Mathematical modeling of 980‐nm and 1320‐nm endovenous laser treatment

Abstract

Endovenous laser treatment (ELT) has been proposed as an alternative in the treatment of reflux of the great saphenous vein (GSV) and small saphenous vein (SSV). Numerous studies have since demonstrated that this technique is both safe and efficacious. ELT was presented initially using diode lasers of 810 nm, 940 nm, and 980 nm. Recently, a 1,320-nm Nd:YAG laser was introduced for ELT. This study aims to provide mathematical modeling of ELT in order to compare 980 nm and 1,320 nm laser-induced damage of saphenous veins. The model is based on calculations describing light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation, and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma, Inc., Arlington, MA). Calculations were performed so as to determine the damage induced in the intima tunica, the externa tunica and inside the peri-venous tissue for 3 mm and 5 mm vessels (considered after tumescent anesthesia) and different linear endovenous energy densities (LEED) usually reported in the literature. Calculations were performed for two different vein diameters: 3 mm and 5 mm and with LEED typically reported in the literature. For 980 nm, LEED: 50 to 160 J/cm (CW mode, 2 mm/second pullback speed, power: 10 W to 32 W) and for 1,320 nm, LEED: 50 to 80 J/cm (pulsed mode, pulse duration 1.2 milliseconds, peak power: 135 W, repetition rate 30 Hz to 50 Hz). Numerical simulations are in agreement with LEED reported in clinical studies. Mathematical modeling shows clearly that 1,320 nm, with a better absorption by the vessel wall, requires less energy to achieve wall damage. In the 810-1,320-nm range, blood plays only a minor role. Consequently, the classification of these lasers into hemoglobin-specific laser wavelengths (810, 940, 980 nm) and water-specific laser wavelengths (1,320 nm) is inappropriate. In terms of closure rate, 980 nm and 1,320 nm can lead to similar results and, as reported by the literature, to similar side effects. This model should serve as a useful tool to simulate and better understand the mechanism of action of the ELT.