Biomedical Engineering Reference
In-Depth Information
when the focus is on the signal subspaces of the sources, i.e., the linear span of their
spatial topographies (or mixing matrix columns, as defined in Sect.
3.3.1
), rather
than the sources themselves. A good example in the context of AF analysis is the
noninvasive measurement of atrial signal organization [
3
]. The working hypothesis
can simply be put as follows: the more complex or disorganized the atrial activations
during AF, the higher the number of spatial topographies required to explain or
reconstruct the observations with certain accuracy (spatial complexity) and the
higher the time variability or nonstationarity of the spatial topographies in the
surface recording (temporal complexity).
To quantify this notion of spatio-temporal complexity, the TQ intervals (contain-
ing atrial activity only) can be concatenated and divided into several consecutive
segments. A BSS model like that in Eq. (
3.17
) is assumed for each segment
c
:
(
c
)
=
H
(
c
)
(
c
)
x
s
.
As explained in Sects.
3.2.2
and
3.3.2
, PCA obtains such a decomposition in which
the sources are uncorrelated and arranged in increasing order of variance (principal
components). We compute the PCA mixing-matrix estimate
ˆ
(1)
from the first
segment, and then project the data of the following segments on its first
k
columns
or spatial topographies, denoted
ˆ
H
(1)
k
H
. Such a projection can be computed as in
Sect.
3.2.2.3
:
(1)
k
(1)
k
(1)
k
(1)
k
=
ˆ
[(
ˆ
)
T
ˆ
]
−
1
(
ˆ
(
c
)
k
(1)
k
(1)
k
)
T
(
c
)
=
U
)
T
(
c
)
x
H
H
H
H
x
(
U
x
,
(1)
k
where
U
contains the orthonormal
k
principal directions of the first segment; see
also Eq. (
3.19
). The normalized MSE between
x
(
c
)
(
c
)
can then be computed
and averaged to quantify how well the dominant principal directions of the first
segment are able to explain the observed data in the remaining segments. This
parameter is computed for
k
=3
on the basis of the classical dipole model, which
assumes that cardiac activity in physiological conditions can be explained by three
components only [
14
]. It turns out [
3
] that this noninvasive index is able to clearly
distinguish two populations of patients that appear to be related, respectively, to type
I (well-organized) and type II/III (disorganized) AF according to Konings' criteria
for invasive atrial recordings [
13
].
and
x
3.4
Conclusion and Outlook
This chapter has examined two problems in cardiology involving the analysis of
the surface ECG, namely, TWA detection and atrial activity estimation during AF.
The diversity or redundancy provided by the spatially separated electrodes and
quasi-periodic waveforms of this noninvasive recording modality can sometimes
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