| United States Patent |
5,782,874
|
|
Loos
|
July 21, 1998
|
Method and apparatus for manipulating nervous systems
Abstract
Apparatus and method for manipulating the nervous system of a subject
through afferent nerves, modulated by externally applied weak fluctuating
electric fields, tuned to certain frequencies such as to excite a
resonance in certain neural circuits. Depending on the frequency chosen,
excitation of such resonances causes relaxation, sleepiness, sexual
excitement, or the slowing of certain cortical processes. The weak
electric field for causing the excitation is applied to skin areas away
from the head of the subject, such as to avoid substantial polarization
current densities in the brain. By exploiting the resonance phenomenon,
these physiological effects can be brought about by very weak electric
fields produced by compact battery-operated devices with very low current
assumption. The fringe field of doublet electrodes that form a
parallel-plate condenser can serve as the required external electric field
to be administered to the subject's skin. Several such doublets can be
combined such as to induce an electric field with short range, suitable
for localized field administration. A passive doublet placed such as to
face the doublet on either side causes a boost of the distant induced
electric field, and allows the design of very compact devices. The method
and apparatus can be used by the general public as an aid to relaxation,
sleep, or arousal, and clinically for the control and perhaps the
treatment of tremors and seizures, and disorders of the autonomic nervous
system, such as panic attacks.
| Inventors:
|
Loos; Hendricus G. (3019 Cresta Way, Laguna Beach, CA 92651)
|
| Appl. No.:
|
788582 |
| Filed:
|
January 24, 1997 |
| Current U.S. Class: |
607/2 |
| Intern'l Class: |
A61N 001/40 |
| Field of Search: |
607/1,2,39,45,46,62,75,115,152
600/26
602/2
128/897,908
|
U.S. Patent Documents
| 1973911 | Sep., 1934 | Ruben | 607/152.
|
Primary Examiner: Kamm; William E.
Parent Case Text
This application is a Continuation-in-part of Ser. No. 08/447,394, May 23,
1995, abandoned which is a continuation of Ser. No. 08/068,748, May 28,
1993, abandoned.
Claims
I claim:
1. Electric field generator for manipulating the nervous system of a
subject, which comprises:
generator means for generating a fluctuating voltage;
at least one doublet having two field electrodes such as to form a
parallel-plate condensor;
distributor means, responsive to the fluctuating voltage, for charging said
at least one doublet;
said at least one doublet to be positioned and oriented such as to render
the subject entirely outside the parallel-plate condensor.
2. The electric field generator of claim 1, further including:
passive doublet having two field electrodes such as to form a
parallel-plate condensor;
a conductor connecting last said two field electrodes;
the passive doublet being positioned outside first said parallel-plate
condenser, such that one of last said two field electrodes is apposed to
one of first said two field electrodes.
3. The electric field generator of claim 1, further including a dielectric
placed between the two field electrodes.
4. The electric field generator of claim 1, further including casing means
for containing the generator means, the distributor means, and said at
least one doublet.
5. A method for manipulating the nervous system of a subject, comprising
the steps of:
generating a fluctuating voltage;
constructing a doublet having two field electrodes such as to form a
parallel-plate condensor;
applying the fluctuating voltage between said two field electrodes to
induce an electric field; and
placing the doublet such as to expose the subject solely to the electric
field outside the parallel-plate condenser.
6. The method of claim 5, further including the steps of:
constructing another doublet having two field electrodes such as to form a
parallel-plate condenser;
connecting last said two field electrodes to each other;
placing said another doublet outside first said parallel-plate condensor,
such that one of last said two field electrodes is apposed to one of first
said two field electrodes;
whereby the electric field polarizes said another doublet; and
whereby said another doublet induces an electric field which boosts first
said electric field at large distances.
7. The method of claim 5, for exciting in the subject a sensory resonance,
the sensory resonance having a resonance frequency, and wherein the
fluctuating voltage has a frequency, the method further including the step
of setting the voltage frequency to the resonance frequency.
8. Electrode for use in an electric field generator for manipulating the
nervous system of a subject, comprising:
an input port;
at least one doublet having two field electrodes such as to form a
parallel-plate condenser;
distributor means, connected to the input port, for charging said at least
one doublet when the input port is energized;
said at least one doublet to be positioned and oriented such as to render
the subject entirely outside the parallel-plate condensor.
9. The electrode of claim 8, further including a dielectric placed between
the two field electrodes.
Description
BACKGROUND OF THE INVENTION
The invention relates to electrical neurostimulation, wherein electric
currents are passed to the brain, the spinal cord, an organ, or peripheral
nerves ›1-3!. Such stimulation has been used with various degrees of
success for anesthesia, induction of relaxation and sleep, as well as for
the treatment of pain, intractable epilepsy, behavioral disorders,
movement disorders, and cardiac arrhythmia. The electric current is
usually delivered by contact electrodes i.e., electrodes that are in Ohmic
contact with the biological tissue. An exception is the capacitor
electrode of Guyton and Hambrecht ›4!, which consists of an implanted
porous tantalum disc with a thin insulating coating of tantalum pentoxide.
After implantation, the pores fill with extracellular fluid and thus
present a large capacitive interface to the fluid. The electrode is
capable of delivering sizable currents to tissue without causing
accumulation of electrochemical byproducts. Mauro ›5! has proposed another
capacitor electrode in which one of the "plates" of a large capacitor is
formed by an electrolyte that is in Ohmic contact with the tissue, via a
thin tube. In both these cases the capacitance employed is large, such as
to pass currents of a magnitude and duration large enough to cause firing
of the nerves, as expressed by the strength-duration curve with typical
times of 0.1 ms and currents of the order of 1 mA ›6,7!. The nerves fire
as a result of substantial depolarization of the nerve membrane by the
applied electric current, a process here called classical nerve
stimulation.
An area of neurostimulation that has attracted much attention is the
induction of relaxation and sleep. One method, called Cranial Electric
Stimulation (CES) involves passing an alternating current through the
brain via contact electrodes attached to the head or held in the mouth.
With properly chosen strength and frequency, these currents may excite or
support brain waves that accompany deep sleep. The method has been
explored extensively in the Former Soviet Union, under the name
"Electrosleep".
A commercially available device is the Japanese "Sleepy" ›8!, which
generates for one hour square pulses of 4 V and 0.2 ms duration, with a
frequency that sweeps from 14 to 0 Hz, every 3 minutes. The device
requires contact electrodes placed on the head. Other commercial CES
devices ›9! are Alpha Stim, Mindman, and Endo Stim, which all require
contact electrodes attached to the head.
Electric currents in biological tissue may also be induced by an electric
field that is generated in the space outside the subject. The external
electric field is set up by applying an electric potential between field
electrodes that do not have Ohmic contact with the tissue. Of course the
arrangement may be seen as a form of capacitive coupling, but with
capacitances very much smaller than in Mauro ›5! or Guyton and Hambrecht
›4!. There is also an important practical difference, in that no bodily
contact with any part of the apparatus is required for the electric field
application by field electrodes.
A neurological effect of external electric fields has been mentioned by
Norbert Wiener ›10!, in discussing the bunching of brain waves through
nonlinear interactions. The electric field was arranged to provide "a
direct electrical driving of the brain" ›10!. Wiener describes the field
as set up by a 10 Hz alternating voltage of 400 V applied in a room
between ceiling and ground.
Brennan ›11! describes an apparatus for alleviating disruptions in the
circadian rythms of a mammal, in which an external alternating electric
field is applied across the head of the subject. The voltage applied to
the electrodes is specified as at least 100 V, and the peak to peak value
of the electric field as at least 590 V/m in free air before deploying the
electrodes across the head of the subject. The frequency of the
alternating electric field is in the range from 5 Hz to 40 Hz. Brennan
states that the method is aimed at subjecting at least part of the
subject's brain to an alternating electric field, in the belief that this
would stimulate an influx of Ca.sup.2+ ions into nerve endings, which in
turn would "regulate and facilitate the release of neurotransmitters".
Embodiments mentioned include electrodes arranged in a head cap, in a bed,
or mounted on the walls of a room. It should be noted that electric
polarization of the head causes the field strength in the narrow space
between electrode and skin to be about a factor h/2d larger than the
free-air field strength, h being the distance between the electrodes and d
the spacing between electrode and skin. For h=17 cm and d=5 mm the factor
comes to 17, so that with the specified free-air field of at least 590
V/m, the field in the gap between electrode and skin is at least 10 KV/m
peak to peak.
A device that involves a field electrode as well as a contact electrode is
the "Graham Potentializer" mentioned in Ref. ›9!. This relaxation device
uses motion, light, and sound as well as an external alternating electric
field, applied predominantly to the head. The contact electrode is a metal
bar in Ohmic contact with the bare feet of the subject; the field
electrode has the form of a hemispherical metal headpiece placed several
inches from the subject's head. According to the brief description in ›9!,
a signal of less than 2 Volts at a frequency of 125 Hz is applied between
the field electrode and the contact electrode. In this configuration, the
contact electrode supplies to the body the current for charging the
capacitor formed by the head-piece field electrode and the apposing skin
area. The resulting electric field stands predominantly in the space
between the head piece and the scalp.
In the three external field methods mentioned, viz., Wiener ›10!, Brennan
›11!, and Graham ›9!, the electric field is applied to the head, thereby
subjecting the brain to polarization currents. These currents run through
the brain in a broad swath, with a distribution determined by
nonuniformities of conductivity and permittivity. The scale of the current
density can be conveniently expressed by the maximum value, over the skin
of the head, of its component perpendicular to the local skin. This scale
is easily for sinusoidal fields as the product of radian frequency,
permittivity, and maximum amplitude of the external field on the head.
Using Brennan's ›11! lowest frequency of 5 Hz, his minimum required
free-air field strength of 590 V/m, and the factor 17 as estimated above
to account for polarization of the head by the applied field, the scale of
the polarization current density in the brain comes to about 280
pA/cm.sup.2. In the absence of an understanding of the neurological
effects involved, it is prudent to avoid exposing the brain to current
densities of such scale, and impose as a limit 1/4000 times the scale
calculated for Brennan's patent. Polarization current densities in the
brain with a scale in excess of 70 fA/cm.sup.2 are henceforth considered
substantial. It is the object of the present invention to obtain a method
and apparatus for manipulating the nervous system by external electric
fields without causing substantial polarization current densities in the
brain.
The use of electric fields raises concerns about possible health effects.
Such concerns have been widely discussed in the media in regard to
electric power lines and electric apparatus ›12!. Answering the pertinent
questions by objective research will take time, but meanwhile governments
have been setting guidelines for safe limits on field strengths. At
present, the strictest conditions of this sort are the Swedish MPRII
guidelines. Magnetic fields are of no concern here, because the currents
involved are so small. However, the electric field strength must be
considered, since even at low voltages strong electric fields can result
from field electrodes placed close to the skin. With respect to extremely
low frequency electric fields, the MPRII guidelines limit the field
strength to 25 V/m in the frequency range from 5 Hz to 2 Khz. In the
Brennan patent ›11! the minimum field strength of 590 V/m violates the
guidelines by a factor 23; when polarization effects are accounted for,
the factor is about 400.
It is a further object of the present invention to manipulate the nervous
system by external electric fields that are in compliance within the MPRII
guidelines.
Brennan ›11! stipulates voltages of at least 100 V, and as high as 600 V
for the preferred embodiment. Generation of such voltages requires a
voltage multiplier stage, if practical battery operation is desired. This
increases the current drain and the size of the generator. The large
voltages also raise safety concerns. It is yet a further object of the
present invention to manipulate the nervous system by external electric
fields, using low voltages that are generated by a small and safe
battery-operated device with low current consumption.
SUMMARY
Experiments have shown that weak electric fields of frequency near 1/2 Hz
applied externally to the skin of a subject can cause relaxation,
doziness, ptosis of the eyelids, or sexual excitement, depending on the
precise frequency used. In these experiments the electric field was
applied predominantly to skin areas away from the head, thereby avoiding
substantial polarization current densities in the brain. Apparently, the
external electric field somehow influences somatosensory or visceral
afferent nerves, which report the effect to the brain. Although the
mechanism whereby the field acts on the afferents is unknown, the effect
must take the form of a slight modulation of the firing patterns of the
nerves, because the polarization current densities induced by the field
are much to small to cause firing of the nerve. If the applied external
field is periodic, so will be the modulation of the firing patterns of
affected afferent fibers, and the brain is then exposed to an evoked
periodic signal input. Apparently, this signal input influences certain
resonant neural circuits, the state of which has observable consequences.
Since the resonances are excited through somatosensory or visceral
afferents, they are called "sensory resonances".
Besides the resonance near 1/2 Hz that affects the autonomic nervous
system, we have also found a resonance near 2.4 Hz which slows certain
cortical processes. For both resonances the electric field strength on the
skin must lie in a certain range of values for the physiological effects
to occur. This "effective intensity window" can be determined accurately
for the 2.4 Hz resonance, by measuring the time needed to count silently
backward from 100 to 70.
The effective intensity window depends on the number of afferents modulated
by the field. This "bulk effect" is important for the proper use of the
invention, and has therefore been explored in preliminary experiments. At
the lower boundary of the windows the external field strengths are very
small, down to 10 mV/m when a large skin area is exposed to the field. The
fact that very small external field strengths suffice for excitation of
sensory resonances through modulation of afferents allows the use of small
battery-powered electric field generators that can be used conveniently by
the general public as an aid to relaxation, sleep, or sexual excitement,
and clinically for the control and perhaps the treatment of tremors and
seizures, and disorders of the autonomic nervous system such as panic
attacks.
Compliance of the devices with the MPRII guidelines on field limits in the
ELF and VLF frequency bands is easily achieved.
The field generators shown involve simple low-voltage generators based on
555-type timer chips, and field electrodes that are small enough to fit
together with the generator in a single small casing, such as a powder
box. A particularly compact field electrode configuration is the doublet,
which has the structure of a parallel-plate condensor; the fringe field of
the doublet is used for the ecitation of sensory resonances in the
subject.
To be effective, the fluctuating electric field need not be sinusoidal or
even periodic. The field may have a complicated spectral power density, as
long as the dominant frequency is close to the resonant frequency of the
sensory resonance of interest. A simple chaotic voltage generator based on
two timer chips is shown. Field electrode configurations of practical
interest include a shielded pair for producing a sharply localized
electric field on two selected skin areas, and a multipole field electrode
which has a very short range. Although the mechanism of electric field
modulation is unknown, candidates for cutaneous receptors that may be
susceptible to this modulation are indicated.
