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Derivation of the respiratory rate from directly and indirectly measured respiratory signals using autocorrelation

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Current Directions in Biomedical Engineering
Aus der Zeitschrift Current Directions in Biomedical Engineering Band 2 Heft 1

Abstract

The estimation of respiratory rates from contineous respiratory signals is commonly done using either fourier transformation or the zero-crossing method. This paper introduces another method which is based on the autocorrelation function of the respiratory signal. The respiratory signals can be measured either directly using a flow sensor or chest strap or indirectly on the basis of the electrocardiogram (ECG). We compare our method against other established methods on the basis of real-world ECG signals and use a respiration-based breathing frequency as a reference. Our method achieved the best agreement between respiration rates derived from directly and indirectly measured respiratory signals.

Keywords: autocorrelation; ECG; respiration; respiratory rate

1 Introduction

The continuous measurement of the respiratory rate is particularly important in the medical environment as well as in the area of sports applications. Here, the most widely used approach is the measurement of the movements due to breathing using a chest strap or an impedance-based pneumographic device [1], [2]. However, there are also algorithms that derive the respiratory frequency noninvasively from other biosignals. It has been shown that the amplitude of the QRS-complex is modulated by chest movements during breathing, which results in a changing R-peak amplitude that correlates highly with the actual respiratory signal (taken from a chest strap or a flow sensor) [3]. From this signal one can estimate the breathing rate using a great variety of algorithms. The most commonly used methods are the Fast-Fourier Transform (FFT-method) and the zero-crossing method. The former estimates the rate from the strongest frequency component in the respiration signal, whereas the latter is based on determining the average duration of each breath [3], [4].

Interferences in the estimated respiration signal can lead to deviations in the estimated respiration rate. In this paper we propose a new method that allows a less interference-prone estimation of the respiratory rate. We applied the method to respiration signals derived both from ECG and a chest strap and evaluated the results in comparison to FFT and zero-crossing based respiration rate estimation methods.

2 Methods

2.1 Estimation of the respiratory rate

As a first step the respiratory signal is extracted from the ECG-signal sampled with the sampling frequency fs. For this purpose, a Hamilton-Tompkins algorithm [5] is used to detect all QRS-complexes in the ECG signal (comp. Figure 1). Next, the amplitude of the R-to-S peak is computed, which provides a robust estimation of the signal amplitude with respect to the baseline [6]. These extracted amplitudes are then interpolated by means of cubic splines to obtain the respiratory signal with the same sampling frequency as the ECG signal. An example for an extracted respiratory signal can be seen in Figure 1. Aside from a phase shift there is a high correlation between the extracted and the reference signal.

Figure 1 Top: baseline-corrected ECG signal with marked R- and S-peaks for the estimation of the R-to-S amplitude; bottom: reference respiratory signal (blue) compared to ECG-derived respiratory signal (orange). Amplitudes are normalized, arbitrary units.
Figure 1

Top: baseline-corrected ECG signal with marked R- and S-peaks for the estimation of the R-to-S amplitude; bottom: reference respiratory signal (blue) compared to ECG-derived respiratory signal (orange). Amplitudes are normalized, arbitrary units.

In order to estimate the respiration rate, the fundamental frequency of the extracted respiratory signal has to be calculated. As mentioned above, this can be done using methods like the FFT in the frequency domain [4] or the zero-crossing method in the time domain [3]. In this paper we present a different approach which is based on the autocorrelation function of the estimated respiratory signal. The autocorrelation function Ψ(i) of the respiratory signal xresp is defined in Eq. 1 [7]:

(1)Ψ⁢(i)=∑n=0Nxresp⁢(n)⁢xresp⁢(n−i)

Here, N and i denote the number of samples and the displacement of the signal towards itself, respectively. Generally, the autocorrelation function describes the similarity of a signal to a shifted version of itself. In the case of periodic signals, this function shows periodic maxima. The displacements i at which those maxima occur correspond to integer multiples of the fundamental period of the signal (here, i.e. the respiratory signal). Employing the Wiener-Khinchin theorem [8] allows an efficient calculation of Eq. 1 on the basis of an FFT. Next, the intervals ti of all neighbouring local maxima of the autocorrelation function are determined. Disturbances in the extracted respiratory signal or its non-stationarity may cause additional local maxima. Figure 2 shows one such example. Here it can be seen that high-frequency disturbances of a respiratory signal lead to local maxima (denoted in red) in the autocorrelation function that are unrelated to the fundamental period of the respiratory signal. To suppress the influence of these additional maxima an empirically estimated threshold is used so that only maxima exceeding this threshold were included in subsequent calculations. To further weaken the influence of highly deviating time intervals their median is usesd as the final estimate for the duration of a breath cycle. The respiratory frequency in breaths per minute (bpm) can then be calculated using Eq. 2.

