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%

THANK YOUTHANK YOUFOR YOUR ATTENTION!FOR YOUR ATTENTION!