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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,
VOL. 44, NO. 3. MARCH 1997, pp. 196208
Sensitivity Distributions of EEG
and MEG Measurements
Jaakko Malmivuo,* Senior Member IEEE, Veikko Suihko and
Hannu Eskola
Abstract  It is generally believed that because
the skull has low conductivity to electric current but is
transparent to magnetic fields, the measurement sensitivity of
the magnetoencephalography (MEG) in the brain region should be
more concentrated than that of the electroencephalography
(EEG). It is also believed that the information
recorded by these techniques is very different. If this were
indeed the case, it might be possible to justify the cost of
MEG instrumentation which is at least 25 times higher than
that of EEG instrumentation. The localization of measurement
sensitivity using these techniques was evaluated
quantitatively in an inhomogeneous spherical head model using
a new concept called halfsensitivity volume (HSV). It is
shown that the planar gradiometer has a far smaller HSV than
the axial gradiometer. However, using the EEG it is possible
to achieve even smaller HSV's than with wholehead planar
gradiometer MEG devices. The microsuperconducting quantum
interference device (SQUID) MEG device does have
HSV's comparable to those of the EEG. The sensitivity
distribution of planar gradiometers, however, closely
resembles that of dipolar EEG leads and therefore, the MEG and
EEG record the electric activity of the brain in a very
similar way.
Index Terms  Bioelectromagnetism,
electroencephalography, magnetoencephalography.
Manuscript received September 28, 1995;
revised October 17, 1996. This work was supported by the
Academy of Finland and the Ragnar Granit Foundation.
Asterix indicates corresponding author.
*J. Malmivuo is with the Ragnar Granit Institute, Tampere
University of Technology, FIN33101 Tampere, Finland (email:
jaakko.malmivuo@tut.fi).
V. Suihko and H. Eskola are with the Ragnar Granit
Institute, Tampere University of Technology, FIN33101
Tampere, Finland.
I. INTRODUCTION
WHEN electrically active tissue
produces a bioelectric field, it simultaneously produces a
biomagnetic field. Thus the origin of both the bioelectric and
the biomagnetic signals is the bioelectric activity of the
tissue.
Magnetic detection of the bioelectric activity introduces
both technical and bioelectromagnetic
differences compared to the electric method.
One technical advantage of
the magnetic method is that biomagnetic signals may be
detected without attaching electrodes to the skin.
Furthermore, superconducting SQUID detectors are capable of
detecting dc currents. On the other hand, biomagnetic
technology needs, especially in brain studies, very expensive
instrumentation and a magnetically shielded room. Their cost
is at least 25 times that of electroencephalography (EEG)
instrumentation
[24].
Bioelectromagnetic differences include differences
in the information contents of the electric and magnetic
signals and in the abilities of these methods to concentrate
their measurement sensitivity or to localize electric sources.
The relative merits of the EEG and magnetoencephalography
(MEG) have been a subject
of very controversial discussion including articles on
scientific experiments [2], [4], [6], scientific
discussions [24], and editorial articles
[5]. With this paper we
participate in this discussion. The results of this paper are
calculated on the basis of the theory we have published
previously [11]  [13], [21].
II. BIOELECTROMAGNETIC BACKGROUND
A. The concept of Lead Field
The bioelectromagnetic differences between EEG and MEG may
be explained by the different sensitivity distributions of
electric and magnetic measurement methods [13]. We have used
the lead field approach to calculate the sensitivity
distributions of the EEG and MEG leads. The lead field is an
electric current field in the volume conductor generated by
feeding a unit current to the lead. (Because the volume
conductor is not superconducting, in magnetic leads an
alternating current having a unit time derivative is used.)
According to the reciprocity theorem of Helmholtz [9], the
current field produced in this manner in the volume conductor
is identical to the distribution of the sensitivity of the
lead.
B. Differences in the Information Contents of the EEG and
the MEG
The initially optimistic view of the new information
content of magnetic recordings was based on consideration of
Helmholtz's theorem which states: "A general vector field,
which vanishes at infinity, can be represented as the sum of
two independent vector fields; one that is irrotational (zero
curl) and another which is solenoidal (zero divergence)."
These vector fields are often referred to as the "flow
source" and the "vortex source", respectively.
In an idealized case where the head is modelled with
concentric conducting spheres it can be shown that the
electric field generated by the current sources of the brain
arises from a flow source and the associated magnetic field
from a vortex source. In the beginning of biomagnetic research
it was believed that because of the Helmholtz Theorem, these
two fields are independent and that as much new information
can be obtained from magnetic recordings as is already present
in electric recordings. However, experimental studies have
demonstrated that these signals look very much the same and
are not fully independent. This apparent contradiction can be
resolved in the following way [13].
The sensitivity of a lead system which detects the dipolar
term of the flow source consists of three orthogonal
components, each of which is linear and homogeneous. The
orthogonality means that none of them can be obtained as a
linear combination of the other two. Thus, the three
sensitivity distributions are fully independent. However, the
electric signals each lead records cannot be completely
independent because each represents a different aspect of the
same volume source.
