Evaluation of a new MEG EEG spatio tempo
Brain Topography, Volume 11, Number 4, 1999
279
Evaluation of a New MEG-EEG Spatio-Temporal
Localization Approach Using a Realistic Source Model
D.P. Schwartz*, J.M. Badier^, R. Bihoue*, and A. Bouliou*
Summary: This paper introduces a new technique for the localization of brain electromagnetic activity: a spatio-temporal fit (SPTF). This algorithm
uses some properties of the principal component analysis and makes no assumptions about the number of sources to be located. It was applied to
both simulated and real MEG/EEG signals and was compared to the well-known moving dipole fit (MDF) technique. For the simulations, we
constructed extended sources, rather than single dipoles, that respected realistic anatomical and temporal properties. From these, we generated,
under different noise conditions, MEG and EEG signals from which localization was performed. The real signals were auditory evoked fields. Firstly,
it appeared that the SPTF was able to separate simultaneously activated sources even on strongly noisy signals while, most of the time, the MDF failed
to give a clear description of the source configuration. Secondly, although we used the same head model to both generate the signals and locate the
sources, localization for EEG was inferior to that for MEG. In conclusion, since in all test conditions the SPTF is found to be far superior to MDF, we
suggest the use SPTF for the localization of equivalent dipoles.
Key words: Spatio-temporal localization; Source model; MEG, EEG.
Introduction
Recording of magnetic fields outside the head (magnetoencephalography or MEG) or electric potential over
the surface of the scalp (electroencephalography or EEG)
give an image of the brain activity with a temporal resolution of a few milliseconds. From these, one can attempt
to localize the sources of the recorded activities by solving
the so-called inverse problem, i.e., the estimation of the
spatial and temporal characteristics of the sources. The
solution of the inverse problem requires solving the forward problem, i.e., the computation of the electric potential and magnetic field, given the conductive current
source distribution within the head and the individual
conductive properties of the internal tissues. This is a
* UPRES EA Cortex cerebral et Epilepsie, Universite de Rennes 1,
Rennes, France.
^ Laboratoire de Neurophysiologie et Neuropsychologie et INSERM CJF 97-6, Universite de la Mediterannee, Marseille, France.
Accepted for publication: December 24,1998.
We thank Pr. J.M. Scarabin, head of the neurosurgical department,
Dr. J. De Graaf, Dr. B. Gibaud, Dr. E. Poiseau, Dr. A. K. Liu and Dr. C.
Liegeois-Chauvel for their valuable contributions in this study. This
study was partly supported by the CNAMTS.
Correspondence and reprint requests should be addressed to Dr.
Denis Schwartz, MGH-NMR Center, Bldg. 149, 13th Street Rm. 2301,
Charlestown MA, 02129, USA.
Fax: 617-726-7422
E-mail: schwarrz@nmr.mgh.harvard.edu
Copyright ©1999 Human Sciences Press, Inc.
well-defined problem, governed by quasi-static limit of
Maxwell's equation. The main issues in the forward
problem, is the choice of appropriate source model and
head model. Note that those models cannot respect all
the properties of real sources and geometrical or conductivity properties of human head. The main difficulty
comes from the inverse problem which is not uniquely
determined. For a given MEG or EEG recording, an
infinite number of source configurations reproducing the
actual data exists. Then, one has to introduce a priori
knowledge (such as the number of sources simultaneously activated) to determine a unique solution. In this
context, it is essential, for a given localization algorithm,
to carefully evaluate its spatial and temporal accuracy.
A widely used method for localization is the so-call
"moving dipole fit" (MDF). This approach consists of the
search at one given moment of the best location of one
single equivalent dipole that fits the recorded data. Using MDF, numerous authors have studied the spatial
localization uncertainties related to the head geometry
and conductivity (Stok 1987; Meijs et al. 1987;
Hamalainen and Sarvas 1989; Cuffin 1990, 1993, 1996;
Bertrand et al. 1991; Yan et al. 1991; Thevenet et al. 1992;
Rothetal. 1993,1997,-Zanow 1995; Yvertetal. 1995,1997).
Although the temporal resolution is the main advantage
of the MEG/EEG recordings, only a few studies dealt
with the temporal accuracy of the localization. Spatiotemporal localization approaches showed that it is possible to localize simultaneously activated sources and to
reconstruct their time course of activation (Scherg 1984,
Schwartz et al.
