Nonlinear Analysis of Surface ECG Atrial Flutter and

Atrial Fibrillation in Man

Tsair Kao

Institute of Biomedical Engineering

National Yang-Ming University

2

Atrial Arrhythmias

Typical atrial flutter (T-AFL)• Single macro-reentrant wave in atrium• Regular conduction to ventricle (2:1, 3:1,6:1)• 240-350 bpm

Atypical atrial flutter (A-AFL)• Irregular conduction to ventricle• Often degenerate into atrial fibrillation• 340-430 bpm

Atrial fibrillation (Af)• Multiple wavelets in atrium• 300-600 bpm

3

Atrial Signals

Intra-atrial electrogram

Epi-cardial electrogram

Surface ECG atrial activity

Atrial flutter– single reentrant circuit (clockwise and counterclockwise)

Atrial fibrillation–simultaneously multi- reentrant circuits

4

Linear Analysis

Time domain• Af/AFL: Ratio between varia

nce and mean of f-wave duration

• Normal/ Af: regularity of RR interval

• Normal/ arrhythmias: ‘P-wave existing’ and ‘ventricular regularity test’

Frequency domain

• Af/ Sinus and AFL: Magnitude squared coherence

• Normal/AFL/Af: ‘dominant frequency’ and spectral

5

Spectral Analysis of Chronic Atrial Fibrillation and Its Relation to Minimal Defibrillation Energy. J Pacing and Clinical Electrophysiology, 25:1747-1751, 2002.

Spectral Analysis

6

Electrophysiological Characteristics and Catheter Ablation in Patients with Paroxysmal Right Atrial Fibrillation. Circulation, 112: 1692-1700, 2005.

Noncontact and Contact Unipolar Electrograms

7

Frequency Domain Analysis

The frequency spectra were plotted and analyzed from 2 to 30 Hz to include only the physiological range of practical interest.

The spectra were normalized by the maximum power of the 64 spectra. For each spectrum, the normalized largest peak, which exceeded 0.2, was identified as the dominant frequency (DF).

Harmonic index (HI), representing the organization of the AF during the 6.82-second time segment.

HI = ( the power of the DF and its harmonic peaks over a 2-Hz window) / (the total power) (from 2 to 30 Hz )

8

Frequency Analysis in Different Types of Paroxysmal Atrial Fibrillation. J Am Coll Cardiol 47:1041-1047, 2006.

Multi-site Bipolar Recordings and Frequency Analysis

Originating from the right superior pulmonary vein (RSPV)

9

Multi-site Bipolar Recordings and Frequency Analysis

Paroxysmal AF originating from the SVC

10

Animal Experiments

Open chest sinus rhythm

induce AF by

electrical stimulation

inject Antiarrhythmic

drugs

restore sinus rhythm

• Nine canines weighted between 10 and 15 kg.

• The 120 electrodes are arranged into 15×8 matrixes.

• The recorded signals included:* sinus rhythm* during AF* AF after injection antiarrhythmic drug * before restoration of normal sinus rhythm

11

Frequency Coherence Mapping

Frequency Coherence Mapping of Canine Atrial Fibrillation: Implication for Anti-arrhythmic Drug-induced Termination

Biomed Eng Appl Basis Comm, 13:56-60, 2003.

12

The earliest depolarization area around SA node (dotted square) is denoted as dominant area (DA). Twenty-four electrodes (about 9×15 cm2) are enclosed by the dotted square.

Isochronal Map in Sinus Rhythm

13

Magnitude-Squared Coherence Map

)()(

)()(

2

fSfS

fSfMSC

yyxx

xy

14

Upper 5 maps represent consecutive 10 s of AF signal.

MSC Map

Lower 5 maps represent 10 s signal just before AF termination

15

Frequency Variations of MSC Maps

16

Independent Component Analysis (ICA)

• ICA is a technique for revealing hidden factors that underlie sets of random signals.

• Blind Source Separation (BSS):• Solving the “cocktail party problem”

17

unknown

s A Wx

s

Mutual Information

•s Unknown

•Mixing matrix A Unknown

•To estimate A and s using only the observed random vector x

•Compute W = A-1

•Obtain ICs from s’ = Wx

Independent Component Analysis

18

Noise Reduction

UnmixingW

Recorded components Independent Components

X1

X2

X6

X3

X4

X5

IC1

IC2

IC3

IC4

IC5

IC6

19

0.0017 0.0005 0.7205 0.0006 0.0011 0.1111 0.9878 0.0057 0.1932 0.0007 0.0001 0.0893 0.0046 0.9177 0.0121 0.0016 0.0281 0.1588 0.0019 0.0065 0.0341 0.9966 0.0003 0.0778 0.0039 0.0663 0.0386 0.0002 0.0194 0.4170 0.0002 0.0033 0.0015 0.0003 0.9509 0.1459

