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Electromagnetic Fields in Biological Systems
For constant conductivity:
• Since ε′ is small compared to ε″ for brain matter at low frequencies, ε′ may be
neglected to obtain a frequency-independent σ. This will result in a closed-form
solution for the induced pulse inside the model.
• Induced pulse inside a spherical model of the brain is a function of the time rate
of change of incident EMP.
• Transmitted pulse amplitude decreases monotonically with increasing distance from the leading (exposed) surface of the sphere, and it is clearly not
symmetrical.
Common Features of These Two Approximation
• The transmitted pulse is oscillatory and has positive and negative contributions,
although the incident Gaussian pulse may be entirely positive.
• The transmitted pulse depends on the time derivative of the impinging EMP.
• The constant conductivity model may be used to estimate maximum transmission. However, it may not be as accurate for spatial distribution predictions of the
transmitted field strength.
• Field coupling is quite small—less than 10 V/m is coupled into a spherical head of
radius 3.5 or 10 cm for a 50-kV/m pulse varying in width from 1 to 10 μs.
• The transmitted EMP amplitude for the 1-μs pulse is approximately 10 times
higher than that for the 10-μs pulse, which is also the case for smaller spheres.
Therefore, a shorter pulse is more readily transmitted into biological objects than
a longer pulse.
1.12.6.3 Typical Electromagnetic Pulse Waveform
in a Spherical Head Model
The salient features include:
• The maxima of transmitted EMP amplitude always occur along the direction of
propagation and through the center of the sphere.
• Transmitted pulse amplitude is highest at the leading surface of the spherical head
and it decreases monotonically with increasing distance into the model.
• The magnitude of transmitted pulses is directly proportional to the size of the
model. For a typical EMP with a peak electric field strength of 50 kV/m, peak
transmitted pulse amplitude in a spherical head of radius 10 cm is 735 V/m and it
occurs at the leading surface. For a brain sphere of radius 3.5 cm, the corresponding transmitted pulse amplitude is 472 V/m.
1.12.6.4 Ultra-Wideband Pulse–Induced Current Inside the Body
The salient features include:
• For a pulse with a rise time of 0.2 ns and total time duration of 7.0 ns, the spectrum
shows that most of the energy in the pulse is concentrated in the 200–900 MHz
band with the peak energy occurring at about 500 MHz.
Electromagnetic Fields in Biological Systems
For constant conductivity:
• Since ε′ is small compared to ε″ for brain matter at low frequencies, ε′ may be
neglected to obtain a frequency-independent σ. This will result in a closed-form
solution for the induced pulse inside the model.
• Induced pulse inside a spherical model of the brain is a function of the time rate
of change of incident EMP.
• Transmitted pulse amplitude decreases monotonically with increasing distance from the leading (exposed) surface of the sphere, and it is clearly not
symmetrical.
Common Features of These Two Approximation
• The transmitted pulse is oscillatory and has positive and negative contributions,
although the incident Gaussian pulse may be entirely positive.
• The transmitted pulse depends on the time derivative of the impinging EMP.
• The constant conductivity model may be used to estimate maximum transmission. However, it may not be as accurate for spatial distribution predictions of the
transmitted field strength.
• Field coupling is quite small—less than 10 V/m is coupled into a spherical head of
radius 3.5 or 10 cm for a 50-kV/m pulse varying in width from 1 to 10 μs.
• The transmitted EMP amplitude for the 1-μs pulse is approximately 10 times
higher than that for the 10-μs pulse, which is also the case for smaller spheres.
Therefore, a shorter pulse is more readily transmitted into biological objects than
a longer pulse.
1.12.6.3 Typical Electromagnetic Pulse Waveform
in a Spherical Head Model
The salient features include:
• The maxima of transmitted EMP amplitude always occur along the direction of
propagation and through the center of the sphere.
• Transmitted pulse amplitude is highest at the leading surface of the spherical head
and it decreases monotonically with increasing distance into the model.
• The magnitude of transmitted pulses is directly proportional to the size of the
model. For a typical EMP with a peak electric field strength of 50 kV/m, peak
transmitted pulse amplitude in a spherical head of radius 10 cm is 735 V/m and it
occurs at the leading surface. For a brain sphere of radius 3.5 cm, the corresponding transmitted pulse amplitude is 472 V/m.
1.12.6.4 Ultra-Wideband Pulse–Induced Current Inside the Body
The salient features include:
• For a pulse with a rise time of 0.2 ns and total time duration of 7.0 ns, the spectrum
shows that most of the energy in the pulse is concentrated in the 200–900 MHz
band with the peak energy occurring at about 500 MHz.