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![Page 1: Nonlinear Analysis of Surface ECG Atrial Flutter and Atrial Fibrillation in Man Tsair Kao Institute of Biomedical Engineering National Yang-Ming University.](https://reader035.fdocuments.net/reader035/viewer/2022062314/56649ebc5503460f94bc573b/html5/thumbnails/1.jpg)
Nonlinear Analysis of Surface ECG Atrial Flutter and
Atrial Fibrillation in Man
Tsair Kao
Institute of Biomedical Engineering
National Yang-Ming University
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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
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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
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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
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Spectral Analysis of Chronic Atrial Fibrillation and Its Relation to Minimal Defibrillation Energy. J Pacing and Clinical Electrophysiology, 25:1747-1751, 2002.
Spectral Analysis
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Electrophysiological Characteristics and Catheter Ablation in Patients with Paroxysmal Right Atrial Fibrillation. Circulation, 112: 1692-1700, 2005.
Noncontact and Contact Unipolar Electrograms
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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 )
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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)
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Multi-site Bipolar Recordings and Frequency Analysis
Paroxysmal AF originating from the SVC
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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
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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.
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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
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Magnitude-Squared Coherence Map
)()(
)()(
2
fSfS
fSfMSC
yyxx
xy
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Upper 5 maps represent consecutive 10 s of AF signal.
MSC Map
Lower 5 maps represent 10 s signal just before AF termination
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Frequency Variations of MSC Maps
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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”
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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
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Noise Reduction
UnmixingW
Recorded components Independent Components
X1
X2
X6
X3
X4
X5
IC1
IC2
IC3
IC4
IC5
IC6
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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
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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
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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.
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Normal Sinus Rhythm
P
I
A
……
……
……
……
…
…
……
……
………
……
……
……
…
…
……
……
………
……
……
……
…
…
……
……
……
……
…
…
……
……
…
AP
IVC
15
4
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Atrial Fibrillation
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AF Before Termination
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Normal Sinus Rhythm
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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
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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
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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
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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
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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
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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
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Preprocessing
Observations (X) Reconstructed signal ( )
ICA
X’
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ICA-estimated Atrial Activities
II V1
T-AFL
A-AFL
AF
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Comparison
• Define the non-QRS region manually
• Root-mean squared error
N
0i
2))i(x)i(x(N
1ErrorRMS
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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
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Reconstructed Atrial Signals
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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
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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
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Surrogate Test
Henon map Xn+1=1-1.4Xn2+0.3Xn
Original data
Surrogate data
max diff: 1.5632×10-13
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Surrogate Test
Henon map Xn+1=1-1.4Xn2+0.3Xn
Original data
Surrogate data
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Surrogate Test
Time reversibility (trev) Correlation dimension (D2)
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Time reversibility (trev) Correlation dimension (D2)
Surrogate Test
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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
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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
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Is Fibrillation Chaos?
Distinguishing Cardiac Randomness from Chaos
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