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We modeled the operative treatment of incompetent truncal veins using endovenous laser ablation (EVLA). The main concern regarding the thermoablative technique is tissue damage, which is correlated with (1) the energy provided by the laser power and (2) temperature distribution. Our objective was to accurate the two functions, namely the fluence rate and the temperature, depending on the thermoablative technique and the endovenous laser treatment (ELT). First, we considered three differential equations: diffusion, heat, and bioheat equations in the endovenous-perivenous multidomain to describe the lumen, the vein wall, the tissue pad, and the skin. Second, we examined the power source according to the Beer-Lambert law in the incident beam irradiance and the heat source as the so-called absorbed optical power density. Third, we checked out the heat transfer at the skin boundary according to Newton’s law of cooling, which stands for a Robin boundary condition. For this new model, we proposed exact solutions: applying differential equations techniques, we solved (1) a diffusion approximation of the radiative transfer equation under the considered power source, and (2) the coupled heat and bioheat equations under the considered heat source accomplished with the Robin boundary condition. Then, we graphically illustrated the fluence rate profile and discussed its time dependence and steady state. Besides, we discuss thermal damage to the vein-tissue system and present open problems.
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Almeida, J., Mackay, E., Javier, J., Mauriello, J., Raines, J. (2009) Saphenous laser ablation at 1470 nm targets the vein wall, not blood. Vascular and Endovascular Surgery, 43(5), 467–472. https://doi.org/10.1177/1538574409335916
Anchala, P., Wickman, C., Chen, R., Faundeen, T., Pearce, W., Narducy, L., Resnick, S. (2010) Endovenous laser ablation as a treatment for postsurgical recurrent saphenous insufficiency. Cardiovascular and Interventional Radiology, 33(5), 983–988. https://doi.org/10.1007/s00270-009-9784-3
Ash, J. L., Moore, C. J. (2010) Laser treatment of varicose veins: Order out of chaos. Seminars in Vascular Surgery, 23(2), 101–106. https://doi.org/10.1053/j.semvascsurg.2010.01.005
Bi, S., Liu, H., Nan, Q., Mai, X. (2023) Study on the effect of micro-vessels on ablation effect in laser interstitial brain tissue thermal therapy based on PID temperature control. Applied Sciences, 13(6), 3751. https://doi.org/10.3390/app13063751
Bianchi, L., Cavarzan, F., Ciampitti, L., Cremonesi, M., Grilli, F., Saccomandi, P. (2022) Thermophysical and mechanical properties of biological tissues as a function of temperature: A systematic literature review. International Journal of Hyperthermia, 39(1), 297–340. https://doi.org/10.1080/02656736.2022.2028908
Caggiati, A., Franceschini, M. (2010) Stroke following endovenous laser treatment of varicose veins. Journal of Vascular Surgery, 51(1), 218–220. https://doi.org/10.1016/j.jvs.2009.07.092
Carradice, D., Mekako, A. I., Mazari, F. A. K., Samuel, N., Hatfield, J., Chetter, I. C. (2011) Clinical and technical outcomes from a randomized clinical trial of endovenous laser ablation compared with conventional surgery for great saphenous varicose veins. British Journal of Surgery, 98(8), 1117–1123. https://doi.org/10.1002/bjs.7615