280
1990; Moscher et al. 1992; Miltner et al. 1994). However,
the spatial and temporal accuracy of such methods is
strongly linked to the temporal properties of the actual
sources (Achim et al. 1988,1990; Baumgartner et al. 1989,
Supek and Aine 1997). Thus, these methods generally
require high skilled users. In the context of a study of the
generators of auditory evoked fields/potentials
(Liegeois-Chauvel et al. 1994), the main goal of this paper
was to evaluate the ability of a new automatic spatio-temporal approach (SPTF) developed by Bouliou (Bouliou et
al. 1994; Bihoue 1996) to overcome the well-known MDF
drawbacks (Scherg 1984, 1990). To evaluate the algorithms accuracy we simulated MEG/EEG signals using
a realistic source model. The properties of the realistic
source (such as its extension, its shape or its temporal
behavior) was defined by the anatomo-functional context
linked to this source. Note that to some degree these
sources may not respect the assumptions of the source
model used by the algorithm. These simulations allowed
us to study the following points:
%o spatial and temporal amplitude of the uncertainties
linked to the properties of the source,
%o behavior of the method when physiological noise is
present,
%o false-positive or false-negative localizations.
After a detailed presentation of the new spatio-temporal algorithm, we present an original simulation method
used to answer the above questions for both MDF and
SPTF. In those simulations, spatial and temporal properties of the sources are described with respect to the a priori
knowledge of the anatomo-functional context. MEG /EEG
signals are simulated on the MEG/EEG sensors that are
used in our real recording. We present the results of 3 tests.
The first test studies the effects of the size of a generator on
the spatial accuracy of our algorithms. The second test
studies the behavior of each localization method using
several simultaneously activated sources with noisy signal. Finally, since simulations cannot describe all the properties of real signals, as a third test, we present the results
of the analysis of real auditory evoked field.
Methods
Spatio-temporal algorithm
In this study, we evaluated a new spatio-temporal fit
(SPTF) algorithm. Classically the SPTF searches for an
equivalent dipole (Deq) to match, through a spatio-temporal analysis, the MEG/EEG data (Sabs) with the computed field/potential (Scomp) that is generated by the
dipole. The underlying idea of the SPTF algorithm is the
application of Principal Component Analysis (PCA)
over a moving short window of time (typically 5 ms or
10 time points) to separate simultaneous, asynchronous
dipolar sources. Let B be the spatio-temporal matrix (Nc
x Nt) containing the signals for Nc sensors at Nt latencies.
The SPTF performs a PCA on the matrix (BBT) (Nc x Nc).
The results are Nc eigenvectors Bj and Nc decreasing
eigenvalues Lj. A discontinuity in the order of magnitude
of the eigenvalues Li indicates the dimension of the signal
subspace Sobs/pca of dimension dims with dims < Nc. Sobs/pca
is then defined as follows:
where a+ are unknown linear coefficients. The dimension
of the signal subspace dims may be determined either
empirically for a given signal or with a criteria as the well
known Kaiser's one (Saporta 1990). In our study, dims
was fixed to three since higher values (4 or 5) did not
change the behavior of the algorithm in our simulations.
Consequently the SPTF minimizes the following
cost-function Err:
The SPTF searches all the dipolar activities belonging to Sobs/pca by minimizing the quantity in equation 2
with respect to both Deq and aj, and therefore performs
its fit on reconstructed data and not on the real data. In
conclusion, the SPTF searches in the signal subspace the
best combinations of Bj representing a dipolar activity.
The minimization is performed with a Newton-Raphson method. The minimization is driven from a set of 30
initial points uniformly located under the MEG channels
or in the entire cerebral space (EEG) (See 2 paragraps
below). From this initial guess, we obtained 30 equivalent
dipoles for each window of time. With the MDF the best
equivalent dipole in term of correlation and goodness of fit
is retained for each latency. Since, from each initial point
the SPTF may converge toward a different Deq and associated aj, it may localize several sources. We then selected
the 3 spatially distinct best equivalent dipoles for each
analyzed window of time. Two dipoles are spatially different if there is more than 2 mm between them.
