#####Heart Rate Variability (HRV), RR-interval and Spectral analysis of Electrocardiogram (ECG) Unevenly spaced signals are met commonly in car industry, communications, medicine and other sciences. In our case, the raw ECG signal is usually unevenly sampled. Heart-rate variability (HRV) signals, which represent the physiological variation in time between heartbeats, are typically unevenly sampled because human heart rates are not constant.
#####Dependencies
- Matlab
- Signal Processing Toolbox
#####RR Intervals
We load our signal in Matlab and perform low or high-pass filtering in order to rule out artifacts.
The filtered signal is presented below.
Then, we find the peaks of the ECG. The amplitude of each point is computed as the inverse of the time difference between consecutive R-Peaks and is placed at the instant of the second R-Peak.
% Find the ECG peaks
[pks,locs] = findpeaks(x,2048, ...
'MinPeakProminence',0.3,'MinPeakHeight',0.2);
% Determine the RR intervals
RLocsInterval = diff(locs);
% Derive the HRV signal
tHRV = locs(2:end);
HRV = 1./RLocsInterval;
% Plot the signal
plot(tHRV,HRV,'LineWidth',4)
xlabel('Time(s)')
ylabel('HRV (Hz)')
We notice that the average heart rate variability is around 1.4, perhaps a sign of arrythmia in our signal. In order to visualize the HRV values better, we plot the RLocsInterval histogram.
% Find sampling interval
figure
hist(RLocsInterval)
grid
xlabel('Sampling interval (s)')
ylabel('RR distribution')
In an ideally perfect result, the sampling intervals of all distributions should have only one value, (equidistant RRs). Here we see 8 different intervals on the axis x.
#####Spectral Analysis The typical frequency bands of interest in HRV spectra are:
- Very Low Frequency (VLF) (3.3 - 40 mHz)
- Low Frequency (LF) (40 to 150 mHz)
- High Frequency (HF) (150 to 400 mHz)
These bands approximately confine the frequency ranges of the distinct biological regulatory mechanisms that contribute to HRV. Fluctuations in any of these bands have biological significance.
We use the Lomb–Scargle periodogram to
calculate the spectrum of the HRV signal. In Matlab, we call plomb.
% Lomb-Scargle Spectral Density Estimate
figure
plomb(HRV,tHRV,'Pd',[0.95, 0.5])
The dashed lines denote 95% and 50% detection probabilities (Pd). These thresholds measure the statistical significance of peaks. The spectrum shows peaks in all 3 bands of interest listed above. However, only the peak located at 74.5 mHz in the LF range shows a detection probability 95%, while only the peak at 231 mHz has a detection probability of 50% in the HF range.