Thermal Distribution Model of THz Radiation Absorption in Biological Tissue
Thermal Distribution Model of THz Radiation Absorption in Biological Tissue
Terahertz radiation falls between the infrared and microwave regions of the electromagnetic spectrum, and it shares some properties with each of these. This Demonstration shows a closed-form thermal-change model due to THz continuous wave (CW) radiation regime absorption in biological tissue at room temperature. It uses the modified heat conduction equation, which assumes no heat response of body tissue homeostatic thermoregulation or convective or radiative heat transfer. Considering a medical application of THz radiation regime absorption in biological tissue, the model involves important parameters such as power density, the calculated beam waist, distance from power source, fraction of transmitted power, penetration depth of THz radiation, scattering and absorption coefficient, all of which are extremely important regarding heat generation due to irradiation on any biological tissue. The amount of heat inside the tissue is highly dependent on its optical properties, such as the absorption and scattering coefficients. Also, the heat transfer depends on some properties of biological tissues, such as thermal diffusivity, thermal and electric conductivity, and so on. Knowledge of some basic concepts of thermodynamics and heat transfer are necessary to understand and to evaluate the effects of THz radiation regime absorption on biological tissues for treatment purposes. You can set the tissue variables, optical parameters, and THz source variables. Vary the THz beam waist radius from sharper to broader or otherwise to see the significant change of temperature against depth of tissue.
w
The temperature increase during the exposure is due to the THz radiation regime absorption in body tissues. This power absorption is characterized by specific absorption rate (SAR), which is related to the THz radiation regime electric field by [1,2]
SAR=exp(-2)exp(-zδ)(W/kg)
2σT
μ
t
2
E
πρδ
2
w
2
r
2
w
μ
t
where () is the electric conductivity of tissue, is the mass density in , =+ () is the total attenuation coefficient absorption and scattering coefficient, () is a spot THz beam waist radius, () is the penetration depth of THz radiation, () is the distance from the power source, is the fraction of transmitted power, and is the root mean square (rms) of THz radiation regime electric field strength in . If there is no response of body tissue, the relation between SAR, duration of exposure , and heat conduction due to change in temperature is
σ
S/mm
ρ
kg/m
μ
t
μ
a
μ
s
-1
mm
w
mm
δ
mm
r
cm
T
E
V/mm
dt
dT
∂T
∂t
2
∇
SAR
C
where is thermal diffusivity in /s, and is the specific heat capacity in . The boundary conditions with respect to the equation corresponding to the computational domain describe space in the direction starting from the skin surface () and ending at the body core (). In the direction, a given temperature boundary condition is applied at the skin surface, that is, (, ), and at the body core (, ). A numerical solution of the last equation is solved by Mathematica's built-in function NDSolve, and a thermal distribution model of THz radiation regime absorption in tissue is produced by NonlinearModelFit. The analytical expression obtained is useful for describing the tissue temperature distribution in a one-dimensional domain, and is compared with the results of the experiment at the beginning of the time domain.
α=κ/ρC
2
mm
C
J/kg°C
z
z=0
z=L
z
z=0
T=25°C
z=L
T=0