Methodology of Evaluation
Description of the Anatomy and Definition of an
Area of Activity
The auditory cortex and the surrounding areas are
Evaluation of a New MEG-EEG Localization Approach
281
Figure 1. 3D view in sagittal direction of the model constructed from a patient. The numbers I and II respectively indicate
the location of the AoAs I and II, used in the evaluation of the localization algorithms. The contoured areas show the
spatial extension of each AoA. Note the difference in geometrical complexity between the two AoAs. The distance
between the surface of the head and the AoA I is equal to 3.5 cm, the spatial extension is 1.2 cm2. The mean orientation
of AoA I is (x = 0.34, y = -0.67 and z = -0.65, largest angle between two single dipoles = 62°) where x is the medial to lateral
direction, y is the posterior to anterior direction and z is the inferior to superior direction. The AoA II lies in the lateral part
of the Heschl gyrus at 2.5 cm from the surface of the head. Its spatial extension is equal to 1.2 cm2. The distance between
the centers of gravity of the AoAs is equal to 1 cm. The mean orientation of AoA II is (x = -0.52, y = 0.09 and z = 0.84, largest
angle between two single dipoles 158°) . Both AoAs contained 900 single dipoles.
manually segmented on an MRI sagittal view by an anatomist (voxel size of the MRI examination = 1 mm3). In this
study, the segmented region of interest (ROI) contains
Heschl gyrus and the planum temporale from the right
hemisphere of a patient. In order to obtain accurate local
characteristics of the surface of the ROI (such as a normal
to the actual surface), we used a B-spline surface (order =
3) to match our data (figure 1).
An area of activity (AoA) is defined as a dipole layer
constrained on the segmented cortical surface, i.e., by a
given part of the cortical surface and a uniform density
of single dipoles located on the surface with a direction
normal to this surface. We assume that a single dipole
represents an hypercolumn of neurons oriented normally
to the cortical surface. An AoA is then defined by a
location on the surface, a spatial extent, and a single
dipole density (figure 1). The time course of activation
of each AoA is defined as a biphasic curve. When an AoA
is activated, we consider that all the single dipoles of this
AoA are activated simultaneously with exactly the same
time course of activation. The parameters of the time
course of activation are fixed with respect to the a priori
knowledge of the temporal properties of the activities
recorded in the region of interest.
Computation of SEEG, MEG, EEG data
A three shell sphere model is used to describe the
head. The first shell represents the brain (radius r1 = 0.87,
conductivity c1 = 1.0), the second the skull (radius r2 =
0.92, conductivity c2 = 0.0125), and the third the scalp
(radius = 1.0, conductivity = 1.0). For surface EEG, a set
Schwartz et al.
282
of 32 electrodes (subset of the 10-10 system, Chatrian
1985) is modeled. The electrodes are uniformly distributed among the scalp, this configuration is being used in
our real EEG recordings. For MEG, a 37 channels sensor
(equivalent to the Magnes system from BTi) is used. The
center of the sensor is centered over the region of interest
(on EEG electrode T4). Note, we used in these simulations the real geometry of MEG or EEG sensors. Thus,
there were strong differences in spatial sampling between both recording methods.
between channels due to an unexpected source of activity
in the recorded signal. We added the resulting noise to
the simulated signals with a weight that is computed
from the desired signal to noise ratio (SNR). The SNR is
defined as the ratio of the average of the simulated signal
power to the average of the noise power.
To conclude, before the evaluation presented in the
next section, we validated our simulations approach by
estimating its capabilities to reproduce depth recordinglike signals. The methodology and the results are described in (Schwartz 1996a).
Computation of the contributions of the AoAs
For one AoAk, the simulated EEG and MEG signals
are the sum of the contributions of its single dipoles
weighted over time by the value of its time course of
activation. There exists a simple linear relationship between electric and magnetic recordings and the moment
of a dipole at any location in the brain. Let sk(t) be the
value of the time course of activation of the AoAk at a
latency t and mi(t) the measurements (MEG or EEG) at a
latency t for the sensor i. Then
where Gk represents the gain matrix of the AoAk. The
components gijkare non-linear functions of both the sensor locations and the model of the head. NAOAK is the
number of single dipoles in the AoAk; Mk is the signals
generated by the AoAk over the time; and SK is the time
course of activation of the AoAk. Then, when the activity
of N AoAs is combined, the final measurement M is
Criteria of evaluation
Let t be a latency, and AoAk an area of activity. To
evaluate each algorithm two errors are computed: The
localization error of the AoAk at t is defined as the distance between the location of equivalent dipole Deq and
the center of gravity of AoAk (i.e., the center of gravity of
the single dipoles belonging to AoAk). In addition, to
determine if Deq is in the neighborhood of an AoA with
respect to the area of this AoA, we define the following
relative error:
where XiAOAOK is the center of gravity of AoAk and xiDeq the
location of the localized equivalent dipole Deq.
