國立東華大學物理系 蕭又新 4/29/2006

1. Detrended Fluctuation Analyses of Electrocardiagrams from Ventricular Fibrillation Patients and Cardiac Tissue Simulations 國立東華大學物理系 蕭又新 4/29/2006

2. Outline • Oscillations in nature • Non-stationary time series analysis: circle map and DFA • Arrhythmias and spiral waves • Statistical signatures of myocardial fibrosis

4. Damped oscillations

5. Oscillations and ping pong

6. Chaotic (or stochastic) oscillations

7. Cardiac activity and ECG

10. 正常人的心率及R-R分佈圖 食用搖頭丸的女性患者

11. Nonlinear noise-reduction applied to RR intervals

12. Concept of nonlinear dynamics: circle map analysis Reference: N. B. Janson et al., Physiological Measurement 22, 565 (2001)

13. Circle map analysis for a marathon player (5 min ECG recording)

14. Circle map analysis for ICU patients

15. DFA algorithm 1. Integrating : i-th interbeat interval time series : average interbeat interval 2. Divided into boxes of equal length n 3. In each box of length n, least-squares line fitting  : local trend in each box(order l) 4. Calculating Fractal correlation measure : DFA • [2] Detrended Fluctuation Analysis(DFA,QISA) • To quantify the fractal-like scaling properties of the R-R interval time series at different temporal scales • Scaling exponent represents the slope() of regression line which related log(fluctuation) to log(window size)  Low exponent values : magnitude of beat-to-beat HRV is close to magnitude of long-term variability(Anti correlation)  High exponent values : magnitude of long-term variability is substantially higher than beat-to-beat variability(Strong correlation) • Scaling-law exponent(=2-1)1) • - fractal-like signal :  = 1 • - White noise :  = 0.5 (ACor : <0.5, Cor : >0.5) • - Brownian motion : = 1.5 1) N. Iyengar, C. Peng, R. Morn, A. Goldberger and L. Lipsitz, Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics, Am. J. Physiol. 271, R1078-R1084(1996). 2) H. Shono et al., Changes in fractal structure of heart rate variability during a nap in one case, Psychiatry Clin. Neurosci. 55, 175-176(2001)

18. Correlations in sleep states • One night HRV of a healthy subject • Long-range correlation (DFA2) • REM sleep. • Decreased correlation • light, deep sleep 1) A. Bunde et. al., Correlated and Uncorrelated regions in HRV fluctuation during sleep, PRL, V85, 3736 (2000)

19. Action Potential in a ventricular muscle fibre 舒張區間 動作電位週期

20. APD V.S. DI

21. Restitution Curve by Experiment Restitution Curve in canine endocardial muscle Koller, Marcus L. et al. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am. J. Physiol. 275(Heart Circ. Physiol. 44): H1635-H1642, 1998.

22. APD、DI and T(CL)

23. A+D=T Restitution Curve 1:1 2:2

24. Conduction Block Spatially distributed action potential dynamics in a canine cardiac Purkinje fiber Jeffrey J. Fox et al. Spatiotemporal Transition to Conduction Block in Canine Ventricle. Circ Res. 2002;90:289-296

25. Normal Rhythm & Arrhythmias • Normal sinus rhythm 60~100 beats per minute • Ectopic rhythms For example： Ventricular tachycardia(心室頻脈) Ventricular fibrillation(心室顫動)

26. Ventricular Tachycardia (VT) • Ventricular tachycardia (VT) is a tachydysrhythmia originating from a ventricular ectopic focus, characterized by a rate typically greater than 120 beats per minute and wide QRS complexes. • VT may be monomorphic or polymorphic. Nonsustained VT is defined as a run of tachycardia of less than 30 seconds duration; a longer duration is considered sustained VT. Reference http://www.emedicine.com/

27. Ventricular Fibrillation (VF) • What is ventricular fibrillation? The heart beats when electrical signals move through it. Ventricular fibrillation is a condition in which the heart's electrical activity becomes disordered. When this happens, the heart's lower chambers contract in a rapid, unsynchronized way. The heart pumps little or no blood.

28. VT & VF in Electrocardiogram Normal Beats (NB) NB to VT VT to VF Reference: Chaos, Solitons and Fractals Vol.13 (2002) 1755.

29. Normal Rhythm • ventricle cells • 2.5 days in culture • 8 day old embryo • 0.8 ml plating density • recorded temp: 36 deg. C • each frame is approximately 1 cm square Reference： Optical Mapping Image Database http://www.cnd.mcgill.ca/bios/bub/imagebase.html

30. Spiral Waves • ventricle cells • 2 days in culture • 8 day old embryo • recorded temp: 36 deg C. • each frame is approximately 1 cm square Reference： Optical Mapping Image Database http://www.cnd.mcgill.ca/bios/bub/imagebase.html

31. Spiral Waves Breakup • ventricle cells • 2 days in culture • 8 day old embryo • 0.4 ml plating density • alphaGA acid 50ul • recorded temp: 36 deg C. • each frame is approximately 1 cm square Reference： Optical Mapping Image Database http://www.cnd.mcgill.ca/bios/bub/imagebase.html

32. Experimental Results for Multi-armed Spirals in Cardiac Tissue Reference: PNAS, vol. 101, p15530 (2004).

33. Cable Theory

34. Normal Rhythm & Conduction Block Simulation results of normal rhythm and conduction block

35. Spiral Waves Formation and Breakup

36. Simulated 3D Spirals Based on MRI Images

40. Statistical Analyses on Human Recordings and Model Results

43. Model Results

45. A comparison between experimental and simulated exponents

46. Effects of obstacles on wave propagation: myocardial fibrosis