Similarly, the sensitivity distribution of a lead system
for the detection of the dipolar term of the vortex source
also has three orthogonal components. Each component can be
represented by a set of concentric circles such that the lead
sensitivity is always tangential to the symmetry axis. The
magnitude of the sensitivity is proportional to the radial
distance from the symmetry axis. Again, because the
sensitivity distributions of these three components are
orthogonal, none of them can be constructed as a linear
combination of the other two. Thus, all three magnetic
sensitivity distributions are also fully independent. However,
as before, the three signals detected by the magnetic leads
are not fully independent because each represents a different
aspect of the same volume source.
It is now possible to resolve the paradox involving
Helmholtz's Theorem. What the Helmholtz Theorem expresses is
not the independence of electric and magnetic signals, but the
independence of the sensitivity distributions of the
recordings of the flow and vortex sources, i.e., the electric
and magnetic lead fields. It indicates that the three electric
lead fields are orthogonal to the three magnetic lead fields.
However, the six signals, measured by the dipolar electric and
magnetic leads cannot be completely independent as they all
arise due to different aspects of the underlying current
source where the activation of the cells is strongly
interconnected.¹ On the other hand, if
the sensitivity distributions of two detection methods 
regardless of whether they are electric or magnetic  are
identical in the source region, the signals and their
information contents are also identical.
¹ We may illustrate this principle with
a mechanical analog: Though we live in a threedimensional
world, the movement of a body is not restricted to
movement in three dimensions. In addition to the linear
movement in the directions of the three coordinate axes, a
body may also rotate around these three coordinate
axes. These six directions are mutually independent and are
analogous to the sensitivity distributions of the measurement
of dipolar electric and magnetic sources.
C. Ability of a Lead to Concentrate its Measurement
Sensitivity
Although the geometric form of certain electric and
magnetic leads might be similar, if one of these had its
measurement sensitivity concentrated in a smaller region,
i.e., were capable of measuring a source region with smaller
dimensions or of localizing an equivalent dipole with better
accuracy, it would be considered superior for brain research.
Localization of a source is not possible with a lead whose
sensitivity is homogeneously distributed. Such a lead can
be used only for determining the magnitude and orientation
of the source. Therefore the electric and also magnetic
leads used for localizing the source have forms different
from those described in the previous section.
D. Application of the Results to Electric and Magnetic
Stimulation
Because of reciprocity, the sensitivity distributions of
electric and magnetic leads can be directly applied to
electric and magnetic stimulation. In that case the
sensitivity distributions can be understood as stimulation
energy distributions. This is easy to understand because what
is done when calculating the lead fields is actually feeding a
unit current to the lead which can be thought of as a
stimulating current.
In practice the physical dimensions of the coils in
magnetic stimulation are much larger than those used in
measuring the biomagnetic fields. Therefore, the results of
this paper concerned with the calculations of magnetic lead
fields are not as directly applicable to stimulation problems
as are those of the electric lead fields.
III. METHODS
A. The Concept of HalfSensitivity Volume
To investigate the EEG and MEG detectors' ability to
concentrate their measurement sensitivity we use the concept
halfsensitivity volume (HSV). The HSV is the volume of
the source region in which the magnitude of the detector's
sensitivity is more than one half of its maximum value in the
source region [13]. If a source is
homogeneously distributed,
the smaller the HSV is, the smaller is the region from which
the detector's signal originates.
In comparing the EEG and MEG detectors' merits the
criterion has usually been either their accuracy in localizing
a source dipole or in differentiating between two nearby
dipoles [23]. In a clinical measurement,
however, a
neurologist is interested in measuring the electric activity
of brain tissue from a limited region. That is a volume
source, not a discrete dipole. These are, of course,
mathematically related concepts.
B. Head Model
Lead fields for the EEG and MEG leads were calculated in
the spherical head model introduced by Rush and Driscoll [17], Fig. 2(a).
It
includes three concentric spheres with the radii
r t = 9.2 cm, r
s = 8.5 cm, and r
b = 8 cm
bounding the regions of the scalp, skull, and brain,
respectively. The conductivities of the scalp and brain
regions are sigma t = sigma
b = 0.45
(Ohm·m)1
and that of
the skull is 80 times smaller being sigma
s = 0.0056
(Ohm·m)1 . When
evaluating the effect of the distance between the cortex and
the skull on the HSV's and the maximum sensitivities we used a
model with four concentric spheres.
Then the radius of the sphere bounding the brain was r
b
= 7.8 cm and 7.6 cm. The sphere representing the cerebrospinal
fluid (CSF) had three times the conductivity of the brain and
the scalp being sigma c = 1.35
(Ohm·m)1.
This relative value of the conductivity of
CSF has been generally used in modelling work like in [1], [17],
[19]. Though the absolute values of the
conductivities in those
works differ from those of the original paper of Rush and
Driscoll [17], the conductivity ratios
are the same. The
results of this paper depend only on the conductivity ratio
(excluding the absolute value of the maximum sensitivities).
A spherical model was selected because of its mathematical
simplicity and because it may be considered accurate in a
limited region. For coils which are coaxial with the
spherical model, the lead fields in the brain region are not
affected by the inhomogeneities of the model due to
cylindrical symmetry. The equations for calculating
electric lead fields and halfsensitivity volumes in a four
concentric spheres model is given in the Appendix.