The orientation error is defined as the angle between
the orientation of the equivalent dipole Deq and the mean
orientation of AoAk (i.e., the mean orientation of the single
dipoles belonging to AoAk). In addition, we define a
relative error of orientation as follow (Stok 1987):
Addition of noise
In order to study the effects of the noise level on the
accuracy of localization, noise was added to the simulated signals. The noise was issued from EEG/MEG
spontaneous activities recorded from an adult subject
(length = 200 ms, sampling rate = 0.920 ms, filtered with
a band-pass filter 1-120 Hz) and is used to match as much
as possible the spectral characteristics of real measurements. Since the simulations are performed in the context of evoked potential/field, each noise epoch is
constructed by 10 averages of 100 ms of spontaneous
activity taken randomly from the original epoch of 200
ms. This average reduces the possible signal correlation
where DiA°Ak is the mean direction of AoAk and DiDeq the
direction of the localized equivalent dipole Deq. These
values are reported over time to study the accuracy and
the stability of the results in term of localization and
direction errors.
Results
Effects of the variation of area of the AoA
We simulated the MEG/EEG signal with one AoA
without noise. The area of the AoA varied from a single
Evaluation of a New MEG-EEG Localization Approach
Figure 2. Accuracy of localization and orientation for
several areas of an AoA located in the medial part of
Heschl gyrus. (Distance from the surface of the head 4.5
cm; mean orientation mainly tangential; the AoA contains
900 dipoles whatever the area). (A-top) Error of localization for MEG (white) and EEG (black). (B-bottom) Orientation accuracy. Note that on those noiseless signals both
MDF and SPTF gave the same results.
point source to 4 cm2 (figure 2). The localization accuracy
on EEG signals decreased when the area of the AoA
increases from 0 mm for a single point source up to 27
mm (Eri = 140%) for 4 cm2. On the contrary, the MEG
accuracy remains under 7 mm (Erl = 45%) for all areas of
the AoA. Regarding orientation the effect was inverse,
i.e., the accuracy of the results on MEG signals decreased
when the area of the AoA increases from 0° (Erd = 0%) for
0 cm2 to 8° (E rd = 24%) for 4 cm2 while the EEG orientation
accuracy remained superior to 1° (Erd = 3%).
Test with two simultaneous activated sources
Analysis on MEG signals
When only one of the AoAs was activated, the accuracy of localization was most of the time very good when
SNR = 100 (errors < 0.75 mm (Erl = 7%)) with both MDF
and SPTF. The performance of the SPTF remained almost
constant whatever the noise level (figure 3A and table I).
When both AoAs were activated (between 40 and 50 ms)
the SFTF localized both AoA I and AoA II with a very good
283
Figure 3. Localization errors with two simultaneous activated sources for MEG signals. Dotted lines represent
localization results for AoA I and plain lines represents
localization results for AoA II. (A) Localization errors using
SPTF (SNR = 100). (B) Localization errors using MDF (SNR =
100). (C) Localization errors using SPTF (SNR = 1). (D)
Localization errors using MDF (SNR = 1). The bottom curve
represents the time course of activation of AoA I (dotted
line) and AoA II (plain line). The temporal overlaping
between both AoAs is equal to 75% of their time of activation. Note that the MDF localizes 1 equivalent dlpole
per latency and the SPTF may localize up to 3 equivalent
dipoles per latency. The grey bold rectangles in (C)
above the results of the SPTF indicate the latencies when
the SPTF found more equivalent dipoles than the actual
number of activated sources. The labels "begin" and
"end" indicate the time range when the activation is
effectively different from zero. The horizontal bold line on
the time axis represents the width of the window of analysis
used for the SPTF.
accuracy (errors < 1 mm (£,./ = 9%) for AoA I and errors <
2 mm (Erl = 18%) for AoA II) with SNR = 100 (figures 4
and 5). Whereas the MDF produced a set of spurious
localizations between AoAs (15 mm from AoA 1 and 7 mm
from AoA II). Moreover, this set of localization was
linked to AoA I and AoA II by equivalent dipoles producing an artificial displacement of the source of activity.
