Functional Constraints Added to an
ICA Separating Algorithm: an Example on
Magnetoencephalographic Signals
Marco Balsi
1
, Giuseppe Filosa
1
, Roberto Sigismondi
1
, Giancarlo Valente
1
,
Giulia Barbati
2
, Filippo Zappasodi
3
, Sara Graziadio
4
, Camillo Porcaro
2
,
Franca Tecchio
3
1
Dipartimento di Ingegneria Elettronica, Università “La Sapienza”, Rome, Italy
2
AFaR – Center of Medical Statistics & IT, Fatebenefratelli Hospital, Rome, Italy
3
ISTC-CNR, Rome, Italy
4
Dipartimento di Fisica, Università “La Sapienza”, Rome, Italy
Abstract. A constraint function expressing a priori information about the
structure of data recorded in a MEG experiment is used to bias ICA towards a
more realistic decomposition. To do so, a function measuring sensitivity to the
stimulation considered is added to the usual contrast function to be optimized.
Experiments show that the proposed algorithm effectively succeeds in
separating physiologically significant activities that standard ICA fails to
distinguish in half of the cases.
1 Introduction
Physiological activity in the brain can be evaluated by means of non-invasive
techniques based on measurement of the electric or magnetic field generated by
electrical neuronal currents (e.g. electroencephalogram - EEG, magnetoencephalo-
gram - MEG). However, relevant signals, related to significant activity, are mixed and
embedded in unstructured noise and in other physiological signals, non relevant to the
desired observation. For this reason, extraction of information from such signals
amounts to blind separation of sources in presence of noise, filtering, and interference,
at least as long as we may assume all phenomena to be linear, as is usual and most
often reasonable.
One of the most promising techniques to tackle such task is Independent
Co
mponent Analysis (ICA) [1,2]. Several studies have proved its effectiveness in
extracting relevant activations from MEG and EEG signals [3-6]. Nevertheless, in
some cases signals are not effectively separated in single components, as they can
remain partially mixed, or split into more than one component. Moreover, ICA may
fail in presence of strong noise, showing very rapid degradation of performance
under a certain SNR [7].
Balsi M., Filosa G., Sigismondi R., Valente G., Barbati G., Zappasodi F., Graziadio S., Porcaro C. and Tecchio F. (2005).
Functional Constraints Added to an ICA Separating Algorithm: an Example on Magnetoencephalographic Signals.
In Proceedings of the 1st International Workshop on Biosignal Processing and Classification, pages 35-41
DOI: 10.5220/0001196300350041
Copyright
c
 SciTePress

ICA does not take other information into account than the statistics of the data.
However, sometimes quite accurate information on some parameters of the signals
we want to separate is known, and more often only general characteristics are
known, such as regularities generally valid on a broad class of natural signals.
Some of the authors have developed a modified ICA algorithm that takes
available general a priori information into account explicitly, and proved its
effectiveness on artificial [8] and real fMRI [9] data. In this paper, such technique is
applied to MEG recordings taken in experiments concerning individual finger
stimulation. We show how addition of appropriate information to the separating
algorithm allows to distinguish more satisfactorily activity from neural networks
devoted to individual finger representation, with respect to standard ICA.
The paper is organized as follows. Section 2 describes the physiological
background, and reviews the modified ICA technique employing additional
information, and experimental methods. In section 3 we discuss results, and
conclusions are drawn in section 4.
2 Physiological Background, Materials and Methods
2.1 EEG and MEG
Neurophysiological techniques (EEG and MEG), by allowing direct investigation of
the electrical neuronal activity, obtain measures with the same time resolution as
the cerebral processing itself. For this reason, EEG and MEG could be used to
investigate cerebral connectivity as expressed in the inter- and intra-regional
activity synchronization. The crucial problem is to gain access to the inner neural
code, starting from the extra-cranial recorded EEG and MEG raw signals. The main
approach has been, up to now, to solve the so-called ‘inverse problem’, i.e. to use
Maxwell’s equations to calculate spatial distribution of the intra-cerebral currents
starting from the magnetic and/or electric field detected in a wide enough area of
the scalp surface. Substantial theoretical and technical difficulties are present in
solving the inverse problem [10].
A different approach has been recently considered, based on statistical properties
of sources composed in the observed signals: ICA was applied by the EEG/MEG
researchers not only as a computational technique able to remove artifacts, but also
as a powerful tool in discriminating functionally different neural sources, possibly
overlapping in time and space [11-13].
2.2 ICA with Prior Information
ICA applies to blind decomposition of a set of signals x that is assumed to be
obtained as a linear combination (through an unknown mixing matrix A) of
statistically independent non-Gaussian sources s:
Asx
=
. (1)
36

