Ventricular Activity Signal Removal in Atrial Electrograms of Atrial

Fibrillation

Bahareh Abdi

, Richard C. Hendriks

, Alle-Jan van der Veen

and Natasja M. S. de Groot

Circuits and Systems (CAS) Group, Delft University of Technology, Delft, The Netherlands

Department of Cardiology, Erasmus University Medical Center, Rotterdam, The Netherlands

Keywords:

Atrial and Ventricular Source Separation, Low-rank and Sparse Matrix Decomposition, Atrial Fibrillation,

Atrial Electrogram.

Abstract:

Diagnosis and treatment of atrial ﬁbrillation can beneﬁt from various signal processing approaches employed

on atrial electrograms. However, the performance and interpretation of these approaches get highly degraded

by far-ﬁeld ventricular activities (VAs) that distort the morphology of the pure atrial activities (AAs). In this

study, we aim to remove VAs from the recorded unipolar electrogram while preserving the AA components.

To do so, we have developed a framework which ﬁrst removes the VA-containing segments and interpolates the

remaining samples. This will also partly remove the atrial components that overlap with VA signals, e.g., du-

ring atrial ﬁbrillation. To reconstruct the AA components, we estimate them from the removed VA-containing

segments based on a low-rank and sparse matrix decomposition and add them back to the electrograms. The

presented framework is of rather low complexity, preserves AA components, and requires only a single EGM

recording. Instrumental comparison to template matching and subtraction and independent component analy-

sis shows that the proposed approach leads to smoother results with better similarity to the true atrial signal.

1 INTRODUCTION

Atrial ﬁbrillation (AF) is one of the most com-

mon age related cardiac arrhythmia whose persistence

and progression is rooted in impaired electrical con-

duction known as electropathology. Atrial electro-

grams (EGMs), i.e. a record of changes in the electri-

cal potential of the (many) cells in the neighborhood

of an electrode that is positioned on the heart surface,

play an important role in the analysis of AF and ex-

amining the level of electropathology in human tis-

sue (Yaksh et al., 2015). However, these electrograms

suffer from far-ﬁeld ventricular activities (VAs) cau-

sed by ventricular depolarizations. Although during

sinus rhythm (SR), atrial activity (AA) and VA are se-

parated in time, they might overlap during AF. These

strong VAs distort the morphology of the pure AAs,

complicate their further analysis and affect their ﬁ-

nal interpretations. Therefore, a required step before

any further processing of the recorded electrograms is

to estimate the pure atrial activities by removing the

VAs.

Reita et al. in (Rieta and Hornero, 2007) catego-

rizes the developed algorithms for VA removal into

three groups. The ﬁrst group of algorithms is based

on template matching and subtraction (TMS) (Shku-

rovich et al., 1998). A second group is based on

adaptive ﬁltering using a VA reference (Petrutiu et al.,

2006), which is obtained using a reference ECG lead.

The third group of VA removal algorithms is based on

blind source separation approaches that try to separate

the components based on the assumption that VA and

AA are uncorrelated, orthogonal, or statistically in-

dependent from beat to beat over time or over space

in multichannel recordings. Independent component

analysis (ICA) is one of the most widely used appro-

aches from this group (Rieta et al., 2004). None of

above mentioned approaches results in a pure AA es-

timate. A perfect performance, however is hampered

by the fact that these signals share overlapping com-

ponents in both time and frequency domain and are

also partially correlated over time and space.

In this study we develop a new framework for re-

moving VA which is based on a sparse and low rank

matrix decomposition. Initially, VA-containing seg-

ments are detected, removed and replaced with subse-

quent spline interpolation. However the performance

of this approach is limited during AF, as VAs might

overlap with the depolarization phase of AAs. In our

approach, we propose to reconstruct AAs in the remo-

Abdi, B., Hendriks, R., van der Veen, A. and S. de Groot, N.

Ventricular Activity Signal Removal in Atrial Electrograms of Atrial Fibrillation.

DOI: 10.5220/0007388901790184

In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019), pages 179-184

ISBN: 978-989-758-353-7

179

ved segments and adding them back to the interpola-

ted signal. Finally, using simulations, we compare the

performance of the proposed algorithm with two other

approaches, TMS and ICA.