Figure 2 Top: ECG-derived respiratory signal (example); bottom: local maxima belonging to the fundamental period (green) and local maxima caused by artifacts (red).
Figure 2

Top: ECG-derived respiratory signal (example); bottom: local maxima belonging to the fundamental period (green) and local maxima caused by artifacts (red).

(2)fresp=60fs/Tresp

The first reference method to estimate respiratory rates is the FFT. It is used to calculate the spectrum of the respiratory signal. The frequency component fmax with the highest amplitude is thaken as the respiratory frequency. This frequencies can be converted to the respiratory rate in bpm using Eq. 3.

(3)fresp=60⁢fmax

For the zero-crossing method, i.e. the second reference method, the first step is to center the signal at zero by subtracting the mean respiratory signal from each sample. After that, all zero-crossings ti are detected. The respiratory rate can finally be estimated by calculating the mean of all detected zero-crossings using Eq. 4.

(4)fresp=602N⁢∑i=1Nti

2.2 Simulation setup

Simultaneous recordings of ECG and respiration were used to evaluate the method. The recordings of 13 subjects with a length of 30 min each were taken from the Combined Measurement of ECG, Breathing and Seismocardiogram (CEBS) database [9], [10]. All datasets contained an ECG-signal as well as a respiratory signal measured by a chest strap. The datasets were converted to a MATLAB-readable format using the WFDB toolbox [11]. From each dataset ECG and respiratory signal were obtained and resampled to a sampling frequency of fs = 250 Hz. Both signals were subdivided into sliding windows of length Tmeas = 30 s and an overlap of 15 s. Baseline removal was applied to the ECG-signal [12]. Furthermore, the 50 Hz powerline interference was removed using an IIR-Notch-Filter. The respiratory signal was smoothed using an FIR-lowpass-filter (fcut = 2 Hz). The method described in section 2.1 was used for the estimation of the respiratory rate by means of directly measured respiratory signals (chest strap) and ECG signals. Subsequently, the results are then compared to the ones obtained for the FFT-method and the zero-crossing method.

3 Results

Figure 3 shows the raw results of all evaluated methods. The horizontal axis represents estimated respiratory rate based on the ECG and the vertical axis represents the respiratory rate based on the chest strap signal. All methods show a high correlation between respiratory rates estimated from ECG and chest strap. Both the autocorrelation method (r = 0.86, p < 10−3) and the zero-crossing method (r = 0.88, p < 10−3) exhibit a strong linear relationship between both estimated respiratory rates whereas this relation is much weaker for the FFT-method (r = 0,6, p < 10−3). The statistical significance of the correlation was tested using a t-test. It can be seen that the reference-based respiratory rate estimated by means of the FFT-method shows discrete values. This is due to the finite frequency resolution. The ECG-based respiration frequency does not show this effect. This is due to the spline interpolation of the R-to-S peak amplitudes leading to slightly varying sample-sizes for each time window and thus to varying frequency resolutions depending on the length of the time window Tmeas.

Figure 3 Correlation between respiration-derived respiratory rate and ECG-derived estimated respiratory rate using the autocorellation method (A), FFT-method (B) and zero-crossing method (C).
Figure 3

Correlation between respiration-derived respiratory rate and ECG-derived estimated respiratory rate using the autocorellation method (A), FFT-method (B) and zero-crossing method (C).

The error between ECG- and chest-strap-based respiration rates for each method is displayed in Figure 4. A Kolmogorov-Smirnov Test was used to compare the error distibutions. It turned out that all distributions were statistically significantly different (p < 10−3). While the median of the autocorrelation method is located around zero, the median of the FFT-method lies above zero and shows a higher spread. The median of the zero-crossing method is also close to zero. However, its error distribution exhibits an asymmetric deviation from the median. Values for mean and variance of the error are shown in Table 1. It can be seen that the autocorrelation method has a smaller error in average than any of the reference methods. In contrast to the zero-crossing method there is a huge difference regarding the variance of the error between autocorrelation- and FFT-method.

Figure 4 Comparison of the error of respiration-based and ecg-based estimation of the respiratory rate using all methods considered. Boxes show interquartile range (IQR = Q0.75 − Q0.25) and median. Outliers are depicted as dots outside of the boxes.
Figure 4

Comparison of the error of respiration-based and ecg-based estimation of the respiratory rate using all methods considered. Boxes show interquartile range (IQR = Q0.75 − Q0.25) and median. Outliers are depicted as dots outside of the boxes.

Table 1

Mean and variance of the error distributions shown in Figure 4.

