10
0
10
1
10
2
10
3
10
4
10
5
ε"
ε'
Complex dielectric constant
10
4
10
5
10
6
10
7
44
Electromagnetic Fields in Biological Systems
1.12.2 Gaussian Electromagnetic Pulse inside
a Planar Biological Medium
The ratio of the transmitted electric field at a given depth in a biological medium and the
incident field at z = 0 is defined as the steady state transfer function. It characterizes the
steady state transfer properties of the medium as a function of frequency. For a planar
biological medium with complex dielectric permittivity
ε* = ε′ − ε″
(1.52)
or
ε*(ω) = ε h + (ε l − ε h )/(1 + jω/ω s )
(1.53)
where the indices h and l characterize the complex dielectric permittivity values far
above and below the critical frequency ω s , respectively. The values for ω s , ε l , and ε h in the
frequency range of interest are approximated by 160π, 2.55 × 10 6 , and 0.2 × 10 6 , respectively, for musclelike tissues. The behaviors of ε′ and ε″ as a function of frequency are
shown in Figure 1.19. The steady state transfer function is given by
H(z,ω) = E t (z,ω)/E 0 (0,ω) = 2/[1 + (ε*) 0.5 ] exp (−αz) exp (−jβz)
(1.54)
At the surface where z = 0, the transfer function is equal to T, the transmission coefficient. As the frequency is reduced such that ω << ω s , it becomes
T = 2/[1 + (ε*) 0.5 ] ~ 0.00125[l + j0.922(ω/ω s )]
(1.55)
ω = 2πf
FigurE 1.19 Complex dielectric constant or permittivity of muscle at low frequencies. (From
Lin, J. C. 1975. Interaction of electromagnetic transient radiation with biological materials. IEEE
Trans Electromagn Compat 17:93–7. With permission.)