The remainder of this paper is as follows. In

Section 2 we formulate the ventricular and atrial acti-

vity separation problem and present our proposed fra-

mework for solving the problem. In Section 3 we pre-

sent the results and compare them with two other met-

hods. Finally, in Section 4, conclusions are drawn.

2 METHOD

2.1 Electrogram Model

We consider a sampled unipolar atrial electrogram

m ∈ R

N×1

with N the number of time samples. We

assume that m is the summation of AAs and VAs, mo-

deled as

m = a + v, (1)

where vectors a, and v contain the AA and VA sam-

ples produced by atrial and ventricular sources re-

spectively. From the physiological point of view, the

AA is composed of two phases, the depolarization

phase and the repolarization phase. The depolariza-

tion phase is of most interest and consists of a pre-

dominantly positive spike followed by a sharp ne-

gative deﬂection. It mostly contains high frequency

AA components and shows a sparse representation

in time. The repolarization phase on the other hand,

changes very smoothly in time and contains very low

frequency components. These repolarization activi-

ties are often viewed as baseline wandering and may

even fade out in some recordings. Depending on the

homogeneity of the depolarization wavefront and the

speed of the electrical propagation in the tissue, the

morphology of these two components may vary from

activity to activity even during SR and they cannot be

simply considered as a shifted version of each other,

especially during AF.

2.2 Data Matrix Formation

To overcome the unnecessary introduction of arti-

facts, we use the concept of minimal processing and

process only VA-containing segments. In this study,

we used a simultaneously recorded ECG as reference

signal to specify the VA-containing segments in the

electrogram which coincide with the QRS complexes

in ECG. Since the QRS complex or the R peak is ea-

sily detectable, any simple detection algorithm could

be used. A rectangular window centered at each de-

tected R peak with a ﬁxed width W is used to mark

the onset and offset of the VA and to denote the VA-

containing segments that might also contain AA du-

ring AF.

The baseline wandering of the electrogram is

mainly caused by the repolarization phase of AA. To

remove the VA without affecting this component, we

ﬁrst remove the VA-containing segments and then re-

place them by spline interpolation applied on the re-

maining data samples. This can to some extend re-

place the removed baseline in the VA segment and

is one of the most basic and efﬁcient approaches for

VA cancellation during SR (Ahmad et al., 2011). The

interpolated data is denoted by m

and has the same

length as the recorded electrogram m. During SR

and in some cases during AF, the VA does not over-

lap with the depolarization phase of AA, and leaves

this component unaffected. Removal and interpola-

tion cancels the VAs thus sufﬁciently and no further

processing would be necessary, cf. the input signal m

and interpolated signal m

in the ﬁrst VA-containing

segment of Figure 1. However, unlike during SR, it

is likely that during AF the depolarization phase of

the AA and the VA completely or partially overlap.

In this case VA removal and interpolation also re-

moves the overlapping depolarization phase of AA.

Therefore, processing the removed component, i.e.,

x = m − m

, is required to extract the potentially re-

moved atrial components and add them back to the

interpolated data, cf. the m, m

and the removed sig-

nal x in the second and third VA-containing segments

of Figure 1.

Before employing any further processing, we con-

struct an appropriate data matrix X of size W × K,

where each column of X = [x

, x

, ..., x

]

is one VA-

containing segment (of length W) of x stored in the

vector x

, k ∈ 1, 2, .., K, and where K is the total num-

ber of detected segments. The data matrix X is mo-

deled as the sum of two components (i) matrix V con-

taining the aligned ventricular activities and (ii) ma-

trix A containing the randomly occurring atrial acti-

vities that coincided with the VA-containing segment,

i.e.

X = A + V. (2)

2.3 VA and AA Separation

We now formulate the problem of decomposing the

data matrix X into its two components, V and A.

