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Electromagnetic Fields in Biological Systems
where q cond is the heat flux (W), k is the thermal conductivity (W/m · K), A is the area
(m 2 ), and ΔT/ΔX is the temperature gradient in the direction of heat flow. Combining
Equations 7.4 and 7.5 results in the following general heat transfer equation:
2
∂T
k∇ T + S = ρc ∂t
(7.6)
where the first term is the temperature gradient in all directions, S is the heat generation, and the right-hand side of the equation is the change in temperature over time.
This equation basically describes the “build up” and distribution of heat in the irradiated
tissue.
Convection plays a role in heat transfer when a fluid present can circulate the heat
away from an area. Consequently, convection should be considered at tissue surfaces
where heat can be lost to the surrounding air. Convection is described by the following:
q′′ = ( − T
h T
)
(7.7)
conv
S
a
where q″ is the heat flux (W/m 2 ), h the convection coefficient (W/m 2 · K), T s the temconv
perature of the tissue, and T a the surrounding temperature.
Radiative heat transport is defined as the spontaneous emission of EM waves by matter. This type of radiation is attributed to the changes in the electron configuration of
the atoms within matter. Radiation mechanisms are not prominent for the transfer of
heat to surrounding tissue, and such mechanisms are not expected to play a major role
in the heat transfer of THz skin interactions. However, for completeness, the Stefan–
Boltzmann law that describes these processes is provided:
4
4
rad
S
a
q = σε (T − T )
(7.8)
where q rad is the heat flux (W), σ is the Stefan–Boltzmann constant (5.67 × 10 −8 Wm −2 K −4 ),
ε is emissivity (i.e., a measure of how well a surface radiates energy), T s is the tissue temperature, and T a is the surrounding temperature.
7.4.5 Thermal History: Temperature Damage Zones
and Associated Biological Effects
When THz radiation is passed into skin, chromophores absorb the photons and heating occurs. Heating triggers a temperature rise that increases the kinetic energy of the
molecules. Once the kinetic energy is greater than the intramolecular bonds that hold
the molecules together, the molecules begin to denature. In an attempt to better characterize these effects, the term thermal history was established. Thermal history is defined
as the temperature profile and time at which the tissue is subjected to elevated temperatures. Thermal-induced biological effects are commonly grouped into three temperature
damage zones: low temperature (43°C–100°C), middle temperature (100°C–300°C), and
high temperature (300°C–1000°C). Figure 7.17 contains data for the effects commonly
Electromagnetic Fields in Biological Systems
where q cond is the heat flux (W), k is the thermal conductivity (W/m · K), A is the area
(m 2 ), and ΔT/ΔX is the temperature gradient in the direction of heat flow. Combining
Equations 7.4 and 7.5 results in the following general heat transfer equation:
2
∂T
k∇ T + S = ρc ∂t
(7.6)
where the first term is the temperature gradient in all directions, S is the heat generation, and the right-hand side of the equation is the change in temperature over time.
This equation basically describes the “build up” and distribution of heat in the irradiated
tissue.
Convection plays a role in heat transfer when a fluid present can circulate the heat
away from an area. Consequently, convection should be considered at tissue surfaces
where heat can be lost to the surrounding air. Convection is described by the following:
q′′ = ( − T
h T
)
(7.7)
conv
S
a
where q″ is the heat flux (W/m 2 ), h the convection coefficient (W/m 2 · K), T s the temconv
perature of the tissue, and T a the surrounding temperature.
Radiative heat transport is defined as the spontaneous emission of EM waves by matter. This type of radiation is attributed to the changes in the electron configuration of
the atoms within matter. Radiation mechanisms are not prominent for the transfer of
heat to surrounding tissue, and such mechanisms are not expected to play a major role
in the heat transfer of THz skin interactions. However, for completeness, the Stefan–
Boltzmann law that describes these processes is provided:
4
4
rad
S
a
q = σε (T − T )
(7.8)
where q rad is the heat flux (W), σ is the Stefan–Boltzmann constant (5.67 × 10 −8 Wm −2 K −4 ),
ε is emissivity (i.e., a measure of how well a surface radiates energy), T s is the tissue temperature, and T a is the surrounding temperature.
7.4.5 Thermal History: Temperature Damage Zones
and Associated Biological Effects
When THz radiation is passed into skin, chromophores absorb the photons and heating occurs. Heating triggers a temperature rise that increases the kinetic energy of the
molecules. Once the kinetic energy is greater than the intramolecular bonds that hold
the molecules together, the molecules begin to denature. In an attempt to better characterize these effects, the term thermal history was established. Thermal history is defined
as the temperature profile and time at which the tissue is subjected to elevated temperatures. Thermal-induced biological effects are commonly grouped into three temperature
damage zones: low temperature (43°C–100°C), middle temperature (100°C–300°C), and
high temperature (300°C–1000°C). Figure 7.17 contains data for the effects commonly