Chaar, C. I. O., Hirsch, S. A., Cwenar, M. T., Rhee, R. Y., Chaer, R. A., Hamad, G. A., Dillavou, E. D. (2011) Expanding the role of endovenous laser therapy: Results in large diameter saphenous, small saphenous, and anterior accessory veins. Annals of Vascular Surgery, 25(5), 656–661. https://doi.org/10.1016/j.avsg.2011.02.031
Chebotarev, A. Y., Pak, N. M., Kovtanyuk, A. E. (2023) Analysis and numerical simulation of the initial-boundary value problem for quasilinear equations of complex heat transfer. Journal of Applied and Industrial Mathematics, 17, 698–709. https://doi.org/10.1134/S1990478923040026
Consiglieri, L. (2016) Analytical solutions in the modeling of the local RF ablation. Journal of Mechanics in Medicine and Biology, 16(05), 1650071. https://doi.org/10.1142/S0219519416500718
Consiglieri, L. (2012) Continuum models for the cooling effect of blood flow on thermal ablation techniques. International Journal of Thermophysics, 33(5), 864–884. https://doi.org/10.1007/s10765-012-1194-0
Consiglieri, L. (2013) An analytical solution for a bio-heat transfer problem. International Journal of Bio-Science and Bio-Technology, 5(5), 267–278. https://doi.org/10.14257/ijbsbt.2013.5.5.26
Consiglieri, L., dos Santos, I., Haemmerich, D. (2003) Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies. Physics in Medicine and Biology, 48(24), 4125–4134. https://doi.org/10.1088/0031-9155/48/24/010
Doganci, S., Demirkilic, U. (2010) Comparison of 980 nm laser and bare-tip fibre with 1470 nm laser and radial fibre in the treatment of great saphenous vein varicosities: A prospective randomised clinical trial. European Journal of Vascular and Endovascular Surgery, 40(2), 254–259. https://doi.org/10.1016/j.ejvs.2010.04.006
Etlik, O., Korkmaz, A. A., Uckurt, Y., Indelen, S., Gundogdu, R., Ozturk, A., al-Salehi, S. K., Aung, S. M. (2013) Endovenous laser ablation for saphenous vein insufficiency: Long-term results. Turkish Journal of Medical Sciences, 43(3), 470–473. https://doi.org/10.3906/sag-1206-68
Firouznia, K., Ghanaati, H., Hedayati, M., Shakiba, M., Jalali, A. H., Mirsharifi, R., Dargahi, A. (2013) Endovenous laser treatment (EVLT) for the saphenous reflux and varicose veins: A follow-up study. Journal of Medical Imaging and Radiation Oncology, 57(1), 15–20. https://doi.org/10.1111/j.1754-9485.2012.02457.x
Gale, S. S., Lee, J. N., Walsh, M. E., Wojnarowski, D. L., Comerota, A. J. (2010) A randomized, controlled trial of endovenous thermal ablation using the 810-nm wavelength laser and the ClosurePLUS radiofrequency ablation methods for superficial venous insufficiency of the great saphenous vein. Journal of Vascular Surgery, 52(3), 645–650. https://doi.org/10.1016/j.jvs.2010.04.030
Goldman, M., Mauricio, M., Rao, J. (2004) Intravascular 1320-nm laser closure of the Great Saphenous Vein: A 6- to 12-month follow-up study. Dermatologic Surgery, 30(11), 1380–1385. https://www.ncbi.nlm.nih.gov/pubmed/15522018
González-Suárez, A., Trujillo, M., Burdío, F., Andaluz, A., Berjano, E. (2014) Could the heat sink effect of blood flow inside large vessels protect the vessel wall from thermal damage during RF-assisted surgical resection? Medical Physics, 41(8), 083301. https://doi.org/10.1118/1.4890103
Goode, S., Chowdhury, A., Crockett, M., Beech, A., Simpson, R., Richards, T., Braithwaite, B. (2010) Laser and radiofrequency ablation study (LARA study): A randomised study comparing Radiofrequency Ablation and Endovenous Laser Ablation (810nm). European Journal of Vascular and Endovascular Surgery, 40(2), 246–253. https://doi.org/10.1016/j.ejvs.2010.02.026