C. Electric Leads
The electrodes were assumed to be point electrodes. The
difference in results between point electrodes and real EEG
electrodes with a radius of a few millimeters was found to
be negligible [22]. The electric leads
included two and
threeelectrode leads. In the threeelectrode leads, the
third electrode was added midway between the two other
electrodes forming one terminal, and the lateral electrodes
were connected together to form the other terminal. (High
input impedance amplifiers are, of course, needed after the
electrodes before the connection is made.) This electrode
configuration produces a more radially oriented sensitivity
distribution.
For EEG leads the HSV was calculated as a function of
electrode separation,
Fig. 1(a) and 1(b).
The electrode separation is expressed as an angle between the
electrodes in the spherical model or as a distance along the
surface of the model.
The equations for calculating the electric lead fields and
HSV's can be found from [16], [17], [21], [22].
Fig. 1. Measurement configurations and
dimensions for electric and magnetic leads: (a) twoelectrode
electric lead, (b) threeelectrode electric lead, (c) axial
gradiometer, and (d) planar gradiometer.
D. Existing MEG Measurement Systems
In biomagnetic measurements two kind of detectors are
used. These are axial and planar gradiometers.
Two different kinds of measurement systems are used in the
most advanced MEG experiments. Clinicaltype measurements
are made with a wholehead mapping system which has a
very large number of channels (more than 100) in a helmetlike
dewar. Regardless of whether the detectors in the whole
head system are axial or planar gradiometers, differences
between signals from adjoining channels are usually
calculated during signal analysis. Thus, multichannel axial
gradiometer systems actually operate like planar
gradiometers. The coil radii in wholehead systems are
usually about 10 mm. The measurement distance of the coils
from the scalp is at least 20 mm and because patients have
different head sizes, it may often be considerably larger.
Another important MEG instrument design is the
microSQUID [3] in which the
detector coil is situated
in the vacuum space allowing measurements at very small
measurement distances, being down to 1.5 mm from the scalp.
The
coil radius is approximately 1 to 2 mm. Such a device has only
a few channels and it can be used only in a limited region of
the head at a time.
E. Magnetic Leads
In our calculations the axial gradiometer coil
radius was 10 mm. The distance of the detector coil from the
scalp was 20 mm being thus 32 mm from the surface of the
brain. These dimensions are typical of wholehead multichannel
MEG devices. The HSV was calculated as a function of the
baseline (coil separation in the radial direction),
Fig. 1(c).
In MEG measurement devices the baselines usually vary between
30 and 100 mm. As discussed above, multichannel MEG devices
built from axial gradiometers actually operate as planar
gradiometers. Therefore, these calculations have more
theoretical than practical value.
In the planar gradiometer calculations the coil
radius was either 10 mm or 1 mm. For the 10 mm coil the
measurement distance from the scalp was 20 mm, representing
the
wholehead MEG devices. The 1 mm coil radius represents the
microSQUID device. For the measurement distance, values
between 20 mm and 0 mm were used. The 0 mm distance is a
theoretical minimum which is impossible to achieve with a
superconducting device. Decreasing the coil radius below 1
mm would not significantly change the shape of the lead
field at the measurement distances used [13]. The HSV was
again calculated as a function of the baseline,
Fig. 1(d).
The coils were coaxial with the spherical head model and
the baseline could be expressed as an angle between the
coils or distance along the scalp. The equations for
calculating the magnetic lead fields are found from [10], [11], [13].
IV. RESULTS
A. The Forms of the Lead Fields of Electric and Magnetic
Leads
The lead fields for twoelectrode leads with
180°,
60° and 20° electrode separations are shown in
Fig. 2(a),
(b) and
(c).
The lead fields are displayed with lead field current flow
lines (thin solid lines).² The
illustration also includes the isosensitivity lines (dashed
lines). The HSV's are indicated with shading. The insulating
effect of the skull causes the sensitivity to distribute quite
homogeneously within the brain region. At large electrode
separations the sensitivity is directed mainly radially and at
small electrode distances mainly tangentially to the head.
Fig. 2. The EEG lead fields for twoelectrode
leads with (a) 180°, (b) 60° and (c) 20° electrode
separations.
The thin solid lines represent the lead field current flow
lines. The dashed lines represent the isosensitivity surfaces.
The HSV's are shown with shading.
² Note that in addition to representing
the path of certain electrons, the lead field current lines
represent the
current density. Thus, the space between two lines represents
a certain amount of current. Because the volume conductor
thickness is larger in the center, the current density
decreases more than it would decrease only on the basis of its
width. Therefore, some of the lines have to end in the volume
conductor region. If the thickness of the volume conductor
were constant, all current lines would be continuous.
The lead field for the threeelectrode lead is
presented in
Fig. 3.
The sensitivity is mainly radial
underneath the central electrode in the region of the HSV.
This holds true at all electrode separations although the lead
field current flow lines spread more when the electrode
separation is small. When the separation of the distal
electrodes in the threeelectrode lead reaches 360°, it is
identical to the twoelectrode lead with 180° electrode
separation.
Fig. 3. The EEG lead field for a
threeelectrode lead.
Fig. 4 illustrates the lead field
for an axial
gradiometer. It has a tangential sensitivity distribution
throughout the brain region. The sensitivity is zero at the
symmetry axis. This is called zero sensitivity line [8]
and it is represented by a thick dashed line. The sensitivity
increases as a function of the radial distance from the
symmetry axis.
