spectral analysis and heart rate variability: principles...
TRANSCRIPT
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Spectral Analysis and Heart Rate Variability:Principles and Biomedical Applications
Dr. Harvey N. Mayrovitz
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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’!
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Signal
Filtered
Spectrum
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How do youextract spectral (frequency)
components present in physiological signals?
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Power Spectral DensityAmount 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!
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Example with Simulated Signals
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A1.0 Hz
B0.3 Hz
C0.065 Hz
A+ B+ C
Dr. H. N. Mayrovitz
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OK Resolution
Dr. HN Mayrovitz
100 secA+ B+ C
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Much BetterResolution
1000 secA+ B+ C
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Generating a time series signal from the Electrocardiogram
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R- R Time Series
(R- R)i (R- R)I+1
R - R Interval varies with time
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Supine rest Mental Arithmetic
CongestiveHeart Failure
Exercise
R- R Time Series
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Heart Rate Variability
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Heart Rate Variability (HRV)
HFLF
RSA
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ULF: <0.003 Hz
VLF: 0.003 - 0.04 Hz
LF: 0.04 - 0.15 Hz
HF: 0.15 - 0.40* HzRespiratory Sinus Arrhythmia (RSA)Cardiac Vagal Activity Change
Baroreceptors phase delay Sympathetic & Parasympathetic
Peripheral Vascular& Thermoregulatory
Heart Rate Variability (HRV)
HFLF
RSA
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RSA Main Source of HF peak
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Parasympathetic(Vagus)
Heart Rate Brake
Inspiration(inhibits
vagus nerveoutflow impulses)
HR changes
Respiratory Linkage to HF & LF
• Centrally?• Increased venous return
BaroreflexVagus ~ Fast ~ HF Sympathetic
Sympathetic ~ Slow ~ Phase Delay ~ LF
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(100 sec)
Peroneal nervesympathetic
Paced BreathingAt 0.2 Hz
Importance of Respiration
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Slow rate allows fuller expression of Ach effectsResulting in greater HF power at lower frequencies
Note HR itselfDOES NOT CHANGE!
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Relationship to Neural Signals
Cardiac Nerve Traffic
R-R Interval
Sympathetic
Vagal
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Enhancement of Sympathetic Modulation
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24 Hour Recording
Physiological Correlatesnot known yet constitutes
Largest Power!
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Time Analysis of HRVuses standard deviation or variance
of (normal) R-R intervals
Coefficient of variance = SD/mean= SDNN/mean
mean
Dr. H. N. Mayrovitz
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Spectral Analysis Considerations
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For a given sampling rate the length of time a signal is sampled sets the
Frequency Resolution
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Signal80 cyclesof a 1 Hz
sinewave
Fourier Power SpectrumPower Spectral Density (PSD)
Dr. HN Mayrovitz
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Signal40 cyclesof a 1 Hz
sinewave
Dr. HN Mayrovitz
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Signal20 cyclesof a 1 Hz
sinewave
Dr. HN Mayrovitz
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Signal10 cyclesof a 1 Hz
sinewave
Dr. HN Mayrovitz
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Dr. HN Mayrovitz
Signal5 cyclesof a 1 Hz
sinewave
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Signal2 cyclesof a 1 Hz
sinewave
Dr. HN Mayrovitz
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Seperating frequency components requires adequate resolution
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1.0 Hz
0.3 Hz
A
B
A + B
Dr. HN Mayrovitz
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A + B
Dr. HN Mayrovitz
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A1.0 Hz
B0.3 Hz
C0.065 Hz
A+ B+ C
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100 sec
OK Resolution
Dr. HN Mayrovitz
A+ B+ C
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1000 sec
Much BetterResolution
Dr. HN Mayrovitz
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PPG ~ HR
RESP
Flow F2
Flow F4
45 second sample
Dr. HN Mayrovitz
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De‐Trending
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R-R Interval series as obtained
FFT
AR
DetrendedOriginal
DetrendedOriginal
Detrended Series
Power Spectral Density(PSD) of R-R Series
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Effect of Detrending
R-R Interval series as obtained
Detrended Series
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Basic Definitions
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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
[K(f)]2
SBP * HRV
resp
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Aliasing Artifacts
Samplingrate > fN
Samplingrate < fN
Erroneousfolded
spectrum
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Windowing
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Autocorrelation Function
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Broad Band Smoothing
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Chaos
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Another Type of ExperimentDr. H. N. Mayrovitz
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Experiment
Blood FlowFinger 2
Blood FlowFinger 4
PPG
RESP
60 sec/div
45 minutes Dr. HN Mayrovitz
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Experiment
Blood FlowFinger 2
Blood FlowFinger 4
PPG
RESP
60 sec/div1 sec/div
45 seconds Dr. HN Mayrovitz
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PPG ~ HR
RESP
Flow F2
Flow F4
Dr. HN Mayrovitz
45 minute sample
Why 2 peaks?
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Physiological signals whose spectral content changes with time
Principle of STFTShort Time Fourier Transform
Dr. H. N. Mayrovitz
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PPG - 45 minute sample using STFT
Dr. HN MayrovitzTi
me
Frequency
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Seg
1
2
3
4
5
6
7
8
9
10T1
T2
T5
T9
T1
T2
T10
T10 = Ttotal - Nprecision/FS= 1200 - 819.2 = 380.7 sec= (Nsegs-1) x S = 9 x 846/20 = 9 x 42.3 sec = 380.7 sec
Ttotal = 20 minutes =1200 sec, FS =20 s/secNprecision = 16384 = 16384/20 = 819.2 secFprecision=(1/819.2) = 0.0012 Hz
S
Principles of Short Time Fourier Transform Analysis
Dr. HN Mayrovitz
Time
Frequency (Hz)
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RESP 45” sample using STFT
Dr. HN Mayrovitz
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Flow F2 45”
Dr. HN Mayrovitz
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Flow F4 45”
Dr. HN Mayrovitz
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HNM: 20” moor signal at 20 s/sec = 24000 pts on left hand =24000/20=1200 secprecision=16384, #seg=10 therefore step =1756precision ~ 16384/20 = 819.2 sec; step ~ 846/20 = 42.3 sec
Precision=number of points per spectrumStep = S = number of points from start of one spectrum to start of the next
Dr. HN Mayrovitz
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HNM: 20” moor signal at 20 s/s = 24000 pts on LH, both with precision = 8192, Fs = 20
A
B
#seg=70step=229
#seg=10step=1756
Dr. HN Mayrovitz
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