Regarding orientation accuracy (figure 6), both
methods had the same behavior as that previously described for localization accuracy. The SPTF gave good
orientations and the accuracy remained very high (errors
279
Evaluation of a New MEG-EEG Spatio-Temporal
Localization Approach Using a Realistic Source Model
D.P. Schwartz*, J.M. Badier^, R. Bihoue*, and A. Bouliou*
Summary: This paper introduces a new technique for the localization of brain electromagnetic activity: a spatio-temporal fit (SPTF). This algorithm
uses some properties of the principal component analysis and makes no assumptions about the number of sources to be located. It was applied to
both simulated and real MEG/EEG signals and was compared to the well-known moving dipole fit (MDF) technique. For the simulations, we
constructed extended sources, rather than single dipoles, that respected realistic anatomical and temporal properties. From these, we generated,
under different noise conditions, MEG and EEG signals from which localization was performed. The real signals were auditory evoked fields. Firstly,
it appeared that the SPTF was able to separate simultaneously activated sources even on strongly noisy signals while, most of the time, the MDF failed
to give a clear description of the source configuration. Secondly, although we used the same head model to both generate the signals and locate the
sources, localization for EEG was inferior to that for MEG. In conclusion, since in all test conditions the SPTF is found to be far superior to MDF, we
suggest the use SPTF for the localization of equivalent dipoles.
Key words: Spatio-temporal localization; Source model; MEG, EEG.
Introduction
Recording of magnetic fields outside the head (magnetoencephalography or MEG) or electric potential over
the surface of the scalp (electroencephalography or EEG)
give an image of the brain activity with a temporal resolution of a few milliseconds. From these, one can attempt
to localize the sources of the recorded activities by solving
the so-called inverse problem, i.e., the estimation of the
spatial and temporal characteristics of the sources. The
solution of the inverse problem requires solving the forward problem, i.e., the computation of the electric potential and magnetic field, given the conductive current
source distribution within the head and the individual
conductive properties of the internal tissues. This is a
* UPRES EA Cortex cerebral et Epilepsie, Universite de Rennes 1,
Rennes, France.
^ Laboratoire de Neurophysiologie et Neuropsychologie et INSERM CJF 97-6, Universite de la Mediterannee, Marseille, France.
Accepted for publication: December 24,1998.
We thank Pr. J.M. Scarabin, head of the neurosurgical department,
Dr. J. De Graaf, Dr. B. Gibaud, Dr. E. Poiseau, Dr. A. K. Liu and Dr. C.
Liegeois-Chauvel for their valuable contributions in this study. This
study was partly supported by the CNAMTS.
Correspondence and reprint requests should be addressed to Dr.
Denis Schwartz, MGH-NMR Center, Bldg. 149, 13th Street Rm. 2301,
Charlestown MA, 02129, USA.
Fax: 617-726-7422
E-mail: schwarrz@nmr.mgh.harvard.edu
Copyright ©1999 Human Sciences Press, Inc.
well-defined problem, governed by quasi-static limit of
Maxwell's equation. The main issues in the forward
problem, is the choice of appropriate source model and
head model. Note that those models cannot respect all
the properties of real sources and geometrical or conductivity properties of human head. The main difficulty
comes from the inverse problem which is not uniquely
determined. For a given MEG or EEG recording, an
infinite number of source configurations reproducing the
actual data exists. Then, one has to introduce a priori
knowledge (such as the number of sources simultaneously activated) to determine a unique solution. In this
context, it is essential, for a given localization algorithm,
to carefully evaluate its spatial and temporal accuracy.
A widely used method for localization is the so-call
"moving dipole fit" (MDF). This approach consists of the
search at one given moment of the best location of one
single equivalent dipole that fits the recorded data. Using MDF, numerous authors have studied the spatial
localization uncertainties related to the head geometry
and conductivity (Stok 1987; Meijs et al. 1987;
Hamalainen and Sarvas 1989; Cuffin 1990, 1993, 1996;
Bertrand et al. 1991; Yan et al. 1991; Thevenet et al. 1992;
Rothetal. 1993,1997,-Zanow 1995; Yvertetal. 1995,1997).
Although the temporal resolution is the main advantage
of the MEG/EEG recordings, only a few studies dealt
with the temporal accuracy of the localization. Spatiotemporal localization approaches showed that it is possible to localize simultaneously activated sources and to
reconstruct their time course of activation (Scherg 1984,
Schwartz et al.
