Analytical solutions in the modeling of the endovenous laser ablation

TL;DR

This paper develops exact analytical solutions for modeling endovenous laser ablation, incorporating detailed heat transfer and laser irradiance effects to improve understanding of the procedure.

Contribution

It introduces a comprehensive mathematical model with exact solutions for heat transfer in EVLA, considering laser irradiance and boundary conditions.

Findings

Exact solutions for heat, diffusion, and bioheat equations in EVLA

Enhanced modeling accuracy by including Beer-Lambert law

Discussion of open problems in the modeling approach

Abstract

We model the operative treatment of incompetent truncal veins using endovenous laser ablation (EVLA). Three differential equations, namely the diffusion, the heat and the bioheat equations, are considered in the endovenous-perivenous multidomain, describing the lumen, the vein wall, the tissue pad and the skin. Exact solutions are provided. Our main concern is to accurate the heat source by taking the Beer--Lambert law into account in the irradiance of the incident beam. To accurate the heat transfer at the skin boundary, the Newton law of cooling is considered as a Robin boundary condition. Open problems are presented.