Fig. 4. The lead field for an axial
magnetometer with 10 mm coil radius and 20 mm measurement
distance from the scalp. The lead field, shown with thin solid
lines, is everywhere tangential to the head model and
circulates around the symmetry axis which is drawn as a thick
dashed line. The sensitivity is zero on the symmetry axis and
it is therefore called the zero sensitivity line. The thin
dashed lines represent the isosensitivity surfaces.
Fig. 5(a) and
(b)
illustrate the form of the lead field for a
planar gradiometer in two orthogonal planes. Because
all magnetic leads in spherical volume conductors are
tangentially oriented, the planar gradiometer also has a
sensitivity distribution tangential to the spherical head
model surface. Because the coil configuration is
quadrupolar when the baseline is small, the sensitivity has
its maximum value under the common center of the two coils.
The sensitivity is linear in the region of the HSV. In
Fig. 6 this is illustrated with lead
sensitivity vectors
calculated in an infinite homogeneous volume conductor at
two planes
[14], [15].
Fig. 5.The lead field
for a planar gradiometer with 10 mm coil radii and 20 mm
baseline shown in two planes: (a) in the plane of the coil
axes and (b) in the plane normal to that. The approximated
lead field is shown with thin solid lines. It is everywhere
tangential to the head model and has a quadrupolar form. The
thin dashed lines represent the isosensitivity surfaces. The
thick dashed line is the zero sensitivity line.
Fig. 6. The lead field for a planar
gradiometer in a plane at a distance of (a) one coil radius
and (b) three coil radii from the coil plane. In (b) the lead
field current density vectors are multiplied by factor of 7.2,
compared to (a) to make them observable. This result is
calculated for an infinite homogeneous volume conductor.
With electric leads it is possible to detect both radially
and tangentially oriented sources. Because the lead field
flow lines of all magnetic leads are always tangential to
the spherical volume conductor, the magnetic leads detect
only sources oriented tangentially to the head. Thus, from
the three orthogonal components of every source, all three
can be detected with electric leads but only the two
tangential ones can be detected with magnetic leads; see
Fig. 7.
Fig. 7. The EEG is sensitive to all the three
components of the electric activity of the brain. The MEG is
sensitive only to the two tangential components.
B. HalfSensitivity Volumes of Electric and
Magnetic Leads
1) Display of the Results: The HSV's for electric
and magnetic leads are displayed as a function of detector
separation in Fig. 8. The detector
separation is given both in
degrees and in circumferential distance on the scalp. For
axial gradiometers the baseline is given on the same
separation scale, though the distance between the coils is not
measured along the scalp but in the radial direction. The
HSV's are given in cm3 of brain region volume.
Fig. 8(a)
illustrates the results for baselines 0°  180°. The
most interesting region, that where the baselines are 0° 
20°, is illustrated in
Fig. 8(b).
Fig. 8.(a) The HSV's of two and
threeelectrode EEGleads and axial and planar gradiometers.
The gradiometers have a measurement distance of 20 mm from the
scalp and coil radii of 10 mm. Arrows indicate the electrode
distances for a 21electrode EEG system (d = 72 mm )
and an electrode system having an electrode distance of half
of that (d = 36 mm). The most interesting region where
the electrode distance/gradiometer baseline is 0° 
20° is magnified.
(b) The HSV's of two and threeelectrode EEG leads and planar
gradiometers for electrode distance/gradiometer baseline
0°  20°. The gradiometers have coil radii of 10 mm
and 1 mm. The measurement distance for the 10 mm coil is 20
mm. For the 1 mm coil the measurement distances are 20, 15,
10, 5, and 0 mm. (The axial gradiometer baseline is not
commensurable with the planar gradiometer baseline and the EEG
lead separation, but for simplicity the HSV of the axial
gradiometer is plotted in the same coordinates.)
2) HalfSensitivity Volumes in the Standard Head
Model: With the twoelectrode lead at 1°
separation an HSV of 1.2 cm³ is obtained. Then it
increases as a function of separation having its maximum at
about 60° separation. From there it decreases slightly,
being 25 cm³ at 180° separation; see
Fig. 8
and Table I.
TABLE I.
HSV OF TWO AND THREEELECTRODE EEG LEADS AND
AXIAL AND
PLANAR GRADIOMETER MEG LEADS WITH h = 20 mm, r =
10 mm GIVEN IN [cm³].
Separation 
EEG 
MEG 
2electr. 
3electr. 
Axial 
Planar 
20° 32 mm 
8.0 
2.4 
39 
5.6 
10° 16 mm 
2.8 
0.67 
31 
3.8 
5° 8.0 mm 
1.5 
0.3 
26 
3.5 
1° 1.6 mm 
1.2 
0.21 
22 
3.4 
At small baselines the HSV of the threeelectrode
lead is 0.2 cm³, i.e., 1/6 of the twoelectrode lead.
The HSV increases monotonically as a function of electrode
separation. When the electrode separation reaches 180° the
HSV is equal to that of the twoelectrode arrangement.
The HSV of an axial gradiometer with h = 20
mm and r = 10 mm has its minimum at minimum coil
separation and increases as a function of coil separation,
approaching that of a single coil magnetometer. At 1.6 mm coil
separation, the HSV of the axial gradiometer is 22 cm³,
see Table I. At 300 mm coil
separation it is 61 cm³.
