Optimized Positioning of ECG Electrodes for WSN Applications - Application and Multidisciplinary Aspects of Wireless Sensor Networks - page 193

where AE ¢ is the AE matrix represented in the TS 1 coordinate system. A hypothesis
of this algorithm is that AE ¢ can be considered as an approximation of the unknown
X (presented in the

TS coordinate system).
The last step of the algorithm will return AE ¢ to the original coordinate system
[ 26 ]:

1

( ) =

T

T

AE TS · ( AE¢ ) , (9.24)

1

where AE is an approximation of the X (measured MECG). The reconstructed
12-lead ECG can be extracted from AE . PCs calculated from the X and data from
only four optimal leads, obtained from X , were used to reconstruct 12-lead ECG.
The target 12-lead ECG, extracted directly from

X , is used to evaluate the obtained

reconstructed results.
The described methodology is based on the assumption that the optimal leads
are known. The procedure for their determination is described in the next section.

9.4.3.2 Optimal Leads Selection with PCA

The optimal leads selection algorithm, based on PCA, is shown in the flowchart
(Fig. 9.10 ).
The trine participation of the MECG can be observed in the above algorithm.
First, it is used to calculate PC; second, to generate the target 12-lead ECG; and
third, to form all possible sets of four reconstruction leads. For every set of four
reconstruction leads, a reconstructed 12-lead ECG is calculated according to the
procedure described in Section 9.4.3.1 . All reconstructed 12-lead ECGs are
compared to the target 12-lead ECG, according to the similarity measures described
in Section 9.4.2 and classified by the similarity factors. The four reconstruction
leads that result in the best similarity factor are considered to be the best leads for
the reconstruction.
Different similarity measures (see Section 9.4.2 ) have usually been observed to
result in the same set of best leads [ 27 ]. It can be concluded that all the described
similarity measures are acceptable; therefore, anyone of them can be selected.

9.4.4 Multivariate Linear Regression

An alternative approach, based on Multivariate Linear Regression (MLR), has been
used to model the relationship between a 12-lead ECG and a set of reconstruction
leads composed of three differential leads, each implemented by two closely placed
electrodes, as described previously. In Section 9.4.3.1 , the MECG was denoted as:

X X = { (1), ……… , Xi Xj Xm ( ), , ( ), , ( )}. (9.25)

As already explained, the differential lead (DL) is the difference between two
unipolar leads: