Mathematical modeling of heart rate tracking in motion affected PPG signals

Figures

• 

  Fig. 1. An example of a clean multi-channel PPG signal taken from subject 1 of the training dataset. (a) and (b) show the PPG channels and ACC channels, respectively. Similarly, (c) and (d) represent the Chirplet Z Transform (CZT)-based spectra for the mentioned signals. In the figure, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_1$$\end{document}P1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_2$$\end{document}P2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_1$$\end{document}A1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

• 

  Fig. 2. An example noisy PPG signal from subject 2 of the training dataset. The third and second peaks from PPG1 and PPG2 refer the actual heart rate instead of the main peaks in PPG1 and PPG2 spectra (c). In the figure, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_1$$\end{document}P1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_2$$\end{document}P2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_1$$\end{document}A1, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

• 

  Fig. 3. Figure shows an example of PPG affected by motion artifacts. Here the samples shown are taken from subject 2 of the training dataset. All the major peaks in both PPGs are random, and a small peak represents of the actual heart rate in PPG1 (Fig. 3). Major peaks are more reflective of the peaks in the acceleration signals.

• 

  Fig. 4. An overview of key steps in the calculation of heart rate from PPG signals. The general flow of heart rate calculation involves pre-processing, calculation of golden seeds, and heart rate calculation based on the CZT spectrum. To handle signals affected by noise and MAs, the spectral solution space is extended and a golden seed algorithm is utilized. In the figure, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}δ represents the unidirectional search area for the next heart rate and spectral length for CZT/FFT (Table 1).

• 

  Fig. 5. Bland-Altman plot and Pearson’s correlation for the complete set of 22 signals in the SPC dataset. (a) shows the Bland-Altman plot, where it can be seen that most of the heart rates are within +1.96 and −1.96 standard deviations. (b) presents the correlation plot of ground truth versus estimated heart rates.

• 

  Fig. 6. Detailed output of the system for a clean signal and a signal affected by noise and MAs. (a) Figure 6a shows the tracking performance of the algorithm for a comparatively clean signal of subject 8 from the test set. (b) The tracking performance of our technique for a very noisy signal with MAs. Figure 6b presents the HR tracking for subject 1 of the test dataset.

• 

  Fig. 7. A noisy PPG sample where both the PPG channels (a-b) lack the spectral peak corresponding to the heart rate. PPG channel 2 (g) is dominated by spectral contents similar to ACC channels.