The problem can be considered as a highly under-

determined blind source separation where the num-

ber of unknowns, A and V, is twice the number of

given measurements, X. However, prior knowledge

of the two sources can be employed to derive use-

ful approximate solutions: (i) The aligned VAs in V,

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180

from beat-to-beat, have an almost similar morphology

which indicates that V is a low-rank matrix while the

occurrence of AA and its morphology in these seg-

ments is random indicating that A is not a low-rank

matrix, (ii) When presented in frequency domain, the

VAs are much sparser, and (iii) AAs are sharper and

more spiky in time domain compared to VAs, matrix

A can therefore be constrained to be sparse. Exploi-

ting these three properties, we formulate the separa-

tion problem as

min

{A,V}

rank(V) +βkΨ

+ αkAk

s. t. X = A + V, (3)

where rank(·) is the rank operator, kAk

∑

i j

| is

the l

-norm of A, Ψ

performs the two-dimensional

cosine transform (DCT), and α and β are the penali-

zation parameters.

Since the rank function is non-differentiable and

non-convex, it is in most studies approximated with

the nuclear norm, kVk

∗

∑

i=1

(V), that is the sum-

mation of all sorted (from largest to smallest) singular

values σ

of matrix V. However, minimizing the trun-

cated nuclear norm (TNN) kVk

∑

k=r+1

(V), that

is the summation of the K −r smallest singular values,

performs better in minimizing the rank function than

minimizing the nuclear norm (Hu et al., 2013). The

TNN, on the other hand, is non-convex and it cannot

be minimized directly. To overcome this issue, the

TNN is initially approximated by its convex surrogate

(Hu et al., 2013)

kVk

∑

i=r+1

(V) = kVk

∗

−

∑

i=1

(V)

= kVk

∗

− max

=I,H

Tr(U

), (4)

where Tr(·) indicates the trace of a matrix, and U

and H

are matrices containing the ﬁrst r columns of

the left and right singular vectors of V respectively,

where V = Udiag(σ)H

is the singular value decom-

position (SVD) of V. Using Equation (4), the new

optimization problem for separation of VA and AA

can be written as

min

{A,V}

{kVk

∗

− max

=I,H

Tr(U

)

+ βkΨ

+ αkAk

}

s. t. X = A + V. (5)

Generally, the lower K (i.e., the number of VA-

containing segments in M), the less accurate the SVD

will be. This might lead to AA components errone-

ously ending up in the low-rank matrix V. Constrai-

ning V to be sparse in the frequency domain using the

regularization on Ψ

V overcomes that AA compo-

nents, that are constrained to be sparse in time dom-

ain, end up in the V matrix. Notice that we did not

extensively search for efﬁcient dictionaries for Ψ. Ho-

wever, we found that the application of the DCT was

computationally of rather low complexity, while lea-

ding to good performance.

A variety of numerical approaches can be used

to solve the optimization problem in Equation (5),

among which we opt for the alternating direction met-

hod of multipliers (ADMM) (Boyd et al., 2011). This

algorithm solves a convex optimization problem by

breaking it into smaller pieces which are simpler to

implement. Furthermore, ADMM has a fast conver-

gence rate to a reasonable precision in practice. To

solve Equation (5), we follow the same approach and

algorithmic steps introduced in (Xue et al., 2018).

The estimated AAs in A are added back to the corre-

sponding samples in the interpolated electrogram m

using a rectangular window. This results in the ﬁnal

estimated atrial activity

a. The ventricular activities

in V are also added to their corresponding samples in

a zero signal of same length as m using a rectangular

window.

3 RESULTS

The proposed framework, from here on referred to as

low-rank and sparse matrix decomposition (LRSD)

method, is tested on clinically recorded epicardial

unipolar electrograms. The electrograms consist of

10 s of induced AF signals recorded at similar loca-

tions on the right atrium of multiple patients, ﬁlte-

red (bandwidth 0.5 to 400 Hz) and sampled (1 kHz).

More details on the electrode speciﬁcations can be

found in (Yaksh et al., 2015). To provide a clear

understanding of the steps of the algorithm and ena-

ble visual inspection of the results, we initially em-

ploy it on the clinically recorded data and demonstrate

the output of each step. However, in Section 3.2 a

more detailed evaluation will be performed on synt-

hetic data. The results are evaluated using instrumen-

tal measures and will also be compared with TMS and

ICA approaches.