280
1990; Moscher et al. 1992; Miltner et al. 1994). However,
the spatial and temporal accuracy of such methods is
strongly linked to the temporal properties of the actual
sources (Achim et al. 1988,1990; Baumgartner et al. 1989,
Supek and Aine 1997). Thus, these methods generally
require high skilled users. In the context of a study of the
generators of auditory evoked fields/potentials
(Liegeois-Chauvel et al. 1994), the main goal of this paper
was to evaluate the ability of a new automatic spatio-temporal approach (SPTF) developed by Bouliou (Bouliou et
al. 1994; Bihoue 1996) to overcome the well-known MDF
drawbacks (Scherg 1984, 1990). To evaluate the algorithms accuracy we simulated MEG/EEG signals using
a realistic source model. The properties of the realistic
source (such as its extension, its shape or its temporal
behavior) was defined by the anatomo-functional context
linked to this source. Note that to some degree these
sources may not respect the assumptions of the source
model used by the algorithm. These simulations allowed
us to study the following points:
%o spatial and temporal amplitude of the uncertainties
linked to the properties of the source,
%o behavior of the method when physiological noise is
present,
%o false-positive or false-negative localizations.
After a detailed presentation of the new spatio-temporal algorithm, we present an original simulation method
used to answer the above questions for both MDF and
SPTF. In those simulations, spatial and temporal properties of the sources are described with respect to the a priori
knowledge of the anatomo-functional context. MEG /EEG
signals are simulated on the MEG/EEG sensors that are
used in our real recording. We present the results of 3 tests.
The first test studies the effects of the size of a generator on
the spatial accuracy of our algorithms. The second test
studies the behavior of each localization method using
several simultaneously activated sources with noisy signal. Finally, since simulations cannot describe all the properties of real signals, as a third test, we present the results
of the analysis of real auditory evoked field.
Methods
Spatio-temporal algorithm
In this study, we evaluated a new spatio-temporal fit
(SPTF) algorithm. Classically the SPTF searches for an
equivalent dipole (Deq) to match, through a spatio-temporal analysis, the MEG/EEG data (Sabs) with the computed field/potential (Scomp) that is generated by the
dipole. The underlying idea of the SPTF algorithm is the
application of Principal Component Analysis (PCA)
over a moving short window of time (typically 5 ms or
10 time points) to separate simultaneous, asynchronous
dipolar sources. Let B be the spatio-temporal matrix (Nc
x Nt) containing the signals for Nc sensors at Nt latencies.
The SPTF performs a PCA on the matrix (BBT) (Nc x Nc).
The results are Nc eigenvectors Bj and Nc decreasing
eigenvalues Lj. A discontinuity in the order of magnitude
of the eigenvalues Li indicates the dimension of the signal
subspace Sobs/pca of dimension dims with dims < Nc. Sobs/pca
is then defined as follows:
where a+ are unknown linear coefficients. The dimension
of the signal subspace dims may be determined either
empirically for a given signal or with a criteria as the well
known Kaiser's one (Saporta 1990). In our study, dims
was fixed to three since higher values (4 or 5) did not
change the behavior of the algorithm in our simulations.
Consequently the SPTF minimizes the following
cost-function Err:
The SPTF searches all the dipolar activities belonging to Sobs/pca by minimizing the quantity in equation 2
with respect to both Deq and aj, and therefore performs
its fit on reconstructed data and not on the real data. In
conclusion, the SPTF searches in the signal subspace the
best combinations of Bj representing a dipolar activity.
The minimization is performed with a Newton-Raphson method. The minimization is driven from a set of 30
initial points uniformly located under the MEG channels
or in the entire cerebral space (EEG) (See 2 paragraps
below). From this initial guess, we obtained 30 equivalent
dipoles for each window of time. With the MDF the best
equivalent dipole in term of correlation and goodness of fit
is retained for each latency. Since, from each initial point
the SPTF may converge toward a different Deq and associated aj, it may localize several sources. We then selected
the 3 spatially distinct best equivalent dipoles for each
analyzed window of time. Two dipoles are spatially different if there is more than 2 mm between them.
