The work was carried out within the state assignment of NRC “Kurchatov institute”. Conflict of interest disclosure : None References [1] M.R. Aslam, H.M. Asif, K. Ahmad, S. Jabbar, A. Hayee, M.S. Sagheer, J.U. Rehman, S. Khalid, A.S. Hashmi, S.R. Rajpoot, A. Sharif, Global impact and contributing factors in varicose vein disease development, SAGE Open Med. 10 (2022). https://doi.org/10.1177/20503121221118992.[2] K.A. Teter, L.S. Kabnick, M. Sadek, Endovenous laser ablation: A comprehensive review, Phlebology 35 (9) (2020) 656-662. https://doi.org/10.1177/0268355520937619.[3] W.S.J. Malskat, A.A. 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Bushukina, et al., Optimization of endovenous laser coagulation: in vivo experiments, Lasers Med. Sci. 35 (2020) 867–875. https://doi.org/10.1007/s10103-019-02874-6.[36] V.P. Minaev, N.V. Minaev, V.Yu. Bogachev, K.A. Kaperiz, V.I. Yusupov, Endovenous laser coagulation: modeling in blood plasma. Phisics of Waves Phenomenon. (2025) in print.[37] Kim C, Sohn IB, Park H, Lee YJ, Lee H. Comparison of laser-assisted damage in soft tissue using bi-directional and forward-firing optical fiber. Optics & Laser Technology. 2014 Mar 1;56:196-201 Information & Authors Information Version history V1 Version 1 11 July 2025 Peer review timeline Published Physica Scripta Version of Record 25 Nov 2025 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords comsol explosive boiling heat and mass transfer laser vein treatment thermal modeling Authors Affiliations Vladimir I. Yusupov 0000-0002-9438-6295 [email protected] NRC “Kurchatov Institute View all articles by this author Alexey Konovalov NRC “Kurchatov Institute View all articles by this author Metrics & Citations Metrics Article Usage 210 views 134 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Vladimir I. Yusupov, Alexey Konovalov. OPTICAL AND COMPUTATIONAL MODELING OF LASER-INDUCED PROCESSES IN ENDOVENOUS LASER ABLATION: HEAT TRANSFER, FLUID DYNAMICS, AND TISSUE COAGULATION. Authorea . 11 July 2025. DOI: https://doi.org/10.22541/au.175221959.93895795/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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