Page 280 - Computational Modeling in Biomedical Engineering and Medical Physics

Hyperthermia and ablation 269

Table 8.4 Physical quantities used in the mathematical models.
Symbol (unit) Quantity
E (V/m) Electric field strength (in complex)
H (A/m) Magnetic field strength (in complex)
μ 0 (H/m) Free space magnetic permeability
ε (F/m) Complex permittivity ε 5 ε 2 jσ=ω, ε 5 σ=jω
ε (F/m) Dielectric permittivity ε 5 ε r ε 0
ε 0 (F/m) Free space dielectric permittivity
Dielectric constant (relative permittivity)
ε r
σ (S/m) Complex conductivity σ 5 σ 1 jωε
σ (S/m) Electrical conductivity
ω (rad/s) Angular frequency
p ffiffiffiffiffiffiffiffi
j Complex number j 5 2 1
3
ρ (kg/m ) Mass density
3
ρ b (kg/m ) Mass density of blood
-1
ω b (s ) Blood perfusion rate
C (J/kg K) Specific heat coefficient
C b (J/kg K) Specific heat coefficient of blood
T (K) Tissue temperature
T b (K) Blood temperature
k (W/m K) Thermal conductivity
3
Q emf (W/m ) Resistive heat (density of the absorbed power)
u (m/s) Velocity field
η (Pa s) Dynamic viscosity
p (Pa) Pressure
I Unity matrix
m (kg) Mass
W (J) Electric energy

Table 8.5 Physical properties used in the model (Andreuccetti et al., 1997; Morega et al., 2008).

Hepatic tissue
jσ
ε 5 ε 0 ε r 2 , where ε 0 5 10 29 F and ω 5 2πf
ω 36π m
σ 5 1:686 S=m and ε r 5 43:035 for the frequency f 5 2:45 GHz
ρ 5 1060 kg=m 3 C 5 3600 J=kg K k 5 0:502 W=mUK

Blood
σ b 5 2:545 S=m and ε rb 5 61 for the frequency f 5 2:45 GHz
ρ 5 1000 kg=m 3 C b 5 4180 J=kg K k b 5 0:543 W=mUK
b
s
ω b 5 6:4 3 10 23 21 η 5 0:05 PaUs
b
Dielectric of coaxial cable PTFE catheter
σ dielec 5 0; ε r dielec 5 2:03 σ PTFE 5 0; ε r PTFE 5 2:6