# Finite Element Method (FEM) Modeling of Laser-Tissue Interaction during Hair Removal
## 4 Discussion  
This is the first report of an approach to realistic modeling of skin and hair in which laser beam-tissue interaction was studied within an FEM framework. A modeling approach allowed us to examine temperature and thermal damage distributions following irradiation at a wavelength of 1064 nm for three combinations of fluence and pulse duration, with and without forced cooling. Our approach also accounted for the presence of angled hair and hair arrays and is comprehensive enough that it could be applied to further clinical research studies. In this paper, we have undertaken a parametric study by varying light fluence and pulse duration, closely following the clinical study [37]. We have found that for all combinations of fluence and pulse duration, at least a partial necrosis of the hair follicle at a depth of 2.5 mm occurred, which corroborated the outcomes of the clinical study [37]. Increasing fluence resulted in an increased area of necrosis, particularly in the epidermis and dermis, which again agreed with the clinical study where an increase in the likelihood of damage to the epidermis and dermis was demonstrated, typically manifesting as erythema and perfocal edema [37]. The use of forced cooling made the area of necrosis less extensive, especially in the epidermis, which again agreed with the findings of the clinical study [37]. We have shown that the hair follicle of a hair exiting the skin surface at an angle undergoes less thermal damage than the follicle of a straight hair. In addition, we observed that the thermal exposure of hair follicles on the periphery of an irradiated array of hair may be insufficient for reaching necrosis. This is possibly a partial explanation for why laser hair removal does not remove all of the hair, since during the hair removal procedure, the laser beam is not centered on each hair separately but on a given area. Finally, our simulation study indicated that the pulse itself and a short relaxation time after the pulse contributed the most to the final thermal damage to the hair follicle. We have also demonstrated that the FEM model of light-tissue interaction in combination with measurements of surface temperature has proven useful in assessing the absorption coefficients of human epidermis and hair. We attempted to develop, verify, and pilot a protocol for in vivo assessment of absorption coefficients of epidermis and hair in humans that could efficiently account for inter-subject variability. As the protocol of our study is simple and comprehensive enough, it may be potentially helpful in a clinical setting. Because pulses significantly shorter than the hair's thermal relaxation time are expected to provide the highest temperatures, the initial hair removal lasers were Q-switched Nd:YAG lasers with nanosecond-long pulse durations [40]. However, since the achievable pulse energies of Q-switched lasers limited the fluences to below 2-4 J/cm\({}^{2}\) for spot radiases of 6-4 mm, and typically required using a topical carbon-based solution to enhance hair absorption, most of today's hair removal procedures are performed with lasers operating in the millisecond (1-50 ms) pulse duration regime [1; 3; 41; 42]. The longer Nd:YAG laser pulse durations, in the range of 25-50 ms, as used in our simulations, are often a preferred choice in order to avoid overheating of the epidermis with a shorter thermal relaxation time. However, our model can be easily adapted to incorporate shorter pulses. Another potential extension of our FEM modeling approach would be to simulate laser treatment of keratinocyte carcinoma [43]. An obvious extension of our study would be to consider thinner hair at different depths and different dimensions of the epidermis, dermis, and subcutis. Another possibility would be to vary skin and hair types. While our study specifically focused on the Nd:YAG laser, it could be easily applied to other lasers operating at shorter wavelengths and then compared to the results of corresponding clinical studies.