Spectral Analysis and Heart Rate Variability: Principles and Biomedical Applications. Dr. Harvey N. Mayrovitz

Transcription

1 Spectral Analysis and Heart Rate Variability: Principles and Biomedical Applications Dr. Harvey N. Mayrovitz

2 Why Spectral Analysis? Detection and characterization of cyclical or periodic processes present in physiological signals Rhythms are present in nearly all physiological signals - but not always evident to the naked eye!

3 Signal Filtered Spectrum

4 How do you extract spectral (frequency) components present in physiological signals?

5 Power Spectral Density Amount of power per unit (density) of frequency (spectral) as a function of frequency PSD describes how the power (or variance) of a time series is distributed with frequency!

6 Example with Simulated Signals

7 A 1.0 Hz B 0.3 Hz C Hz A+ B+ C Dr. H. N. Mayrovitz

8 A+ B+ C 100 sec OK Resolution Dr. HN Mayrovitz

9 A+ B+ C 1000 sec Much Better Resolution

10 Generating a time series signal from the Electrocardiogram

11 R- R Time Series R - R Interval varies with time (R- R) i (R- R) I+1

12 R- R Time Series Supine rest Mental Arithmetic Exercise Congestive Heart Failure

13 Heart Rate Variability

14 Heart Rate Variability (HRV) LF HF RSA

15 Heart Rate Variability (HRV) Peripheral Vascular & Thermoregulatory Baroreceptors phase delay Sympathetic & Parasympathetic Respiratory Sinus Arrhythmia (RSA) Cardiac Vagal Activity Change ULF: <0.003 Hz VLF: Hz LF: Hz HF: * Hz LF HF RSA

16 RSA Main Source of HF peak

17 Respiratory Linkage to HF & LF Parasympathetic (Vagus) Heart Rate Brake HR changes Inspiration (inhibits vagus nerve outflow impulses) Centrally? Increased venous return Baroreflex Vagus ~ Fast ~ HF Sympathetic Sympathetic ~ Slow ~ Phase Delay ~ LF

18 Importance of Respiration (100 sec) Peroneal nerve sympathetic Paced Breathing At 0.2 Hz

19 Slow rate allows fuller expression of Ach effects Resulting in greater HF power at lower frequencies Note HR itself DOES NOT CHANGE!

20 Relationship to Neural Signals R-R Interval Cardiac Nerve Traffic Sympathetic Vagal

21 Enhancement of Sympathetic Modulation

22 24 Hour Recording Physiological Correlates not known yet constitutes Largest Power!

23 Time Analysis of HRV uses standard deviation or variance of (normal) R-R intervals Coefficient of variance = SD/mean = SDNN/mean mean Dr. H. N. Mayrovitz

24 Spectral Analysis Considerations

25 For a given sampling rate the length of time a signal is sampled sets the Frequency Resolution

26 Signal 80 cycles of a 1 Hz sine wave Fourier Power Spectrum Power Spectral Density (PSD) Dr. HN Mayrovitz

27 Signal 40 cycles of a 1 Hz sine wave Dr. HN Mayrovitz

28 Signal 20 cycles of a 1 Hz sine wave Dr. HN Mayrovitz

29 Signal 10 cycles of a 1 Hz sine wave Dr. HN Mayrovitz

30 Signal 5 cycles of a 1 Hz sine wave Dr. HN Mayrovitz

31 Signal 2 cycles of a 1 Hz sine wave Dr. HN Mayrovitz

32 Seperating frequency components requires adequate resolution

33 A 1.0 Hz B 0.3 Hz A + B Dr. HN Mayrovitz

34 A + B Dr. HN Mayrovitz

35 A 1.0 Hz B 0.3 Hz C Hz A+ B+ C

36 A+ B+ C 100 sec OK Resolution Dr. HN Mayrovitz

37 1000 sec Much Better Resolution Dr. HN Mayrovitz

38 PPG ~ HR RESP Flow F2 45 second sample Flow F4 Dr. HN Mayrovitz

39 De Trending

40 R-R Interval series as obtained Detrended Series Original Detrended FFT Power Spectral Density (PSD) of R-R Series Original Detrended AR

41 Effect of Detrending R-R Interval series as obtained Detrended Series

42 Basic Definitions

43 Coherence Function Degree of linear correlation as fn of frequency Gxx, Gyy and Gxy are spectra of x(t), y(t) and crosspectrum of x and y SBP * HRV [K(f)] 2 resp

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45 Aliasing Artifacts Sampling rate > f N Sampling rate < f N Erroneous folded spectrum

46 Windowing

47 Autocorrelation Function

48 Broad Band Smoothing

49 Chaos

50 Another Type of Experiment Dr. H. N. Mayrovitz

51 Experiment 60 sec/div Blood Flow Finger 2 Blood Flow Finger 4 PPG RESP 45 minutes Dr. HN Mayrovitz

52 Experiment 60 1 sec/div Blood Flow Finger 2 Blood Flow Finger 4 PPG RESP 45 seconds Dr. HN Mayrovitz

53 PPG ~ HR Why 2 peaks? RESP Flow F2 Flow F4 45 minute sample Dr. HN Mayrovitz

54 Physiological signals whose spectral content changes with time Principle of STFT Short Time Fourier Transform Dr. H. N. Mayrovitz

55 PPG - 45 minute sample using STFT Frequency Time Dr. HN Mayrovitz

56 Principles of Short Time Fourier Transform Analysis Seg T1 T2 S 5 6 T9 7 8 T T10 Frequency (Hz) T2 T1 Time Ttotal = 20 minutes =1200 sec, FS =20 s/sec Nprecision = = 16384/20 = sec Fprecision=(1/819.2) = Hz T10 = Ttotal -Nprecision/FS = = sec = (Nsegs-1) x S = 9 x 846/20 = 9 x 42.3 sec = sec Dr. HN Mayrovitz

57 RESP 45 sample using STFT Dr. HN Mayrovitz

58 Flow F2 45 Dr. HN Mayrovitz

59 Flow F4 45 Dr. HN Mayrovitz

60 HNM: 20 moor signal at 20 s/sec = pts on left hand =24000/20=1200 sec precision=16384, #seg=10 therefore step =1756 precision ~ 16384/20 = sec; step ~ 846/20 = 42.3 sec Precision=number of points per spectrum Step = S = number of points from start of one spectrum to start of the next Dr. HN Mayrovitz

61 HNM: 20 moor signal at 20 s/s = pts on LH, both with precision = 8192, Fs = 20 A #seg=70 step=229 B #seg=10 step=1756 Dr. HN Mayrovitz

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