At small coil separations the HSV of a planar gradiometer
with h = 20 mm and r = 10 mm is much smaller
than that of the axial gradiometer, being 3.4 cm³ at
1° coil separation, as shown in
Table I. At larger than
about 20° separation the planar gradiometer HSV starts to
increase rapidly and at very large separation it is about
twice that of the axial gradiometer.
Decreasing the planar gradiometer coil radius to r
= 1 mm decreases the HSV at 1° coil separation
approximately 20% to 2.7 cm³, as illustrated in Fig. 8(b)
and
Table II.
Decreasing the measurement distance to h
= 15, 10, 5, and 0 mm decreases the HSV at 1° coil
separation to 1.7, 0.97, 0.48 and 0.16 cm³, respectively.
As discussed earlier, the measurement distance h = 0 mm
cannot be achieved with superconducting technology, but it
represents the theoretical minimum measurement distance.
TABLE II.
HSV OF PLANAR GRADIOMETERS WITH h = 0 ...
20 mm, r = 1 mm GIVEN IN [cm³].
Separation 
Gradiometer coil distance 
20 mm 
15 mm 
10 mm 
5 mm 
0 mm 
20° 
5.0 
3.8 
3.0 
2.4 
2.3 
10° 
3.2 
2.2 
1.4 
0.8 
0.41 
5° 
2.8 
1.8 
1.1 
0.55 
0.19 
1° 
2.7 
1.7 
0.97 
0.48 
0.16 
3) Effect of Skull Conductivity on the Halfsensitivity
Volumes:Some uncertainty exists in the literature
concerning the conductivity of the skull. We investigated the
effect of the skull conductivity on the HSV's of the
electric leads by decreasing it by 25% from 1/80 to
1/100 times the conductivities of the brain and the scalp.
These results are illustrated in
Fig. 9 and
Table III.
Below 5° electrode separation, its effect on the HSV was
marginal. At 20° electrode separation the HSV was
increased only about 10%.
Fig. 9. The effect of skull conductivity on
the HSV's of the two and threeelectrode EEG leads. The
results are calculated with skull conductivities of (1/80)
sigma b and (1/80)
sigma b where
sigma b
is the conductivity of brain (and scalp).
TABLE III.
EFFECT OF SKULL CONDUCTIVITY ON THE HSV OF TWO
AND THREEELECTRODE EEG LEADS.
HSV'S ARE GIVEN IN [cm³] WITH (1/80)
sigma b AND (1/100)
sigma b SKULL
CONDUCTIVITIES.
Separation 
2electrode EEG 
3electrode EEG 
(1/80)sigma b 
(1/100)sigma b 
(1/80)sigma b 
(1/100)sigma b 
20° 
8.0 
8.5 
2.4 
2.6 
10° 
2.8 
3.0 
0.67 
0.89 
5° 
1.5 
1.5 
0.3 
0.3 
1° 
1.2 
1.2 
0.21 
0.22 
In a spherical model the skull conductivity does not have
any effect on the lead fields of the magnetic leads.
4) Effect of the distance between the cortex and the
skull on the halfsensitivity volumes: In the real head
the cortex does not touch the skull but there is a space
filled by cerebrospinal fluid. We investigated the effect of
the distance between the cortex and the skull (i.e., the
cerebrospinal fluid) by using values 0 mm, 2 mm and 4 mm to
represent this distance. We used for the cerebrospinal fluid
the conductivity of three times that of the brain being
sigma c =
1.35 (Ohm·m)1. The
corresponding HSV's for the electric and magnetic leads are
shown in Fig. 10 and
Table IV.
The effect is quite
remarkable in the electric leads. At 1° separation
the 2 and 4 mm distances magnified the HSV by factors of 2.7
and 4.4 for the twoelectrode lead and by factors 2.4 and 3.5
for the threeelectrode lead, respectively. When the
separation increases, the relative increase of the HSV
decreases. In
Table IV
we have also given the HSV's calculated with the same CSF
conductivity as that of the
brain to give the reader a possibility to estimate the
effect of the CSF conductivity.
Fig. 10. The effect of the distance of the
cortex from the skull on the HSV's of electric and magnetic
leads. The HSV's of two and threeelectrode electric leads
and of planar and axial gradiometers plotted as a function of
electrode distance/gradiometer coil separation. The results
are calculated for 0 mm, 2 mm and 4 mm distances between skull
and cortex.
TABLE IV.
EFFECT OF THE DISTANCE BETWEEN THE CORTEX AND
THE SKULL TO THE HSV OF
TWO AND THREEELECTRODE EEG LEADS.
HSV'S ARE GIVEN IN [cm³] FOR 0mm, 2mm AND 4mm
DISTANCES
BETWEEN THE CORTEX AND THE SKULL.
CONDUCTIVITY OF THE CSF IS sigma c
= 1.35 (Ohm·m)1 BEING THREE TIMES THAT OF THE BRAIN
AND SCALP. RESULTS ARE ALSO CALCULATED FOR
sigma c =
sigma t =
sigma b.