Sources s are estimated (up to arbitrary scaling and permutation) by independent
components (IC) y as
Wxy
=
,
where unmixing matrix W is to be estimated along with the ICs.
ICA can be cast as an optimization process that maximizes independence as
described indirectly by a suitable contrast function. As ICA only takes cumulative
statistics of signals into account, other structural aspects remain irrelevant to the
decomposition. For instance, temporal order of samples of a signal defined over
time is indifferent.
Biomedical signals can often be assumed as generated through a linear mixing
process as Eq. 1, where independent sources are supposed to model activities (of the
brain in this case) that originate from separate causes, but coexist in adjacent and
possibly overlapping volumes. In fact, strict independence of such sources is
probably in many cases unrealistic, but using such hypothesis has proved very
effective in many contexts, even if a posteriori we may observe that perfect
independence is never achieved.
Often, however, we know more about such causes and signals. In particular, when
a stimulation protocol is applied, we may make strong assumptions on the localiz-
ation of response in time.
Some of the authors [8] have developed a modified ICA technique that explicitly
uses such additional information to bias the decomposition procedure towards
solutions that satisfy such assumptions, trading off some independence of the
extracted signals. The method is based on optimizing a modified contrast function
HJF
λ
+
=
where J is any function as normally used for ICA, while H accounts for the prior
information we have on sources. Parameter λ is used to weigh the two parts of the
contrast function. If λ is set to zero, maximization of F leads to pure independence.
2.3 Experimental Setup
Magnetoencephalographic data were recorded from 16 healthy volunteers (8
female, mean age 31±2 years), during separate electrical stimulation of their right
thumb or little finger. Ring electrodes were used to deliver the stimulus which
consisted of 0.2-ms-long electric pulses (cathode proximal), with an inter-stimulus
interval of 631 ms; stimulus intensities were set at about twice the subject’s sensory
threshold. The subjects had signed an informed consent and the experimental
protocol followed the standard ethical directives of the declaration of Helsinki.
Brain magnetic fields were recorded from the left rolandic region, i.e., contra-
laterally to the stimulation, after positioning the central of the 28 sensors of the
MEG system over the C3 site of the International 10–20 electroencephalographic
system; a total area of about 180 cm
2
was covered. Data were filtered through a
0.16–250-Hz bandpass and gathered at 1000-Hz sampling rate. The noise spectral
density of each magnetic sensor was 5–7 fT/Hz
1/2
at 1 Hz. About 280 single trials
were recorded for each of the two stimulus conditions.
37

2.4 Functional Constraints
In order to identify neural networks devoted to individual finger central
representation, the ‘reactivity’ to the stimuli was taken into account. It was defined
as follows:
1) the evoked activity (EA) was computed separately for the two sensorial
stimulations, by averaging signal epochs centered on the corresponding stimulus
(EA
T
, thumb; EA
L
, little finger).
2) the reactivity coefficient (R) was computed as
∑∑
−
−==
−=
10
30
X
40
20
X
)(EA)(EA
tt
X
ttR
with X = T, L, and t=0 corresponding to the stimulus arrival. The time interval
ranging from 20 to 40 ms includes the maximum activation [14] and the baseline
(no response) was computed in the pre-stimulus time interval (-30 to -10 ms).
3) The constraint function was then chosen as
X
H
(
)
kRH
XX
,
ϕ
=
,
where
()
⎩
⎨
⎧
≤
=
else 1
when
X
kRkR
R
X
X
ϕ
and k is a suitable parameter measuring the required minimum response.
In order to separate contributions generated by individual stimulations, we started
by using constraint
, and extracted a single component. Then, after projecting
residuals on the orthogonal space w.r.t. the extracted component, we repeated the
procedure using
. From then on, we applied a composite
L
H
T
H
TL
HHH +
=
. This
procedure was motivated by the fact that thumb representation is physiologically
larger than little finger one. Therefore, by operating in this way we meant to favour
extraction of the naturally weaker components first.
The same data were also analyzed by unconstrained ICA, using the popular
fastICA algorithm [15]. Both algorithms were applied after the PCA whitening
without dimensionality reduction.
For comparison, the positions of the known markers of signal arrival in the primary
sensory cortex, occurring at around 20 ms from the stimulus (M20), were calculated
by standard procedure of averaging original channel signals.
As a main criterion to evaluate the ‘goodness’ of extracted ICs in representing
individual fingers, we observed their spatial position. To this aim, ICs representing
thumb and little finger were separately retro-projected, so as to obtain their field
distribution. A moving equivalent current dipole (ECD) model inside a
homogeneous best-fitted sphere was used. ECD coordinates were expressed in a
right-handed Cartesian coordinate system defined on the basis of three anatomical
landmarks (x-axis passing through the two preauricolar points directed rightward,
the positive y-axis passing through the nasion, the positive z-axis consequently).
Only sources with a goodness-of-fit exceeding 80% and within a pre-defined
physiological volume (a cube of 5 cm side, centred in x=-33, y=9, z=100, i.e. the
38

