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Fok et al. Skin temperature of laser for Nevus of Ota

specific blood and tissue, respectively; Tb and T (℃) relaxation time (τ) should be taken into account when
are temperatures of blood and tissue, respectively; Q m applying the thermal wave equation. This factor τ is
(W/m ) is the metabolic rate of tissue; Q (W/m ) is the neglected in the Pennes equation. Usually the thermal
3
3
r
volumetric heating rate; and τ (kg/m ) is the density of relaxation time τ for general homogeneous materials
3
tissue. [33] is very low, i.e. between 10 -10 s. Thermal waves
[31]
-14
-8
showed no clear effect during heat transfer except when
Because the thermal wave equation is hyperbolic, there was a marked change in the heat flux rate. τ in
it is common to use a numerical analysis instead of biological systems has been predicted to be 20-30 s. [31,32]
an analytic solution. Furthermore, due to the large
temperature gradient observed in a thermal energy In 1995, researchers like Mitra et al., [37] conducted
input spot on the skin surface when the laser is experiments on processed meat and obtained the
heating the tissue for a short time, we can neglect the following result: τ is 16 s. Currently most studies of
temperature diffusion on the skin surface and focus biological tissues use a τ of 20 s. [34,35] In this study τ is
primarily on heat transfer, which occurs in the same also set at 20 s. This concept is very important for laser
direction as the thermal energy input. The equation surgeons to choose the correct τ for the treatment of
can be simplified as a one-dimensional equation for hyperpigmented lesions such as Nevus of Ota.
applying to the definite difference model to find the
solution to the thermal wave equation. [34-36] Since laser illumination requires using an extremely
short amount of time and its heat flux being tremendously
At a high energy and a high heat flux of laser illumination, high, the thermal wave effect is very clear during
the heat convection effect is not apparent, and can heat transfer, and therefore, our study conducted an
be disregarded. The temperature of the surrounding analysis with the thermal wave equation to be able to
environment was also not a significant factor. However, observe and determines skin heat transfer. Currently
temperature decreases when the thickness of tissue the most common lasers used in cutaneous surgery
increases. As human skin tissue contains three layers - for Nevus of Ota are the Q-switched ruby lasers. The
epidermis (thickness is 0.00008 m), dermis (thickness wavelength of the QSRL is 694 nm, and the pulse duration
is 0.002 m) and hypodermis (thickness is 0.01 m) - is 25 ns. Regarding the input of laser energy, the use
the thickness of human tissue would be 0.01208 m. of a fixed illumination time on a surface as a boundary
When including laser illumination on the skin surface, condition must also be considered. In order to obtain
the difference between Boundary Conditions and attainable results, the boundary condition was divided
Initial Conditions should be considered. During laser in terms of the energy density of input energy. As to
application, it is necessary to consider burn injury when the analytic solution, the separation variable method
the skin temperature is 44 ℃. [37] Second or third-degree and superposition principle theory was used to obtain
burns on the skin will result if temperature increases results. This made the discussion of skin heat transfer
and it is therefore necessary to carefully control skin easier and more precise.
surface temperature. Because of the close relationship
between the temperature of the skin surface and the With an ambient skin temperature of 30 ℃ and to
energy density of laser illumination, it is important to ensure that the epidermal temperature does not
avoid burn injury when using lasers of different energy exceed 70 ℃ after pulsed laser exposure, the highest
densities within certain times and areas. permissible “T-jump” (ΔT LASER ) is 40 ℃. If a preliminary
sub-therapeutic diagnostic laser pulse, D , produces
0
Since the characteristic time of tissue (τ) has significant a T-jump (because incident energy density is directly
influence on temperature prediction, the result derived proportional to ΔT LASER ) then the threshold for epidermal
using the thermal wave equation with the thermal damage (D ) is D = 40 D /ΔT LASER .
E
E
0
wave effect can be more accurate. For biological
tissues, τ is defined as the characteristic time needed Consider a simple example to illustrate the principle
for accumulating the thermal energy required for in a patient with a normal skin surface temperature of
propagative transfer to the nearest element within 30 ℃: one joule of laser energy delivered to the skin
nonhomogeneous inner structures. That is, it is the time produces a T-jump of 8 ℃. Therefore, in order to keep
needed for the temperature of objects to drop by half the T-jump after laser illumination at less than 40 ℃,
from the warmest temperature after being illuminated such that the epidermal temperature does not exceed
with a laser. 70 ℃, the boundary condition should be divided in
terms of the energy density of input energy. As to the
For general homogeneous materials, τ is defined as analytic solution, the separation variable method and
the thermal relaxation time. The effect of the thermal superposition principle theory can be used to obtain
6 Plastic and Aesthetic Research ¦ Volume 4 ¦ January 19, 2017