Separation 
2electrode EEG 
3electrode EEG 

sigma c =
1.35 
sigma b =
0.45 

sigma c =
1.35 
sigma b =
0.45 
0 mm 
2 mm 
4 mm 
2 mm 
4 mm 
0 mm 
2 mm 
4 mm 
2 mm 
4 mm 
20° 
8.0 
15.6 
20.6 
11 
14.3 
2.4 
4.7 
5.9 
3.6 
4.6 
10° 
2.8 
5.9 
8.6 
4.1 
5.7 
0.67 
1.5 
2.0 
1.2 
1.5 
5° 
1.5 
3.8 
6.1 
2.4 
3.9 
0.3 
0.72 
0.98 
0.51 
0.77 
1° 
1.2 
3.2 
5.3 
2.0 
3.4 
0.21 
0.5 
0.74 
0.3 
0.57 
As shown in Fig. 10 and
Table V,
in the magnetic leads the effect is smaller. (Because
the vertical scale in
Fig. 10 is the same as in
Figs. 9 and
8, the HSV's of the
axial gradiometer at 2 and 4 mm distance between the cortex
and the skull did not fit to the figure and they can be found
only from
Table V.)
At 1° separation the 2 and 4 mm
distances magnified the HSV by factors of 1.07 and 1.2 for the
planar gradiometer lead and by factors 1.2 and 1.3 for the
axial gradiometer lead, respectively. When the separation
increases the relative increase of the HSV slightly decreases.
(The CSF conductance does not have any effect to the HSV in a
magnetic lead.)
TABLE V
EFFECT OF THE DISTANCE BETWEEN THE CORTEX AND
THE SKULL TO THE HSV OF AXIAL AND PLANAR GRADIOMETERS WITH
h = 20 mm, r = 10 mm.
HSV's ARE GIVEN IN [cm³] for 0, 2, and 4 mm DISTANCES
BETWEEN THE CORTEX AND THE SKULL.
Separation 
Axial gradiometer 
Planar gradiometer 
0 mm 
2 mm 
4 mm 
0 mm 
2 mm 
4 mm 
20° 32 mm 
39 
44 
48 
5.6 
5.9 
6.2 
10° 16 mm 
31 
34 
38 
3.8 
4.2 
4.6 
5° 8.0 mm 
26 
30 
33 
3.5 
3.8 
4.3 
1° 1.6 mm 
21 
25 
28 
3.4 
3.6 
4.2 
C. Maximum Sensitivities of Electric and Magnetic Leads
1) Maximum Sensitivities in the Standard Head
Model: When the electrode separation decreases, the
maximum sensitivity of the electric leads decreases
from amaximum of
JLE = 147 A/m² at
180° separation to 11 A/m² and 1.5 A/m² for the
two and threeelectrode leads at 1° separation,
respectively. It reaches the 3 dB values at about 18.5°
and 25° separations, respectively,
Fig. 11(a) and
Table VI.
Fig. 11. The maximum sensitivity of (a) the two
and threeelectrode EEG leads and b) the MEG leads of axial
and planar gradiometers with coil radii of 10 mm plotted as a
function of electrode distance/gradiometer separation.
TABLE VI
MAXIMUM SENSITIVITIES OF TWO AND
THREEELECTRODE EEG AND OF AXIAL AND PLANAR GRADIOMETERS WITH
h = 20 mm, r = 10 mm.
SENSITIVITIES FOR THE ELECTRIC LEADS ARE GIVEN IN [A/m²]
WHILE THESE FOR THE MAGNETIC LEADS ARE GIVEN IN [nA/m²].
Separation 
2electrode
[A/m²] 
3electrode
[A/m²] 
Axial gradiometer [nA/m²] 
Planar gradiometer [nA/m²] 
180° 289 mm 
150 
150 
9.2 
9.6 
90° 145 mm 
140 
140 
9.1 
11 
30° 48 mm 
120 
110 
8.2 
19 
20° 32 mm 
108 
97 
7.5 
17 
10° 16 mm 
82 
62 
5.5 
11 
5° 8.0 mm 
51 
28 
3.6 
5.7 
1° 1.6 mm 
11 
1.5 
0.89 
1.2 
The sensitivity of the magnetic leads is
illustrated in Fig. 11(b) and
Table VI.
The maximum sensitivity of axial gradiometers at large
coil separation approaches the value obtained for a single
coil magnetometer and is equal to 9.3 µA/m². It
reaches the 3 dB value at a coil separation of approximately
23 mm. The planar gradiometer has its maximum
sensitivity at about 30° coil separation and reaches the
3 dB value at about 14° separation.
2) Effect of Skull Conductivity on the Maximum
Sensitivities:
Fig. 12
and
Table VII
illustrate the effect of the skull conductivity on the maximum
sensitivity of the electric leads when decreasing its
value by 25%. At 1° baseline the maximum sensitivity of
two and threeelectrode EEG's decreases some 15%, at 20°
baseline the decrease is about 18%.
Fig. 12. The effect of
the skull conductivity on
the maximum sensitivity of the two and threeelectrode
EEGleads. The results are calculated with skull
conductivities of (1/80)
sigma b and (1/100)
sigma b where
sigma b is the conductivity of
brain (and scalp).
TABLE VII.
EFFECT OF THE SKULL CONDUCTIVITY ON THE MAXIMUM
SENSITIVITY OF TWO AND THREEELECTRODE EEG LEADS GIVEN IN
[A/m²] WITH (1/80)
sigma b AND (1/100)
sigma b SKULL
CONDUCTIVITIES.