mean centre of hand cortical representation in a healthy population) [14] were
accepted. It is to be noted that the field distribution obtained by retro-projecting
only one IC, is time-invariant up to a scale factor. Consequently, the subtending
current distribution (ECD position in our case) is time-independent.
Table 1. Average and s.d. across subjects (number of subjects, #) of IC
T
and IC
L
characteristics, fast_IC
T
, fast_IC
L
and fast_IC
T;L
(a unique IC responding best to both
stimulations, found in 50% of the cases using fastICA): spatial position S
X
(x, y, z) with their
explained variance (e.v.); the evoked activity indexes (R
T
and R
L
). Mean M20
T
and M20
L
positions are reported.
S
X
(mm)
# e.v. x y z R
T
R
L
IC
T
16
0.95±0.05 -41±9 9±12 88±11 11.6±4.1 1.2±1
IC
L
16
0.94±0.05 -35±11 5±12 100±14 7.2±5.5 13.3±5.3
fast_IC
T
8
0.94±0.05
-44±13 10±38 83±19 8.5±5.1 1.9±3.5
fast_IC
L
7
0.97±0.04
-38±13 6±22 98±11 4.3±4.7 9.2±7
fast_IC
T;L
8
0.94±0.08
-38±14 9±6 96±13 7.9±5.2 8.4±3.6
M20
T
16
0.96±0.18 -42±8 11±11 91±10
M20
L
16
0.94±0.06 -33±10 6±13 100±10
3 Experimental Results
The activity of the source representing a finger is compared when stimulating the
finger itself with respect to when an other finger is stimulated. To do this, the defined
indexes R
T
and R
L
, describing respectively the responsiveness to thumb and little
finger stimulations, were both tested for each of the two functional sources IC
L
and
IC
T
. The evoked activity of the two extracted sources (IC
T
and IC
L
), resulted
significantly higher when the finger that source represents was stimulated (Table 1,
R
T
> R
L
for thumb source (IC
T
), p <.0001 ; R
L
> R
T
for little finger source (IC
L
),
p=.001).
Components obtained by fastICA failed in half of cases (8 out of 16) to separate
thumb and little finger response: in those cases a unique IC was selected that
responded best to both stimulations (fast_IC
T;L
) . Moreover, in one subject out of the
eight showing the thumb source (fast_IC
T
), the little finger one lacked. Therefore, in
the fastICA case, R
L
and R
T
were tested for the three types of sources obtained,
including for each test only those subjects for whom the components considered were
indeed found. Results were positive for two out of the three comparisons (Bonferroni
post-hoc comparisons): R
L
> R
T
for fast_IC
L
(p=0.02) and for fast_IC
T;L
versus
fast_IC
T
(p=0.04), but not significantly difference was found between fast_IC
L
and
fast_IC
T;L
(p=0.95). R
T
did not result significantly different for any contrast between
pairs of obtained sources.
As shown in Table 1, dipole coordinates (x,y,z) were computed from the two retro-
projected components IC
T
and IC
L
in our 16 subjects group. We have to note that for
4 subjects, localization of the retro-projected IC
T
was not possible (variance explained
39

< 0.8, dipole not accepted). The same retro-projection was performed for the fastICA
sources.
A General Linear Model (GLM) for repeated measures was estimated to test for
differences in source localization: as dependent variables the 3-dimensional
coordinates vectors obtained for each subject were used, with the two levels Finger
(Thumb, Little) as within-subjects factor. Factor Finger resulted significant
(F(3,9)=16.512, p=0.001), corresponding to S
T
(position of retro-projected IC
T
)
significantly lateral, anterior and lower with respect to S
L
(position of retro-projected
IC
L
). This was in agreement with M20 ECD positions when stimulating respectively
thumb and little finger (Table 1).
Testing the seven subjects for whom thumb and little finger response was separated,
for the position of retro-projected ICs (fast_S
T
and fast_S
L
resp.), factor Finger
resulted not significant at the standard threshold p value of 0.05 (F(3,4)=4.37, p=0.09;
x and y axes not significantly different, z axis at p=0.06). Moreover, dipole
coordinates of fast_S
T;L
(retro-projected fast_IC
T;L
) with respect to fast_S
T
and
fast_S
L
resulted not significantly different (Kruskal-Wallis test, p>0.05).
It can be noted that the first two functionally-constrained components (IC
T
and
IC
L
), well positioned in agreement with homuncular distribution, were characterized
by non-Gaussian kurtosis values: normalized kurtosis median=0.84; interquartile
range=[0.36-1.02]. The remaining components, having excluded the artifactual
abnormally peaked ones [5], tended to Gaussianity, confirming that the main ICA
criteria work properly: normalized kurtosis median=0.11; interquartile range=[0.05-
0.23]. This difference was found statistically significant (Mann-Whitney p-
value<0.0001).
Kurtosis differences in the fastICA components resulted less evident between
task-related and non task-related components: fast_IC
T
, fast_IC
L
and fast_IC
T;L
had
normalized kurtosis median=1.5; interquartile range=[0.88-1.99]. The remaining
components had normalized kurtosis median=0.91; interquartile range=[0.43-1.5],
Mann-Whitney p-value=0.06.
4 Conclusions
The proposed procedure proved able to extract somatotopically consistent sources.
A specific added value of the ICA approach lies in detecting the complete time
course of the estimated sources, trial by trial, instead of describing the activations
by averaging all sensors channels and only in specific instants, as usually done in
the standard procedures.
On the other hand, standard ICA failed in half of the examined subjects to
separate the two sources, producing in that cases a "mixed finger" source, both in
spatial position and in task reactivity.
40

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