Differentiating the PPG signal
Contents
Differentiating the PPG signal¶
In this tutorial we will learn how to differentiate physiological signals.
Our objectives are to:
Apply SciPy functions for differentiating signals.
View typical shapes of the first and second derivatives of PPG signals.
Context: Differentiating the PPG signal is a key step in identifying fiducial points on PPG pulse waves.
Setup¶
These steps have been covered in previous tutorials, so we’ll just re-use the code here.
# Import packages
import sys
from pathlib import Path
!pip install wfdb==4.0.0
import wfdb
Requirement already satisfied: wfdb==4.0.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (4.0.0)
Requirement already satisfied: requests<3.0.0,>=2.8.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (2.28.1)
Requirement already satisfied: numpy<2.0.0,>=1.10.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (1.23.1)
Requirement already satisfied: SoundFile<0.12.0,>=0.10.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (0.10.3.post1)
Requirement already satisfied: matplotlib<4.0.0,>=3.2.2 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (3.5.2)
Requirement already satisfied: scipy<2.0.0,>=1.0.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (1.8.1)
Requirement already satisfied: pandas<2.0.0,>=1.0.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from wfdb==4.0.0) (1.4.3)
Requirement already satisfied: cycler>=0.10 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (0.11.0)
Requirement already satisfied: pyparsing>=2.2.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (3.0.9)
Requirement already satisfied: fonttools>=4.22.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (4.34.4)
Requirement already satisfied: python-dateutil>=2.7 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (2.8.2)
Requirement already satisfied: pillow>=6.2.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (9.2.0)
Requirement already satisfied: packaging>=20.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (21.3)
Requirement already satisfied: kiwisolver>=1.0.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (1.4.3)
Requirement already satisfied: pytz>=2020.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from pandas<2.0.0,>=1.0.0->wfdb==4.0.0) (2022.1)
Requirement already satisfied: urllib3<1.27,>=1.21.1 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from requests<3.0.0,>=2.8.1->wfdb==4.0.0) (1.26.10)
Requirement already satisfied: certifi>=2017.4.17 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from requests<3.0.0,>=2.8.1->wfdb==4.0.0) (2022.6.15)
Requirement already satisfied: idna<4,>=2.5 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from requests<3.0.0,>=2.8.1->wfdb==4.0.0) (3.3)
Requirement already satisfied: charset-normalizer<3,>=2 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from requests<3.0.0,>=2.8.1->wfdb==4.0.0) (2.1.0)
Requirement already satisfied: cffi>=1.0 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from SoundFile<0.12.0,>=0.10.0->wfdb==4.0.0) (1.15.1)
Requirement already satisfied: pycparser in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from cffi>=1.0->SoundFile<0.12.0,>=0.10.0->wfdb==4.0.0) (2.21)
Requirement already satisfied: six>=1.5 in /opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages (from python-dateutil>=2.7->matplotlib<4.0.0,>=3.2.2->wfdb==4.0.0) (1.16.0)
# The name of the MIMIC-IV Waveform Database on PhysioNet
database_name = 'mimic4wdb/0.1.0'
