Optical-thermal mathematical model for endovenous laser ablation of varicose veins

Abstract

Endovenous laser ablation (EVLA) is successfully used to treat varicose veins. However, the exact working mechanism is still not fully identified and the clinical procedure is not yet standardized. Mathematical modeling of EVLA could strongly improve our understanding of the influence of the various EVLA processes. The aim of this study is to combine Mordon's optical-thermal model with the presence of a strongly absorbing carbonized blood layer on the fiber tip. The model anatomy includes a cylindrically symmetric blood vessel surrounded by an infinite homogenous perivenous tissue. The optical fiber is located in the center of the vessel and is withdrawn with a pullback velocity. The fiber tip includes a small layer of strongly absorbing material, representing the layer of carbonized blood, which absorbs 45% of the emitted laser power. Heat transfer due to boiling bubbles is taken into account by increasing the heat conduction coefficient by a factor of 200 for temperatures above 95 °C. The temperature distribution in the blood, vessel wall, and surrounding medium is calculated from a numerical solution of the bioheat equation. The simulations were performed in MATLAB™ and validated with the aid of an analytical solution. The simulations showed, first, that laser wavelength did virtually not influence the simulated temperature profiles in blood and vessel wall, and, second, that temperatures of the carbonized blood layer varied slightly, from 952 to 1,104 °C. Our improved mathematical optical-thermal EVLA model confirmed previous predictions and experimental outcomes that laser wavelength is not an important EVLA parameter and that the fiber tip reaches exceedingly high temperatures.