3.1 Experiments on Clinical Data

Figure 1 visualizes a fragment of each stage of the

proposed framework, employed on 10 s of clinically

recorded electrogram during induced AF. The electro-

gram is normalized such that the average ventricular

activity has a maximum amplitude of -1. The 10 se-

conds contain K = 16 VA-containing segments, each

Ventricular Activity Signal Removal in Atrial Electrograms of Atrial Fibrillation

181

6400 6600 6800 7000 7200 7400 7600 7800 8000

Figure 1: The input electrogram m and output signals at

each stage of the algorithm with

v and

a as the ﬁnal ex-

tracted VA and AA output. The onset and offset of VA-

containing segments are denoted by red vertical lines. The

segments where AA and VA overlap are also denoted by *.

windowed with a rectangular window with a ﬁxed

length of W = 100 samples (100 ms). Since the fo-

cus of this study is on introducing the algorithm itself

and not on optimal tuning of its parameters, we used

values that yielded visually good source separation,

that are, α = 0.5, β = 0.8, and r = 3.

The input signal is shown as m in Figure 1. The

VA-containing segments are initially removed and in-

terpolated and the result is shown as m

. LRSD is

employed on the data matrix X containing the VA-

containing segments of x = m − m

. The separa-

ted atrial and ventricular activities resulting from the

LRSD are plotted as a

and

v respectively.

a = a

demonstrates the ﬁnal atrial activity estimated from

the input signal m. For an easier visual inspection,

we show for both

a and v in Figure 2 a zoomed ver-

sion of 3 VA-containing segments from the example

in Figure 1.

To compare the performance of the algorithm with

two other approaches we select the TMS (Shkurovich

et al., 1998) and ICA (Rieta et al., 2004) approaches.

TMS, similar to the LRSD, only requires one electro-

gram as well as the ECG signal for detection of VA-

containing segments and is computationally of low

complexity. However, to separate the two sources,

ICA requires the whole ECG signal. Moreover, ta-

king care of the permutation and scaling in the result

of ICA is complicated and can affect its performance.

Figure 3 demonstrates four clinically recorded elec-

trograms m from four different patients as well as

the three estimated atrial components for each patient.

As we can see, LRSD visually provides the best and

smoothest output. The smoothness of the atrial com-

20 60 100 20 60 100 20 60 100

Figure 2: Zoomed version of the three speciﬁed VA-

containing segments in Figure 1 as well as

v and

a as the

ﬁnal extracted atrial and ventricular activity.

ponent is of high importance for further processing of

the data, since any added distortion might be misin-

terpreted as fractionated AAs.

3.2 Performance Evaluation

Evaluating the performance of the proposed method

using instrumental measures, requires the pure AA

and VA, which are not available from clinically re-

corded data. On the other hand, due to the big range

of variations in AAs and VAs morphology during AF,

generating realistic data for a fair performance eva-

luation is difﬁcult. To avoid these complications and

test the framework on realistic data, we generated the

synthesized data in two steps. First we select a sample

VA-containing segment from the electrogram and we

make sure it does not coincide with AA. We then ex-

tract the VA in this segment using spline interpolation

and subtraction. Since VA does not overlap with AA,

this provides us with well separated AA and VA com-

ponents. The separated VA, referred to as pure VA,

is then added to another location on the same EGM

where it overlaps with pure AA and not with anot-

her VA. The pure VA is also shifted in small steps

(10 ms) to create different degrees of overlap with the

AA. The same steps are also performed on the ECG

signal. Finally, TMS, ICA, and LRSD are employed

on the synthesized data.

To evaluate the performance of the introduced ap-

proaches in separating the AA and VA components,

we use four different instrumental measures. The ﬁrst

instrumental measure we use is the normalized cross-

correlation coefﬁcient between the pure AA a and the

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182

2400 2600 2800 3000 3200 3400 3600 3800

1600 1800 2000 2200 2400 2600 2800 3000

(a) (b)

2200 2400 2600 2800 3000 3200 3400 3600

1800 2000 2200 2400 2600 2800 3000 3200

Figure 3: The signals from before are respectively the clinically recorded electrogram m from four different patients (a) to

(d), and the separated atrial activity after employing TMS, ICA and the LRSD. The vertical lines indicate the onset and offset

of VA-containing segments. Overlapping AA and VA are indicated by *.