μ (err)Var (err)
Autocorrelation−0.153.68
FFT−0.817.54
Zero-crossing−0.442.7

An inter-subject analysis emphasizes these findings. It can bee seen in Figure 5 that the error of the zero-crossing method shows a higher spread than the error of the autocorrelation method. We have omitted the FFT-method since we consider it unsuited here due to its discrete-valued results.

Figure 5 Error of the autocorrelation- and zero-crossing method on an inter-subject level. Boxes show interquartile range (IQR = Q0.75 − Q0.25) and median. Outliers are depicted as dots outside of the boxes.
Figure 5

Error of the autocorrelation- and zero-crossing method on an inter-subject level. Boxes show interquartile range (IQR = Q0.75 − Q0.25) and median. Outliers are depicted as dots outside of the boxes.

4 Discussion

We compared ECG-derived and chest-strap-derived respiratory rates using three different methods, i.e. FFT, zero-crossing and the newly proposed autocorrelation method. It became apparent that there is a high correlation between the results of zero-crossing and the autocorrelation. Yet, the correlation between the FFT-method and the two others is considerably lower. The results also show a low variance of the error for zero-crossing and autocorrelation as opposed to the FFT-method. However, the ECG-based respiratory rate estimates by means of zero-crossing are systematically lower than the chest-based estimation. Apparently, the autocorrelation method is less prone to interferences in the respiratory signal than the other methods. These interferences can be caused by either artifacts in the ECG signal or as a result of natural changes of the breath frequency in the analysed time interval. Another disadvantage of the FFT-method is its finite frequency resolution in the time window under consideration. It is also possible that an insufficient baseline removal leads to low-frequency components in the derived respiratory signal and therefore to a larger error. This effect was reduced by calculating the amplitude of the R-peak with respect to the S-peak but can not be completely eliminated.

Algorithms used for preprocessing can also have a deteriorating effect on the estimation of the respiratory frequency. FIR-filters used to enhance the signal-to-noise ratio almost always also remove important signal components, which in turn can lead to changed R-peak amplitudes. Other techniques (i.e. wavelet filters) might help to mitigiate this effect.

We have shown that the proposed autocorrelation method is generally feasible for the estimation of the respiration rate from both ECG-based and chest strap based respiratory signals. It is applicable to the long-term monitoring of patients in a clinical environment without directly measuring the respiratory signal. This is particularly useful, e.g. during rehabilitation after a surgical intervention. The used data exhibits a rather low variability in terms of respiratory frequency. An evaluation of our method using very low and very high respiratory frequencies is necessary to further substantiate its usefulness. An extension of our method to PPG signals may also be conceivable.

Author’s Statement

Research funding: This work was funded by the Federal Ministry of Education and Research (BMBF) (FKZ 03FH032IX5). 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 conducted research is not related to either human or animal use.

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Published Online: 2016-9-30
Published in Print: 2016-9-1

