397
Terahertz Radiation
Thermal damage has been shown to be exponentially dependent on temperature and
linearly dependent on time of exposure (Beckham et al. 2004), and is commonly defined
using the following equation:
⎛ C 0 ⎞
t p
Ω = ln ⎝ ⎜
⎠ ⎟ = ∫ Aexp( −E a /RT )d t
(7.9)
C t
( )
0
where Ω is the tissue damage, A the frequency factor (i.e., damage rate [1/second]), E a
the activation energy (J/mole), T the temperature of exposure ( o K), R the gas constant
(8.32 J/mol K), and the integral is over the time of the heat exposure. The Arrhenius integral takes into account temperature–time history of the sample to predict tissue damage
based on the damage threshold. The threshold for tissue damage is usually determined
by pathological analysis and is a ratio of the concentration of native (undamaged) tissue
before irradiation exposure (C 0 ) to the concentration of native tissue at the end of the
exposure time (Ct). The threshold for determination of damaged to undamaged tissue is
arbitrarily selected. Importance of tissue damage calculations will become more clear in
discussions regarding THz safety standards (Section 7.4.7).
7.4.6.2 Computational Modeling and Empirical Measures
of Terahertz-Induced Skin Damage
Conventional computational modeling techniques have been used to simulate the propagation of THz radiation in biological tissues. Such efforts have also been extended to
predict tissue-damage thresholds for skin exposed to THz radiation (Ibey et al. 2008).
A recent study examined these processes using a two-dimensional, cylindrically symmetrical tissue construct (Ibey et al. 2008). In this work, an approximate solution to the
bioheat equation was computed using source terms generated from either an optical or
a radio-frequency model. The optical model source term was estimated from a simple
linear absorption model (Eq. 7.2), whereas the radio-frequency model source term was
formulated using finite-difference time-domain (FDTD) computational electrodynamic
techniques (Ibey et al. 2008). The FDTD techniques were used to predict the specific
absorption rate (SAR) generated within single and multislab skin models. Each source
term was entered into the bioheat equation to predict the thermal history (temperature
and time) for THz-exposed skin. After the bioheat equation was used to determine the
tissue’s thermal history, damage thresholds were computed using the Arrhenius equation (see Eq. 7.9). Figure 7.18 contains the plots of the predicted temperature rise and
tissue-damage thresholds at THz frequencies. Knowledge of tissue-damage thresholds
is vital for the safe use of THz radiation in real-world applications. Such information is
also critical in the design of effective medical procedures.
Our research group has also conducted several experiments to explore THz-induced
tissue damage (McQuade et al. 2007; Dalzell et al. 2010). The results of these studies
have been used to provide empirical data to support current THz standards. In these
studies, we used the FEL at Jefferson Laboratory (υ = 0.1–1.0 THz, E = 2.0–14.0 mW/cm 2 ,
2 seconds) and wet chamois cloths. Thresholds were determined using conventional
damage score determination and probit analysis techniques, and tissue temperatures
were measured using IR thermographic techniques. Using the experimental data,
Terahertz Radiation
Thermal damage has been shown to be exponentially dependent on temperature and
linearly dependent on time of exposure (Beckham et al. 2004), and is commonly defined
using the following equation:
⎛ C 0 ⎞
t p
Ω = ln ⎝ ⎜
⎠ ⎟ = ∫ Aexp( −E a /RT )d t
(7.9)
C t
( )
0
where Ω is the tissue damage, A the frequency factor (i.e., damage rate [1/second]), E a
the activation energy (J/mole), T the temperature of exposure ( o K), R the gas constant
(8.32 J/mol K), and the integral is over the time of the heat exposure. The Arrhenius integral takes into account temperature–time history of the sample to predict tissue damage
based on the damage threshold. The threshold for tissue damage is usually determined
by pathological analysis and is a ratio of the concentration of native (undamaged) tissue
before irradiation exposure (C 0 ) to the concentration of native tissue at the end of the
exposure time (Ct). The threshold for determination of damaged to undamaged tissue is
arbitrarily selected. Importance of tissue damage calculations will become more clear in
discussions regarding THz safety standards (Section 7.4.7).
7.4.6.2 Computational Modeling and Empirical Measures
of Terahertz-Induced Skin Damage
Conventional computational modeling techniques have been used to simulate the propagation of THz radiation in biological tissues. Such efforts have also been extended to
predict tissue-damage thresholds for skin exposed to THz radiation (Ibey et al. 2008).
A recent study examined these processes using a two-dimensional, cylindrically symmetrical tissue construct (Ibey et al. 2008). In this work, an approximate solution to the
bioheat equation was computed using source terms generated from either an optical or
a radio-frequency model. The optical model source term was estimated from a simple
linear absorption model (Eq. 7.2), whereas the radio-frequency model source term was
formulated using finite-difference time-domain (FDTD) computational electrodynamic
techniques (Ibey et al. 2008). The FDTD techniques were used to predict the specific
absorption rate (SAR) generated within single and multislab skin models. Each source
term was entered into the bioheat equation to predict the thermal history (temperature
and time) for THz-exposed skin. After the bioheat equation was used to determine the
tissue’s thermal history, damage thresholds were computed using the Arrhenius equation (see Eq. 7.9). Figure 7.18 contains the plots of the predicted temperature rise and
tissue-damage thresholds at THz frequencies. Knowledge of tissue-damage thresholds
is vital for the safe use of THz radiation in real-world applications. Such information is
also critical in the design of effective medical procedures.
Our research group has also conducted several experiments to explore THz-induced
tissue damage (McQuade et al. 2007; Dalzell et al. 2010). The results of these studies
have been used to provide empirical data to support current THz standards. In these
studies, we used the FEL at Jefferson Laboratory (υ = 0.1–1.0 THz, E = 2.0–14.0 mW/cm 2 ,
2 seconds) and wet chamois cloths. Thresholds were determined using conventional
damage score determination and probit analysis techniques, and tissue temperatures
were measured using IR thermographic techniques. Using the experimental data,