Application of DFA to heart Application of DFA to heart rate variabilityrate variability
Mariusz SozańskiMariusz Sozański**, Jan Żebrowski, Jan Żebrowski**, Rafał Baranowski, Rafał Baranowski++
*Faculty of Physics, Warsaw University of Technology
+National Institute of Cardiology, Warsaw
1. Intro – overview of DFA1. Intro – overview of DFA1. Intro – overview of DFA1. Intro – overview of DFAR
R
1. Intro – overview of DFA1. Intro – overview of DFA
If we observe scaling:If we observe scaling:
• We may conclude that:We may conclude that:– For For =0.5 fluctuations are not self-correlated;=0.5 fluctuations are not self-correlated;– For 0.5<For 0.5<1 long-range correlations exist;1 long-range correlations exist;– For 0<For 0< long-range anticorrelations exist; long-range anticorrelations exist;
– =1=1 corresponds to flicker (corresponds to flicker (11//ff) noise;) noise;
– =1.5 corresponds to Brownian noise;=1.5 corresponds to Brownian noise;
• In other words:In other words:the „smoother” the time series, the bigger the „smoother” the time series, the bigger is obtained. is obtained.
nnF ~)(
1. Intro – overview of the 1. Intro – overview of the methodmethod
22.. Scale-independent Scale-independent DFA DFA
*Goldberger,Peng et al., PNAS 99, supp.1, 2466(2002)
2. Scale-dependent version2. Scale-dependent version
*K. Saermark et al., Fractals 8, 4,
315-322 (2000).
3. coronary disease3. coronary disease
1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4
0
4
8
12
16
20F(n =1 6 )
coronary d isease
healthy
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
4
8
12
16a lfa 1coronary d isease
healthy
scale-independent scale-dependent
3. cardiomiopathy3. cardiomiopathy
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3
0
2
4
6F(n=1 6 )
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
2
4
6
8
le g e n dcard iom iopathy
healthy
a lfa 1
scale-independent scale-dependent
3. cardiac infarction3. cardiac infarction
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
0
2
4
6
8
a lfa 1after in farct
healthy
0.5
1
1.5
2
2.5
3
3.5
n=4 n=8 n=16 n=32 n=64
F(n )
scale-independent scale-dependent
3. cardiac infarction3. cardiac infarction
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
0
2
4
6
8
F(n =1 6 )after in farct
healthy
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3
0
4
8
12
16
F(n =8 )card iom iopathy
hea lthy
window length=16 RR window length=8 RR
4. Comparison with SDNN4. Comparison with SDNN
4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0
0
2
4
6
8
1 0
S t. d e via tio nafter in farct
healthy
sensitivity specifity pred. accuracyF(n=16) 55% 67% 74%F(n=8) 53% 67% 72%SDNN 51% 77% 78%
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