Respiratory signals are required in a large variety of applications not only in medicine. For instance, the diagnosis of sleep disorders and the detection of apnea is carried out measuring respiration during the night. In addition, the performance of professional athletes can be improved by monitoring their respiration during physical activity. Furthermore, stress assessment and management can be evaluated by considering respiration signals. However, measuring and quantifying respiration can become a tedious job. Typically, the measurement is carried out using spirometers or acquiring transthoracic impedance. They have the disadvantage of requiring additional medical equipment and often disturbing the normal respiration of the subject. Therefore, the ECG derived respiration (EDR) appeared as a low cost convenient alternative. For this method only the ECG is needed which is already available in many cases. Respiration has a direct effect on the ECG due to three major coupling mechanisms. First, the electrodes used to record the ECG move with respect to the heart as the thorax inflates and deflates. Therefore, the projection of the mean electrical axis of the heart on the given electrodes changes with ribcage movement. Second, the electrical impedance of the torso changes depending on the volume of air present in the lungs. Air, and consequently the lungs have a significantly different electrical permittivity than the organs in the thorax. Since the lungs are between the heart and the electrodes on the chest, the potential difference measured by them changes depending on respiration. Third, a physiological phenomenon called respiratory sinus arrhythmia (RSA), which is a direct modulation of the heart rate by respiration rate. The modulation is achieved because during the inspiration the heart beats slower while during exhalation the heart rate accelerates. In the past, these three coupling mechanisms have been used to create different methods to extract a respiration signal from the ECG. In general, they have a direct influence on the baseline of the ECG, its amplitude through a modulation process and the instantaneous heart rate. In this work, we implemented a group of commonly used EDR methods and found an optimal linear combination of them in order to build a better reconstruction of the real breathing signal.
2.1 Data used in this study
In order to develop and test our algorithms, two well known data sets from Physionet  were used. The first data set is the Fantasia database (Fantasia). It contains a total of 40 recordings from 20 young and 20 elderly subjects in resting state while watching the Disney movie Fantasia. One ECG channel and one respiratory signal are present. The signals were digitized at 250 Hz. The second database is the MIT-BIH Polysomnographic Database (SLP). It contains a total of 18 recordings from 16 subjects that were evaluated for chronic obstructive sleep apnea syndrome. Among other physiologic signals, one ECG channel and one respiratory signal are present. The recordings have a duration between 2 and 7 hours depending on the subject. The signals were digitized at 250 Hz.
2.2 Preprocessing the ECG signal
When preprocessing ECG signals for EDR methods, it is of highest priority to fully suppress baseline wander. The majority of EDR methods try to reflect amplitude fluctuations in the ECG caused by respiration and are thus corrupted by low frequency artifacts. In order to estimate and then subtract the baseline, a concatenation of two median filters was applied. Median filters work analogously to moving average filters but they calculate the median signal value within a sliding window. The width of the sliding windows for the median estimation was chosen to be 200 ms and 600 ms respectively. This approach eliminates baseline wander while retaining P-QRS-T waves. A demonstration of the method is shown in figure 1. High frequency noise and power line interference were filtered using Gaussian kernels.
2.3 EDR methods used
A large number of algorithms have been developed in the past to estimate respiration from the ECG. An introduction to this topic is given by Bailón  and O’Brien . In this work, we implemented a total of 13 methods. As mention in the introduction, they are based on one of the three phenomena that couple respiration and ECG. Out of the 13 methods, 6 of them deal with the amplitude modulation caused on the QRS complex (first principal component (PCA), QRS integral, QR slope, QRS width, R peak and RS amplitude) and 4 of them on the T wave (T integral, T peak, T slope, RT peak). One of the methods uses the statistical properties of the ECG in every beat (kurtosis). Another one extracts the spectral properties of the signal below 0.5 Hz using the discrete wavelet transform (wavelet). Finally, the last method uses time distance between each QRS complex (RR interval). Since the majority of the methods do not deliver a continuous signal but rather one sample point per beat, an interpolation has to be carried out. We chose a low pass filter with a cutoff frequency equal to halve of the mean heart rate of the subject. Using this interpolation method we minimize additional frequency content that was not present in the original respiration signal. The functionality of the R peak method is displayed in figure 2.
