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Generation of Poincaré Plot from ECG Analysis |
| Tags | pre-process☁ecg☁poincare |
The Poincaré Plot defines a geometrical and non-linear approach for studying heart rate variability and in a more generic perspective is also a methodology to quantify the level of chaos in periodic processes.
This structure consists in a bidimensional plot, where each of its points has as coordinates the duration of two consecutive RR intervals ( $RR[i]$, $RR[i + 1]$ ), i.e. from tachogram each pair of samples i and i + 1 define a point in the Poincaré Plot.
There are two reference lines mathematically defined by the following equations:
| \begin{equation} RR[i + 1] = RR[i] \end{equation} | \begin{equation} RR[i + 1] = -RR[i] + 2 avg(RR) \end{equation} |
If the dispersion of Poincaré points in relation to these lines is high, than it can be concluded that heart rate variability is high.
1 - Importing needed packages
# biosignalsnotebooks own package for loading and plotting the acquired data
import biosignalsnotebooks as bsnb
# Scientific packages
import numpy
import math
2 - Load of acquired ECG data
# Load of data (using a relative path of the project)
data, header = bsnb.load("/signal_samples/ecg_5_min.h5", get_header=True)
3 - Identification of mac address of the device and the channel used during acquisition
channel = list(data.keys())[0]
4 - Storage of sampling frequency and acquired data inside variables
# Sampling frequency and acquired data
fs = header["sampling rate"]
# Signal Samples
signal = data[channel]
time = numpy.linspace(0, len(signal) / fs, len(signal))
5 - Generation of tachogram
tachogram_data, tachogram_time = bsnb.tachogram(signal, fs, signal=True, out_seconds=True)
6 - Axes of Poincaré plot
rr_i = tachogram_data[:-1]
rr_i_plus_1 = tachogram_data[1:]
7 - Generation of Poincaré Plot
8 - Determination of SD1 and SD2 parameters
These parameters quantify the dispersion level of the Poincaré samples regarding to each reference line, being proportional to the short and long-term heart rate variability, respectively.| \begin{equation} SD1 = \sqrt{\frac{SDSD^2}{2}} \end{equation} | \begin{equation} SD2 = \sqrt{2 \times SDNN^2 - SD1^2} \end{equation} |
| \begin{equation} SDSD = \sqrt{\frac{\sum_{i=2}^N ((RR[i] - RR[i - 1]) - \overline{RR_i - RR_{i - 1}})^2}{N - 1}} \end{equation} | \begin{equation} SDNN = \sqrt{\frac{\sum_{i=1}^N (RR[i] - \overline{RR})^2}{N - 1}} \end{equation} |
| $\overline{RR_i - RR_{i - 1}}$ is the average value of the first derivative of tachogram, while $\overline{RR}$ is the average value of the tachogram samples |
tachogram_diff = numpy.diff(tachogram_data)
SDSD = numpy.std(tachogram_diff)
SDNN = numpy.std(tachogram_data)
SD1 = numpy.sqrt(0.5 * numpy.power(SDSD, 2))
SD2 = numpy.sqrt(2 * numpy.power(SDNN, 2) - numpy.power(SD1, 2))
avg_rr = numpy.average(tachogram_data)
9 - Representation of Poincaré Plot with associated parameters
This procedure can be automatically done by poincare function in process module of biosignalsnotebooks package
x_axis, y_axis, SD1, SD2 = bsnb.poincare(signal, fs, signal=True, in_seconds=False)
We hope that you have enjoyed this guide.
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