1. Introduction
The term “dose” as applied to electromagnetic safety parallels its use in
pharmacology; it refers to the quantity of an agent (in this case electrical
energy) that can potentially result in a biological effect. Past editions of this Dosimetry Handbook have
focused on methods for measuring or calculating the absorption of electromagnetic
energy by the human body, that is, the administered “dose.” In this work, I intend to go beyond an
exposition of the absorption and distribution of electrical energy in the body.
It would be a laudable achievement if I could specify a safe “dose” of
electrical energy and explain how to measure it. But the subject is far too complex to be
reduced to a number, or even a single table of numbers. Instead, we are faced with a myriad of
physical and biological relationships that account for human reactions to
electrical energy – relationships that involve spatial and temporal
characteristics of the electrical forces within the body, factors related to
the human subject, the method of application of the energy, and the
environment. To further complicate the
problem, we are confronted with variations in the outcomes of biological
experiments that defy causal explanations, and for which we are consequently
reduced to formulations based on probability to describe adverse biological
reaction thresholds. Even the definition
of “adverse” is not obvious and requires careful delineation.
Considering these complications, I believe the subject of electrical
dosimetry is best approached through an exposition of the biophysical forces
and mechanisms that account for human reactions, whether adverse, beneficial,
or benign. I have attempted to take this
approach in this chapter for the portion of the
electromagnetic spectrum below 100 kHz.
The investigator who develops standards for electrical exposure needs an
understanding of underlying biophysical mechanisms to help interpret
experimental data, extrapolate from particular experimental conditions to more
general conditions that may require regulation, and devise methods whereby the
important quantities can be measured or calculated.
Numerous mechanisms have been advanced to account for human reactions to
electrical energy. Among these, it is
important to distinguish between established
and proposed mechanisms. An established
mechanism is defined here as one having
the following properties: (a) it can be used to predict biological effects in humans; (b) it can be
explicitly modelled using equations or parametric relationships; (c) it has
been verified in the intact human; (d) it is supported by strong evidence; (e)
it is widely accepted among experts in the scientific community. Mechanisms not having these characteristics
are classified as proposed. I have identified established and proposed
mechanisms based on these criteria in my recent book [Reilly,
1998a], and in other publications; [Reilly, 2000a, 2000b, 2002]. I will draw from these and other publications
in this chapter.
Of the established mechanisms, the one that has the most impact on
standards at the relatively low frequencies treated in this chapter is an
excitable tissue effect, referred to here as electrostimulation; another established electrical mechanism for
biological reactions is a thermal
one. At frequencies below 100 kHz,
electrostimulation reaction thresholds will typically be lower than thermal
reaction thresholds. Above 100 kHz,
thermal effects typically exhibit lower thresholds of reaction than do
electrostimulation effects. However,
with pulsed waveforms of low duty factor, the frequencies at which
electrostimulation thresholds are lower than thermal thresholds can extend into
the megahertz region.
Electrostimulation produces short-term effects, that is, it results in
acute reactions that are manifested within seconds, (usually a fraction of a
second) after the exposure begins. It
dominates over thermal thresholds at frequencies below 100 kHz and as low
as 1 Hz. Below that, magnetohydrodynamic
mechanisms can be the most sensitive ones responsible for the human reactions.
Although there are
many questions remaining about electrostimulation effects, we largely
understand the underlying mechanisms, we can verify theoretical mechanisms in humans and animals, the experimental
results are robust, and we can define biological end points in the intact
human. It is therefore valuable to
define limits to human exposure based on our understanding of acute excitable
tissue effects.
Other mechanisms of interaction that fit into the proposed category relate to long-term or chronic exposure effects [Olden, 1999; Reilly, 1998a]. These mechanisms are typically mentioned in
connection with hypotheses concerning adverse health effects, including cancer,
reproductive effects, and nervous system disorders from chronic exposure to
low-level electric and magnetic fields.
Standard-setting and advisory groups, while not dismissing long-term
exposure mechanisms as irrelevant, have concluded that the evidence and body of
knowledge concerning them is presently insufficient to derive a human exposure
limit [ICNIRP, 1998; IEEE, 2002]. Progress in research on proposed mechanisms
should nevertheless be monitored and evaluated as to whether any one can be
included in the list of established mechanisms.
1. Principles
of nerve and muscle excitation
Every biological cell
maintains a potential difference between its interior and exterior; usually the
interior is negative with respect to the exterior. Nerve and muscle cells
respond to electrical stimuli by becoming “excited,” a state in which the neural membrane
undergoes a marked change of conductivity that leads to a large change in the
cellular potential. The excited state is
triggered when the potential difference across the cellular membrane is
sufficiently reduced from its normal resting state. This potential change, called an action potential, propagates along the
nerve’s axon. In an afferent neuron
(e.g., a nerve conveying information from a sensory receptor to the brain) the
action potential normally travels to the spinal cord and thence to the central
nervous system (CNS). In an efferent
nerve cell (e.g., one conveying information from the brain to muscle cells),
the action potential is initiated in the CNS, from whence it propagates to
muscle connections called motor end
plates. Communication from one nerve
cell to another or at the motor end plate takes place across junctions called synapses, most typically by means of
chemical agents called neurotransmitters.