Horng, T.-L., Lin, W.-L., Liauh, C.-T., Shih, T.-C. (2007) Effects of pulsatile blood flow in large vessels on thermal dose distribution during thermal therapy. Medical Physics, 34(4), 1312–1320. https://doi.org/10.1118/1.2712415
Katta, N., Santos, D., McElroy, A. B., Estrada, A. D., Das, G., Mohsin, M., Donovan, M., Milner, T. E. (2022) Laser coagulation and hemostasis of large diameter blood vessels: Effect of shear stress and flow velocity. Scientific Reports, 12, 8375. https://doi.org/10.1038/s41598-022-12128-1
Kotte, A. N. T. J., van Leeuwen, G. M. J., Lagendijk, J. J. W. (1999) Modelling the thermal impact of a discrete vessel tree. Physics in Medicine & Biology, 44(1), 57–74. https://doi.org/10.1088/0031-9155/44/1/006
Marqa, M., Mordon, S., Hernandez-Osma, E., Trelles, M., Betrouni, N. (2013) Numerical simulation of endovenous laser treatment of the incompetent great saphenous vein with external air cooling. Lasers in Medical Science, 28(3), 833–844. https://doi.org/10.1007/s10103-012-1141-0
Memetoglu, M. E., Erbasan, O., Ozel, D. (2012) Follow-up results of laser saphenous ablation. Dicle Tip Dergisi, 39(3), 331–335. https://doi.org/10.5798/diclemedj.0921.2012.03.0153
Min, R. J., Khilnani, N. M., Zimmet, S. E. (2003) Endovenous laser treatment of saphenous vein reflux: Long-term results. Journal of Vascular and Interventional Radiology, 14(8), 991–996. https://doi.org/10.1097/01.RVI.0000082864.05622.E4
Mordon, S., Wassmer, B., Zemmouri, J. (2006) Mathematical modeling of endovenous laser treatment (ELT). BioMedical Engineering OnLine, 5, 26. https://doi.org/10.1186/1475-925X-5-26
Oh, C. K., Jung, D.-S., Jang, H. S., Kwon, K. S. (2003) Endovenous laser surgery of the incompetent Greater Saphenous Vein with a 980-nm diode laser. Dermatologic Surgery, 29(11), 1135–1140. https://www.ncbi.nlm.nih.gov/pubmed/14641341
Olver, F. (1972) Bessel functions of integer order. In M. Abramonitz I. Stegun (Eds.), Handbook of mathematical functions with formulas, graphs, and mathematical tables (pp. 355–389).
Ozisik, M. (2012) Appendix IV: Bessel Functions. In Heat conduction (pp. 691–706). John Wiley & Sons, Ltd. https://doi.org/10.1002/9781118411285.app4
Ozkan, U., Sariturk, C. (2012) Early clinical improvement in chronic venous insufficiency symptoms after laser ablation of saphenous veins. Diagnostic and Interventional Radiology, 18(6), 594–598. https://doi.org/10.4261/1305-3825.DIR.5917-12.1
Palombi, L., Morelli, M., Bruzzese, D., Martinelli, F., Quarto, G., Bianchi, P. G. (2024) Endovenous laser ablation (EVLA) for vein insufficiency: two-year results of a multicenter experience with 1940-nm laser diode and a novel optical fiber. Lasers in Medical Science, 39, 61. https://doi.org/10.1007/s10103-024-04000-7
Poluektova, A., Malskat, W., Gemert, M. V., Vuylsteke, M., Bruijninckx, C., Neumann, H., van der Geld, C. (2014) Some controversies in endovenous laser ablation of varicose veins addressed by optical-thermal mathematical modeling. Lasers in Medical Science, 29, 441–452. https://doi.org/10.1007/s10103-0131450-y
Prahl, S. A. (1995) The diffusion approximation in three dimensions. In A. J. Welch M. J. C. Van Gemert (Eds.), Optical-thermal response of laser-irradiated tissue (pp. 207–231). Springer US.
