# Blood Pressure Estimation by Photoplethysmogram Decomposition into Hyperbolic Secant Waves
## 3 Results  
Multiple regression was performed between PDA (Gaussian and sech) on plethysmographic data and the continuous blood pressure measurement data from the 10 subjects (60 segments of 8 s, for each subject), as discussed in Section 2. Initially, we studied multiple correlations between BP and PDA parameters independently for each subject. For each subject's data (60 8-s segments), the average Gaussian PDA and sech PDA parameters in the 8-s segments were used to determine the multiple correlation coefficient against the corresponding average BP ground truth in the same segments (Figure 6a). Moreover, in Figure 6a, using similar data segmentation and multiple  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Combination of Features**} \\ \hline
**Subject Number** & **Sech-PDA** & **Gaussian-PDA** \\ \hline
1 & \(\Delta\)t\({}_{0,1}\), FWHM\({}_{2}\) & \(\Delta\)t\({}_{0,2}\), a\({}_{1}\), a\({}_{2}\), FWHM\({}_{1}\), FWHM\({}_{2}\), FWHM\({}_{3}\) \\
2 & a\({}_{3}\), FWHM\({}_{1}\), FWHM\({}_{2}\), FWHM\({}_{3}\) & \(\Delta\)t\({}_{0,2}\), FWHM\({}_{1}\) \\
3 regression, we show the correlation coefficient of the Leave One Out (59:1) BP prediction vs. the corresponding average BP ground truth in the segment left out. This correlation coefficient was thus calculated using 60 data points per volunteer, since the Leave One Out (LOO) procedure was executed comprehensively for all 8-s segments of each subject. In Figure 6a, all results are calculated on an individual-by-individual basis. Figure 7 shows a scatterplot with all the 600 data points (for all 10 subjects), where the BP was predicted using the regression model learned with each subject data individually. We call this \"training data\". Note that the Gaussian PDA (R\({}^{2}\) = 0.77, \(p\) = 0.0000) underperformed compared with the prediction power of the sech PDA (R\({}^{2}\) = 0.81, \(p\) = 0.0000). Figure 8 is similar to Figure 7, but each one of the 600 data points was generated by an LOO prediction ('test data'), with an underlying regression model learned for each subject data individually. For each subject, 60 data points were generated by LOO 59:1. Again, the Gaussian PDA (R\({}^{2}\) = 0.58, \(p\) = 0.0000) underperformed compared with the prediction power of the sech-PDA (R\({}^{2}\) = 0.76, \(p\) = 0.0000). To further investigate possible performance differences between Gaussian PDA and sech PDA, we reanalyzed the data produced for Figure 6a. First, we averaged the multiple correlation coefficients, and the correlation coefficient, both from Figure 6a, which were determined independently for each one subject. The result of such an average is shown in Figure 6b. There was no statistically significant difference between the performance of the Gaussian PDA and the sech PDA by this analysis. Figure 6: Multiple correlation coefficients for each subject data as the training data and the correlation coefficients calculated by Leave One Out for each subject dataset. (**a**) Results for each subject independently. (**b**) Mean value of results from (**a**). For the group, the differences between the Gaussian and sech results are not statistically significant. Finally, Figure 9 shows multiple regression and correlation coefficients (from LOO) conducted on the data of all the subjects processed together (600 segments). Notice in Figure 9, there is a reduction in the multiple correlation coefficient, and in the correlation coefficient compared to regressions with the data of only one subject at a time, as in Figure 6b. Again, there was no statistically significant difference between the performance of Gaussian PDA and the sech PDA. This seems to indicate that, for long timeframes, Gaussian PDA and sech PDA, on average, converge to the same prediction power. For completeness, we show in Figure 10 mean squared errors (MSE) between the original pulse wave and the reproduced wave based on Gaussian PDA or Sech PDA in each subject (for all data regressions, analogous to Figure 7).