2.4 Quantifying quality of EDR methods
In order to benchmark the EDR methods implemented in this work and choose the best ones to combine later, the maximal correlation between the measured and the estimated respiration was used. The procedure was carried out on non overlapping windows of the signal with a width of 20 s. A median correlation value was calculated in the end. This way, every method received a score between 0 and 1 for every signal. In the end, we chose the best four methods (PCA, R peak, QRS integral and RS amplitude) and they all turned out to be QRS complex based estimations. In order to include new information from other ECG waves and thus different time points, we also considered the best two T wave methods (T peak and T integral). The performance of each method on the Fantasia data set can be seen in figure 3.
2.5 Optimal linear combination of EDR methods to improve estimation
An optimal linear combination of the chosen EDR methods can be found (equation 1). For this purpose, a pre-possessing step is needed first. Every EDR method delivers a signal with its own amplitude and phase. In order to compensate amplitude differences between the methods, every EDR signal was normalized to have a unitary variance. Phase shift among EDR signals was corrected using the cross correlation between the PCA method and each of other methods. The time point of maximal cross correlation was subtracted from every EDR signal so that no time shift between the methods was present in the end.(1)
The vector of coefficients was obtained using an optimization algorithm. The resulting EDR signal should be as similar as possible to the reference respiration measurement. Similarity was quantified in a correlation sense. In order to avoid linearly dependent parameter sets, we also restrained the values of each coefficient to be in the interval [0; 1] and to sum up to 1. Thus, the problem can be formulated as a minimization of a target function (equation 3). The optimization was carried out using the function fmincon implemented in MATLAB®.(2)(3)
For each subject in the Fantasia database, an optimal parameter set was calculated. It turned out that every signal had a different optimal coefficient vector. Therefore, the median parameter set among the complete database was fixed and defined as global optimum. In order to test the performance of this globally optimal parameter vector, it was compared to other three estimations. First, every single EDR method prior to optimal linear combination was considered. Second, the best performing EDR method for each subject was taken into account. Third, the locally best linear combination of methods for each subject was considered too. In addition, the optimal parameter vector was tested without modifications on the SLP database. Moreover, the comparison was carried out in the same way as for the Fantasia database.
3.1 Optimal linear combination of EDR methods for the Fantasia database
Optimal coefficient vector obtained for the Fantasia can be seen in table 1. Figure 4 shows the results of the performance of the linear combination of EDR methods in the Fantasia database. It can be observed that the median performance of the combined EDR signal was higher than the median of every single EDR method. In addition, even though a fixed set of coefficients was used, the combined signal competes with the best single EDR method and linear combination of methods for every patient. The fixed coefficient vector achieved a median cross correlation coeffi-cient of almost 0.8.
3.2 Performance of the algorithm on the SLP database
Figure 5 shows the results of the performance of linear combination of EDR methods on the SLP database using the fixed parameter vector obtained from the Fantasia database. The results are qualitatively similar to the ones presented in the previous section. However, in this data set the fixed coefficient vector achieved a median cross correlation coefficient of almost 0.9, which was larger than the one obtained for the Fantasia dataset.
The magnitude of each coefficient in the parameter vector reflects the performance of each EDR method. Higher values are in accordance with better performance. It was also possible to demonstrate that a fixed set of coefficients can deliver a median performance that is better than each of the single EDR methods. This is in accordance with the theory of optimal linear estimation. Furthermore, the fixed set of parameters performed almost as good as the specially chosen estimations for each subject. Since in the majority of EDR applications no prior knowledge about the quality of each EDR method is available, a fixed vector of coeffi-cients for the linear combination is a promising approach to this problem. The fixed set of parameters has the disadvantage of not adapting from subject to subject. This can be problematic if for one particular subject an EDR method is specially noisy. In that case, it would be convenient to reduce its corresponding coefficient in the linear combination. It was also very interesting to see that a fixed parameter vector that was originally obtained using the Fantasia database could be generalize to the new and up to that point unknown SLP database. This result proves that a fixed set of parameters can be used for general applications with different subjects, recording devices and ECG leads.
5 Limitations and outlook
The proposed algorithm has two significant drawbacks. First, the coefficient vector for the linear combination is fixed. In future, the algorithm could be extended to deliver a coefficient vector that changes in time and adapts its components to local signal quality. Second, the algorithm does not include all EDR methods. It would be interesting to optimally integrate all EDR methods to the existing algorithm and reevaluate its performance. Adding new EDR methods not mentioned here, together with an ECG multilead approach could significantly improve the performance of the algorithm even further.
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About the article
Published Online: 2015-09-12
Published in Print: 2015-09-01
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.