# Finite Element Method (FEM) Modeling of Laser-Tissue Interaction during Hair Removal
## 1 Introduction  
In recent decades, laser technology has become an increasingly prevalent tool for hair removal, both for aesthetic and health-related purposes [1; 2; 3; 4]. When compared to conventional practices such as shaving, waxing, chemical peilatories, and electrolysis, laser hair removal procedures appear to be fast, with long-lasting results and minimal side effects [5; 6]. The mechanism of laser hair removal has been well described and is based on irreversible photothermal damage to hair follicles through the use of a light source at the red or infrared end of the spectrum [1]. Among the critical factors influencing the effectiveness of laser hair removal are the laser wavelength, duration of the pulse, fluence, and cooling method [1]. The main advantage of laser hair removal is selective photthermolysis, while most complications can be prevented by correctly selecting the laser type tailored to each patient and adjusting parameters and cooling [7]. It is imperative to have well-trained personnel with in-depth knowledge of the procedures to perform laser treatments effectively and safely [7]. The most frequently used laser hair removal systems are ruby laser (694 nm), alexandrite laser (755 nm), pulsed diode lasers (800, 810 nm), and Nd:YAG laser (1064 nm); in addition, intense pulsed light (IPL) sources with a broad spectrum (within 500-1200 nm) are also being used for hair removal [7]. In this article, we exclusively focus on the long-pulse Nd:YAG laser (1064 nm), which is characterized by the largest penetration within skindue to its low absorption and scattering, while at the same time the absorption in the hair follicle is sufficiently high to achieve irreversible damage to this area. Ideally, the duration of the laser pulse should be shorter than the thermal relaxation time of the hair and longer than that of the epidermis in order to achieve effective hair removal while avoiding unnecessary skin damage [1]. However, since the epidermal and hair relaxation times both vary in the range of 1-100 ms, with thinner hair having a shorter relaxation time, this approach may not always be viable [8]. For example, one of the challenges involved with commercial diode laser hair removal systems is their very long pulse duration [1]. Most commonly, induced skin cooling is used to prevent epidermal damage. The fastest cooling method, albeit with certain risks involved, is a cryogenic cooling spray that evaporates immediately and very quickly removes heat from the epidermis without substantially changing the temperature in the deeper layers of the skin [9; 10]. Safer methods include contact cooling with cold metal and induced cooling with cold air [11; 12]. Most recently, a DMC (Dry Molecular Cooling) technology has been introduced that is based on a controlled fine water spray, combining the positive features of the cryogenic spray and cold air cooling [13]. Numerical modeling of laser-tissue interaction is useful as it can aid in optimizing the design and validation of laser hair removal protocols and systems by methodically assessing the influence of various parameters before submitting patients to unnecessary clinical trials. It is therefore somewhat surprising that, according to our knowledge, there has been only one published study [14] that applied an adequately realistic numerical modeling technique to simulate light and heat transport during laser hair removal. Specifically, [PERSON] et al. [14] systematically simulated hair removal with an IPL device for wavelengths between 400 and 1200 nm, with fluences from 5.0-7.0 J/cm\({}^{2}\) and pulse lengths of 2.5-25 ms. Their approach was based on the three-dimensional modular adaptable grid model of [PERSON] et al. [15] and contained epidermis and dermis, while the hair was approximated as a cylindrical sleeve with a truncated sphere. The primary aim of the present study was to extend the formalism of [PERSON] et al.