DESCRIPTION OF THE DRAWINGS
FIG. 1 depicts a preferred embodiment, and shows the deployment of field
electrodes external to the body of the subject.
FIG. 2 illustrates the electric field generated between the field
electrodes and the subject's body.
FIG. 3 shows an embodiment which generates an electric field that
fluctuates as a rounded square wave, and includes an automatic shutoff.
FIG. 4 shows an embodiment which generates an electric field that
fluctuates as a rounded square wave, and which includes an automatic
frequency shift and automatic shutoff.
FIG. 5 shows an embodiment which generates an electric field that
fluctuates as a rounded square wave with a chaotic time dependence, and
which includes an automatic shutoff.
FIG. 6 shows the map of time intervals between consecutive transitions of
the chaotic square wave generated by the circuit of FIG. 5.
FIG. 7 shows an embodiment with the field electrodes and generator
contained in a powder box.
FIG. 8 shows a doublet field electrode.
FIG. 9 depicts a multipole field electrode for producing a short-range
electric field.
FIG. 10 shows schematically a shielded pair of electrodes.
FIG. 11 illustrates the electric field of a doublet placed near a subject.
FIG. 12 provides information for estimating the polarization current and
the maximum electric field induced on the subject's skin by a doublet.
FIG. 13 shows a doublet with distant field enhancer.
FIG. 14 shows the effective intensity window for currents passed by contact
electrodes to the skin overlaying the vagus nerve.
FIG. 15 shows the effective intensity window for large skin area exposure
to the field from a doublet placed some distance from the subject.
FIG. 16 is a replot of the data of FIG. 15, to serve in a comparison with
the data of FIGS. 17 and 18.
FIG. 17 shows the effective intensity window for an experiment using a
shielded electrode pair placed on the thighs.
FIG. 18 shows the effective intensity window for an experiment using a
shielded electrode pair placed on the finger tips.
DETAILED DESCRIPTION
The invention is based on the discovery, made in our laboratory, that
neurological effects can be induced by weak external electric fields of a
precisely tuned frequency near 1/2 Hz, when applied to skin areas away
from the head. The observed effects include ptosis of the eyelids,
relaxation, drowziness, the feeling of pressure at a centered spot on the
lower edge of the brow, seeing moving patterns of dark purple and greenish
yellow with the eyes closed, a tonic smile, a tense feeling in the
stomach, and sexual excitement, depending on the precise frequency used.
These effects were observed initially for external field strengths in the
range from 1 to 25 V/m, but recent experiments have shown effects with
much weaker and stronger fields.
In these experiments the polarization current densities produced in
biological tissue by the applied external electric field are much too
small to cause classical nerve stimulation, yet a central nervous system
response is evoked. Experiments have shown that signal pathways other than
afferent nerves are not involved. It follows that weak external electric
fields can evoke some sort of signal that is carried by afferent nerves.
Since classical nerve stimulation cannot occur, these signals must have
the form of a modulation of spontaneous firing patterns. The simplest such
modulation is frequency modulation (fm), but more subtle modulation modes
›26! may be involved. For simplicity of description however, we will refer
to the modulation as fm. In our experiments the modulation depth is very
small, but for field frequencies that are close to a resonant frequency of
receptive neural circuits the weak incoming fm signal can evidently cause
excitation of the resonance with observable consequences. Since the
applied fields are much too weak to cause nerves to fire, the sensory and
visceral receptors and afferents susceptable to modulation must exhibit
spontaneous firing.
Since the resonances are excited through somatosensory or visceral afferent
nerves, they are here called sensory resonances. The sensory resonance
near 1/2 Hz involves the autonomic nervous system and is therefore called
the 1/2 Hz autonomic resonance.
Exploitation of sensory resonances and reliance on modulation of
spontaneous firing patterns rather than classical nerve stimulation makes
it possible to manipulate the nervous system with very small electric
fields, induced by low voltages. Moreover, employing the natural pathways
of afferent nerves into the brain allows application of the field to skin
areas away from the head. The invention thereby meets the stated objects
of providing manipulation of the nervous system without causing
substantial polarization current densities in the brain, compliance with
MPRII field limits, and use of a low-voltage battery-operated generator
with low current consumption.
The invention provides a method and apparatus for manipulating the nervous
system of human subjects. Such manipulation comprises relaxation and the
induction of sleep or arousal, as well as the control and perhaps the
treatment of tremors, seizures, and disorders resulting from malfunctions
of the autonomic nervous system, such as panic attacks.
In the early experiments the excitation of the sensory resonance occurred
through modulation of cutaneous nerves by the applied external electric
field. In later experiments with larger field strengths, similar
physiological effects have been obtained by applying the field to the skin
overlying the vagus nerve or the sciatic nerve. It appears that excitation
of sensory resonances can be achieved through any afferent pathway,
provided that it is broad.
A new sensory resonance has been found at 2.4 Hz, characterized by a
pronounced increase in the time needed for counting silently backward from
100 to 70. Prolonged exposure to the 2.4 Hz excitation is found to have a
sleep-inducing and dizzying effect. Recent experimental results will be
discussed towards the end of the specification.
The equipment suitable for the generation of the weak electric fields used
for the modulation of afferent nerves consists of field electrodes and a
voltage generator. The field electrodes can simply be conductive foils,
wires, or meshes that may optionally be covered on one or both sides with
an insulating layer. The field electrodes are to be electrically connected
to the generator, but insulated from the subject. The voltage generator is
to produce a low fluctuating voltage. The time dependence of the
fluctuating voltage need not be sinusoidal or even periodic, but may have
a complicated spectrum, as long as the dominant frequency of the voltage
is at or near the resonance frequency for the sensory resonance of
interest, or can be tuned to this effect; a tuning range from 0.1 to 3 Hz
was used for the early experiments in which the 1/2 Hz resonance was
found. The dominant frequency is here defined as the frequency at the
global maximum of the spectral power density. In the rare case that there
is more than one such maximum, the dominant frequency is formally taken as
the least of the frequencies for the global maxima. The dominant frequency
of the output of a generator can be easily measured, and those skilled in
the art can readily design a generator with a specified or tunable
dominant frequency and desired spectral properties. Harmonic content needs
to be considered for compliance with the MPRII guidelines, if the
amplitude of the field applied to the skin is large. An automatic shutoff
can be provided, such as to limit the duration of field application.
It has been found that a single 1/2 hour application of the field is
usually sufficient to induce sleep, if the frequency of the wave is tuned
correctly for the individual to a frequency near 1/2 Hz. Shorter
application times are typically sufficient for inducing relaxation. The
effects of the applied electric field are usually noticeable after half a
minute or so.
A preferred embodiment of the invention is shown in FIG. 1, where the
voltage generator 1, labeled as GEN, is connected to the field electrodes
2 by wires 3; the field electrodes 2 are positioned away from the subject
4. The voltage generator may be tuned manually with the tuning control 21.
As an option, sheet conductors 43 and 43' such as aluminum foils may be
placed near the subject in order to diminish interference from a 60 Hz or
50 Hz house field, to be discussed. Referring to FIG. 2, application of a
voltage between the field electrodes 2 produces an electric field 5
between field electrodes 2 and the subject 4, for the case that the sheet
conductors 43 and 43' of FIG. 1 are absent. The field is applied
predominantly to skin areas away from the head of the subject; in the
setup of FIG. 1 these areas comprise skin area 36 on the hips, buttocks,
and lower back, and skin area 36' on the back side of the thighs and
knees.
A suitable voltage generator, built around two RC timers, is shown in FIG.
3. Timer 6 (Intersil ICM7555) is hooked up for astable operation; it
produces a square wave voltage with a frequency determined by resistor 7
and capacitor 8. The square wave voltage at the output 9 drives the LED
10, and appears at one of the output terminals 11, after voltage division
by potentiometer 12. The other output terminal is connected to an
intermediate voltage produced by the resistors 13 and 14. As a result, the
voltage between the output terminals 11 alternates between positive and
negative values. Automatic shutoff of the voltage that powers the timer,
at point 15, is provided by a second timer 16 (Intersil ICM7555), hooked
up for monostable operation. The shutoff occurs after a time interval
determined by resistor 17 and capacitor 18. Timer 16 is powered by a 3 V
battery 19, controlled by the switch 20. The output terminals 11 are
connected to the field electrodes 2 by conductors 3. The resistors 13 and
14 not only serve as a voltage divider that gives the intermediate voltage
needed to produce an alternating square wave, but these resistors also
provide current limitation. A further decrease of the currents induced in
the subject is caused by the output capacitor 22, in a manner to be
discussed. There is the option of including a switch 44 in the output
circuit, in order to prevent polarization of the electrode assembly by a
60 Hz or 50 Hz house field when the device is inactive, to be discussed.
A time variation of frequency may be accomplished by manipulating the
control voltage of one section of a dual timer with the output of the
other section. An embodiment for this type of operation is shown in FIG.
4. The dual timer 23 (Intersil ICM7556) is powered at point 24 by voltage
from the output 15 of timer 16 (Intersil ICM7555), which serves as an
automatic shutoff after a time interval determined by resistor 17 and
capacitor 18. The timer operation is started by closing switch 20. The
voltage at output 25 of the dual timer 23 drives the LED 10, and is
applied, via the variable resistor 12, to one of the outputs 11 of the
voltage generator. Resistors 14 and 13 serve to provide an intermediate
voltage at the other output terminal 11, such as to result in a potential
difference between the output terminals that alternates between positive
and negative values of substantially equal magnitudes. The frequency of
the square wave voltage at point 25 depends on resistor 7 and capacitor 8.
The frequency is also influenced by the control voltage applied to the
timer. A frequency upshift can be obtained by applying the output of the
second section of the dual timer 23 to the control voltage pin of the
first timer section, via resistor 26. This second timer section is hooked
up for monostable operation. The output terminals 11 are connected by
conductors 3 to the field electrodes 2, which are pieces of aluminum foil,
covered by insulating tape on both sides.
The automatic shutoff and time variation of the frequency are examples of
automatic control of the fluctuating voltage generated by the generator.
Low frequencies can be monitored with an LED 10 of FIG. 3. The LED blinks
on an off with the square wave, and doubles as a power indicator. The
frequency can be determined by reading a clock and counting LED light
pulses. For higher frequencies a monitoring LED can still be used, if it
is driven by a wave obtained by frequency division of the generator output
wave.
The voltage generators discussed above have oscillators of the RC type, but
other types of low-voltage oscillators can be used as well. For instance,
the voltage generator can be built as a digital device, in which a square
wave output is derived from a clock signal by means of frequency division.
Chaotic signals, time variation of frequency, programmed frequency
sequences, automatic turn on and shutdown, frequency adjustment, and
frequency monitoring may also be accomplished digitally. A computer that
runs a simple timing program can be used for the generation of all sorts
of square waves that can be made available at a computer port. An economic
and compact version of such arrangement is provided by the Basic Stamp
›30!, which has an onboard EEPROM that can be programmed for the automatic
control of the fluctuating voltage generated, such as to provide desired
on/off times, frequency schedules, or chaotic waves. In the interest of
controlling polarization current peaks or complying with MPRII guidelines,
the square waves can be rounded by RC circuits, and further smoothed by
integration and filtering. In this manner, near-sinusoidal output can be
achieved. Such output can also be obtained with a digital sine-wave
generator based on a walking-ring counter ›31!, or with a waveform
generator chip such as the Intersil ICL8038. Analog circuits for tunable
sine wave generators based on LC oscillators with passive inductance and
capacitance are not practical because of the very large component
parameter values required at the low frequencies involved. Large
inductances can be produced by a compact active stage, or one can use two
separate RC phase shift circuits connected in a loop with an amplitude
limiter ›32!. Tuning may be done with a single potentiometer.
Applications are envisioned in which the field electrodes are driven with a
fluctuating voltage that is chaotic. Such a voltage is here defined as a
signal for which the times of zero crossings or peaks, or both, form a
pseudo-random sequence. A simple example is provided by a square wave for
which the transition time intervals form a pseudo-random sequence, within
upper and lower limits. The brain is adaptive, but the chaotic transitions
are difficult to learn and anticipate, and therefore a field with a
slightly chaotic square wave can thwart habituation. A sensory resonance
can still be excited by such a wave, if the dominant frequency of the wave
is close to the resonant frequency. The chaotic wave can also be used to
upset pathological oscillatory modes in neural circuitry, such as to
control tremors in Parkinson patients.
An embodiment which involves a chaotic square wave electric field is shown
in FIG. 5. The dual timer 23 (Intersil ICM7556) is powered, at point 24,
by the output 15 of timer 16 (Intersil ICM7555), hooked up for monostable
operation, such as to provide automatic shutoff after a time determined by
resistor 17 and capacitor 18. Operation of timer 16 is started by closing
switch 20. Both sections of the dual timer 23 are hooked up for bistable
operation, with slightly different RC times. The voltage at output 25 of
the first timer section is used to drive the LED 10; after voltage
division by the variable resistor 12, the voltage is applied to one of the
outputs 11. The other output 11 is an intermediate voltage from the
voltage divider formed by resistors 14 and 13. The outputs 11 are
connected to the field electrodes 2 through conductors 3. The RC time of
the first timer section is determined by resistor 7 and capacitor 8. The
RC time of the second timer section is determined by resistor 27 and
capacitor 28. The two timer sections are coupled by connecting their
outputs crosswise to the control voltage pins, via resistors 29 and 30,
with capacitors 31 and 32 to ground. For a proper range of component
values, easily found by trial and error, the square wave output of each of
the timer sections is chaotic.
An example for chaotic output is shown in FIG. 6, where the points plotted
correspond to transitions (edges) of the square wave. Abscissa 33 and
ordinates 34 of a plotted point are time durations between consecutive
transitions of the square wave output; for any transition, the abscissa is
the time to the preceding transition, and the ordinate is the time to the
next transition. Starting with transition 35, consecutive transitions are
found by following the straight lines shown. The transition times follow a
pseudo random sequence, with some order provided by the oval attractor.
The results shown in FIG. 6 were measured for the device of FIG. 5, with
the following component values: R.sub.7 =1.22 M.OMEGA., R.sub.27 =1.10
M.OMEGA., R.sub.29 =440 K.OMEGA., R.sub.30 =700 K.OMEGA., C.sub.8 =0.68
.mu.f, C.sub.28 =1.0 .mu.f, C.sub.31 =4.7 .mu..mu.f, and C.sub.32 =4.7
.mu.f. In the above list, R.sub.i is the resistance of component i in FIG.
5, and C.sub.j is the capacitance of component j.