Preprocessing

mixing

A

Reconstruction signalsIndependent Components

IC1

IC2

IC3

IC4

IC5

IC6

S’1

S’2

S’6

S’3

S’4

S’5

20

Original Signals vs. Reconstruction Signals

Original Signals Reconstruction signals

0.639

0.634

0.638

0.002

0.704

0.699

Correlation coefficient

20 40 60 80 100

1

2

3

4

x 104

20 40 60 80 100

1

2

3

4

x 104

20 40 60 80 100

1

2

3

4

x 104

20 40 60 80 100

2000400060008000

1000012000

20 40 60 80 100

1

2

3

4

x 104

20 40 60 80 100

2

4

6x 10

4

20 40 60 80 100

1

2

3

4x 10

4

20 40 60 80 100

1

2

3

x 104

20 40 60 80 100

1

2

3

x 104

20 40 60 80 100

5

10

15

x 104

20 40 60 80 100

0.51

1.52

2.5x 10

4

20 40 60 80 100

0.51

1.52

2.5x 10

4

S’1

S’2

S’6

S’3

S’4

S’5

S1

S2

S6

S3

S4

S5

21

How Many Components ?

PCA W S CoherenceX

Mutual Information

Coherence >= 0.5

If the coherence value is greater than 0.5, the ICA process was repeated with a reduced number of output components until the coherence value between each component was smaller than 0.5.

22

Normal Sinus Rhythm

P

I

A

……

……

……

……

…

…

……

……

………

……

……

……

…

…

……

……

………

……

……

……

…

…

……

……

……

……

…

…

……

……

…

AP

IVC

15

4

23

Atrial Fibrillation

24

AF Before Termination

25

Normal Sinus Rhythm

26

No. NSR AFBD1 AFBD2 AFAD1 AFAD2 AFBT Drug

A11 3Hz(1.8) 10Hz(1.8)10Hz(3.6)

8Hz(1.4)9Hz(3.7)

7Hz(2.6)7Hz(1.6)

7Hz(3.8)7Hz(1.6)

6Hz(1.5) P

A13 2Hz(1.1) 13Hz(2.2)14Hz(1.8)15Hz(2.11)

13Hz(2.5)14Hz(0.5)

5Hz(1.8)5Hz(1.3)

4Hz(2.4)4Hz(1.2)

4Hz(2.3)4Hz(1.5)

P

A17 2Hz(1.2) 12Hz(2.7)12Hz(3.3)11Hz(1.9)

9Hz(2.0)10Hz(2.4)10Hz(1.5)

6Hz(1.8)7Hz(2.1)7Hz(2.5)

5Hz(3.7)6Hz(2.4)

4Hz(3.2) P

A18 3Hz(1.6) 12Hz(1.1)12Hz(2.6)7Hz(1.9)

11Hz(3.4)10Hz(2.9)10Hz(2.7)

6Hz(2.4)8Hz(1.0)

6Hz(3.7)8Hz(1.0)

5Hz(1.5) P

A19 2Hz(1.7) 12Hz(0.6)10Hz(3.6)

11Hz(1.11)10Hz(2.12)

7Hz(1.12) 5Hz(1.1)7Hz(1.13)

4Hz(1.7) P

A21 3Hz(1.5) 8Hz(1.0)9Hz(3.5)10Hz(0.5)

6Hz(0.9)8Hz(3.6)

7Hz(2.12)8Hz(1.3)8Hz(2.1)

7Hz(2.11)7Hz(2.1)

7Hz(1.3)4Hz(2.1)

S

A31 2Hz(1.1) 11Hz(1.7)11Hz(2.1)13Hz(2.9)

11Hz(3.0)11Hz(2.8)12Hz(1.5)

6Hz(1.3)8Hz(3.6)

6Hz(2.10)8Hz(1.1)

3Hz(1.3)8Hz(0.5)

S

P=procainamide, S=sotalol, NSR=normal sinus rhythm, AF= atrial fibrillationAFBD1,AFBD2: Two AF segments before drug injection AFAD1,AFAD2: Two AF segments after drug injectionAFBT: AF just before termination

27

Independent Component Approach to the Analysis of Epicardial Atrial Electrograms of Electrically Induced Atrial Fibrillation. J Biol Med Eng 25: 93-97, 2005.

中國工程師學會 95年工程論文獎

28

Nonlinear Analysis

Nonlinear Analysis of Epicardial Atrial Electrograms of Electrically Induced Atrial Fibrillation in Man

Hoekstra BPT et al.: J Cardiovasc Electrophysiol, 1995;6:419-440

I

3 pts

II

3 pts

III

3 pts

4 sec ECG

1 KHz

29

Nonlinear Analysis

Correlation dimension and maximal Lyapunov exponent

Correlation dimension and correlation entropy

Discriminate type I, II and III atrial fibrillation

Type I not generated by linear stochastic dynamics

Is heart activity nonlinear dynamics ?