These normal processes
can be activated or modified by electrical forces introduced into the body
through applied current or electromagnetic induction for medical diagnosis or therapy. If uncontrolled, the same forces can be
detrimental.
Excitable tissue
effects are typically observed shortly after the application of the stimulus,
often within milliseconds to seconds.
These "acute" effects stand in contrast to responses to
chronic electromagnetic exposure effects that many investigators have studied
at much lower exposure levels for possible implications on human health.
Biological cells
normally maintain a potential, Vr, in which the interior of the cell is negative
with respect to its exterior. Typical
values of Vr for nerve and muscle cells are -65 and -90 mV respectively. Considering the membrane potential (≈
0.1 V) and thickness (≈ 10-8 m), the
electric field developed across the resting membrane is around 107 V/m. The
conductivity of the excitable membrane is controlled by the this enormous
electric field. Disturbances from the
resting condition can lead to profound changes in the membrane's electrical
properties, and ultimately initiate the functional responses of nerve and
muscle.
Figure 1.
Representation of current flow around elongated cell placed in medium having a
uniform electric field (uniform current density). The membrane is assumed to be semi-permeable
to current flow.
Figure 1 illustrates
the distribution of current flow around an elongated cell within a medium
having a uniform electric field (i.e., uniform current density). The cell is presumed to be oriented with its
long axis parallel to the undisturbed field.
The flux lines suggest that the current through the membrane, and hence
the disturbance of membrane polarisation, is greatest at the ends of the
fibre. The anode-facing end of the cell
will be hyperpolarised, and the cathode-facing end will be depolarised. In an alternating field, the sites of
hyperpolarisation and depolarisation alternate every one-half cycle of the
field oscillation.
We can analyse the
potential disturbances of the elongated cell using the theory of electrical
coaxial cables. Consider a cable of
length 2L in a longitudinal static
field of strength E. The steady-state solution for membrane
voltage is given by [Sten-Knudsen, 1960]:
where X = x/l, x is the longitudinal distance from the centre
of the cell, l is the space constant, and 2L is the length of the cell. X
= 0 is taken as the centre of the cell, and the ends are at ± L.
The space constant l, also known as the electrotonic distance of the membrane, defines the distance along
the membrane that a steady-state voltage disturbance due to point current
injection will decay to e-1 of the value at the disturbed location. Space constants for invertebrate nerve are in
the range 0.23 - 0.65 cm [Rall, 1977].
Figure 2. Normalised
membrane voltage of a finite cable immersed in a static field of strength E.
Cable length = 2L. Voltage has odd-valued symmetry about X = 0.
Figure 2 illustrates
Eq. (1) for several cable lengths. Since
Vm has odd-valued symmetry about X = 0, only one quadrant of the function
needs to be illustrated. The maximum
membrane voltage occurs at the ends of the fibre, and has the value
For very long cells L ® ¥, and the voltage at the cell's terminus is El, a value which is closely approached even for
fibres of modest length. For instance,
with L/l = 2 (total length = 4l), the membrane
voltage at the ends is ±0.964El.
As evident in Eqs. (1)
and (2), the fundamental force for membrane polarisation is the in-situ electric field, E, rather than current density, J.
Although it is also possible to describe electrostimulation effects in
terms of current density, as has been a common practice in the past [Bernhardt, 1988; ICNIRP, 1998; IEEE, 1999], the in situ electric field is a more fundamental descriptor. Of course, we can relate the two by J = Es, where s is the conductivity
of the medium. However, the conversion introduces an additional parameter (s) about which there
may be some additional uncertainty in an applied situation. The calculation of
the in situ electric field is less
sensitive to assumptions of tissue conductivities compared to internal current
density. Consequently, it is preferable
to express membrane polarisation effects, including nerve and muscle excitation,
in terms of the in-situ E-field
rather than current density. To my
knowledge, the IEEE low-frequency standard
[IEEE, 2002] is the first to
specify basic restrictions for the general public in terms of the in-situ electric field.
1.2. Polarisation of nerve cells within an electric
field
A nerve cell is an extremely elongated cell:
the length of a sensory nerve innervating the fingertip or toe has a length of
about one metre. Figure 3 illustrates modes of stimulation of a nerve
cell, designated as
end, bend, and spatial gradient
modes [Reilly, 1998a; Reilly and Diamant, 2003]. The illustration shows a myelinated nerve,
which, due to its significantly lower threshold as compared with an
unmyelinated nerve, is a good choice for
electrical stimulation models.
An action potential is initiated by depolarisation of the cellular
membrane from its resting potential. Depolarisation
occurs at points along the membrane experiencing current efflux. As illustrated in the figure, current efflux
could occur at a site where the nerve is terminated, such as with a sensory
receptor or motor end plate, where the nerve undergoes a sharp bend, or where a
spatial gradient of the electric field exists.
In practice, all three of these modes can be take place at one
time. The site where excitation first occurs
will be the one in which the depolarisation is maximal, and this site determines
the threshold of excitation.
Figure 3