Tests with a subject who is not a Parkinson patient, but who has a hand
tremor of another origin, have shown good control of the tremor by a
square wave electric field with the chaotic time dependence shown in FIG.
6. The device of FIG. 5 was used in these tests, with electrodes placed
vertically on two opposite vertical sides of the seat cushion of an easy
chair.
In the present invention, the external field is applied predominantly to
certain selected areas of the skin of the subject, such as the areas as 36
and 36' in FIG. 2. Areas of predominant field application are here defined
to consist of all points of the skin at which the absolute value of the
resultant field strength is at least twice the average over the skin. The
resultant field includes the field produced by polarization charges on the
skin of the subject. The resultant field is perpendicular to the skin when
the polarization keeps up with changes in the applied field, as is the
case for the low frequencies involved, if sharp transitions are avoided.
Of convenience in social settings is an embodiment in which the two field
electrodes and the signal generator are contained in a single casing such
as a small box, purse, powder box, or wallet. An embodiment is shown in
FIG. 7, where the generator 1' with tuning control 21' is placed inside a
powder box casing 45 with hinge 49. The field electrodes 2 and 2' are
contained in the casing 45. The field electrodes 2 are connected to the
generator 1' by conductors 3. For brevity, field electrodes mounted on the
outside surface of a casing are considered as contained in the casing.
The peak-to-peak variation of the output voltage of the voltage generators
discussed above cannot exceed 16 V, because of supply voltage limitations
for the CMOS timer chip. However, much lower output voltages suffice for
most applications. An output voltage of 2.4 V peak to peak is adequate for
the setup of FIG. 1. Such an output voltage is provided by the signal
generators of FIGS. 3 and 4, when powered by a 3 V battery. Such small
voltages suffice even for embodiments in which the generator and field
electrodes are mounted in a single small casing, in spite of the small
area available for the electrodes.
An electric field outside the body of the subject is called an external
electric field.
In applications of modulation of cutaneous nerves by an external electric
field there is usually also present a 60 Hz or 50 Hz house field, an
electric field emanating from house wiring, electric apparatus and
electric power lines. House fields can have considerable strength; Becker
and Marino ›15, table 10.4! list the electric field, at 1 ft distance from
an electric blanket, broiler, refrigerator, food mixer, hairdryer, and
color TV, respectively as 250, 130, 60, 50, 40, and 30 V/m. The electric
field 1 ft away from a light bulb is listed as 2 V/m. The house field may
cause inadvertent modulation of cutaneous nerves. In distinction with this
inadvertent modulation, there is the purposeful modulation which is the
subject of the present invention. The house field intensities mentioned
above suggest that the house field may interfere with the purposeful
modulation. The interference can be diminished by reducing the strength of
the house field incident on the subject. This may be done by placing near
the subject a sheet conductor oriented roughly parallel with the local
house field. An example is shown in FIG. 1, where a sheet conductor in the
form of aluminum foils 43 is placed against the underside of the bed, and
a continuation 43' of the aluminum foil covers the back of the headboard.
The house-field-diminishing effect of a properly placed and oriented sheet
conductor can be readily understood as due to electric polarization of the
sheet conductor by the house field.
There further is concern about the effect of house field induced electric
polarization of the electrode assembly, that may occur at times when no
external electric field is being generated by the apparatus, although the
field electrodes are electrically connected through the device. This state
occurs during most of the night, if the apparatus of FIGS. 3 or 4 is used
as a sleeping aid with permanently placed field electrodes, after the
automatic shutoff has cut the power to the oscillator. Of concern is the
circuit comprised of the two field electrodes, their connections to the
signal generator, and pertinent output circuitry in the signal generator.
Referring to FIG. 3, it is seen that this circuit includes the capacitor
22 and part of the potentiometer 12. The house field generally induces
polarization currents in this circuit. The resulting polarization charges
on the field electrodes induce an electric field with a nonuniformity
scale comparable to the electrode spacing. This 60 Hz field may cause
modulation of the same afferent nerves as those involved in the purposeful
modulation by the apparatus field. The inadvertent modulation may cause
weak fm signals of 60 Hz frequency in receptive neural circuitry, and the
signals may be so weak as to sneak by nuisance-guarding circuitry. The
unwanted signals may be diminished by using the house-field-diminishing
sheet conductor described above. Alternatively, or in addition,
polarization of the electrode assembly by the house field may be prevented
by breaking the electric connection between the field electrodes by means
of a switch (44 in FIG. 3) in one of the output leads of the signal
generator. This switch may be ganged with the power switch.
The external electric field must be predominantly applied to skin regions
away (at least 10 cm) from the head of the subject. Furthermore,
substantial polarization current densities in the subject's brain must be
avoided. The scale of these current densities is expressed here for
sinusoidal fields as the product of permittivity, radian frequency of the
field, and maximum external electric field amplitude on the head; this
product should not exceed 70 fA/cm.sup.2. Satisfying this condition and
that of predominant field application to skin areas away from the head
requires calculation of external field strengths on the subject's skin,
for the field electrode configuration and deployment considered. This can
be done along the following lines.
First, the electric field produced by a field electrode at distance .gamma.
is given by the well known Coulomb formula, for .gamma. considerably
larger than the electrode dimensions. For elongated electrodes, the
two-dimensional Coulomb formula can be used for intermediate distances
that are large compared to a significant dimension of the cross section
but small compared to the electrode length. The presence of the subject
can be accounted for by the well-known method of images ›27!. The field
produced by a field electrode in its immediate vincinity can be calculated
with simple models that are appropriate to the situation at hand, and are
well known to those skilled in the art. Of course, these calculations need
only be approximate or furnish reliable upper bounds of the field strength
considered. Field calculations will be shown here for several field
electrode configurations and settings of practical interest.
Presently, the experiments that underlie the invention will be discussed.
The experiment setup used was much like the one shown in FIG. 1, with
variations as to the skin area of predominant field application. The
voltage applied between the field electrodes was usually a square wave
with a frequency that can be manually tuned from 0.1 to 3 Hz, by adjusting
the tuning control 21 on the generator 1 of FIG. 1; the voltage of the
square wave was about 3 V. Frequencies at which a physiological effect
occurs were found by manual frequency scanning. We needed a way to tell
whether the nervous system of the subject was being affected by the
external electric field. Invasive procedures were ruled out. Extensive EEG
measurements were done on the scalp over appropriate points on the
postcentral gyrus, using the method of averaging over many sweeps, in
order to recover evoked potentials ›13!. No evoked potentials showed up,
even after averaging over 8000 sweeps, which brought the sensitivity to
100 nV. This showed that if anything is going on with the cutaneous nerves
in the skin areas exposed to the field, it is not classical nerve
stimulation. It was noticed that, at frequencies of about 1/2 Hz, the
subject became drowsy and the EEG eventually showed increased amplitudes
of slow waves, as judged by the signal waveform. The experiments need to
be repeated, using hardware or software that provides for fast spectral
analysis. Lacking this equipment, we looked for another indicator and
found one in the form of ptosis of the eyelids.
When voluntary control of the eyelids is relinquished, the eyelid position
is determined by the state of the autonomic nervous system. There are two
ways in which this indicator may be used. In the first the subject simply
relaxes control over the eyelids, and makes no effort to correct for any
drooping. The more sensitive second method requires the subject to first
close the eyes about half way. While holding this eyelid position, the
subject rolls the eyes upward, while giving up voluntary control of the
eyelids. With the eyeballs turned up, ptosis will decrease the amount of
light admitted into the eyes, and with full ptosis the light is completely
cut off. The second method is very sensitive because the pressure exerted
on the eyeballs by partially closed eyelids increases parasympathetic
activity. As a result the eyelid equilibrium position becomes labile, as
evidence by a slight flutter. The labile state is sensitive to small
shifts in the activities of the sympathetic and parasympathetic nervous
system. The method works best when the subject is lying flat on the back
and is viewing a blank wall that is dimly to moderately illuminated.
With this arrangement maximum ptosis occurred at a frequency near 1/2 Hz,
with external electric field amplitudes on the skin ranging from 1 V/m to
25 V/m, where field amplitude is defined as half the peak-to-peak
variation of the field strength. Immediately after onset, the ptosis
frequency, defined as the frequency for maximum ptosis, slowly decreases
until a steady frequency is reached in 5 to 10 minutes. It is believed
that this is due to changes in the chemical environment of the resonating
neural circuitry, caused by changes in the concentration of
neurotransmitters or hormones that accompany or result from the resonance
or from the subsequent shift in the autonomic nervous system state. The
effect is here called "chemical detuning" of the ptosis frequency. The
slow shift of ptosis frequency initially is so large that ptosis is lost
if the frequency is not adjusted. The ptosis is accompanied by a state of
deep relaxation, and a slight dull pressure at a spot about 1 cm above the
point midway between the eyes.
As directly demonstrated by the ptosis experiments, the method of the
present invention can be used for inducing relaxation in a subject. In
further experiments with the device of FIG. 3 it has been found that, in a
narrow range of frequencies around the ptosis frequency, the subject
became very relaxed after a few minutes of field application, using peak
field strengths on the subject's skin of about 1 V/m. The field was
induced by field electrodes placed on the sides of the seat cushion of an
easy chair. The ptosis frequency is higher in the evening than in the
morning, just after awakening. For the subject tested, the evening ptosis
frequency was 0.512 Hz at the onset, slowly shifting downwards to 0.465 Hz
in about 10 minutes. Other autonomic responses can be obtained as well;
tuning to a frequency of 0.540 Hz brings forth a tonic smile, provided
that the subject gives up voluntary control of the facial muscles
involved, so that the smile is controlled by the autonomic nervous system.
Relaxation was experienced in the frequency range from 11% below to 4%
above ptosis frequency. In the morning, the ptosis frequency at the onset
was 0.490 Hz initially, shifting downwards to 0.460 Hz in about 7 minutes.
The method can also be used for the induction of sleep. Long-term tests
running for about 400 nights were conducted on a subject who had trouble
sleeping due to prolonged severe situational stress. In these tests, an
external electric field was set up by applying a square-wave voltage of 20
V peak to peak between two field electrodes placed directly underneath the
bed sheet on both sides of hips. Good results were obtained with
frequencies of about 1/2 Hz. More recently, the device of FIG. 4 with a 3
V battery has been used successfully by the same subject for about 300
nights, under the same stressful conditions. Among the various electrode
positions tried, the placement depicted in FIG. 1 was found to be most
effective for inducing peaceful sleep. In this configuration the field
electrodes 2 are located directly under the mattress, in the vertical mid
plane through the longitudinal axis. The maximum electric field amplitude
on the subject's skin is estimated as about 1 V/m. Two modes of operation
were used. In the first mode, the unit was turned on at bedtime, at a
frequency of 0.545 Hz, and thereafter left alone. After 15 minutes, the
device automatically shifts the frequency upward by 3%, and turns off the
oscillator after another 15 minutes. The subject usually fell asleep
before automatic shutoff had occurred. A second mode of operation involves
initial tuning for ptosis, followed by manual tracking of the slowly
downshifting ptosis frequency, using the tuning control 21 shown in FIG.
1. About 5 minutes after a steady ptosis frequency is reached, the device
is shut off manually. Tracking the ptosis frequency during its downward
shift brings an increasingly deep state of relaxation and detachment.
Sleep usually follows shortly after the device is shut off manually.
In regard to electrode placement there is a fundamental neurological
difference between antisymmetric and symmetric excitation, in which the
skin polarization is respectively antisymmetric and symmetric with respect
to the midsagittal plane. In antisymmetric excitation, the weak fm signals
from the modulated afferents act antisymmetrically on the brain. As a
consequence, resulting resonances in neural circuits exhibit antisymmetry
in left and right hemispheres, and the corpus callosum is "caught in the
middle". In symmetric excitation, resonant modes occur synchronously in
both hemispheres, and the corpus callosum is less involved, if at all.
Experiments have shown that induction of sleep occurs with both
excitations, but the symmetric excitation gives a somewhat softer feeling.
At frequencies somewhat different from the ptosis frequency, sexual arousal
has been observed. In a male subject 67 years of age, the incidence of
morning erections increased considerably when a square wave voltage was
applied to field electrodes 2 placed as shown in FIG. 1, at a frequency of
0.563 Hz, and also, to a lesser extent, at a frequency of 0.506 Hz. These
frequencies were found by manual scanning the range from 0.1 to 3 Hz. The
signal generator of FIG. 3 was used, powered by a 3 V battery. For
frequencies near 0.55 Hz, rather intense sexual excitement lasting for up
to an hour has been induced in a male subject 70 years of age, by applying
the external electric field predominantly to a skin area that includes the
perinaeum skin.
Cutaneous receptors are particularly dense in glabrous skin, such as found
on the palms of the hand, footsoles, areas of the genitals, nipples,
areola, and lips. In the somatosensory map between areas of skin, the
thalamus, and sensory cortex, the representation of these glabrous skin
areas is greatly amplified. As a consequence, external electric field
modulation of cutaneous nerves in glabrous skin is expected to excert a
particularly strong effect on the central nervous system. We feel that
this should be avoided by the general public; the effects are already
ample when the field is applied predominantly to areas of the skin which
are innervated sparsely, such as the thighs and the back. In particular,
the lips should not be exposed strongly to the field, so that the areas of
predominant application of the electric field by the general public should
be away (say, at least 10 cm) from the head. Another reason for such
choice is the avoidance of substantial polarization current densities in
the brain, as discussed above.
Fixing experiment parameters except for the field strength, the described
physiological effects are observed only for field intensities in an
interval, called here "the effective intensity window". This feature of
sensory resonances may be understood as due to nuisance-guarding neural
circuitry that blocks impertinent repetitive sensory signals from higher
processing. For the guarding circuitry to spring into action, the
amplitude of the nuisance signal needs to exceed a certain threshold. This
explains the upper boundary of the effective intensity window. The lower
boundary of the window is due to the detection threshold of the sensory
signals.
There needs to be concern about kindling ›13, 18! of epileptic seizures in
susceptable individuals. Kindling has traditionally involved the passage
of electric currents of the order of 0.1 mA directly to a part of the
brain, such as the amygdala. Although in the present invention substantial
polarization current densities in the brain are avoided, an effect similar
to kindling might occur if critical neural circuits are subjected to
repeated sessions of periodic fm signals from somatosensory or visceral
afferents. To guard against such an effect, the frequency of modulation of
afferents for use by the general public should be chosen away from the
frequencies involved in epileptic seizures. Modulation frequencies below 2
Hz appear to qualify in this regard.
