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where
S
is the reconstructed lead, α
i
are constant coefficients, and
L
i
are measured
leads from a limited lead system composed of
p
leads. The above equation can be
written in a matrix form for
r
reconstructed leads:
S A
=
,
·
where
A
is an
[
r
×
matrix,
L
and
S
are vectors of
p
input leads from limited
system, and
r
output reconstructed leads, respectively. The transformation coeffi-
cients are time-independent and the same for all investigated subjects.
]
9.4
New Methodology for Wireless Electrode Positioning
and Reconstruction of 12-Lead ECG
9.4.1
Input Data
The input data set should be as large as possible, i.e., as many test electrodes as possible
should be used. Larger numbers of test electrodes increase the chances of better selec-
tion of an optimal subset of electrodes. Our input data sets were measurements from
31-channel MECG, 10 s long (10,000 samples per channel), either consecutive from the
same subject or single measurements from a number of subjects. Note that an MECG
measurement has enough leads, placed at appropriate positions, to generate the target
12-lead ECG, which is the same as the one obtained by a standard measurement.
For detailed verification of the selection algorithm it is useful to have several test
MECG measurements from the same patient. The first MECG measurement is used to
calculate the transformation coefficients required by the reconstruction algorithm, and
to select a set of the best electrodes for the reconstruction of the standard 12-lead ECG.
Note that the remaining MECGs are, in fact, not known in real situations, where only
measurements from a limited number of leads will be available. But if available, they
can be used for the evaluation of the obtained reconstruction parameters - differential
lead positions and transformation coefficients.
In this way, validation of the reconstruction algorithm is possible using different
measurements from the same subject, taken on different occasions, for example,
before and after heart surgery. If only a single test MECG measurement is available,
we can still evaluate the derived reconstruction coefficients, with some confidence.
In this work we evaluated the algorithms for selecting optimal differential leads with
31-channel test MECG measurement that contains, beside the normal sinus rhythm,
a single supraventricular extrasystole. Such a reconstruction can be regarded as sig-
nificantly harder than just the reconstruction of a normal sinus rhythm.
9.4.2
Time Series Similarity Factors
ECG recordings are generally composed of more than a single lead, as in the
12-lead ECG, and a MECG which has 31 or 35 leads. In the terminology of time
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