Synthetic photoplethysmogram generation using two Gaussian functions

Figure 1. The main idea of the proposed modeling method. The blue color represents the systolic wave, and the red color represents the diastolic wave. (a) One-beat PPG waveform. (b) The circular motion principle. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document}ω is the angular velocity; it is fixed per pulse, but changes with different pulses. This figure shows how the circular motion will be used to generate a PPG waveform in a periodical manner.

Figure 2. Synthesized PPG signal using (a) excellent pulse template and (b) acceptable template. The optimal parameters for generating synthesized PPG signals based on these templates are shown in Table 1. An excellent PPG template means that the systolic and diastolic waves are salient (more clinical features, including heart rate, can be determined). An acceptable PPG template means that the systolic and diastolic waves are not salient (only heart rate can be determined). Here, MSE is the mean square error between the synthetic PPG and the template PPG, and r is the correlation coefficient. This figure shows that the model can generate excellent and acceptable PPG pulses with high correlation and low MSE.

Figure 3. Comparison of HRV between the real PPG and the synthetic PPG over 5-min duration in 116 subjects. (a), (c), (e), (g), (i) and (k) are Normalized Bland-Altman Plots of SDNN, RMSSD, LF, HF, SD1 and SD2, respectively. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Average = (simulate' + real')/2$$\end{document}Average=(simulate′+real′)/2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$difference = real' - simulate'$$\end{document}difference=real′-simulate′ where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$real'$$\end{document}real′ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

Figure 4. Comparisons of synthetic PPGs with different noises. (a) Three different low-frequency noise levels were added. The amplitudes of noise signals are 0.3, 0.4 and 0.1, and the frequencies are 0.3 Hz, 0.2 Hz and 0.9 Hz, respectively.(b) Five different high-frequency noise signals were added. The amplitudes of noise signals are 0.1, 0.03, 0.05, 0.04 and 0.05, and the frequencies are 50 Hz, 60 Hz, 70 Hz, 90 Hz and 100 Hz, respectively. (c) Five different noise signals were added. The amplitudes of noise signals are 0.4, 0.2, 0.3, 0.02 and 0.04, and the frequencies are 0.1 Hz, 0.7 Hz, 0.5 Hz, 70 Hz and 90 Hz, respectively. The blue part in (b) is the systolic wave and the red part is the diastolic wave. This figure shows that the synthetic PPG generated by the proposed model is similar to the real PPG in the MIMIC III database.

Figure 5. Synthesized PPG waveform based on the unfit template. The optimal parameters of the synthesized unfit PPG waveform are shown in the row corresponding to the unfit group in Table 1. Unfit means that the heart rate cannot be determined and the systolic and diastolic waves cannot be distinguished. Here, MSE is the mean square error between the synthetic PPG and the template PPG, and r is the correlation coefficient. This figure shows that the proposed model cannot synthesize the unfit PPG pulses.

Figure 6. Motion trajectory of a single synthesized PPG waveform. The simulated PPG waveform is based on an excellent PPG template (associated model parameters are shown in Table 1). The blue curve represents the first Gaussian, which corresponds to the systolic wave, and the red curve represents the second Gaussian, which corresponds to the diastolic wave. (a) Synthesized PPG waveform trajectory of one heartbeat in 3-D space, and the dotted part is the unit cycle. (b) Changes to the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document}x in one period. (c) Changes to the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y$$\end{document}y in one period. (d) Changes to the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…