The pathological oscillatory neural activity involved in epileptic seizures
›13! is influenced by the chemical milieu of the neural circuitry
involved, specifically through concentrations of GABA, glutamate, and
aspartate ›18!, and perhaps .beta.-endorphin. Since excitation of the 1/2
Hz sensory resonance may cause a shift in some of these neurotransmitter
concentrations, the application of external electric fields may be useful
for control and perhaps treatment of seizures. For this purpose, the
patient wears compact field electrodes and a generator, to be manually
activated upon experiencing a seizure precursor or aura. For patients with
infrequent seizures, a small unit that contains the field electrodes as
well as the generator, in the form of a small box, wallet, purse, or
powderbox, may be particularly suitable.
The modulation of afferents by external electric fields may also be used
for the control of tremors in Parkinson patients, by interfering with the
underlying pathological oscillatory activity. According to Ref. ›14!,
Scientific American of 1892 contains an article about controlling
Parkinson symptoms by means of a vibrating helmet placed on the patient's
head. For a 10 Hz vibration frequency, the subject is reported to
experience, within a few minutes, a general lassitude and a tendency to
sleep. Modulation of afferent nerves by a properly tuned periodic external
electric field affords another and far less conspicuous excitation method,
which is expected to have a similar result. The method of upsetting
pathalogical oscillatory activity by applying an external electric field
for modulating afferent nerves in skin areas away from the head may also
be used for the control of seizures.
The method may be applied for the control of panic attacks, when these
involve an abnormally high activity of the sympathetic nervous system. The
experiments on ptosis, relaxation, and sleep show that the application of
alternating external electric fields can diminish the activity of the
sympathetic nervous system. The apparatus of FIG. 3 may be used, tuned to
a frequency just below ptosis, or, for severe cases, right at ptosis. In
this application it is convenient to use a generator and field electrodes
mounted in a small single casing, such as a small box, wallet, purse, or
the powder box of FIG. 7.
The question arises whether in the weak-field experiments discussed above
the observed physiological effects are perhaps due to mechanisms other
than the response of afferent nerves to the applied field. Candidates for
such alternate mechanisms are polarization currents induced in the brain,
and currents carried along high-conductivity paths provided by the
cerebrospinal fluid, blood, and lymph, and subsequently detected by
receptors. These alternate mechanisms are ruled out by experiments in
which a sharply localized electric field is applied to the dorsum of the
feet. The usual array of physiological responses was found in these
experiments. It is therefore concluded that for weak aplied electric
fields the observed physiological effects are indeed instigated by a
response of afferent nerves to the external electric field.
The manipulation of the nervous system by external electric fields tuned to
a sensory resonance frequency is subject to habituation, sensitization,
classical conditioning, and the placebo effect. To minimize habituation in
the use as a sleeping aid, the field should be predominantly applied to a
different skin area each night. Sensitization, the placebo effect, and
positive classical conditioning enhance the efficacy of the method.
Clinical trials can be designed such that the placebo effect does not
contribute to the statistical mean. This is done by arranging the
generator output to the field electrodes to be passed or blocked by
computer, according to a pseudo-random sequence with a seed that is
changed from run to run, as determined for instance by date and time.
Whether the field was on or off is unknown until the run is complete and
the response of the subject has been entered into the computer. The
arrangement is equivalent to a trully double-blind study.
The following considerations are important for proper design and use of the
field generator, as well as for the planning and interpretation of
experiments.
When an external electric field is applied to an isolated conductor,
electric currents will flow that drive charges to the conductor surface.
In steady state, these charges are distributed in such a way that the
total electric field inside the conductor vanishes and the conductor
surface is equipotential. These surface charges and electric currents are
here called respectively "polarization charges" and "polarization
currents". Although mainly used in the context of dielectrics, the wording
is proper for isolated conductors as well.
Since the human body is a good conductor of electricity, exposure of an
isolated subject to an alternating external electric field will cause
polarization currents to flow broadly through the subject's body. The
currents are of course accompanied by an ("internal") electric field,
which turns out to be a very small fraction of the applied external field.
In principle the polarization current and accompaning internal electric
field may act on receptors, axons, synapses, and dendrites. As a purely
electrical effect, the polarization current causes a polarization of the
body, in which electric charges accumulate on the skin, if the latter is
dry and the body is substantially insulated from its surroundings. The
polarization charge density on the skin tracks the fluctuations in the
applied external field. For an external electric field that varies as a
square wave, the polarization currents flow only as brief pulses in
response to the edges of the square wave. The polarization current pulses
then have sharp leading edges, followed by an exponential decay with an
e-folding time
T.sub.c =(.di-elect cons./.di-elect cons..sub.o).di-elect cons..sub.o
.eta.,(1)
where .di-elect cons..sub.o is the permittivity of free space
(8.85.times.10.sup.-12 farads/m), .di-elect cons./.di-elect cons..sub.o
the /average dielectric constant of the biological tissue, and .eta. the
average resistivity. T.sub.c is called the charge relaxation time. Using
the dielectric constant .di-elect cons./.di-elect cons..sub.o and
resistivity .eta. for muscle tissue ›16, FIG. 3--3!, we find the estimate
T.sub.c =710 ns. (2)
After each square wave edge, the current flow in the subject's body becomes
negligibly small after a few times T.sub.c. For square wave edges that are
rounded with a rise time considerably larger than T.sub.c, the
polarization current pulses are broadened to the rise time of the edges.
If spatial averages are used for the dielectric constant and resistivity,
the charge relaxation time expressed by (1) is a spatial average. However,
local relaxation times can differ substantially from the spatial average;
for instance, the relaxation time of membranes ranges from 0.7 ms to 24 ms
for the cases listed by Katz ›17, table 1!.
For external electric fields that vary slowly compared to the charge
relaxation time (2), the polarization keeps up with the field. The
resultant electric field, i.e., the sum of the applied field and the field
due to polarization, is then essentially always perpendicular to the skin
of the subject, and the electric field on the skin is proportional to the
surface density of electric polarization in the skin. As will be
discussed, experiments have shown that weak external field modulation of
cutaneous nerves is due to electric polarization of the skin.
The polarization currents are subject to the skin effect ›19, p. 5-85!, in
which the current density falls of exponentially, from the skin into the
body, with e-folding distance
##EQU1##
where .function. is the frequency of the applied field, .mu. the
permeability, and .eta. the resistivity of the body tissue. Calculation of
the skin depth .delta..sub.s for the frequencies involved in the present
invention gives values in excess of 1 m. It follows that the polarization
current paths are not restricted by the skin effect.
The scale of the polarization current densities can be determined from the
peak polarization current induced in the subject's body by the applied
external field. This peak current can easily be calculated for the case
that the applied electric field varies as a rounded square wave. The
calculation is illustrated here for the field generator of FIG. 3. Let the
resistors 13 and 14 and the potentiometer 12 all have the same resistance
R.sub.o, and let the potentiometer wiper be set at fraction .alpha. of the
total resistance R.sub.o. With a 3 V battery, the output voltage of timer
16 at point 15 is 2.5 V. Therefore, timer 6 produces a square wave with a
voltage of V.sub.o =2.5 V. A short calculation shows that the voltage
between the two output terminals 11 swings from .alpha.V.sub.o /3 to
-.alpha.V.sub.o /3, and that the output impedance, in the absence of
output capacitor 22, is
R.sub.out =.alpha.(3-2.alpha.)R.sub.o /3. (4)
Hence, with an output capacitor C.sub.o, the peak polarization current
through the body of the subject is
##EQU2##
where C.sub.eb is the part of the capacitance between the field electrodes
calculated from electrode charges at the end of electric field lines that
go to the subject's body, and C.sub.ee is the remaining part of the
capacitance between the field electrodes. Eq. (5) holds, provided that
R.sub.O is much larger than the impedance of the subject's body, a
condition that is satisfied in practice. The rise time of the external
electric field is
##EQU3##
provided that T.sub.f is much larger than the charge relaxation time (2)
of the subject's body. This condition is satisfied in practice, unless
.alpha. is very small. For the device of FIG. 3, with an output capacitor
C.sub.O =1000 pf, R.sub.O =1 M.OMEGA., .alpha.=1, V.sub.O =2.5 V, and the
electrode configuration of FIG. 1, with the estimates C.sub.eb =1 pf,
C.sub.ee =1 pf, the peak current I.sub.max of (5) becomes
I.sub.max =5.0 nA, (7)
and the rise time T.sub.f of (6) is found to be
T.sub.f =0.33 ms. (8)
Although these results were derived for the generator of FIG. 3, under the
assumption that the timer produces a square wave with sharp edges, they
will remain valid for rise times up to 100 ns. Comparison of the peak
polarization current (7) with the 1 mA or so required for classical nerve
stimulation ›6,7! shows that the latter does not occur in the experiments
under discussion. Estimating, for the setup of FIG. 1, the area of the
skin that is subjected to appreciable field strengths as 2 A=600 cm.sup.2,
the peak polarization current density has over this area a spatial average
<j>=I.sub.max /A, which comes to
<j>=17 pA/cm.sup.2. (9)
Using .eta.=400 Ohm cm as an average tissue resistivity ›16, FIG. 3--3!,
the spatial averaged peak internal electric field strength <E.sub.i > that
accompanies the average peak current density <j> of (9) is
<E.sub.i >=6.8 nV/cm, (10)
for the case considered. These results are spatial averages of temporal
peaks. In order to estimate the deviations from the average caused by
nonuniformities in conductivity, consider a membrane with surface
resistivity of 4000 Ohm cm.sup.2 ›17, table 1! subject to the
perpendicular current density (9). The potential difference across the
membrane is then perturbed by a mere 68 nV. Even if a factor 10 is used to
account for the local nonuniformities in current density, the resulting
peak membrane potential perturbation of 680 nV is about a factor 58000
below the membrane depolarization required for firing. This again shows
that classical nerve stimulation does not occur. Since the applied field
acts on the nerves, as evidenced by the observed physiological effects,
the action must be a modulation of the spontaneous firing pattern of the
nerve. The question remains whether the modulation is caused by the
polarization currents or by the polarization charges on the skin.
In order to investigate this question, two experiments were performed. The
field generator of FIG. 3 was used in both, with a 1000 pf output
capacitor 22, V.sub.O =2.5 V, and R.sub.O =1 M.OMEGA., where R.sub.O is
the resistance of resistors 13 and 14, and potentiometer 12. The field
electrodes were aluminum foil rectangles of 8.times.17 cm, placed over the
upper skin of the subject's feet, with 1.5 cm insulation between the skin
and the foils. The field electrodes were shielded on the outside with
8.5.times.20 cm rectangular pieces of grounded aluminum foil, separated
from the field electrodes by a 0.5 cm thick layer of insulation. The
subject's feet, fitted with the shielded field electrode assemblies, were
placed in a 36.times.31.times.53 cm cardboard box, covered on the outside
with grounded aluminum foil; the front opening of the box was shielded by
a curtain of grounded insulated strips of aluminum foil. With this
arrangement, the electric field was mainly confined to the 1.5 cm space
between each field electrode and the opposing area of skin; any field
spilling out from this space was essentially kept in the box by the
grounded shield on the outside of the box and by the grounded curtain in
front. The capacitance between the field electrodes via the subject's body
is estimated as C.sub.eb =11 pf, using a dielectric constant of 2.6 for
the styrofoam insulation. The remaining capacitance between the field
electrodes is estimated as C.sub.ee =33 pf. With the output capacitor
C.sub.O =1000 pf, V.sub.O =2.5 V and R.sub.O =1 M.OMEGA., Eq. (5) gives a
peak polarization current of I.sub.max =53 nA, multiplied by a factor that
ranges from 1/3 to 1, as the intensity control potentiometer is advanced
from small .alpha. to .alpha.=1. Full ptosis was observed with intensity
control potentiometer settings from .alpha.=1 to .alpha.=0.06, at a
frequency near 0.53 Hz.
Next, the experiment was repeated with one modification: the upper skin of
the subject's feet, in the area opposite the field electrodes, was covered
with a layer of conductive jelly, followed by a thin layer of overlapping
strips of aluminum foil, and a thin insulating plastic sheet. In this
arrangement, the polarization currents in the subject's body end up not on
the subject's skin opposite the field electrodes, but on the aluminum foil
covering of that skin area. The conductive jelly between skin and aluminum
foil assures that the polarization charges make their way to the foil
without delay beyond the charge relaxation time T.sub.c of (2). As a
result, the polarization currents that flow in the subject's body are the
same as in the previous experiment, but during the plateaus of the square
wave, after a few times T.sub.c, the skin is not subjected to an electric
field. With intensity control settings .alpha. ranging from 1 down to
0.06, and tuning through the frequency range from 0.490 to 0.589 Hz, only
very faint and fleeting ptosis was sporadically experienced for very short
times; it could not be tracked in the usual manner by slowly tuning to
lower frequencies. This result is to be compared with the full ptosis
occurring in the previous experiment in which the feet were not covered
with the highly conductive layer.
Varying the intensity control settings a in the two experiments gave pairs
of settings in which the polarization current densities on the skin in the
areas opposite the field electrodes is the same for the two experiments.
For each of these pairs, the values of .alpha. are somewhat different,
because the metal covering of the skin used in the second experiment
extends to border areas for the purpose of capturing the edge field flux;
therefore, the effective area of skin involved in the second experiment is
slightly larger than in the first experiment. Considering the existence of
these pairs of .alpha. settings for which the polarization current
densities on the skin are the same for the two experiments, and the
essential absence of ptosis in the second experiment, it is concluded that
ptosis is essentially not caused by polarization currents in the skin.
Moreover, settings with the same .alpha. give about the same polarization
currents in the rest of the subject's body, away from the skin area
opposite the field electrodes. It is therefore concluded that ptosis is
essentially not due to stimulation or modulation of nerves other than
cutaneous nerves, and it is not due to polarization currents in the brain
either. It also follows that the ptosis is essentially not due to any
stray electric field standing on the scalp or any other part of the skin
other than the skin area lying directly across the field electrodes. It is
concluded that the ptosis is essentially due to external electric field
effects other than the polarization current, and that ptosis occurs
essentially through cutaneous sensory nerves.
What are the effects of the external electric field, besides the
polarization current? One such effect is the force exerted by the external
field on hairs. However, experiments in which the field is exclusively
applied to glabrous skin also give ptosis; hence, hairs are not involved
in an essential way. The only possibility remaining is a shallow
penetration of the external electric field into the subject's skin. Two
such mechanisms have come to mind.