Prince, E., Soares, G., Silva, M., Taner, A., Ahn, S., Dubel, G., Jay, B. (2011) Impact of laser fiber design on outcome of endovenous ablation of lower-extremity varicose veins: Results from a single practice. Cardiovascular and Interventional Radiology, 34(3), 536–541. https://doi.org/10.1007/s00270-010-9922-y
Proebstle, T., Krummenauer, F., Gul, D., Knop, J. (2004) Nonocclusion and early reopening of the great saphenous vein after endovenous laser treatment is fluence dependent. Dermatologic Surgery, 30, 174–178. https://doi.org/10.1067/mva.2002.121132
Puggioni, A., Kalra, M., Carmo, M., Mozes, G., Gloviczki, P. (2005) Endovenous laser therapy and radiofrequency ablation of the great saphenous vein: Analysis of early efficacy and complications. Journal of Vascular Surgery, 42(3), 488–493. https://doi.org/10.1016/j.jvs.2005.05.014
Rasmussen, L. H., Lawaetz, M., Bjoern, L., Vennits, B., Blemings, A., Eklof, B. (2011) Randomized clinical trial comparing endovenous laser ablation, radiofrequency ablation, foam sclerotherapy and surgical stripping for great saphenous varicose veins. British Journal of Surgery, 98(8), 1079–1087. https://doi.org/10.1002/bjs.7555
Rathod, J., Taori, K., Joshi, M., Mundhada, R., Rewatkar, A., Dhomane, S., Gour, P. (2010) Outcomes using a 1470-nm laser for symptomatic varicose veins. Journal of Vascular and Interventional Radiology, 21(12), 1835–1840. https://doi.org/10.1016/j.jvir.2010.09.009
Roggan, A., Friebel, M., Doerschel, K., Hahn, A., Mueller, G. J. (1999) Optical properties of circulating human blood in the wavelength range 400-2500 nm. Journal of Biomedical Optics, 4(1), 36–46. https://doi.org/10.1117/1.429919
Schmedt, C.-G., Blagova, R., Karimi-Poor, N., Burgmeier, C., Steckmeier, S., Beck, T., Hecht, V., Meier, R., Sadeghi-Azandaryani, M., Steckmeier, B., Sroka, R. (2010) Update of endovenous laser therapy and the latest application studies. Medical Laser Application, 25(1), 34–43. https://doi.org/10.1016/j.mla.2009.11.004
Schwarz, T., von Hodenberg, E., Furtwängler, C., Rastan, A., Zeller, T., Neumann, F.-J. (2010) Endovenous laser ablation of varicose veins with the 1470-nm diode laser. Journal of Vascular Surgery, 51(6), 1474–1478. https://doi.org/10.1016/j.jvs.2010.01.027
Sharif, M. A., Soong, C. V., Lau, L. L., Corvan, R., Lee, B., Hannon, R. J. (2006) Endovenous laser treatment for long saphenous vein incompetence. British Journal of Surgery, 93(7), 831–835. https://doi.org/10.1002/bjs.5351
Star, W. M. (1995) Diffusion theory of light transport. In A. J. Welch M. J. van Gemert (Eds.), Optical-thermal response of laser-irradiated tissue (pp. 131–206). Springer US.
Theivacumar, N., Gough, M. (2011) Endovenous Laser Ablation (EVLA) to Treat Recurrent Varicose Veins. European Journal of Vascular and Endovascular Surgery, 41(5), 691–696. https://doi.org/10.1016/j.ejvs.2011.01.018
Tseng, Y.-H., Chen, C.-W., Wong, M.-Y., Yang, T.-Y., Lin, Y.-H., Lin, B.-S., Huang, Y.-K. (2022) Blood flow analysis of the great saphenous vein in the supine position in clinical manifestations of varicose veins of different severities: Application of phase-contrast magnetic resonance imaging data. Diagnostics, 12(1). https://doi.org/10.3390/diagnostics12010118
Van Ruijven, P., Poluektova, A., Van Gemert, M., Neumann, H., Nijsten, T., Van der Geld, C. (2014) Optical-thermal mathematical model for Endovenous Laser Ablation of varicose veins. Lasers in Medical Science, 29, 431–439. https://doi.org/10.1007/s10103-013-1451-x
Vuylsteke, M., Martinelli, T., Van Dorpe, J., Roelens, J., Mordon, S., Fourneau, I. (2011) Endovenous Laser Ablation: The role of intraluminal blood. European Journal of Vascular and Endovascular Surgery, 42(1), 120–126. https://doi.org/10.1016/j.ejvs.2011.03.017
Zhang, Y., Xie, H. (2018) The effect of a bifurcation structure on the heat transfer and temperature distribution of pulsatile blood flow. International Journal of Heat and Mass Transfer, 118, 663–670. https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.055
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