extracted AA

a, referred to as the similarity metric,

that is

Si =

cov(a,

std(a)std(

, (6)

where cov(·) is covariance and std(·) is the standard

deviation. The closer this variable is to 1, the more

similar the signals are. The second instrumental mea-

sure is the mean square error (MSE) between a and

denoted by MSE

. The smaller this value is, the bet-

ter the results. The third instrumental measure is the

ventricular depolarization reduction(VDR) deﬁned as

(Rieta and Hornero, 2007)

VDR =



1 −

max(

)

max(

)



(7)

where max(|v|) is the maximum amplitude of ventri-

cular activity that coincides with the R-peak in ECG

and max(|

v|) is the maximum amplitude of extrac-

ted ventricular activity. The smaller the VDR is, the

better the ventricular reduction. We also introduce a

new instrumental measure that measures smoothness,

abbreviated as Sm. It is calculated as the the standard

deviation of the ﬁrst time derivative of the difference

Table 1: Summary of instrumental measures.

MSE

Si MSE

VDR Sm

P1 0.005 TMS 0.96 0.005 0.19 0.01

ICA 0.29 0.124 0.59 0.03

LRSD 0.75 0.031 0.26 0.02

P2 0.008 TMS 0.89 0.008 0.13 0.01

ICA 0.80 0.058 1.53 0.02

LRSD 0.97 0.007 0.06 0.01

P3 0.021 TMS 0.82 0.02 0.25 0.01

ICA 0.53 2.250 2.64 0.09

LRSD 0.86 0.01 0.04 0.01

P4 0.071 TMS 0.71 0.07 0.32 0.04

ICA 0.36 0.958 2.64 0.09

LRSD 0.84 0.038 0.15 0.03

P5 0.148 TMS 0.68 0.148 0.28 0.07

ICA 0.25 2.820 2.52 0.19

LRSD 0.79 0.038 0.15 0.03

between a and

a, which is

Sm = std



d(a −



. (8)

The smaller this value is, the less fractionated the re-

sults are.

Table 1 shows the results of the instrumental me-

Ventricular Activity Signal Removal in Atrial Electrograms of Atrial Fibrillation

183

asures evaluated on synthesized data of ﬁve different

patients, where the VAs and AAs are separated using

the three introduced approaches TMS, ICA and the

LRSD. The patients are sorted based on the regula-

rity in their VA-containing segments, where the mean

square error between the average of all segments and

the pure VA denoted by MSE

is used as the indicator

of the regularity. For all patients, the added pure VA

overlaps with several randomly selected AAs, with

different levels of overlap, except for patient 2 where

we purposely chose samples with no overlap with

AA. The performance of ICA in our simulations is

relatively bad. This might be partly due to (i) the low

quality of the ECG signal we had access to in this

experiment and (ii) the errors in handling the permu-

tation and scaling issues in ICA.

As can be seen, the results with respect to simi-

larity and MSE are quite comparable for all patients,

however as the regularity in VA-containing segments

decreases, the LRSD outperforms the other two ap-

proaches in almost all measures. Only for the ﬁrst pa-

tient with very regular segments, TMS performs bet-

ter than the proposed LRSD. As previously mentio-

ned, the smoothness is of high importance since the

added distortions might be misinterpreted as fracti-

onated electrograms. However our simulations on

synthesized data show that if the AA is already fracti-

onated, the added distortions after employing TMS

and ICA completely change the morphology of pure

AA, while the LRSD preserves the pure AA morpho-

logy, resulting in better performances.

4 CONCLUSION

In this study we proposed a new framework for re-

moval of VA from atrial electrograms, which is based

on interpolation and subtraction followed by low-rank

and sparse matrix decomposition. The proposed fra-

mework is of low complexity, does not require high

resolution multi-channel recordings, or a calibration

step for each individual patient. The approach outper-

forms the reference methods TMS and ICA with re-

spect to instrumental measures. In particular in cases

where the ventricular activities are less regular. It pro-

vides smooth AA estimates, which is of high impor-

tance for signal processing applications that are based

on the fractionation evaluation in atrial activities.

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