# Segment for analysis
segment_names = ['83404654_0005', '82924339_0007', '84248019_0005', '82439920_0004', '82800131_0002', '84304393_0001', '89464742_0001', '88958796_0004', '88995377_0001', '85230771_0004', '86643930_0004', '81250824_0005', '87706224_0003', '83058614_0005', '82803505_0017', '88574629_0001', '87867111_0012', '84560969_0001', '87562386_0001', '88685937_0001', '86120311_0001', '89866183_0014', '89068160_0002', '86380383_0001', '85078610_0008', '87702634_0007', '84686667_0002', '84802706_0002', '81811182_0004', '84421559_0005', '88221516_0007', '80057524_0005', '84209926_0018', '83959636_0010', '89989722_0016', '89225487_0007', '84391267_0001', '80889556_0002', '85250558_0011', '84567505_0005', '85814172_0007', '88884866_0005', '80497954_0012', '80666640_0014', '84939605_0004', '82141753_0018', '86874920_0014', '84505262_0010', '86288257_0001', '89699401_0001', '88537698_0013', '83958172_0001']
segment_dirs = ['mimic4wdb/0.1.0/waves/p100/p10020306/83404654', 'mimic4wdb/0.1.0/waves/p101/p10126957/82924339', 'mimic4wdb/0.1.0/waves/p102/p10209410/84248019', 'mimic4wdb/0.1.0/waves/p109/p10952189/82439920', 'mimic4wdb/0.1.0/waves/p111/p11109975/82800131', 'mimic4wdb/0.1.0/waves/p113/p11392990/84304393', 'mimic4wdb/0.1.0/waves/p121/p12168037/89464742', 'mimic4wdb/0.1.0/waves/p121/p12173569/88958796', 'mimic4wdb/0.1.0/waves/p121/p12188288/88995377', 'mimic4wdb/0.1.0/waves/p128/p12872596/85230771', 'mimic4wdb/0.1.0/waves/p129/p12933208/86643930', 'mimic4wdb/0.1.0/waves/p130/p13016481/81250824', 'mimic4wdb/0.1.0/waves/p132/p13240081/87706224', 'mimic4wdb/0.1.0/waves/p136/p13624686/83058614', 'mimic4wdb/0.1.0/waves/p137/p13791821/82803505', 'mimic4wdb/0.1.0/waves/p141/p14191565/88574629', 'mimic4wdb/0.1.0/waves/p142/p14285792/87867111', 'mimic4wdb/0.1.0/waves/p143/p14356077/84560969', 'mimic4wdb/0.1.0/waves/p143/p14363499/87562386', 'mimic4wdb/0.1.0/waves/p146/p14695840/88685937', 'mimic4wdb/0.1.0/waves/p149/p14931547/86120311', 'mimic4wdb/0.1.0/waves/p151/p15174162/89866183', 'mimic4wdb/0.1.0/waves/p153/p15312343/89068160', 'mimic4wdb/0.1.0/waves/p153/p15342703/86380383', 'mimic4wdb/0.1.0/waves/p155/p15552902/85078610', 'mimic4wdb/0.1.0/waves/p156/p15649186/87702634', 'mimic4wdb/0.1.0/waves/p158/p15857793/84686667', 'mimic4wdb/0.1.0/waves/p158/p15865327/84802706', 'mimic4wdb/0.1.0/waves/p158/p15896656/81811182', 'mimic4wdb/0.1.0/waves/p159/p15920699/84421559', 'mimic4wdb/0.1.0/waves/p160/p16034243/88221516', 'mimic4wdb/0.1.0/waves/p165/p16566444/80057524', 'mimic4wdb/0.1.0/waves/p166/p16644640/84209926', 'mimic4wdb/0.1.0/waves/p167/p16709726/83959636', 'mimic4wdb/0.1.0/waves/p167/p16715341/89989722', 'mimic4wdb/0.1.0/waves/p168/p16818396/89225487', 'mimic4wdb/0.1.0/waves/p170/p17032851/84391267', 'mimic4wdb/0.1.0/waves/p172/p17229504/80889556', 'mimic4wdb/0.1.0/waves/p173/p17301721/85250558', 'mimic4wdb/0.1.0/waves/p173/p17325001/84567505', 'mimic4wdb/0.1.0/waves/p174/p17490822/85814172', 'mimic4wdb/0.1.0/waves/p177/p17738824/88884866', 'mimic4wdb/0.1.0/waves/p177/p17744715/80497954', 'mimic4wdb/0.1.0/waves/p179/p17957832/80666640', 'mimic4wdb/0.1.0/waves/p180/p18080257/84939605', 'mimic4wdb/0.1.0/waves/p181/p18109577/82141753', 'mimic4wdb/0.1.0/waves/p183/p18324626/86874920', 'mimic4wdb/0.1.0/waves/p187/p18742074/84505262', 'mimic4wdb/0.1.0/waves/p188/p18824975/86288257', 'mimic4wdb/0.1.0/waves/p191/p19126489/89699401', 'mimic4wdb/0.1.0/waves/p193/p19313794/88537698', 'mimic4wdb/0.1.0/waves/p196/p19619764/83958172']
# Segment 3 and 8 are helpful
rel_segment_n = 8
rel_segment_name = segment_names[rel_segment_n]
rel_segment_dir = segment_dirs[rel_segment_n]
Extract one minute of PPG signal from this segment¶
These steps have been covered in previous tutorials, so we’ll just re-use the code here.
