5.5.1
The bias and variance of theNFB
On simulated data, the NFB algorithm yielded estimates with bias and variance approaching zero with increasing input SNR values. The simulations showed that the sensitivity of the NFB algorithm to its parameters (i.e., the filter bank resolution F and the forgetting factorδ) depends on the input SNR. A second input to the NFB algorithm reduced the estimation bias and variance by up to 50% compared to using a single input with a larger effect on the bias than on the variance.
Figure 5.10: The reference and NFB estimate BRs for Subject 1 during exercise. The mean absolute error over the length of the record was 1.61 brpm.
Figure 5.11: The reference and NFB estimate BRs for Subject 2 during exercise. The mean absolute error over the length of the record was 3.71 brpm.
5.5.2
The performance of theW-OSC and NFB algorithms on resting data
Both the W-OSC and the NFB methods yielded instantaneous BR estimates in a continuous and automatic manner, without requiring special adjustments based on subject characteristics. Furthermore, sudden changes in the BR estimate because of abnormal beats or bad quality seg- ments in the recordings were rectified within a limited number of iterations due to the recursive- ness of both methods, thus no special data-dependent pre-processing was needed.
Since the number of input signals in the W-OSC and NFB algorithms is not limited, the breathing-related waveforms extracted from more than one ECG lead can be used to estimate the BR. In fact, other inputs containing the breathing modulation can be used as well. In particular, the RSA extracted from photoplethysmogram (PPG) recordings and the pulse transit time (PTT) are candidates as seen from their power spectral densities (PSD) in Figure 5.12. They both contain the breathing modulation of the heart rate similarly to the RSA and RPA of ECG. PPG waveforms are somewhat popular for the estimation of the cardiac and breathing parameters in a non-invasive and easy manner [139, 219] and the PTT can be derived by using ECG and PPG recordings, and also carries the breathing modulation of the cardiac rhythm [243]. Figure 5.13 shows a snapshot of a demonstration created for the startup company Leman Micro Devices6 in a collaborative project. In this demonstration, the BR was estimated from the ECG RSA and RPA, RSA from PPG signals acquired in red and infrared (IR) illuminations, the PTT and several combinations of them.
Figure 5.12: The PSD of the ECG and PPG RSA and the PTT. All contain the breathing modu- lation as seen in the peak at around 0.2 Hz.
From real ECG data, the NFB estimated the BR with a smaller error and less delay (nearly half less) than the W-OSC method. When the mean delay was introduced in the estimates, the errors were smaller for both algorithms, as expected.
On the ECG data, the estimation error of the NFB method was consistent with the results of the simulations in terms of variations with respect to the parameter choice and the number of in- puts. The estimation delay appeared to be directly related toδ. On the other hand, the resolution (F) did not seem to have a specific relationship with the delay, but it had an effect on the complex- ity of the algorithm. A mid-range value of the two parameters provided an acceptable error-delay compromise. Nonetheless, over the range of tested values, the error varied at most by 0.31 brpm, which is not a large variation considering that the reference BR was on average 17.34 brpm. In comparison with the W-OSC, the NFB algorithm showed a considerably smaller sensitivity to its
Figure 5.13: Estimating the BR from several ECG and PPG breathing modulations: (a) The PPG and ECG and the heart beats; (b) the reference breathing waveform and the RSA extracted from the ECG and the PPG; (c) The BR estimated with the W-OSC method.
parameter choice. This property is especially beneficial in real biomedical applications, in which there is a large variability in the signals between individuals and even within one individual. It is therefore beneficial to use a method, which does not require much adjustment of its parameters.
Using the RSA and RPA, separately, was also by far not as good as using both together, which shows the importance of the additional information. The RPA alone yielded better results than the RSA alone. This result is not in line with other studies [138]. In [138], all the inputs were narrow-band filtered to avoid the baroreflex oscillation. However, in the event of a low BR (lower than 0.2 Hz equivalent to 12 brpm), the breathing-related component would not be correctly extracted. The results were good regardless, because in the “Fantasia” data set, the BR is always above 12 brpm. The filtering operation removed the unwanted baroreflex influence without removing breathing-related oscillations. It seems that indeed, in the present study, the large baroreflex amplitude interferes with the identification of the breathing-related component of the RSA (wide-band). It is important to note that without prior knowledge about the BR, which is normally the case in an application, one cannot justify using only the narrow-band RSA. In a spirit of objectivity, we respected this condition in this study.
Results obtained in the present study can be compared to those of Orphanidou et al. [138], which were also presented on the “Fantasia” data set. It must be noted that the others used the same AR-based frequency estimation method on both the ECG-derived breathing waveform and the breathing signal to derive estimated BRs and reference BRs. A degree of correlation may therefore exist between the derived BRs. Furthermore, a validity criterion was used to exclude up to 35% of the data. In the present study, the W-OSC tracking method was excluded for reference estimation in order to avoid bias in the results. Due to the unavoidable differences in methodology and the different reference BR, the W-OSC and NFB estimates are not directly comparable to Orphanidou et al.’s. However, the order of magnitude of the errors in the present study are similar, despite using the entire data set, and not imposing restrictive bandwidths in the filtering processes.
Unlike the AR-based method of Orphanidou et al., both the W-OSC and the NFB methods are automatic and instantaneous, robust to abnormal beats and segments of bad quality data. The delay in the estimates of Orphanidou et al. is half the window length, which is 30 s. Both methods in this chapter were implemented in a truly real-time manner, such that heart beats were processed in chronological order, and the BR estimates were updated with information from each
new beat.
5.5.3
The performance of theNFB method on physical activity data
On the data acquired during physical activity, the NFB method was robust and tracked the rapidly varying BR accurately and with no need for any special adjustments compared to its application to resting-state signals, except for a slightly larger application bandwidth.
It must be noted that the W-OSC method was also applied to the task of etimating the BR during exercise. The results were similar to those of the NFB with a larger estimation delay, as expected. Due to the small amount of data available, we chose not to carry out an extensive analysis on the exercise data.
5.5.4
Limitations
On the real data, i.e. the “Fantasia” data set and the VO2MAX data, the reference BR was computed with automated methods. Despite our best care and intentions, the automatic reference could be influenced by noise and artifacts and does not fully represent a ground-truth.
As discussed in Chapter 3, in the supine position, the RSA is generally the largest component of the R-R intervals. In the orthostatic position, the baroreflex activity influence is larger than at supine, and may be confused for the breathing-related component. This problem even occurred in the “Fantasia” supine data in [138]. Other studies have also highlighted that estimating the BR in positions other than supine or seated is more difficult [224]. Most of the results presented in this chapter were also on supine data. It must be noted that estimating the BR regardless of the position my be more challenging than on supine resting data. However, interestingly, on the exercise data, this problem did not arise. This could be due to the more prominent breathing patterns and the autonomic particularities of exercise.