Noninvasive Cardiac Signal Analysis Using Data Decomposition Techniques - Modeling in Computational Biology and Biomedicine - page 92

a b

600

400 1

200

0 0

−200

−400 −1

−600

0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800

T−wave index, i T−wave index, i

Fig. 3.7 TWA detection during angioplasty. ( a ) First component of vector θ i in model ( 3.12 )
estimated by the PCA-based method of Sect. 3.2.3 . The alternans of the parameter appears in the
range 300 ≤ i ≤ 650 .( b ) Welch's t test output for p< 0 . 01 from the PCA results displayed in ( a ).
Changes in alternans phase (0 , 1 , − 1) are clearly visible

in [ 16 ] by considering the matrix made up of the N available T-wave realizations:
X =[ x 1 , x 2 ,..., x N ] ∈R L×N . The rank- k subspace best describing in the least

square sense the observation space, i.e., the subspace spanned by the columns of X ,
is spanned by the columns of any given rank- matrix A and the ( k− ) dominant left

singular vectors of matrix I − A ( A

T X . Fixing k =3 and A = 1I ,this
result yields the sample version of the above derivations. To enhance the varying
nature of the TWA phenomenon, the data can be transformed according to the
derivative operator δ x i =( x i − x i− 1 ) before applying the detection method.
The PCA-based approach described in this section is valid for any extended
model of observation disturbances. For instance, a detrending step can also be
applied as in [ 17 ], where a more refined model accounting for an affine baseline
wandering has also been proposed in the context of noninvasive atrial activity
extraction during AF using a similar framework.

T

A ) − 1 A

3.2.4 Success Story: T-Wave Alternans Detection During

Angioplasty

The TWA detection approach described in the previous section has been applied
to real data acquired during angioplasty (STAFF III database) [ 15 ]. Angioplasty
consists in the inflation of a balloon in the coronary artery to treat arterial stenosis.
This procedure temporarily provokes ischemia and induces changes in cardiac cell
properties that may cause TWA. Figure 3.7 a displays the first entry of vector

θ i in

model ( 3.12 ) (or of vector ˜ θ i in Eqs. ( 3.14 )and( 3.15 )) when using δ x i from the

T-wave dataset.