Methodology of Evaluation
Description of the Anatomy and Definition of an
Area of Activity
The auditory cortex and the surrounding areas are
Evaluation of a New MEG-EEG Localization Approach
281
Figure 1. 3D view in sagittal direction of the model constructed from a patient. The numbers I and II respectively indicate
the location of the AoAs I and II, used in the evaluation of the localization algorithms. The contoured areas show the
spatial extension of each AoA. Note the difference in geometrical complexity between the two AoAs. The distance
between the surface of the head and the AoA I is equal to 3.5 cm, the spatial extension is 1.2 cm2. The mean orientation
of AoA I is (x = 0.34, y = -0.67 and z = -0.65, largest angle between two single dipoles = 62°) where x is the medial to lateral
direction, y is the posterior to anterior direction and z is the inferior to superior direction. The AoA II lies in the lateral part
of the Heschl gyrus at 2.5 cm from the surface of the head. Its spatial extension is equal to 1.2 cm2. The distance between
the centers of gravity of the AoAs is equal to 1 cm. The mean orientation of AoA II is (x = -0.52, y = 0.09 and z = 0.84, largest
angle between two single dipoles 158°) . Both AoAs contained 900 single dipoles.
manually segmented on an MRI sagittal view by an anatomist (voxel size of the MRI examination = 1 mm3). In this
study, the segmented region of interest (ROI) contains
Heschl gyrus and the planum temporale from the right
hemisphere of a patient. In order to obtain accurate local
characteristics of the surface of the ROI (such as a normal
to the actual surface), we used a B-spline surface (order =
3) to match our data (figure 1).
An area of activity (AoA) is defined as a dipole layer
constrained on the segmented cortical surface, i.e., by a
given part of the cortical surface and a uniform density
of single dipoles located on the surface with a direction
normal to this surface. We assume that a single dipole
represents an hypercolumn of neurons oriented normally
to the cortical surface. An AoA is then defined by a
location on the surface, a spatial extent, and a single
dipole density (figure 1). The time course of activation
of each AoA is defined as a biphasic curve. When an AoA
is activated, we consider that all the single dipoles of this
AoA are activated simultaneously with exactly the same
time course of activation. The parameters of the time
course of activation are fixed with respect to the a priori
knowledge of the temporal properties of the activities
recorded in the region of interest.
Computation of SEEG, MEG, EEG data
A three shell sphere model is used to describe the
head. The first shell represents the brain (radius r1 = 0.87,
conductivity c1 = 1.0), the second the skull (radius r2 =
0.92, conductivity c2 = 0.0125), and the third the scalp
(radius = 1.0, conductivity = 1.0). For surface EEG, a set
Schwartz et al.
282
of 32 electrodes (subset of the 10-10 system, Chatrian
1985) is modeled. The electrodes are uniformly distributed among the scalp, this configuration is being used in
our real EEG recordings. For MEG, a 37 channels sensor
(equivalent to the Magnes system from BTi) is used. The
center of the sensor is centered over the region of interest
(on EEG electrode T4). Note, we used in these simulations the real geometry of MEG or EEG sensors. Thus,
there were strong differences in spatial sampling between both recording methods.
between channels due to an unexpected source of activity
in the recorded signal. We added the resulting noise to
the simulated signals with a weight that is computed
from the desired signal to noise ratio (SNR). The SNR is
defined as the ratio of the average of the simulated signal
power to the average of the noise power.
To conclude, before the evaluation presented in the
next section, we validated our simulations approach by
estimating its capabilities to reproduce depth recordinglike signals. The methodology and the results are described in (Schwartz 1996a).
Computation of the contributions of the AoAs
For one AoAk, the simulated EEG and MEG signals
are the sum of the contributions of its single dipoles
weighted over time by the value of its time course of
activation. There exists a simple linear relationship between electric and magnetic recordings and the moment
of a dipole at any location in the brain. Let sk(t) be the
value of the time course of activation of the AoAk at a
latency t and mi(t) the measurements (MEG or EEG) at a
latency t for the sensor i. Then
where Gk represents the gain matrix of the AoAk. The
components gijkare non-linear functions of both the sensor locations and the model of the head. NAOAK is the
number of single dipoles in the AoAk; Mk is the signals
generated by the AoAk over the time; and SK is the time
course of activation of the AoAk. Then, when the activity
of N AoAs is combined, the final measurement M is
Criteria of evaluation
Let t be a latency, and AoAk an area of activity. To
evaluate each algorithm two errors are computed: The
localization error of the AoAk at t is defined as the distance between the location of equivalent dipole Deq and
the center of gravity of AoAk (i.e., the center of gravity of
the single dipoles belonging to AoAk). In addition, to
determine if Deq is in the neighborhood of an AoA with
respect to the area of this AoA, we define the following
relative error:
where XiAOAOK is the center of gravity of AoAk and xiDeq the
location of the localized equivalent dipole Deq.
The orientation error is defined as the angle between
the orientation of the equivalent dipole Deq and the mean
orientation of AoAk (i.e., the mean orientation of the single
dipoles belonging to AoAk). In addition, we define a
relative error of orientation as follow (Stok 1987):
Addition of noise
In order to study the effects of the noise level on the
accuracy of localization, noise was added to the simulated signals. The noise was issued from EEG/MEG
spontaneous activities recorded from an adult subject
(length = 200 ms, sampling rate = 0.920 ms, filtered with
a band-pass filter 1-120 Hz) and is used to match as much
as possible the spectral characteristics of real measurements. Since the simulations are performed in the context of evoked potential/field, each noise epoch is
constructed by 10 averages of 100 ms of spontaneous
activity taken randomly from the original epoch of 200
ms. This average reduces the possible signal correlation
where DiA°Ak is the mean direction of AoAk and DiDeq the
direction of the localized equivalent dipole Deq. These
values are reported over time to study the accuracy and
the stability of the results in term of localization and
direction errors.
Results
Effects of the variation of area of the AoA
We simulated the MEG/EEG signal with one AoA
without noise. The area of the AoA varied from a single
Evaluation of a New MEG-EEG Localization Approach
Figure 2. Accuracy of localization and orientation for
several areas of an AoA located in the medial part of
Heschl gyrus. (Distance from the surface of the head 4.5
cm; mean orientation mainly tangential; the AoA contains
900 dipoles whatever the area). (A-top) Error of localization for MEG (white) and EEG (black). (B-bottom) Orientation accuracy. Note that on those noiseless signals both
MDF and SPTF gave the same results.
point source to 4 cm2 (figure 2). The localization accuracy
on EEG signals decreased when the area of the AoA
increases from 0 mm for a single point source up to 27
mm (Eri = 140%) for 4 cm2. On the contrary, the MEG
accuracy remains under 7 mm (Erl = 45%) for all areas of
the AoA. Regarding orientation the effect was inverse,
i.e., the accuracy of the results on MEG signals decreased
when the area of the AoA increases from 0° (Erd = 0%) for
0 cm2 to 8° (E rd = 24%) for 4 cm2 while the EEG orientation
accuracy remained superior to 1° (Erd = 3%).
Test with two simultaneous activated sources
Analysis on MEG signals
When only one of the AoAs was activated, the accuracy of localization was most of the time very good when
SNR = 100 (errors < 0.75 mm (Erl = 7%)) with both MDF
and SPTF. The performance of the SPTF remained almost
constant whatever the noise level (figure 3A and table I).
When both AoAs were activated (between 40 and 50 ms)
the SFTF localized both AoA I and AoA II with a very good
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Figure 3. Localization errors with two simultaneous activated sources for MEG signals. Dotted lines represent
localization results for AoA I and plain lines represents
localization results for AoA II. (A) Localization errors using
SPTF (SNR = 100). (B) Localization errors using MDF (SNR =
100). (C) Localization errors using SPTF (SNR = 1). (D)
Localization errors using MDF (SNR = 1). The bottom curve
represents the time course of activation of AoA I (dotted
line) and AoA II (plain line). The temporal overlaping
between both AoAs is equal to 75% of their time of activation. Note that the MDF localizes 1 equivalent dlpole
per latency and the SPTF may localize up to 3 equivalent
dipoles per latency. The grey bold rectangles in (C)
above the results of the SPTF indicate the latencies when
the SPTF found more equivalent dipoles than the actual
number of activated sources. The labels "begin" and
"end" indicate the time range when the activation is
effectively different from zero. The horizontal bold line on
the time axis represents the width of the window of analysis
used for the SPTF.
accuracy (errors < 1 mm (£,./ = 9%) for AoA I and errors <
2 mm (Erl = 18%) for AoA II) with SNR = 100 (figures 4
and 5). Whereas the MDF produced a set of spurious
localizations between AoAs (15 mm from AoA 1 and 7 mm
from AoA II). Moreover, this set of localization was
linked to AoA I and AoA II by equivalent dipoles producing an artificial displacement of the source of activity.
Regarding orientation accuracy (figure 6), both
methods had the same behavior as that previously described for localization accuracy. The SPTF gave good
orientations and the accuracy remained very high (errors