Vascular waveform analysis using Bayesian pulse deconvolution

Figures

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  Fig. 1 |. Signal filtering accuracy in simulation. (a) A typical 2nd-order 0.5-12Hz Butterworth bandpass filter incompletely attenuates noise and introduces phase distortions in the physiological frequency range. Bayesian pulse deconvolution (PD) achieves greater noise attenuation across all frequencies. Shaded regions represent ±1 standard deviation across 100 simulations. (b) Bayesian pulse deconvolution (PD) recovers the waveform with less filter distortion than a typical filter. (c) Across 100 simulated waveforms, Bayesian pulse deconvolution achieves the best noise attenuation. Each point represents one simulated waveform. (Baseline algorithms are defined in Table 1.)

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  Fig. 2 |. Timing detection accuracy in simulation. (a) Typical pulse timing features are extracted from heuristic positions on a pre-filtered signal, such as the local maximum systolic peak (SP), local minimum onset (ON), peak first derivative (U), or peak 2nd derivative (A). (b) Bayesian pulse deconvolution (PD) aligns timing to the entire heartbeat cycle. (c) Across 100 simulated waveforms, Bayesian pulse deconvolution achieves the best root-mean-square error (RMSE). The “Ideal Filter” baseline takes the peak first derivative (U) from the true noiseless waveforms from simulation. This baseline has a higher median RMSE than Bayesian PD (p=1e–5). Each point represents one simulated waveform. (Baseline algorithms are defined in Table 1.)

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  Fig. 3 |. Shape extraction accuracy in simulation. (a) Typically, pulse shapes are extracted by aligning and averaging a filtered signal based on heuristic timing markers, ignoring overlaps between pulses. (b) Bayesian pulse deconvolution (PD) explicitly models overlaps in pulse shapes. (c) Across 100 simulated waveforms, Bayesian pulse deconvolution achieves the lowest percent error of the pulse shape area. The “Ideal Filter” baseline is the average pulse shape from the true noiseless signal using the true exact pulse times from simulation. Each point represents one simulated waveform. (Baseline algorithms are defined in Table 1.)

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  Fig. 4 |. Pulse timing evaluation on human recordings. (a) Pulse timing analysis of experimental recordings from a 48-year-old supine participant. Peaks of the electrocardiogram (ECG) are a proxy ground truth for evaluating the accuracy of pulse intervals extracted from a typical PyPPG (U) algorithm (defined in Table 1) and Bayesian pulse deconvolution (PD). (b) Pulse intervals extracted from the waveforms above. Dashed gray lines represent integer multiples of the sample period 1/fs. (c) Across 105 human recordings, Bayesian pulse deconvolution has a lower median root-mean-square error (RMSE) relative to ECG (p=1e–10). Each point represents one vascular waveform. Values are on a logarithmic scale.

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  Fig. 5 |. Uncertainty quantification. The true signal is derived from a 5-second photoplethysmogram waveform (only the first 3 seconds are plotted). Noisy signals are simulated with different sampling rates (fs) and signal-to-noise ratios (SNR). Shown in red are the maximum a posteriori (MAP) estimates and 99% credible intervals (CI) of the posterior were computed from 10,000 Monte Carlo Markov Chain (MCMC) samples. The marginal posterior distributions for the pulse times are shown as kernel density estimates (KDE) from the MCMC posterior samples. (a) High fs = 64 Hz, high SNR = 10. (b) Low fs = 16 Hz, high SNR = 10. (c) High fs = 64 Hz, low SNR = 1. (d) Low fs = 16 Hz, low SNR = 1.

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  Fig. 6 |. Analytical model of vascular waveforms. (a) Generative equations describing timing, shape, and noise components of observed signal y(t). (b) Bayesian graphical network representation. Arrows represent conditional dependence between variables. (c) Illustration of selected variables in the generative model.