The first mechanism is due to thermal motion of the ions, that cause a
smearing of the polarization charges through a Debye layer at the skin
surface. The scale of such penetration in an electrolyte with monovalent
ions of opposite charge is given by the Debye length ›20!
##EQU4##
where .di-elect cons. is the permittivity, e the elementary electric
charge, n the concentration of one of the ion species deep in the
electrolyte, and V.sub.T =kT/e is the thermal voltage (26 mV at the normal
skin temperature of 34.degree. C.); k is the Boltzmann constant and T the
absolute temperature. If the electrolyte is exposed to an external
electric field E.sub.o perpendicular to its boundary, then at
thermodynamic equilibrium the potential at depth z in the electrolyte is
approximately
V(z)=E.sub.o .delta..sub.d e.sup.-z/.delta..sbsp.d, (12)
where .delta..sub.d is the Debye length given by (11), and the voltage is
taken with respect to points deep in the electrolyte. The approximation
(12) is good if E.sub.O .delta..sub.d <<V.sub.T. From (12) one has for the
electric field
E(z)=E.sub.o e.sup.-z/.delta..sbsp.d. (13)
These results are easily derived from balancing conduction and diffusion
currents, together with the Poisson equation that relates the potential to
the charge distribution. The calculation can be readily extended to the
case of bivalent ions, and to mixtures of ions with different valences.
The above considerations for an electrolyte are applicable to the dermis,
because of its considerable fluid content. But one may apply the theory
also to the epidermis. This outer layer of the skin contains horny cells
that suppress the mobility of ions. However, the relation between mobility
and diffusivity of ions is still given by the Einstein relation.
Therefore, the equilibrium thermodynamics of ions in the epidermis is the
same as in an electrolyte. Since the ion concentration in the epidermis is
relatively small, the Debye length is relatively large; for example, for
an ion density of 10.sup.7 per cm.sup.3 and a dielectric constant of 4,
the Debye length (11) is 0.54 mm. Sensory receptors in dermal papilla that
protrude into the base of the epidermis are then subjected to the remnant
of the electric field as it penetrates from the outside, in the manner
shown by Eq. (13). If the cytoplasm of the receptor is at the same
potential as the deep body tissue, then the membrane potential at the tip
of the receptor is perturbed by the about the voltage (12), using for z
the thickness of the epidermis. Taking 0.2 mm for that thickness, and
parameters of the epidermis as in the above example, an external field of
1 V/m on the skin is found to perturb the membrane potential of the
receptor tip by about 0.4 mV.
Such a change in membrane potential is much too small to fire the nerve.
However, as pointed out by Terzuolo and Bullock in a classical paper ›25!,
modulation of the frequency of an already active neuron can be achieved
with voltages very much lower than those needed for the excitation of a
quiet neuron. Voltage gradients as small as 1 V/m across the soma were
sufficient to cause a marked change of firing of adaptive stretch
receptors of crayfish ›25!. Terzuolo and Bullock further remark ›25! that
the value of the critical voltage gradient for this effect may actually be
much smaller than 1 V/m. The 0.4 mV membrane voltage perturbation
calculated above for the example may be sufficient to cause frequency
modulation of the firing pattern of the receptors investigated by Terzuolo
and Bullock. Perhaps the same behavior occurs for other slowly adapting
mechanoreceptors that exhibit spontaneous firing, such as Ruffini endings
and Merkel cells, which are found roughly at a depth of 0.2 mm in the skin
›21, 23, 34!.
A second mechanism for penetration of the external field into the epidermis
is provided by sweat ducts. These narrow ducts are normally kept at least
partially filled by the sweat glands and capillary action. The highly
conducting thin sweat column in the duct will be polarized by the external
electric field. As a result the field will be severely distorted, causing
the equipotential surfaces to crowd together near the tips of the columns,
and dip deep into the epidermis in between the sweat ducts. As a result, a
local field that is a small fraction of the external field E.sub.O acts on
cutaneous receptors which lie in papilla that protrude into the base of
the epidermis. The associated potential must be added to that due to the
first mechanism.
Cold receptors also lie at shallow depths ›22! and exhibit spontaneous
firing, so that they need to be considered as candidates for modulation by
externally applied weak electric fields. Therefore, an experiment was
performed in which steady electric fields of up to 1 KV/m were applied to
the skin. If modulation occurs, these electric fields may induce a
sensation of skin temperature change. No such sensation was experienced.
However, there may have been rapid adaption to the electric field
stimulus, and the effect of the field on the firing pattern of cold
receptors may differ in nature from the pattern change due to temperature.
The latter possibility is suggested by the complicated coding of
temperature information, which is much more intricate than mere frequency
modulation ›26!. Therefore, the observed absence of a temperature
sensation in steady-state electric field application does not quite rule
out modulation of cold receptors by the applied external electric field.
There have been further developments, as follows.
It has been observed that lower field strengths suffice for the excitation
of sensory resonances when the skin area of dominant field application is
increased. This "bulk" effect is important for the proper use of the
invention, and can be understood as follows. The field causes a frequency
modulation of the stochastic firing of the affected afferent fibers. If
these fibers synapse, either directly or indirectly, upon a summing
neuron, then the sequence of current injection spikes into the dendrite of
the neuron will be a slightly modulated Poisson stream. For zero
modulation a Poisson distribution is expected on theoretical grounds if
the number N of synapsing afferents is large, since the afferent spike
trains add and interlace. This results in a high-frequency sequence of
charge injections, in which the features of the individual afferent spike
trains are substantially washed out, in much the same way as density
nonuniformities of a substance suspended in a fluid are removed by
stirring. The Poisson distribution is found to be a good approximation in
computer simulations with N of the order of 4000, substantially
independent of the details of the firing probability distributions for the
individual afferents. As a consequence of the Poisson distribution, the
variance as well as the mean of the number of injection spikes into the
summing neuron that occurs in a fixed time interval .DELTA.t is
.lambda.=N.function..sub.O .DELTA.t, (14)
where .function..sub.O is the average frequency of the afferent spike
train, assumed to be the same in each afferent, for simplicity. For large
N the excitatory synaptic current needs to be balanced with an inhibitory
current, lest the integrated signal by far exceeds the firing threshold
and the summing neuron is locked into a maximal firing state. The balance
requires that, in addition to N excitatory neurons, roughly N inhibitory
neurons also synapse on the summing neuron. The inhibitory current spikes
contribute to the noise, thus increasing the variance by about a factor 2.
Balanced excitatory and inhibitory activity has been recently considered
as a mechanism for rendering cortical neurons sensitive to small
fluctuations in their synaptic current; see ›35! and the references
contained therein. With modulation present, the Poisson distribution still
stands short-term, but .lambda. has now a slow sinusoidal variation with
the frequency of the applied electric field. All modulated afferents
contribute coherently to this sine wave. As a result, the signal-to-noise
ratio of the fm signal that is present in the temporal density of the
current injection spikes is proportional to mN.function..sub.o
/.sqroot.(2.function..sub.o N)=m.sqroot.(.function..sub.o N/2), where m is
the depth of the frequency modulation. The latter is expected to be
proportional to the applied external field amplitude E. Hence, one expects
the signal-to-noise ratio to be proportional to E.sqroot.(.function..sub.o
N). The fm signal is somehow demodulated by subsequent neural circuitry.
The latter contains or is followed by nuisance-guarding circuits, with the
result that the observable response to the field application exhibits an
effective intensity window. One expects the ultimate response to be a
function of the signal-to-noise ratio of the current injections into the
summing neuron, so that
observable response=function of (E.sqroot.(.function..sub.o N).(15)
Eq. (15) shows the bulk effect. For excitation of sensory resonances
through modulation of cutaneous nerves, N is roughly proportional to the
skin area A.sub.s over which the field is predominantly applied, and also
to the surface density .rho. of the affected nerves, so that in (15) one
has
N=c.rho.A.sub.s, (16)
where c is a constant. If the fm detection circuitry receives inputs from M
similar summing neurons, the results (15) and (16) still hold if N is
replaced by MN. Very shallow frequency modulation can be detected amidst
the large fluctuations occurring in the spontaneous firing of the
individual afferents, if the product MN is large. This result is helpful
in understanding the exquisite sensitivity of the human electroception
observed and discussed here. Stochastic resonance ›33! perhaps contributes
to the sensitivity as well.
The peak value (10) of the internal electric field induced by an external
field of 1 V/m with rounded square wave time dependence at a frequency
near 1/2 Hz shows that the internal field is a very small fraction of the
external field. The same conclusion holds for sinusoidal fields, for which
the internal field is easily found to be
E.sub.i =2.pi..function.T.sub.c E.sub.o, (17)
where T.sub.c is the relaxation time (1), .function. the field frequency,
and E.sub.O the external electric field. For .function.=1/2 Hz, and the
value T.sub.c given by (2), Eq. (17) gives for the internal electric field
E.sub.i =2.2.times.10.sup.-6 E.sub.o. (18)
It follows that, for the purpose of calculating the field induced on the
skin by field electrodes, the internal electric field may be neglected, so
that the subject's skin is an equipotential surface. For the configuration
of FIG. 2, the skin voltage is then determined by a capacitive voltage
divider with two capacitors, one formed by the left electrode 2 and the
apposing skin area 36', and the other formed by the right electrode 2 and
the skin area 36. If both electrodes are placed opposite the skin by a
small separation d, the electric field on the skin in the areas 36 and 36'
is approximately
E=V/2d, (19)
where V is the voltage applied between the field electrodes.
For many applications as well as for research purposes it is convenient to
use as field electrodes a doublet, because it is compact and its field can
be easily calculated for several practical settings. Referring to FIG. 8,
the doublet consists of two field electrodes 50 and 51 of identical size
and shape placed parallel and in registration with each other, and
separated by a dielectric layer 52 such as to form a parallel-plate
condensor. The dielectric may just be air. Optionally, insulating sheets
53 may be applied to the outside surfaces of the field electrodes 50 and
51, so that the electrodes, the dielectric layer and the insulating sheets
form a sandwich of five layers that are alternatingly insulating and
conductive. The dielectric and insulating sheets have a slight overlap
with respect to the field electrodes in order to provide effective
insulation. Application of a voltage between the field electrodes causes
charging of the doublet, so that electric charges of opposite sign
accumulate on the electrodes. If the applied voltage fluctuates in time,
so will the electric charge on the electrodes.
The field electrodes of the doublet are connected via conductors 54 to an
input port 55 for receiving a fluctuating voltage difference. This
connection is straightforward for the single doublet of FIG. 8, but for
multiple doublets more complicated connections may be desired, and voltage
dividers may be used as well. Such connections and voltage dividers are
provided by a distributor which charges the doublets, upon receiving a
fluctuating voltage at the input port. Examples for distributors for
multiple doublets are shown in FIGS. 9 and 10, to be discussed. The
straigthforward connections for the single doublet of FIG. 8 are seen as a
special case of a distributor.
In FIG. 8, the doublet formed by the sandwich of conductive foils and
insulating sheets has a plane shape, but the doublet may be curved or
flexible, such as to fit body contours.
Upon charging the doublet, a concentrated field arises between the field
electrodes; the condenser action is mainly due to this field. A much
weaker field occurs in the space outside the parallel-plate condenser,
this space being defined as the set of points P through which no straight
line exists that intersects the two field electrodes at points that are on
opposite sides of P. This "fringe field" is not essential for the
condenser action, but in the present invention it is used as the electric
field to which the subject is exposed. An example configuration of doublet
and subject is shown in FIG. 11, where the doublet 66 is placed near the
subject 4, such as to apply the fringe field predominantly to region 67 of
the skin. The fringe field of a charged doublet in the presence of the
subject is illustrated by several field lines, such as 65. In FIG. 11 the
doublet is oriented parallel to the nearby skin, but other orientations
may be used.
At this point the difference with Brennan ›11! should be noted. In that
patent at least part of the subject's brain region is located between the
pair of electrodes. In contrast, in our doublet the space between the
field electrodes is narrow and occupied only by one or more dielectric
layers; the subject is not exposed to the field between the electrodes,
but to the fringe field, as illustrated in FIG. 11. For the doublet, the
difference with the Brennan patent remains even if the skin area of
predominant application of the fringe field is on the head or close to the
head. The condition of avoiding substantial polarization current densities
in the brain can be met by limiting the peak external field amplitude on
the head such that the scale of the polarization density is below 70
fA/cm.sup.2. With this condition satisfied, the external electric field
will still modulate cutaneous nerves in the scalp.
Experiments have been done with a doublet placed about 10 cm from the top
of the head in an orientation parallel to the local skin. The doublet that
has 45.times.70 mm field electrodes, was contained in a small box that
also contained a generator for producing a near-sinusoidal voltage with 3
V amplitude and a tunable frequency in the range from 0.43 to 0.58 Hz. Use
of this setup as a sleeping aid over a period of about a month has been
very successful.
At distances .gamma. large compared with the doublet dimensions, the fringe
field of a doublet plus the charge displaced in the dielectric is a dipole
field with as source strength the electric dipole moment Q.delta., where Q
is the charge on one of the electrodes of the doublet, and .delta. is the
electrode separation. Using the standard approximation for the capacitance
of a parallel-plate condensor one finds .di-elect cons..sub.o VA for the
dipole moment, where .di-elect cons..sub.O is the vacuum. At distances
.gamma. that are large compared to the doublet dimensions, the dipole
field in free space has the magnitude
##EQU5##
where A is the electrode area, and V the voltage applied between the two
electrodes of the doublet. The factor b is
##EQU6##
where .theta. is the polar angle with respect to the normal to the
electrode surface, as seen from the point where the field is considered.
Eq. (20) is a good approximation if the electrode dimensions and
separation are small compared to the distance .gamma..
For the special case that the electrodes of the doublet are flat circular
discs of radius R, the fringe field on the rotational symmetry axis can be
calculated exactly in the limit of zero electrode separation. In this
limit the dipole moment density on the circular disc is uniform and equal
to .di-elect cons..sub.o V, and the field on the axis is found to be
E=(1/2)VR.sup.2 /(R.sup.2 +z.sup.2).sup.3/2, (22)
where z is the distance to the doublet. Eq. (22) expresses the field in
free space. Presence of a subject near the charged doublet causes the
field to be influenced by polarization charges induced on the subject's
skin by the field. If the doublet is small compared with the subject and
is positioned parallel to the nearby skin at a distance d that is small
compared with the dimensions of the subject, as in FIG. 11, the field at
the intersection of the doublet axis and the skin is approximately
E=VR.sup.2 /(R.sup.2 +d.sup.2).sup.3/2, (23)
as follows readily with the method of image charges ›27!, when the skin
near the doublet may be approximated as flat. For very small or zero
distance d one then finds for the central field
E=V/R, (24)
showing that, counter to intuition, the field does not become large for
small d. That is because for small d the subject's skin is at nearly the
same potential as the doublet electrode nearest the skin, by the action of
the capacitive voltage divider involved.
