Field st
−10.00
−1.00
10.00
1.00
3.00
5.00
Time (10 mm value) in ns
Line---calculated
Point---measured
rength (kV/m)
30.00
50.00
42
Electromagnetic Fields in Biological Systems
FigurE 1.16 A typical electromagnetic pulse waveform. (From Lin, J. C., C. L. Wu, and
C. K. Lam. 1975. Transmission of electromagnetic pulse into the head. Proc IEEE 63:1726–7. With
permission.)
time or in strength (Lin, Wu, and Lam 1975). This EMP waveform can be characterized
by a triple exponential time function such as
e 0 (t) = [A/g(τ r )] [exp (−αt) − a exp (−βt) − (1 − a) exp (−γt)]
(1.51a)
with
g(τ r ) = exp (−ατ r ) − a exp (−βτ r ) − (1 − a) exp (−γτ r )
(1.51b)
where a, α, β, and γ are constants; τ r is the pulse rise time or the time taken for the pulse
to reach its maximum strength; A is the peak electric field strength of the pulse and exp
is the exponential function. The solid line is computed from Equation 1.51a using the
values A = 50 kV/m, a = 0.1497, α = 1.20 × l0 6 , β = 0.11α, γ = 253.62α and τ r = 17.78 ns.
From the Fourier analysis given in Section 1.12.2, the transmitted pulse inside a homogeneous spherical model of the head is related to the time rate of change of the incident
EMP. Representative results using an effective average conductivity of 0.2 S/m for the
brain are shown in Figures 1.17 and 1.18. The sphere of radius 10 cm (Figure 1.17) simulates an adult human−size head and the spherical model of radius 3.5 cm (Figure 1.18)
mimics the head of an animal such as an adult cat or a rhesus monkey. The incident
pulse is normalized to 1 V/m. The transmitted pulse along the z axis is shown since the
maxima of transmitted EMP amplitude always occur along the direction of propagation
and through the center of the sphere. It can be seen that the transmitted pulse amplitude
is the highest at the leading surface of the spherical head for both cases and decreases
monotonically with increasing distance into the model.