Event Detection - R Peaks (ECG)
Difficulty Level:
Tags detect☁ecg☁r-peaks

One of the distinctive characteristics of the electrocardiographic (ECG) signals is their periodicity, something that is not common in physiological terms.

Due to this characteristic, the study of cardiac cycle variability (heart rate variability) defines an important segment of ECG analysis.

However, heart rate variability analysis is dependent of the detection of ECG R peaks, which is the main topic of the present Jupyter Notebook . This task can be achieved by applying the Pan-Tompkins algorithm, translated to Python paradigm by Raja Selvaraj

1 - Importation of the needed packages and definition of auxiliary functions

In [1]:
# biosignalsnotebooks python package
import biosignalsnotebooks as bsnb

# Scientific packages
from numpy import linspace, diff, zeros_like, arange, array

2 - Load of acquired ECG data

In [2]:
# Load of data
data, header = bsnb.load_signal("ecg_4000_Hz", get_header=True)

3 - Identification of the device mac-address and the channel used during acquisition

In [3]:
channel = list(data.keys())[0]
In [4]:
print ("Channel: " + str(channel))
Channel: CH1

4 - Storage of sampling rate and acquired data inside variables

In [5]:
# Sampling rate.
sr = header["sampling rate"]

# Signal Samples.
signal = data[channel]

4.1 - A time-axis should be generated in order to a more intuitive interpretation of the final results

In [6]:
time = bsnb.generate_time(signal)

5 - Simplification of ECG signal (isolation of abrupt transitions)
5.1 - Step 1 of Pan-Tompkins Algorithm - ECG Filtering (Bandpass between 5 and 15 Hz)

In [7]:
# Step 1 of Pan-Tompkins Algorithm
filtered_signal = bsnb.detect._ecg_band_pass_filter(signal, sr)
In [8]:
bsnb.plot_ecg_pan_tompkins_steps(time, signal, filtered_signal, sr, titles=["Original Signal", "Post Filtering Signal"])

5.2 - Step 2 of Pan-Tompkins Algorithm - ECG Differentiation

In [9]:
# Step 2 of Pan-Tompkins Algorithm
differentiated_signal = diff(filtered_signal)
In [10]:
bsnb.plot_ecg_pan_tompkins_steps(time, filtered_signal, differentiated_signal, sr, titles=["Post Filtering Signal", "Post Differentiation Signal"])

5.3 - Step 3 of Pan-Tompkins Algorithm - ECG Rectification

In [11]:
# Step 3 of Pan-Tompkins Algorithm
squared_signal = differentiated_signal * differentiated_signal
In [12]:
bsnb.plot_ecg_pan_tompkins_steps(time, filtered_signal, squared_signal, sr, titles=["Post Differentiation Signal", "Post Rectification Signal"])

5.4 - Step 4 of Pan-Tompkins Algorithm - ECG Integration ( Moving window integration )
5.4.1 - Definition of the samples number inside the moving average window

In [13]:
nbr_sampls_int_wind = int(0.080 * sr)

5.4.2 - Initialisation of the variable that will contain the integrated signal samples

In [14]:
integrated_signal = zeros_like(squared_signal)

5.4.3 - Determination of a cumulative version of "squared_signal"

In the cumulative version of the signal under analysis, his sample value $i$ will be sum of all values included between entry 0 and entry $i$ of the studied signal (in our case "squared_signals").

In [15]:
cumulative_sum = squared_signal.cumsum()

5.4.4 - Estimation of the area/integral below the curve that defines the "squared_signal"

Implicitly, with the current procedure, "squared_signal" is divided into multiple rectangles with fixed width (equal 1 sample) and height determined by the sample value under analysis .

In [16]:
integrated_signal[nbr_sampls_int_wind:] = (cumulative_sum[nbr_sampls_int_wind:] - 
                                           cumulative_sum[:-nbr_sampls_int_wind]) / nbr_sampls_int_wind
integrated_signal[:nbr_sampls_int_wind] = cumulative_sum[:nbr_sampls_int_wind] / arange(1, nbr_sampls_int_wind + 1)
In [17]:
bsnb.plot_ecg_pan_tompkins_steps(time, squared_signal, integrated_signal, sr, titles=["Post Rectification Signal", "Post Integration Signal"])