The approximation (23) is inadequate for doublets placed at a distance from
the subject that is considerably larger than the doublet size. The field
due to the polarization charges on the subject's skin can then be
estimated with the image charge method by representing the subject's body
as a conductive sphere. With this crude model one can calculate a
correction factor F for the maximum field on the subject's body. FIG. 12
illustrates the model for the case that the doublet is placed a distance s
from the subject, with the electrodes oriented parallel to the line of
shortest distance between doublet and subject. The subject is modelled as
a conductive sphere 69 with radius .alpha.. The doublet 70 causes electric
polarization of the sphere, such that on the sphere the total electric
field is perpendicular to the spherical surface. The maximum electric
field on the sphere can be expressed as
##EQU7##
where the factor F is read from graph 72. The angle .alpha. at which the
field on the sphere is maximum can be read from graph 71. The graphs 71
and 72 were calculated with the method of images ›27!.
For this model one can also calculate the capacitance C between the doublet
and the sphere. This capacitance determines the total polarization charge
Q on the upper half sphere of FIG. 12, that occurs in response to a
voltage V applied to the doublet,
Q=CV. (26)
The capacitance can be determined from
C=gA/.alpha., (27)
where the factor g can be read from graph 88 of FIG. 12. For a sinusoidal
field with frequency .function., the amplitude of the total polarization
current induced in the sphere is
I=2.pi..function.Q. (28)
Eqs. (27) and (28) provide estimates for the total polarization charge
induced on the skin of the subject by a nearby doublet, and the total
polarization current induced in the subject's body. These results are
valid for the case that the plane of the doublet is oriented parallel to
the shortest line between doublet and subject, as in FIG. 12. Similar
calculations can easily be done for other orientations.
In certain experiments and clinical applications there is a need for an
external electric field that is strictly confined to two selected skin
regions. Such a field can be set up with a shielded electrode pair as
depicted in FIG. 10, where field electrodes 2 and 2' of identical shape
and size are closely apposed, in parallel fashion, respectively by
electrodes 38 and 39 called shield electrodes. The latter have the same
size and shape as the field electrodes 2 and 2', and are positioned and
oriented such as to bring their contours in registration with those of the
corresponding electrodes 2 and 2'. Furthermore, a conductor 40 connects
the shield electrodes, so that they have the same potential. Electrodes 2
and 2' are connected by wires 41 to the input port 55 which is to receive
a voltage from the generator. With the generator voltage applied to the
input port 55, the voltage on the field electrodes 2 and 2' is
respectively V.sub.1 and V.sub.2. Although not shown, insulation is
applied between electrodes 2 and 38, and between electrodes 2' and 39.
Optionally, insulation is applied to the top and bottom of the two
resulting structures as well, resulting in two 5-layer sandwiches. The
latter are positioned in close proximity of the skin 37 of the subject, in
the orientation shown in FIG. 10. If the sandwiches are placed parallel
and at equal distances to the skin 37, then both the skin and the shield
electrodes have the potential (V.sub.1 +V.sub.2)/2, so that no field lines
stand between the shield electrodes 38 or 39 and the subject. It follows
that the external electric field is then confined to four narrow spaces,
viz., the space between electrode 2 and the skin 37, between electrode 2'
and the skin, between electrode 2 and the shield electrodes 38, and
between electrode 2' and shield electrode 39, except for edge fields
pouring from the edges of the narrow spaces. These edge fields extend over
a distance of the order of the electrode separation or the distance from
electrode 2 or 2' to the skin. If these separations are very small, so
will be the spatial extents of the edge fields, and the external field on
the skin then will be essentially confined to the skin areas directly
apposed by the electrodes 2 and 2'. Electrodes 2 and 2' need not be
positioned in close proximity to each other.
In the foregoing discussion the field electrodes 2 and 2' were assumed to
have the same shape, size, and distance to the skin. One can deviate from
these conditions by making adjustments in the distances at which the
shield electrodes are applied over the field electrodes 2 and 2', such as
to assure that the shield electrodes are at the same potential as the
skin. The shield electrodes 38 and 39 may be conductive foils or
conductive meshes. The conductor 40 may be a conductive foil, which may
simply be the continuation of the shield electrodes 38 and 39. If the
field electrodes 2 and 2' are deployed at a short distance from each
other, the shield electrodes 38 and 39, together with the conductor 40 may
be implemented as a single conductive foil.
The shielded electrode pair of FIG. 10 can be seen as two doublets with
opposite electric dipole moment that are connected in series, and
therefore as a special case of doublets with a distributor as discussed
above. In this case the distributor comprises the input port 55, the
connections 41 between the field electrodes and the input port 55, as well
as the connection 40 between the shield electrodes 38 and 39.
A well-designed and deployed shielded pair of field electrodes limits the
field application essentially to the skin area directly apposing the field
electrodes. Therefore, the shielded pair can be used on skin areas very
close to the head, without causing substantial polarization currents in
the brain. An important example of such deployment is localized field
application to the skin overlying the vagus nerve in the neck.
A doublet may be used also in the compact configuration wherein the field
electrodes are contained together with the generator in a single casing,
such as a small electronic project box, or the powder box of FIG. 7. The
distant fringe field can be further increased by placing a conductor in
front or behind the doublet. The conductor will then be polarized, and the
electric dipole formed by the polarization charges will boost the distant
field. A particularly effective conductor for this purpose is shown in
FIG. 13. There, the doublet 42 is apposed, at a short distance d, by a
conductive foil 46 of the same shape, size, and orientation as the
electrodes of the doublet. Another such conductive foil 47 is placed at a
distance S, parallel to foil 46, and the two foils 46 and 47 are connected
by a conductor 48. The conductor comprised of 46, 47, and 48 is polarized
by the fringe field that emanates from the doublet, so that foils 46 and
47 acquire opposite polarization charges of magnitude Q, thereby forming
an electric dipole with moment QS. The orientation of this induced dipole
is the same as that of the doublet. Hence, the foils 46, 47, the wire 48
may be seen as a "passive doublet", which boosts the distant electric
field. The boost factor us the same in all directions. For doublets of
circular shape, a short calculation that uses Eq. (24) gives the result
that the total electric dipole moment, and therefore the distant field, is
increased by at least a factor S/R+1, as compared with the field of the
original dipole by itself. It is readily seen that the same result is
obtained whether the passive doublet is placed in front or behind the
doublet i.e., in FIG. 13, respectively below or above doublet 42. In FIG.
13, the passive doublet should however not be placed on the left or right
of doublet 42, since then the dipole moment induced in the passive doublet
would have a direction opposite the dipole moment of doublet 42, so that
at large distances the electric field would be reduced rather than
boosted. The space between the foils 46 and 47 may be put to good use by
placing the generator there, so that a compact package results that can be
contained in a single small casing, similar to the one shown in FIG. 7. In
spite of its small size, such a device can generate an adequate field at
considerable distance from the subject, because of the electric dipole
moment boost by the passive doublet.
There sometimes is a need for a short-range electric field that is produced
by field electrodes placed some distance away from the subject's body.
This can be accomplished with an assembly of doublets designed such that
their combined field is asymptotically multipole, i.e., at large distances
.gamma., the potential falls off as 1/.gamma..sup.k, with k>2. The integer
k is called the order of the multipole. Such an assembly of doublets is
here called a multipole field electrode. For an assembly of doublets to be
a multipole electrode, certain conditions need to be satisfied. These
conditions are here discussed for an assembly of doublets that is
axisymmetric and lies in a plane. The produced electric field is then
axisymmetric as well, with symmetry axis, say, z. In free space the
potential for such a field has a so-called multipole expansion ›28! with
terms of the order of 1/.gamma..sup.2, 1/.gamma..sup.4, 1/.gamma..sup.6,
etc. The coefficients of these terms depend on the radii and driving
voltages of the m individual doublets that make up the assembly. The radii
and driving voltages can be chosen such that the first m-1 terms in the
multipole expansion vanish. The leading term of the expansion is then of
the order 1/.gamma..sup.2m, so that the field produced by the assembly is
asymptotically multipole of order 2m. The details of the calculation are
not shown here, but can be easily derived by those skilled in the art. The
result of the calculation is as follows.
Consider, in a plane, an assembly of m concentric circular electric
doublets, with radii R.sub.j, and voltages V.sub.j, j=1 to m. The first
m-1 terms in the multipole expansion of the electric potential produced by
the assembly vanish if
.SIGMA.R.sub.j.sup.2 V.sub.j =0, .SIGMA.R.sub.j.sup.4 V.sub.j =0, . . .
.SIGMA.R.sub.j.sup.2m-2 V.sub.j =0, (29)
with the sums taken over j=1 to m. This is a Van der Monde system ›29! that
can be solved, for any m, by a modification of the Pascal triangle for the
binomial coefficients. The modification entails starting each row of the
triangle with the row number, and completing the row by the well-known
Pascal triangle construction. One thus finds for the first row 1, for the
second row 2,1, for the third row 3,3,1, for the fourth row 4,6,4,1, etc.
For the assembly of m doublets, the modified Pascal triangle must be
completed up to row m. The voltages V.sub.j are then to be taken
proportional to the sequence of numbers in the mth row of the triangle,
with alternating signs. The squared radii, R.sub.j.sup.2, of the
individual doublet discs are to be taken proportional to the index j. The
resulting V.sub.j and R.sub.j satisfy Eq. (29), as can be verified by
substitution. The superposition of m doublet discs can be implemented in
practice by adding the voltages in the regions of overlap, and applying
these sums as driving voltages to annular doublets with radii R.sub.j-1
and R.sub.j, R.sub.O being chosen as zero. As an example for m=4, one has
a central doublet disc of radius R driven by a voltage V, an annular
doublet with inner radius R and outer radius R.sqroot.2 driven by the
voltage -3 V, an annular doublet with inner radius R.sqroot.2 and outer
radius R.sqroot.3 driven by a voltage 3 V, and an annular doublet with
inner radius R.sqroot.3 and outer radius 2 R driven by the voltage -V. In
practice the voltages are derived from an accurate resistive divider. The
above calculations give a good approximation if the electrode separations
in the individual doublets are very small compared to the distance
.gamma., so that the fraction of the areas of the electrodes that have
considerable nonuniformities in charge distribution is negligible. If the
order of the multipole field electrode is increased, the asymptotic
multipole field falls off faster, the central lobe narrows, and a larger
driving voltage is required in order to maintain the same field strength
at any far fixed point on the symmetry axis. Furthermore, finer
fabrication tolerances are required, because the multipole action is based
on the cancellation of the lower order pole contributions. The latter two
effects place a practical upper limit on the order of the multipole field
electrode.
The field of a charged doublet polarizes the adjacent doublets. This cross
coupling is unwanted, since it complicates design of the multipole field
electrode. The coupling can be kept to negligible levels by choosing the
distance between the two field electrodes of each doublet very small.
The structure of the multipole electrode of order 8 of the type discussed
above is shown in FIG. 9, as an axisymmetric assembly of individual
doublets 57, 58, 59, and 60 with symmetry axis 56. The doublet 57 has the
shape of a disc, whereas the doublets 58, 59, and 60 have annular shape.
The assembly of doublets is fastened to two adhesive sheets of insulation
61, which are stuck together in the border region 62. An insulating layer
66 is applied between the upper assembly consisting of the doublets 57 and
59, and the lower assembly consisting of the doublets 58 and 60. Each of
the doublets consists of two field electrodes, such as 63 and 64 for
doublet 57, insulated by a dielectric layer 65. Here, the distributor
involves a resistive voltage divider 68 and connections to the various
points in the doublet assembly and to the input port 55 that is to receive
a fluctuating voltage. For readability of the drawing, some of these
connections are implicitly indicated as pairs of identical letters placed
at certain connection points; such point pairs are understood to be
electrically connected.
The multipole electrode of FIG. 9 has four doublets which together cover a
geometric disc without leaving gaps. However, configurations with gaps can
be designed, by considering each gap as an annular doublet with zero
driving voltage. The coefficients R.sub.j.sup.2, R.sub.j.sup.4, etc. in
Eq. (29) are then replaced by differences of powers of the outer and inner
radii of the annular gaps, as will be evident by carrying out the
multipole expansion of the electric potential. The solution by the
modified Pascal triangle no longer holds, but the resulting equations that
express the vanishing of the first m-1 terms in the multipole expansion
can be readily solved numerically. Non-axisymmetric electric multipoles
can be designed as well, but the analysis then requires spherical
harmonics ›28!.
A multipole field electrode of order 8 has been built as a circular planar
sheet, with a central doublet of R=6.25 cm radius. In free space, the
asymptotic field has a central lobe with polar angle of 18.2.degree., and
the electric field on the symmetry axis, at distance z from the plane of
the multipole sheet, is calculated as 17.5 V(R/z).sup.9 V/m, where Vis the
driving voltage on the assembly, in volts. When the multipole is placed
near an isolated subject, the polarization charges on the subject's skin
modify the field, such as to render it perpendicular to the skin. The
field modification can be estimated with the image charge method by
modeling the subject as a conductive sphere. In an application as a
sleeping aid, the 8th order planar multipole field electrode described
above was placed under the mattress of the subject. The external field at
the point P of intersection of the multipole axis with the skin was
calculated to be a factor 2.54 times the free field value, using z=13 cm,
and a radius .alpha.=24 cm for the conductive sphere radius in the model.
Using a rounded square wave generator with a peak to peak voltage of 6 V
connected to the input port (55 of FIG. 9) of the distributor, the total
external field at point P is calculated as 183 mV/m.
The multipole field electrode produces a field with a lobe structure, so
that on the subject's skin there is a set of zones of positive and
negative field amplitudes. In order to discuss these field zones somewhat
quantitatively, it is convenient to use a model in which the skin lies in
a plane, so that the polarization effects can be expressed by a simple
version of image charges ›27!. If the multipole symmetry axis is
perpendicular to the plane, the field zones are bounded by concentric
circles centered at point P. On these circles the field vanishes, and the
field changes sign when crossing the circles. For the deployment described
above these circles are centered at point P and have the radii 3.6, 7.8,
11.0, and 12.8 cm, as follows from a calculation of the multipole field in
the vincinity of a conductive plane. On the plane, the maximum field
amplitude occurs at point P. Going from P through the concentric zones
gives for the field extrema the sequence -0.18, 0.015, -0.00017, and
5.times.10.sup.-7, all relative to the amplitude at P. The sequence of
extrema shows that the field falls off very fast indeed. Similar features
will occur in reality, where the shape of the skin deviates from a plane
at larger distances to point P as contact with the mattress is lost. The
small size of the central zone and the existence of field zones of
alternating field direction have important consequences.
