Photoplethysmography (PPG)
Photoplethysmography (PPG) is a non-invasive optical technique used to measure blood volume changes in the microvascular bed of tissue. PPG signals are often used to measure heart rate, heart rate variability (HRV), respiratory rate, and oxygen saturation (SpO2). In PhysioKit, we provide a variety of routines for processing PPG signals.
Synthetic PPG
We can generate a synthetic PPG signal using the ppg.synthesize function. The function returns a numpy array with the PPG signal. The duration parameter specifies the length of the signal in seconds. The sample_rate parameter specifies the sampling rate in Hz. The heart_rate parameter specifies the heart rate in beats per minute (BPM).
Example
In the following snippet, we generate a synthetic PPG signal with a heart rate of 64 BPM sampled at 1000 Hz.
import physiokit as pk
sample_rate = 1000 # Hz
heart_rate = 64 # BPM
signal_length = 10*sample_rate # 10 seconds
ppg, segs, fids = pk.ppg.synthesize(
signal_length=signal_length,
sample_rate=sample_rate,
heart_rate=heart_rate,
frequency_modulation=0.3,
ibi_randomness=0.1
)
Noise Injection
We can additionally add noise to generate a more realistic PPG signal.
Example
Given the previous synthetic PPG signal, we can add baseline wander, powerline noise, and custom noise sources.
# Add baseline wander
ppg_noise = pk.signal.add_baseline_wander(
data=ppg,
amplitude=1,
frequency=0.5,
sample_rate=sample_rate
)
# Add powerline noise
ppg_noise = pk.signal.add_powerline_noise(
data=ppg_noise,
amplitude=0.05,
frequency=60,
sample_rate=sample_rate
)
# Add additional noise sources
ppg_noise = pk.signal.add_noise_sources(
data=ppg_noise,
amplitudes=[0.05, 0.05],
frequencies=[10, 20],
noise_shapes=["laplace", "laplace"],
sample_rate=sample_rate
)
Sanitize PPG
PPG signals are often corrupted by noise. The ppg.clean function provides a simple way to remove noise from PPG signals. By default, the routine implements a bandpass filter with cutoff frequencies of 0.5 Hz and 4 Hz. The lowcut and highcut parameters can be used to specify the cutoff frequencies. The order parameter specifies the order of the filter. The sample_rate parameter specifies the sampling rate in Hz. The function returns a numpy array with the cleaned PPG signal.
Example
In the following snippet, we clean the noisy PPG signal using a bandpass filter with cutoff frequencies of 0.5 Hz and 4 Hz.
...
# Clean PPG signal
ppg_clean = pk.ppg.clean(
data=ppg_noise,
lowcut=0.5,
highcut=4,
order=3,
sample_rate=sample_rate
)
Extract R-Peaks and RR-Intervals
A common task in PPG processing is to extract systolic peaks and peak-to-peak intervals. This has a 1:1 correspondance with r-peaks and therefore can be used to compute heart rate and HRV.
Example
In the following snippet, we extract systolic peaks and peak-to-peak intervals from the cleaned PPG signal.
...
# Extract s-peaks
peaks = pk.ppg.find_peaks(data=ppg_clean, sample_rate=sample_rate)
# Compute peak-to-peak intervals
rri = pk.ppg.compute_rr_intervals(peaks=peaks)
# Identify abnormal RR-intervals (e.g., ectopic beats)
# Mask is a boolean array where 0 indicates a normal RR-interval
mask = pk.ppg.filter_rr_intervals(rr_ints=rri, sample_rate=sample_rate)
# Keep normal RR-intervals
peaks_clean = peaks[mask == 0]
rri_clean = rri[mask == 0]
Compute Heart Rate
The ppg.compute_heart_rate function computes the heart rate based on the selected method. The peak method computes heart rate based on identified systolic peaks whereas fft method uses FFT to compute the heart rate. The function returns the heart rate in beats per minute (BPM) along with a "quality of signal" (QoS) metric. The QoS metric is a value between 0 and 1 where 1 indicates a high quality signal and 0 indicates a low quality signal. The QoS metric is based on the selected method.
Example
Continuing from the previous example, we can compute the heart rate using the peak method.
# Compute heart rate using FFT
hr_bpm, hr_qos = pk.ppg.compute_heart_rate(
ppg_clean,
method="fft",
sample_rate=sample_rate
)
OUTPUT:
Heart Rate: 64 BPM
Compute HRV Metrics
Refer to HRV Documentation for computing HRV metrics based on systolic peaks.
Derive Respiratory Rate
Respiratory sinus arrhythmia (RSA) is a phenomenon where the heart rate varies with respiration. Specifically, during inspiration, the heart rate increases and during expiration, the heart rate decreases. This is due to the parasympathetic nervous system which is responsible for slowing the heart rate. The ppg.compute_respiratory_rate function computes the respiratory rate based on the RR-intervals. The function returns the respiratory rate in breaths per minute (BPM) along with a "quality of signal" (QoS) metric. The QoS metric is a value between 0 and 1 where 1 indicates a high quality signal and 0 indicates a low quality signal. The QoS metric is based on the selected method. Beyond modulating the peak-to-peak intervals, respiration also modulates the amplitude of the PPG signal.
Example
In the following snippet, we derive the respiratory rate from the PPG signal.
...
# Compute respiratory rate using RIFV method
rr_bpm, rr_qos = pk.ppg.derive_respiratory_rate(
ppg=peaks[mask == 0],
peaks=peaks[mask == 0],
rri=rri[mask == 0],
method="rifv",
sample_rate=sample_rate
)
Respiratory Rate: 18 BPM
Note
In certain conditions such as noisy environments, certain subjects, PPG position, etc., the respiratory rate may not be accurately estimated. In these cases, the QoS metric will be low.
Compute SpO2
Using two PPG signals with different wavelengths, we can compute the oxygen saturation (SpO2). In PhysioKit, we can compute SpO2 in time domain using ppg.compute_spo2_in_time or frequency domain using ppg.compute_spo2_in_frequency.
Example
In the following snippet, we compute SpO2 in time and frequency domain from PPG signals captured by the MAX8614x sensor.
max8614x_coefs = [-16.666666, 8.333333, 100]
# Load PPG signals
ppg_red = ...
ppg_ir = ...
# NOTE: Pass the raw PPG signals as routines need to extract DC component
# Compute SpO2 in time domain
spo2_td = pk.ppg.compute_spo2_in_time(
ppg1=ppg_red,
ppg2=ppg_ir,
coefs=max8614x_coefs,
lowcut=0.5,
highcut=4,
sample_rate=sample_rate
)
# Compute SpO2 in frequency domain
spo2_fd = pk.ppg.compute_spo2_in_frequency(
ppg1=ppg_red,
ppg2=ppg_ir,
coefs=max8614x_coefs,
lowcut=0.5,
highcut=4,
sample_rate=sample_rate
)
SpO2: 98%
Note
When calling ppg.compute_spo2_in_time or ppg.compute_spo2_in_frequency, the coefs parameter must be specified. The coefficients are used to convert the PPG signals to SpO2 via a 2nd order polynomial. The coefficients are specific to the PPG sensor and should be provided by the manufacturer.