•YES

•NO

30

Data Acquisition

• Department of Cardiology, Veterans General Hospital, Taipei

• Catheter ablation• 12-lead ECG (CardioLab system, Prucka GE)

• Sampling frequency: 1kHz• Three types of atrial arrhythmias (10 sec)

• Typical atrial flutter

• Atypical atrial flutter

• Atrial fibrillation

31

Surface ECG

12-lead ECG ICA

V1atrial signal

Surrogate test

Properties analysis

Null hypothesis:

The input signal is generated from linear stochastic system

Remove ventricular activity

Adaptive filtering

Independent component analysis

32

Preprocessing

Observations (X) Reconstructed signal ( )

ICA

X’

33

ICA-estimated Atrial Activities

II V1

T-AFL

A-AFL

AF

34

Comparison

• Define the non-QRS region manually

• Root-mean squared error

N

0i

2))i(x)i(x(N

1ErrorRMS

35

Diagnosis Patient

No.

No. of sources of

ICA component

RMS Error (mean±SD)

No. of sources of

ICA component

RMS Error (mean±SD)

T-AFL Hx018 10 0.0221±0.0025 10,8 0.0121±0.0042 Hx021 7 0.0595±0.0084 7,9 0.0527±0.0119 Hx026 9 0.0210±0.0051 9,11 0.0159±0.0051 Hx030 10 0.0223±0.0068 10,11 0.0203±0.0047 Lx000 6 0.0214±0.0047 6,11 0.0203±0.0052 Lx007 10 0.0275±0.0077 10,11 0.0316±0.0098 Lx008 7 0.0295±0.0061 7,9 0.0171±0.0025 Lx009 7 0.0459±0.0066 7,12 0.0231±0.0082

A-AFL Hx014 8 0.0242±0.0273 × × Hx028 9 0.0275±0.0116 9,8 0.0275±0.0116 Hx029 12 0.0260±0.0097 12,11 0.0260±0.0067 Hx034 12 0.0213±0.0081 12,11 0.0226±0.0071 Lx004 7 0.0283±0.0083 7,8 0.0201±0.0076 Lx006 8 0.0252±0.0069 8,10 0.0236±0.0065 Lx013 8 0.0249±0.0043 × ×

Af Hx003 12 0.0211±0.0053 12,11 0.0105±0.0036 Hx019 9 0.0229±0.0076 9,11 0.0227±0.0052 Hx025 11 0.0231±0.0056 11,7 0.0125±0.0034 Hx032 11 0.0284±0.0051 11,12 0.0298±0.0044 Hx033 10 0.0259±0.0085 10,8 0.0295±0.008 Lx003 10 0.0449±0.0093 10,11 0.0441±0.0101

Notes about ‘×’ There were no other proper sources which can be recognized as atrial sources.

Comparison

36

Reconstructed Atrial Signals

37

Surrogate Test

N surrogate data

Iterative amplitude adjusted Fourier transform (iAAFT)

Time reversibility (trev)

Correlation dimension (D2)

Rank order test Reject, accept

N

1n

3nn

rev )xx(N

1)(t

38

Surrogate Test

Henon map Xn+1=1-1.4Xn2+0.3Xn

Original data

Surrogate data

Mean =0.2574SD = 0.7207

Mean =0.2574SD = 0.7207

39

Surrogate Test

Henon map Xn+1=1-1.4Xn2+0.3Xn

Original data

Surrogate data

max diff: 1.5632×10-13

40

Surrogate Test

Henon map Xn+1=1-1.4Xn2+0.3Xn

Original data

Surrogate data

41

Surrogate Test

Time reversibility (trev) Correlation dimension (D2)

42

Time reversibility (trev) Correlation dimension (D2)

Surrogate Test

43

Surrogate test trev D2 Diagnosis Patient No. DF

Rank Decision Rank Decision Typical atrial flutter HX018 4.375 1 R 1 R

HX021 3.75 1 R 1 R HX026 4.25 1 R 1 R HX030 4.00 38 A 1 R LX000 4.50 1 R 1 R LX007 5.00 1 R 1 R LX008 3.25 1 R 1 R LX009 3.25 1 R 1 R

The proportions of rejecting the null

hypothesis

7/8 8/8

Atypical flutter HX014 6.00 1 R 1 R

HX028 5.625 1 R 1 R HX029 4.625 38 A 2 A HX034 5.125 40 A 14 A LX004 3.875 1 R 4 A LX006 7.00 1 R 1 R LX013 4.125 11 A 1 R

The proportions of rejecting the null

hypothesis

4/7 4/7

Atrial fibrillation HX003 5.875 17 A 12 A

HX019 6.875 1 R 10 A HX025 6.125 34 A 5 A HX032 6.875 29 A 14 A HX033 6.125 16 A 7 A LX003 6.875 26 A 18 A

The proportions of rejecting the null

hypothesis

5/6 6/6

Atrial Arrhythmias and Surrogate tests

44

  D2 1 C

Typical atrial flutter

2.85  0.61 1.64 1.69 97.89  13.74

Atypical atrial flutter

4.13  0.95 10.48  1.23 125.22  8.26

Atrial fibrillation 5.67  0.62 17.34  2.19 141.17  10.70

Nonlinear Characteristics

Differentiation of Atrial Flutter and Atrial Fibrillation

from Surface Electrocardiogram Using Nonlinear Analysis

J Med Biol Eng, 25(3): 117-122, 2005

45

Is Fibrillation Chaos?

Distinguishing Cardiac Randomness from Chaos

46