Separation 
2electrode EEG 
3electrode EEG 
(1/80)sigma b 
(1/100)sigma b 
(1/80)sigma b 
(1/100)sigma b 
20° 
110 
89 
97 
79 
10° 
82 
67 
63 
50 
5° 
51 
42 
28 
23 
1° 
11 
9.2 
1.5 
1.3 
In a spherical model the skull conductivity does not have
any effect on the maximum sensitivity of the magnetic
leads.
3) Effect of the Distance Between the Cortex and the Skull
on the Maximum Sensitivities: At 1° separation,
changing the distance between the cortex and the skull from 0
mm to 2 and 4 mm decreases the maximum sensitivity of
twoelectrode lead some 48% and 65% and threeelectrode
lead some 64% and 79%, respectively. At 20° separation the
relative decrease is smaller, see
Fig. 13(a) and
Table VIII.
Fig. 13. The effect of the distance between the
cortex and the skull on the maximum sensitivity of electric
and magnetic leads. (a) Maximum sensitivities of two and
threeelectrode electric leads. (b) Maximum sensitivities of
planar and axial gradiometers. The results are calculated for
0 mm, 2 mm and 4 mm distances between the cortex and the
skull.
TABLE VIII
EFFECT OF THE DISTANCE BETWEEN THE CORTEX AND
THE SKULL ON THE MAXIMUM SENSITIVITY OF TWO AND
THREEELECTRODE EEG LEADS GIVEN IN [A/m²] FOR DISTANCES
OF 0 mm, 2 mm AND 4 mm BETWEEN THE CORTEX AND THE SKULL. THE
CONDUCTIVITY OF THE CSF sigma c =
1.35 (Ohm·m)1.
Separation 
2electrode EEG 
3electrode EEG 
0 mm 
2 mm 
4 mm 
0 mm 
2 mm 
4 mm 
20° 32 mm 
110 
67 
51 
97 
56 
39 
10° 16 mm 
82 
47 
34 
62 
30 
19 
5° 8.0 mm 
51 
27 
19 
28 
12 
6.9 
1° 1.6 mm 
11 
5.7 
3.9 
1.6 
0.58 
0.33 
In the same situation the maximum sensitivity of axial
gradiometer decreases some 16% and 29% and that of
planar gradiometer some 20% and 33%, respectively. At
20° separation the relative decrease is a little smaller,
as shown in
Fig. 13(b) and
Table IX.
TABLE IX
EFFECT OF THE DISTANCE BETWEEN THE CORTEX AND
THE SKULL ON THE MAXIMUM SENSITIVITY OF AXIAL AND PLANAR
GRADIOMETERS WITH h = 20 mm, r = 10 mm GIVEN IN
[nA/m²] FOR DISTANCES 0 mm, 2 mm, AND 4 mm OF AXIAL AND
PLANAR GRADIOMETERS
WITH h = 20 mm, r = 10 mm GIVEN IN [nA/m²]
FOR DISTANCES 0 mm, 2mm, AND 4 mm .
Separation 
Axial gradiometer 
Planar gradiometer 
0 mm 
2 mm 
4 mm 
0 mm 
2 mm 
4 mm 
20° 32 mm 
7.5 
6.5 
5.6 
17 
15 
12 
10° 16 mm 
6.6 
4.8 
4.2 
11 
8.9 
7.5 
5° 8.0 mm 
3.6 
3.1 
2.6 
5.7 
4.7 
3.9 
1° 1.6 mm 
0.94 
0.79 
0.67 
1.2 
0.96 
0.8 
V. DISCUSSION
A. Forms of the Lead Fields
The radially oriented lead field of a single electrode
electric lead cannot be synthesized with any magnetic leads.
Similarly, the vortexform lead field of an axial gradiometer
cannot be synthesized with any electric leads. Thus, these
leads give most complementary information about the electric
sources of the brain. However, the axial gradiometer has very
large HSV, as seen from Fig. 8(a),
and its signal is thus a
spatial average from a large region of the brain. Therefore it
has very low clinical value.
With short electrode and coil separations, respectively,
the lead fields of the twoelectrode lead and the planar
gradiometer closely resemble each other. Thus, the information
from these leads is most redundant.
B. Half Sensitivity Volumes
Despite the diffusing effect of the skull the electric
leads have smaller HSV's than the typical wholehead MEG
systems. Even with the smallest possible coil separations, the
planar gradiometer requires recording distances of 12 mm or
less to reach the HSV of the twoelectrode EEG lead. The
threeelectrode EEGleads are superior, having HSV comparable
to the theoretical 0 mm microSQUID planar gradiometer
measurement distance.
C. Maximum Sensitivities
When the electrodes or coils are brought closer to each
other the HSV becomes smaller. While this improves the form of
the lead field, it also decreases the sensitivity of the lead.
The important question is whether the signal amplitude is
acceptable at those separations where the HSV is sufficiently
small.
In electric leads the 3 dB signal amplitude is reached
with larger separation than for magnetic leads. This result
means that if identical electrode/coil separations are used in
both electric and magnetic leads, attenuation from the maximum
amplitude with electric signal is greater than with the
magnetic signal. However, because the signaltonoise ratio of
the electric measurement is much greater than in the magnetic
one, the electric measurement is much easier to perform also
with shorter electrode separation.