# time since the start of the segment at which to begin extracting data
start_seconds = 100
no_seconds_to_load = 5
segment_metadata = wfdb.rdheader(record_name=rel_segment_name,
pn_dir=rel_segment_dir)
print(f"Metadata loaded from segment: {rel_segment_name}")
fs = round(segment_metadata.fs)
sampfrom = fs*start_seconds
sampto = fs*(start_seconds + no_seconds_to_load)
segment_data = wfdb.rdrecord(record_name=rel_segment_name,
sampfrom=sampfrom,
sampto=sampto,
pn_dir=rel_segment_dir)
print(f"{no_seconds_to_load} seconds of data extracted from: {rel_segment_name}")
for sig_no in range(0, len(segment_data.sig_name)):
if "Pleth" in segment_data.sig_name[sig_no]:
break
ppg = segment_data.p_signal[:,sig_no]
fs = segment_data.fs
print(f"Extracted the PPG signal from column {sig_no} of the matrix of waveform data.")
Metadata loaded from segment: 88995377_0001
5 seconds of data extracted from: 88995377_0001
Extracted the PPG signal from column 4 of the matrix of waveform data.
Filter the data¶
These steps have been covered in previous tutorials, so we’ll just re-use the code here.
# package
import scipy.signal as sp
# filter cut-offs
lpf_cutoff = 0.7 # Hz
hpf_cutoff = 10 # Hz
# create filter
sos_ppg = sp.butter(10, [lpf_cutoff, hpf_cutoff],
btype = 'bp',
analog = False,
output = 'sos',
fs = segment_data.fs)
w, h = sp.sosfreqz(sos_ppg, 2000, fs = fs)
# filter PPG
ppg_filt = sp.sosfiltfilt(sos_ppg, ppg)
Import the packages required to plot the signal: matplotlib which is used to create plots, and NumPy which is used to create a time vector in this example.
from matplotlib import pyplot as plt
import numpy as np
Plot the original and the filtered PPG signal
fig, ax = plt.subplots()
t = np.arange(0, len(ppg_filt)) / segment_data.fs
ax.plot(t, ppg,
linewidth=2.0,
label = "original PPG")
ax.plot(t, ppg_filt,
linewidth=2.0,
label = "filtered PPG")
ax.set(xlim=(0, no_seconds_to_load))
plt.xlabel('time (s)')
plt.ylabel('PPG')
plt.legend()
plt.show()
We will use the filtered signal instead of the original PPG from now on.
Differentiate the PPG signal¶
Differentiate it once and twice using the Savitzky-Golay filtering function in SciPy
# Calculate first derivative
d1ppg = sp.savgol_filter(ppg_filt, 9, 5, deriv=1)
# Calculate second derivative
d2ppg = sp.savgol_filter(ppg_filt, 9, 5, deriv=2)
Resource: Savitzky-Golay filtering, which is used here to calculate derivatives, is described in this article.
Question: Can you summarise how Savitzky-Golay filtering works? What are its advantages in physiological signal processing?
Plot the PPG and its derivatives¶
from matplotlib import pyplot as plt
import numpy as np
t = np.arange(0, len(ppg_filt))/segment_data.fs
fig, (ax1,ax2,ax3) = plt.subplots(3, 1, sharex = True, sharey = False)
ax1.plot(t, ppg_filt)
ax1.set(xlabel = '', ylabel = 'PPG')
plt.suptitle('The PPG signal and its first and second derivatives')
ax2.plot(t, d1ppg)
ax2.set(xlabel = '',
ylabel = 'PPG\'')
ax3.plot(t, d2ppg)
ax3.set(xlabel = 'Time (s)',
ylabel = 'PPG\'\'')
plt.show()
Question: How would the derivatives have looked different if the PPG signal hadn't been filtered before differentiation?
Hint: In the differentiation step above, try replacing 'ppg_filt' with 'ppg'.
Question: How would the derivatives have been different if the PPG signal had been filtered using different co-efficients?
Hint: Above, try replacing the relatively wide band-pass frequencies '[0.7, 10]' with '[0.8, 3]'.
Consider: Which band-pass frequencies would be most suitable for pulse wave analysis? How about heart rate estimation?
Comparison with typical PPG pulse wave¶
The figure below shows a typical PPG pulse wave recorded from a young, healthy subject.
Source: Charlton PH, Photoplethysmogram (PPG) pulse wave fiducial points, Wikimedia Commons (CC BY 4.0).
_pulse_wave_fiducial_points.svg){kind=link}
Question: How does this pulse wave shape and derivatives compare to the shape of those obtained from MIMIC data above? What might explain the differences?
Extension: Try using 'rel_segment_n=3' above (i.e. analysing segment '82439920_0004'). How do the pulse waves in this signal compare? What might that tell us about this patient?
Further reading: this article provides further information on how age affects the shape of the PPG's second derivative.