First, the small size of central zone affords a sharply localized field
application, in spite of the fact that the multipole field electrode is
some distance (here 13 cm) away from the subject. For example, this is
useful in sexual excitation, which can be arranged by the subject by
taking a position on the mattress such that the central lobe of the
multipole field electrode under the mattress is aimed at the perinaeum.
Second, the modulation of cutaneous nerves in adjacent zones is 180.degree.
out of phase. The same is true for the fm signals received in
corresponding zones of the thalamus, by virtue of the somatotopic map of
the cutaneous sensory system. The resulting fine spatial scale of the
signal structure into the thalamus is expected to have consequences for
the excitation of sensory resonances.
The setup with the multipole field electrode placed under the mattress at
lumbar level has been tested as a sleeping aid for about 30 nights, with
good results.
The main lobe of the multipole field electrode may be aimed at a skin
region on the head or close to the head, as long as the brain is not
exposed to substantial polarization current densities. This condition can
be met by limiting the peak amplitude of the external field on the skin.
The field can still excite sensory resonances, by virtue of the presence
of cutaneous nerves in the skin of the head, including the scalp.
A new sensory resonance has been found near 2.4 Hz. The resonance shows up
as a sharp increase in the time of silently counting backward from 100 to
70, as fast as possible, with the eyes closed. The counting is done with
the "silent voice" which involves motor activation of the larynx
appropriate to the numbers to be uttered, but without the passage of air,
or movement of mouth muscles. The motor activation causes a feedback in
the form of a visceral stress sensation in the larynx. Counting with the
silent voice must be distinguished from merely thinking of the numbers,
which does not produce a stress sensation, and is not a sensitive detector
of the resonance. The larynx stress feedback constitutes a visceral input
into the brain and thus may influence the amplitude of the resonance. This
unwanted influence is kept to a minimum by using the count sparingly in
experiment runs. The protocol adapted in our laboratory, after extensive
trial and error, is to have experiment runs of 40 minutes duration, with
counts taken at times 0, 20, and 40 minutes into the run. In early
experiments the count was done from 100 to 70, but as experience was
gained, we switched to the more sensitive 100-60 counts. Since counting is
a cortical process, the 2.4 Hz resonance is here called a cortical sensory
resonance, in distinction to the autonomic resonance that occurs near 1/2
Hz. In addition to affecting the silent counting, the 2.4 Hz resonance is
expected to influence some other cortical processes as well. It was found
that in the long run the resonance has a sleep inducing effect. Very long
exposures cause dizziness. The frequency of 2.4 Hz raises concerns about
kindling; therefore, the general public should not use the 2.4 Hz
resonance until this concern has been addressed properly in experiments.
The sensitivity and numerical nature of the silent count makes it a very
suitable detector of sensory resonance, thereby affording several
experiments which clarify somewhat the processes involved, and provide
guidance for the proper use of the invention.
First, the experiment aimed at resolving the question whether it are the
polarization currents or the polarization charges that cause the
excitation of the 1/2 Hz autonomic resonance has been repeated for the 2.4
Hz cortical resonance, using the same field strengths applied in the same
manner to the same areas of skin, but with a sine wave instead of a
rounded square wave. The amplitude of the voltage applied to the field
electrodes was 1.45 V, resulting in an external electric field at the skin
with a maximum amplitude of 48 V/m. A frequency of 2.407 Hz was used, and
the counts were done from 100 to 60. As for the 1/2 Hz experiments
discussed, the electric field was applied to the dorsum of the feet in a
localized manner. In the first experiment the silent counts were 37 s at
the start t=0 of the run, 53 s at t=20 minutes, and 75 s at t=40 minutes,
the end of the run. The pronounced increase of counting time shows
excitation of the 2.4 Hz resonance. In the second experiment the
conditions and parameters were the same, except that the skin of the
dorsum of the feet was covered with conductive jelly and aluminum foil,
all insulated from the field electrodes. This arrangement removes the
polarization charges from the skin, whereas the polarization currents in
the skin and the body are the same as before. The counts were 32 s at t=0,
34 s at t=20 minutes, and 33 s at t=40 minutes, so that the resonance was
not excited. Comparison of the two experiments shows that the excitation
of the resonance is not due to polarization currents, but rather to
polarization charges on the skin, in agreement with the conclusion reached
above for the 1/2 Hz autonomic resonance experiments.
The magnitude of the polarization current densities in the subject is
calculated as follows. With an estimated 11 pf capacitance between the
field electrodes via the subject's body, the polarization current
amplitude comes to 241 pA. Assuming that this current is spread over a
skin area that is 10% larger than the area of the nearby field electrode,
the maximum current density in the subject's body is found to be 1.6
pA/cm.sup.2. The experiment shows that such a small current density
applied to cutaneous nerves in the dorsum of the foot is not capable of
exciting the 2.4 Hz resonance, but the accompanying polarization charges
can.
In the described experiments the polarization current through the skin is
concentrated in the skin area S immediately apposing the field electrodes,
fanning out from there into deeper lying tissue. A similar current
distribution can be set up by means of contact electrodes attached to the
skin in the area S. This affords another check on the conclusion that the
resonance is not excited by the currents, in the parameter range
considered. To perform this check, the output of the sinusoidal voltage
generator was connected to the contact electrodes via a small capacitor
which at the low frequencies presents an impedance very much larger than
that of the subject's body. The generator thereby becomes effectively a
current source. The two contact electrodes had the same size and shape as
the field electrodes in the field experiments described above, and each
was attached to the dorsum of the foot through a layer of conductive
jelly. Passing in this manner a sinusoidal current with an amplitude of 48
nA at 2.417 Hz gave rise to a 100-60 count of 35 s at t=0, 36 s at t=20
minutes, and 34 s at t=40 minutes, showing that the resonance was not
excited. The maximum current density in the skin was 321 pA/cm.sup.2,
considerably larger than in the field application discussed. Yet, the
current did not cause excitation of the 2.4 Hz resonance. It may be
remarked that the current density of 321 pA/cm.sup.2 perhaps falls outside
the effective intensity window, but that is not the case, as follows from
the next experiment discussed.
Thus far arrangements have been discussed where the modulation of afferents
by the field occurs in the receptors of afferent fibers. An essentially
different situation of interest occurs when the tissue underlying the skin
area of predominant field application is traversed by a nerve that has no
receptors in the skin area. The question then arises whether the spike
trains carried by the afferent fibers in the nerve can be modulated
without causing classical nerve stimulation. Since polarization charges on
the skin cannot have an effect in this case, any modulation occurring must
be due to the polarization currents. The origin of the currents does not
matter, so that they may as well be introduced by contact electrodes,
since this arrangement affords easier control of the current magnitude for
research purposes. An experiment was done in which currents in the tissue
were produced by contact electrodes (3M red dot.sup..gamma.m, 22.times.22
mm) placed on the skin at the back of the right knee, with a
center-to-center separation of 45 mm, such as to expose the underlying
sciatic nerve to longitudinal currents. For a sinusoidal current with a
peak density amplitude of 3.4 nA/cm.sup.2 at a frequency of 2.410 Hz, the
100-60 counts were 33 s at t=0, 54 s at t=20 minutes, and 67 s at t=40
minutes, showing excitation of the 2.4 Hz resonance. The current density
of 3.4 nA/cm.sup.2 is much too small for causing classical nerve
stimulation. No excitation was found for a similar current injection
transverse to the nerve. The experiments show that indeed, afferent fibers
in a nerve can be modulated by electric currents without undergoing
classical nerve stimulation. The current densities at which modulation
occurred were a factor 10 larger than in the previously discussed
experiment with the dorsum of the foot, wherein the 2.4 Hz resonance was
not excited. The finding that transverse currents do not excite the
resonance shows that the modulation is really done on the afferent fibers,
and not on receptors.
Similar results were found for sinusoidal current applications to the skin
over the right vagus nerve in the neck. Exposure to longitudinal currents
in the range from 200 pA/cm.sup.2 to 60 nA/cm.sup.2 caused excitation of
the 2.4 Hz resonance, but transverse currents showed no effect. The fact
that the current density of 200 pA/cm.sup.2 caused excitation of the
resonance while 321 pA/cm.sup.2 applied to the dorsum of the foot was
ineffective is understandable as due to the bulk effect discussed above;
the afferents are much more numerous in the vagus nerve than in the
affected region in the foot experiment. To get further data on this issue,
we measured the effective intensity window for excitation of the 2.4 Hz
resonance through vagal modulation with longitudinal currents applied by
contact electrodes attached to the overlying skin. The contact electrodes
used were again a pair of 3M red dot.sup..gamma.m electrodes with centers
45 mm apart. To provide longitudinal currents, the electrodes were placed
on the skin of the neck over the right vagus nerve, one above the other
along the direction of the underlying nerve. The results are shown in FIG.
14, where the time needed for the silent count from 100 to 70 is plotted
versus the amplitude of the total current passed through the subject by
the contact electrodes placed on the neck. The current was sinusoidal with
frequency of 2.466 Hz. For a fixed current amplitude, the 100-70 counting
time was measured at the beginning, t=0, of the current application, at
t=20 minutes into the experiment run, and at t=40 minutes at the end of
the run. In FIG. 14 the measured counting times are shown as graph 73 for
t=0, graph 74 for t=20 minutes, and graph 75 for t=40 minutes. The
effective intensity window is clearly seen to extend from about 100 pA to
about 200 nA. The apparant anomaly near point 74 is attributed to chemical
detuning. Dividing by the electrode area of 484 mm.sup.2, the window for
the peak current density in the subject is found to range from 21
pA/cm.sup.2 to 41 nA/cm.sup.2. These current densities are much too small
to cause classical nerve stimulation. The previously discussed modulation
mechanism involving the Debye layer in the epidermis does not apply in
this case since the modulation does not involve receptors, but rather
afferent fibers in a nerve that runs in the tissue underlying the skin
region of the current injection. It must be that longitudinal electric
currents in the tissue surrounding the vagus nerve can affect the
propagation velocity of action potentials in the afferents; fluctuating
applied currents would then result in frequency modulation of the spike
trains received by the brain. Since the propagation velocity of action
potentials along an axon is influenced by the membrane conductance, and
the latter is a sensitive function of the membrane potential ›38!, the
propagation speed can indeed be modulated by perturbations of the membrane
potential brought about by longitudinal currents superimposed on the
currents that accompany the action potential propagation, considering the
nonuniformities of conductivity in the current path distribution. The
modulations of propagation speed brought on by the currents are very
small, but they can produce a fm of signals received by the brain that
suffices for the excitation of a sensory resonance, if the frequency of
the current is chosen properly. The influencing of the action potential
propagation speed along an axon by an external electric field is of great
importance to neural science and needs to be investigated further.
Further experimentation has shown that sensory resonances can be excited by
external fluctuating electric fields with amplitudes on the skin much
lower than 1 V/m. This was already known from experiments with the 1/2 Hz
resonance which shows ptosis of the eyelids occurring at field amplitudes
of 20 mV/m on the skin, using a doublet placed some distance from the
subject, such as to expose a large area of skin to the weak field. The
discovery of the 2.4 Hz resonance with the more sensitive and quantitative
detector in the form of the silent count made measurements at even lower
field strengths possible. In these experiments a doublet with rectangular
field electrodes of 59.times.44 cm was used, oriented as in FIG. 12. The
doublet was driven by a sine wave with amplitude of 1.25 V, at a frequency
near 2.4 Hz. The doublet was placed at various distances from the subject,
about at hip height. The distances were large enough to expose a large
skin area to the field. The maximum field induced on the subject's skin
was estimated with Eq. (25), using a 24 cm radius sphere to model the
subject. The results for the silent 100-40 count are shown in FIG. 15,
where the counting time at the beginning, t=0, of the run, at t=20
minutes, and t=40 minutes is shown respectively by graphs 76, 77, and 78.
The crossover of graphs 77 and 78 is attributed to chemical detuning. A
pronounced slowing of the counting is seen to occur already at a peak
field external field amplitude of 10 mV/m. FIG. 15 shows an effective
intensity window that extends from about 8 to 190 mV/m field amplitude.
With Eqs. (26)-(28), using the values for s/.alpha. for the experiments
together with FIG. 12, the effective intensity window can be expressed in
terms of the polarization current in the subject's body; the window is
found to extend from 0.25 to 5.9 pA.
Since in the experiments the distance s of FIG. 12, measured from the
center of the doublet to the subject's body, varied from 64.5 cm to 208
cm, there was considerable variation of the skin area A.sub.s of
predominant field application, which in first approximation is
proportional to s.sub.2. Therefore it is of interest to consider the bulk
effect discussed above. Using Eqs. (15) and (16), ignoring the effect of
the surface density .rho. of cutaneous nerves, and taking .sqroot.A.sub.s
as the distance s of FIG. 12, the graphs of FIG. 15 may be replotted in
terms of the quantity E.sub.max s. The result is shown in FIG. 16, where
the graphs for t=0, 20, and 40 minutes are shown respectively as 79, 80,
and 81. The effective intensity window is seen to extend from about 17 to
123 mV, in terms of E.sub.max s. That the voltages are comparable to
membrane potentials is deemed fortuitous.
In the above experiment, different field strengths were obtained by putting
the doublet at different distances s from the subject. This resulted of
course in different areas A.sub.s of predominant field application. As a
check on the validity of Eq. (15), an experiment was performed in which
A.sub.s is fixed, and the field strength is varied by changing the voltage
applied to the field electrodes. The latter were a shielded pair as in
FIG. 10, with field electrodes of 223.times.230 mm applied to the thighs
of the subject at a distance of 5 mm from the skin. A sinusoidal generator
voltage was used with frequency of 2.408 Hz and an amplitude of 1.25 V.