D. Effect of the Parameters of the Head Model
A given percentage change in the conductivity of the skull
causes a smaller percentage change in the maximum
sensitivities and HSV's of the electric leads. On the magnetic
leads it does not have any effect. Thus, changing the skull
conductivity is not an important factor.
The distance between the cortex and the skull, i.e., the
effect of the cerebrospinal fluid, has a large effect on the
results. It makes the HSV's larger and the signal amplitudes
smaller in both electric and magnetic leads. The effect on HSV
is larger in electric leads than it is in magnetic leads.
VI. CONCLUSION
Our theoretical analysis shows the following.
1) With the EEG it is possible to record the electric
activity of the brain from a more concentrated
region than with the MEG
2) The sensitivity distributions of such MEG leads
which have small HSV's (planar gradiometers)
resemble very much those of dipolar EEG leads and
therefore they record the electric activity of the
brain in a very similar way
3) The effect of headmodel parameters is either
small or at least similar in both EEG and MEG
leads.
Furthermore it is known that the EEG can record the three
orthogonal components of the electric sources in the cortex
but the MEG can record only the two tangential ones.
In biomagnetic research, recordings are not consistently
compared with corresponding electric recordings. Therefore it
is not usually shown that the results obtained with magnetic
methods could have been obtained equally well or even more
accurately with electric methods. To assess the clinical
diagnostic value of the MEG and to be able to justify its much
higher price compared with electric methods, MEG studies
should be performed parallel with EEG studies.
APPENDIX
EQUATIONS FOR CALCULATING ELECTRIC LEAD FIELDS
AND HALFSENSITIVITY VOLUMES
IN A FOUR CONCENTRICSPHERES MODEL
Assuming solution of the form V = f(r)g(q)h(f)
the general solution can be shown to be [17]
 (A.1) 
where P_{n}^{m}(cosf) is the associated
Legendre polynomial of the first kind. The coefficients A_{m }, B_{m }, C_{n } and D_{n }
are determined from boundary conditions.
For any arbitrary placement of electrodes on the surface of the outer sphere,
the coordinate system can always be oriented in such way that f
will have only even symmetry about f = 0.
Thus the coefficients of sinmf will be zero.
Constant terms representing uniform fields will be neglected and term
D_{n }r^{  (n+1)} will be omitted in the innermost
sphere (brain), since the negative powers of r would cause a singularity
at the origin.
Boundary conditions: The normal component of the current density on the
outermost surface must be zero everywhere except at the electrodes. In these
equations the subscripts have the following meaning: t = scalp, s
= skull, c = CSF, and b = brain.
 (A.2) 
Furthermore, the normal component of the current density and the potential
must be equal everywhere on the corresponding surfaces of the inner spheres.
 (A.3) 
The boundary conditions give seven equations with seven unknowns.
The solution for the potential in the brain can be shown to be
 (A.4) 
where
I_{R} = reciprocal current fed to the electrodes
in which
and
where
and
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Acknowledgement. This work has been supported by the
Academy of Finland and the Ragnar Granit Foundation.

Jaakko Malmivuo
(S'71M'92SM'95) received the M.Sc.
and Ph.D. degrees from Helsinki University of Technology,
Espoo, Finland, in 1971 and 1976, respectively. From 1974 to
1976 he served as researcher at Stanford University.
In 1976 he was appointed as Associate Professor and in
1986 Professor of Bioelectromagnetism at Tampere University of
Technology (TUT), Tampere, Finland. Since 1992 he has been
Director of the Ragnar Granit Institute at TUT. He has served
as Visiting Professor at Technical University of Berlin (West)
(1988), Dalhousie University, Halifax, Canada (1989), and
Sophia University, Tokyo, (1993). He has over 250 scientific
publications and he has cowritten with R. Plonsey,
Bioelectromagnetism, (New York; Oxford Univ. Press,
1995).
Dr. Malmivuo was President of the Finnish Society for
Medical Physics and Medical Engineering in 19871990. He is
founder Member and President of the International Society for
Bioelectromagnetism.


Veikko E. Suihko received the M.Sc. degree in
electrical engineering and the Lic.Tech. degree in biomedical
engineering from Tampere University of Technology, Tampere,
Finland, in 1991 and 1994, respectively. From 1991 to 1996, he
was researcher at the Ragnar Granit Institute at Tampere
University of Technology.
He is currently Associate Physicist at Tampere University
Hospital. His research interests include modeling of
bioelectric phenomena with applications to noninvasive
electric stimulation of central nervous system and measurement
of electric activity of the brain.


Hannu Eskola was born in Honkilahti, Finland, on
November 13, 1954. He received the M.Sc. and Ph.D. degrees in
biomedical engineering from Tampere University of Technology,
Tampere, Finland, in 1979 and 1983, respectively.
Since 1980 he has been Hospital Physicist in various
departments in University Hospitals of Tampere and Kuopio. In
1994 he joined the Ragnar Granit Institute at Tampere
University of Technology and became Associate Professor in
Medical Electronics. His main research interests are in
neurophysiology, especially in modelling of electric fields in
the brain.