Before application to the electrodes, the generator output voltage was
reduced by an adjustable voltage divider. Silent counts from 100 to 60
were done at times t=0, 20, and 40 minutes into the experiment run. The
resulting counting times are plotted as function of E.sqroot.A.sub.s,
where A.sub.s is the skin area of predominant field application, which
here is equal to the electrode area of 513 cm.sup.2. E is the electric
field on the skin apposing the field electrode; E is uniform and equal to
E.sub.max introduced above. The resulting plots are shown in FIG. 17,
where 82, 83, and 84 are respectively the counting time plots for t=0, 20,
and 40 minutes. The anomaly at the data points with E.sqroot.A.sub.s =79.5
may perhaps be attributed to chemical detuning that depresses the counting
times, but the matter needs further investigation. The data reveal an
effective intensity window that extends from 18.2to 158 mV in terms of
E.sqroot.A.sub.s. Comparison with FIG. 16 shows that the windows for the
two experiments are in rather good agreement, considering the crudeness of
the model illustrated in FIG. 12, and the neglect of differences in
surface density .rho. of cutaneous nerves in the skin areas involved; see
Eqs. (15) and (16).
In order to see the effect of surface density .rho. of cutaneous receptors,
another experiment was done in which a shielded pair of small field
electrodes was applied to the tip of the index and middle fingers of the
left hand. Since the receptor density .rho. is larger on the finger tips
than on the thighs, the values for E.sub.max .sqroot.A.sub.s in the window
are expected to be less than for the thighs experiment. The field
electrode area was 15.times.20 mm, and both field electrodes were applied
at an average distance d=0.5 mm from the skin, accounting for the distance
variation due to the ridges on the fingerprint skin. The voltage applied
to the field electrodes (2 and 2' of FIG. 10) was sinusoidal with an
amplitude of 1.15 V, reduced by a resistive divider, so that different
field electrode voltages can be applied from run to run. Counting times
from 100 to 60 are plotted in FIG. 18 versus E.sub.max .sqroot.A.sub.s.
The graphs 85, 86, and 87 show respectively the counting times at t=0, 20,
and 40 minutes into the run. The data reveal an effective intensity window
that extends from 6.6 to 54 mV, in terms of E.sub.max .sqroot.A.sub.s. The
bimodality of graphs 86 and 87 does not appear to be due to chemical
detuning, and needs to be investigated further. Comparison with FIG. 17,
where the window extends from 18.2 to 158 mV, and use of Eqs, (15) and
(16), gives for the surface densities the ratio
.rho..sub.f /.rho..sub.t =2.9, (30)
where .rho..sub.f and .rho..sub.t are respectively the receptor densities
of the affected cutaneous nerves on the finger tips and on the thighs. The
upper window limits have been used in calculating the ratio (30).
The small ratio (30) is surprising, and it may help in identifying which
type afferents are modulated. There are four different kinds of nerve
endings in fingerprint skin: bare intraepidermal terminals, intrapapillary
coils, Merkel cells, and Meissner corpuscules ›34!. The latter have poor
low frequency response. The Merkel cells are mechanoreceptors that are
innervated by slow-adapting (SA) afferents with good low frequency
response, which makes them candidates for electric field modulation with
the frequencies used. The cells sometimes are found to be most profuse
near the entry of sweat ducts into the underside of the epidermis ›34!.
Nearby Merkel cells are thus subjected to a field that is concentrated by
the conductive sweat ducts, so that they may get modulated. The matter
needs further investigation.
It is of interest to compare the ratio of upper to lower limit of the
windows, as it is independent of the receptor density .rho.; this ratio is
here called the span of the window. For FIGS. 16, 17, and 18, the span is
found to be respectively 7.2, 8.7, and 8.2. The good agreement of the
spans of the effective intensity windows for the three experiments with
different skin areas of predominant field application supports the notion
that the nuisance-guarding circuitry is the same in all three cases. In
contrast, the window span is about 2000 in FIG. 14 which pertains to
excitation not by external electric fields, but by longitudinal currents
applied with contact electrodes to the skin overlying the vagus nerve in
the neck. Our comments on this large span of 2000 are as follows. First,
the afferents in the vagus nerve report visceral information, whereas the
cutaneous nerve signals are somatosensory. Since the latter are much more
prone to nuisance signals coming from the environment, the
nuisance-guarding circuitry involved is expected to be more sensitive. It
is even somewhat surprising that such activity is indicated at all for
visceral information. Second, our modulation of the vagus nerve and
cutaneous nerves are of different nature, as evidenced by the large
current densities needed in the former case. Perhaps the modulation of the
propagation speed along the afferents involved is a strongly nonlinear
function of the applied longitudinal current density.
Although an effective intensity window has been noticed in the 1/2 Hz
experiments, the window has not been measured, mainly because we lacked a
sensitive quantitative indicator. Ptosis of the eyelids, the leading
indicator for the 1/2 Hz resonance, is not nearly as suitable a detector
as the 100-60 counting time for the 2.4 Hz resonance. In the absence of
the full window information, one can still see whether effective
intensities for the 1/2 Hz resonance fit the 2.4 Hz windows, in terms of
E.sub.max .sqroot.A.sub.s. For the 1/2 Hz cases we take two experiments
with setups that have given satisfactory results as sleeping aids. The
first of these is illustrated by FIG. 1, with the peak external electric
field amplitude on the skin estimated as 1 V/m. With the area A.sub.s of
predominant field application estimated as 400 cm.sup.2, the product
E.sub.max .sqroot.A.sub.s comes to 200 mV. The second experiment involves
a doublet of 16 cm.sup.2 area driven by 3 V peak to peak, and placed at a
distance s=30 cm from the subject's thighs. Use of Eqs. (25) and FIG. 12
gives for the maximum electric field on the skin E.sub.max =12 mV/m, so
that one has E.sub.max .sqroot.A.sub.s =4 mV, using .sqroot.A.sub.s =s.
The E.sub.max .sqroot.A.sub.s values of 200 mV and 4 mV for these 1/2 Hz
resonance cases can perhaps be reconciled with the 2.4 Hz resonance window
of FIG. 16, considering differences in the density .rho. of affected
cutaneous receptors in the skin areas of predominant field application
involved. This result supports the notion that the nuisance-guarding
circuitry is the same for the 1/2 Hz and 2.4 Hz resonances. Further
experiments are needed to settle the question.
For a sinusoidal external field the polarization current density in the
skin has approximately the amplitude
j=2.pi..function..di-elect cons..sub.O E.sub.O, (31)
where E.sub.O is the external field on the skin, .function. the field
frequency, and .di-elect cons..sub.o the permittivity of free space. For
the 1/2 Hz experiment discussed in regard to Eqs. (4)-(9), the current
density amplitude (31) comes to 2.8 fA/cm.sup.2. This value is of course
very much smaller than the peak current density of 17 pA/cm.sup.2 given by
(9) for the rounded square wave. It has been observed that, in weak field
experiments with cutaneous nerves, sine waves excite the resonance just as
well as square waves of the same amplitude, rounded or not. This is
consistent with our conclusion that it are the polarization charges that
cause the modulation of the cutaneous nerves, not the polarization
currents. Since the polarization currents constitute a foreign intrusion,
sine waves, with their mimimum polarization currents, are to be preferred
from a neurological point of view.
Excitation of the 1/2 Hz resonance is possible with large external electric
fields, up to 10 KV/m, produced by placing insulated field electrodes
directly on the skin of the thighs. In this arrangement, a sweat layer
quickly develops between the skin and the field electrode insulation. This
highly conductive layer removes the polarization charges from the skin so
that the mechanism that relies on the Debye smearing of the polarization
charges in the epidermis cannot operate. Therefore, the modulation of
cutaneous nerves in this case must be due to polarization currents. For
the rounded square wave used, the peak polarization current density in the
skin apposing the field electrodes is found to have an amplitude of about
100 nA/cm.sup.2. This current density lies somewhat outside the window of
FIG. 14, which ranges from 21 pA/cm.sup.2 to 41 nA/cm.sup.2, in terms of
the current density. The discrepancy is believed to be due to the
difference in the density of afferents for the two cases. Since the
afferents of the cutaneous nerves in the dermis are oriented roughly
perpendicular to the skin surface, the local polarization current is
longitudinal with respect to the afferent fibers, so that one expects the
afferents to be subject to modulation by the currents, at least by virtue
of the action potential propagation speed effect discussed. In addition,
the cutaneous receptors may also respond to the large polarization
currents. The modulation of cutaneous nerves by the large external field
of 10 KV/m in the presence of a sweat layer between skin and field
electrode insulation is thereby understood to about the same extent as the
other modulation situations. It is emphasised that the polarization
current density of 100 nA/cm.sup.2 is still much too small to cause
classical nerve stimulation.
Dominant frequencies appropriate for the excitation of sensory resonances
discussed lie near 1/2 Hz and 2.4 Hz. Additional sensory resonances may be
found, with frequencies up to perhaps 45 Hz.
Strong fields applied to areas of skin overlying nerves may be used for
modulating afferent fibers in these nerves, thereby providing a method for
manipulation of the nervous system via visceral afferents, as in the vagus
nerve. The method differs from that of Wernicke et al. ›36! and from that
of Terry et al. ›37!, in that it employs field electrodes rather than
contact electrodes, so that it is noninvasive, and there is no reliance on
classical nerve stimulation, so that current densitites smaller by a
factor 50000 suffice. Furthermore, the present invention uses excitation
of sensory resonance. In our experiments, a shielded pair of insulated
field electrodes is placed on or adjacent to the skin such that the line
connecting their centers is roughly parallel to the underlying nerve,
afferents of which are to be modulated. The field strength needed for the
excitation of sensory resonances can be calculated from (31) if the
necessary current densities are known. For the excitation of the 2.4 Hz
resonance through the vagus nerve, these current densities can be
determined from FIG. 14; accounting for the electrode area of 484
mm.sup.2, the window extends from 21 pA/cm.sup.2 to 41 nA/cm.sup.2. Using
(31), the corresponding field strengths for a sine wave are found to range
from 3.8 KV/m to 7.6 MV/m. A low-voltage sine wave generator suffices for
the production of fields in a low part of this range, if the insulated
field electrodes are placed directly on the skin. For instance, with
insulating tape 0.076 mm thick (3M Scotch.sup..gamma.m Mailing Tape), a
voltage amplitude of 1 V gives a field of 13.2 KV/m.
Strong-field experiments have been conducted on the sciatic nerve
underlying the skin on the back of the knee, using an insulated doublet of
60.times.42 mm area. With the doublet positioned in the skin fold of the
bent knee, and an 162.times.135 mm insulation sheet provided such that the
polarization currents cannot be shortened by apposing skin of calf and
thigh, the sciatic nerve was exposed to longitudinal polarization currents
of the order of 50 pA/cm.sup.2, caused by fields of about 3.7 KV/m set up
by a sine wave voltage of 1.13 V amplitude at a frequency of 2.414 Hz. The
100 to 60 counting times were 34 s at t=0, 54 s at t=20 minutes, and 59 s
at T=40 minutes, showing that the 2.4 Hz resonance was excited.
A similar experiment was done in the right armpit, exposing the ulnar nerve
to longitudinal polarization currents that were caused by the 60.times.42
mm doublet inbedded in the 162.times.135 mm insulation sheet discussed
above, using the same voltage amplitude and frequency as before. The
100-60 counting times were 33 s at t=0, 57 s at t=20 minutes, and 57 s at
t=40 minutes, showing excitation of the 2.4 Hz resonance.
Finally, a strong-field experiment was done on the right vagus nerve in the
neck, using a shielded pair of field electrodes of 22.times.22 mm area, at
a center-to-center distance of 45 mm, oriented such as to expose the nerve
to longitudinal polarization currents. The field electrodes were driven by
a sinusoidal voltage with an amplitude of 1.13 V and a frequency of 2.414
Hz. The 100-60 counting times were 34 s at t=0, 68 s at t=20 minutes, and
74 s at t=40 minutes, showing excitation of the 2.4 Hz resonance. In spite
of the rather close proximity of the skin area of predominant field
application, the brain was not subjected to substantial polarization
current densities, by virtue of the strict field localization by the
shielded field electrode pair.
The experiments discussed show that there are two regimes of afferents
modulation by an electric field applied to a selected skin area. The first
regime involves modulation of cutaneous sensory receptors by polarization
charges in the skin, and is therefore called charge modulation. In the
second regime the polarization currents are strong enough to cause
modulation of the propagation speed of action potentials along axons
exposed to the currents, so that the regime is called current modulation.
In both regimes, the polarization currents are much too weak to cause
classical nerve stimulation. Sensory resonances can be excited in both
regimes, but the effective intensity windows have different spans. In the
charge modulation regime, the window extends roughly from 20 mV to 140 mV
in the parameter E.sub.max .sqroot.A.sub.s, to be adjusted for different
densities of the affected cutaneous receptors. In the current modulation
regime, the effective intensity window extends roughly from 21 pA/cm.sup.2
to 41 nA/cm.sup.2, to be adjusted for the number of affected afferents in
the nerve exposed to the polarization currents. The span of about 2000 for
this window compared to about 8 for the charge modulation regime shows
that different mechanisms operate in the two regimes. Current modulation
is suitable for manipulation of the nervous system through visceral or
somatosensory afferents in large nerves that are, at places, capacitively
accessible through the skin, such as vagus and sciatic nerves. In these
cases, the application of external fields can be done with a shielded pair
of field electrodes, placed on the overlying skin in the direction of the
nerve. When used properly, the shielded electrode pair assures that the
field is applied strictly to the underlying skin, without exposing more
distant regions of the body, such as the brain, to substantial
polarization currents. The field strengths appropriate for exitation of
sensory resonances in the two regimes differ by a large factor; for charge
modulation, typical fields on large skin areas range from 10 to 200 mV/m,
whereas for the current modulation the fields, naturally for localized
small skin area exposure, are of the order of kilovolts per meter. For
both regimes, the proper fields can be produced by the same low-voltage
generator, simply by using different field electrodes and deployment. The
doublet placed some distance from the subject is particularly suitable for
charge modulation of cutaneous receptors over large skin areas, whereas
the shielded pair is the field electrode configuration of choice in the
current modulation regime, although a single doublet may be used for the
special case where it can be completely surrounded by the subject's skin.
The method is expected to be effective also on certain animals, and
applications to animal control are therefore envisioned. The nervous
system of mammals is similar to that of humans, so that sensory resonances
are expected to exist, albeit with somewhat different frequencies. The
disposition toward the 1/2 Hz resonance is thought to have its origin in
the fetal state, developed by the rythmical sensations caused by the
mother's walk, associatively coupled with hormone concentrations. For
mammals, one expects a resonance of this type at about the frequency of
the mother's relaxed walk. Accordingly, in the present invention, the
subjects are mammals.
The invention is not limited by the embodiments shown in the drawings and
described in the specification, which are given by way of example and not
of limitation, but only in accordance with the scope of the appended
claims.
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