©2016 Fabian Schrumpf et al., licensee De Gruyter.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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https://doi.org/10.1515/cdbme-2016-0054
Schlagwörter für diesen Artikel
autocorrelation; ECG; respiration; respiratory rate
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  59. Artificial blood circulatory and special Ultrasound Doppler probes for detecting and sizing gaseous embolism
  60. Detection of microsleep events in a car driving simulation study using electrocardiographic features
  61. A method to determine the kink resistance of stents and stent delivery systems according to international standards
  62. Comparison of stented bifurcation and straight vessel 3D-simulation with a prior simulated velocity profile inlet
  63. Transient Euler-Lagrange/DEM simulation of stent thrombosis
  64. Automated control of the laser welding process of heart valve scaffolds
  65. Automation of a test bench for accessing the bendability of electrospun vascular grafts
  66. Influence of storage conditions on the release of growth factors in platelet-rich blood derivatives
  67. Cryopreservation of cells using defined serum-free cryoprotective agents
  68. New bioreactor vessel for tissue engineering of human nasal septal chondrocytes
  69. Determination of the membrane hydraulic permeability of MSCs
  70. Climate retainment in carbon dioxide incubators
  71. Multiple factors influencing OR ventilation system effectiveness
  72. Evaluation of an app-based stress protocol
  73. Medication process in Styrian hospitals
  74. Control tower to surgical theater
  75. Development of a skull phantom for the assessment of implant X-ray visibility
  76. Surgical navigation with QR codes
  77. Investigation of the pressure gradient of embolic protection devices
  78. Computer assistance in femoral derotation osteotomy: a bottom-up approach
  79. Automatic depth scanning system for 3D infrared thermography
  80. A service for monitoring the quality of intraoperative cone beam CT images
  81. Resectoscope with an easy to use twist mechanism for improved handling
  82. In vitro simulation of distribution processes following intramuscular injection
  83. Adjusting inkjet printhead parameters to deposit drugs into micro-sized reservoirs
  84. A flexible standalone system with integrated sensor feedback for multi-pad electrode FES of the hand
  85. Smart control for functional electrical stimulation with optimal pulse intensity
  86. Tactile display on the remaining hand for unilateral hand amputees
  87. Effects of sustained electrical stimulation on spasticity assessed by the pendulum test
  88. An improved tracking framework for ultrasound probe localization in image-guided radiosurgery
  89. Improvement of a subviral particle tracker by the use of a LAP-Kalman-algorithm
  90. Learning discriminative classification models for grading anal intraepithelial neoplasia
  91. Regularization of EIT reconstruction based on multi-scales wavelet transforms
  92. Assessing MRI susceptibility artefact through an indicator of image distortion
  93. EyeGuidance – a computer controlled system to guide eye movements
  94. A framework for feedback-based segmentation of 3D image stacks
  95. Doppler optical coherence tomography as a promising tool for detecting fluid in the human middle ear
  96. 3D Local in vivo Environment (LivE) imaging for single cell protein analysis of bone tissue
  97. Inside-Out access strategy using new trans-vascular catheter approach
  98. US/MRI fusion with new optical tracking and marker approach for interventional procedures inside the MRI suite
  99. Impact of different registration methods in MEG source analysis
  100. 3D segmentation of thyroid ultrasound images using active contours
  101. Designing a compact MRI motion phantom
  102. Cerebral cortex classification by conditional random fields applied to intraoperative thermal imaging
  103. Classification of indirect immunofluorescence images using thresholded local binary count features
  104. Analysis of muscle fatigue conditions using time-frequency images and GLCM features
  105. Numerical evaluation of image parameters of ETR-1
  106. Fabrication of a compliant phantom of the human aortic arch for use in Particle Image Velocimetry (PIV) experimentation
  107. Effect of the number of electrodes on the reconstructed lung shape in electrical impedance tomography
  108. Hardware dependencies of GPU-accelerated beamformer performances for microwave breast cancer detection
  109. Computer assisted assessment of progressing osteoradionecrosis of the jaw for clinical diagnosis and treatment
  110. Evaluation of reconstruction parameters of electrical impedance tomography on aorta detection during saline bolus injection
  111. Evaluation of open-source software for the lung segmentation
  112. Automatic determination of lung features of CF patients in CT scans
  113. Image analysis of self-organized multicellular patterns
  114. Effect of key parameters on synthesis of superparamagnetic nanoparticles (SPIONs)
  115. Radiopacity assessment of neurovascular implants
  116. Development of a desiccant based dielectric for monitoring humidity conditions in miniaturized hermetic implantable packages
  117. Development of an artifact-free aneurysm clip
  118. Enhancing the regeneration of bone defects by alkalizing the peri-implant zone – an in vitro approach
  119. Rapid prototyping of replica knee implants for in vitro testing
  120. Protecting ultra- and hyperhydrophilic implant surfaces in dry state from loss of wettability
  121. Advanced wettability analysis of implant surfaces
  122. Patient-specific hip prostheses designed by surgeons
  123. Plasma treatment on novel carbon fiber reinforced PEEK cages to enhance bioactivity
  124. Wear of a total intervertebral disc prosthesis
  125. Digital health and digital biomarkers – enabling value chains on health data
  126. Usability in the lifecycle of medical software development
  127. Influence of different test gases in a non-destructive 100% quality control system for medical devices
  128. Device development guided by user satisfaction survey on auricular vagus nerve stimulation
  129. Empirical assessment of the time course of innovation in biomedical engineering: first results of a comparative approach
  130. Effect of left atrial hypertrophy on P-wave morphology in a computational model
  131. Simulation of intracardiac electrograms around acute ablation lesions
  132. Parametrization of activation based cardiac electrophysiology models using bidomain model simulations
  133. Assessment of nasal resistance using computational fluid dynamics
  134. Resistance in a non-linear autoregressive model of pulmonary mechanics
  135. Inspiratory and expiratory elastance in a non-linear autoregressive model of pulmonary mechanics
  136. Determination of regional lung function in cystic fibrosis using electrical impedance tomography
  137. Development of parietal bone surrogates for parietal graft lift training
  138. Numerical simulation of mechanically stimulated bone remodelling
  139. Conversion of engineering stresses to Cauchy stresses in tensile and compression tests of thermoplastic polymers
  140. Numerical examinations of simplified spondylodesis models concerning energy absorption in magnetic resonance imaging
  141. Principle study on the signal connection at transabdominal fetal pulse oximetry
  142. Influence of Siluron® insertion on model drug distribution in the simulated vitreous body
  143. Evaluating different approaches to identify a three parameter gas exchange model
  144. Effects of fibrosis on the extracellular potential based on 3D reconstructions from histological sections of heart tissue
  145. From imaging to hemodynamics – how reconstruction kernels influence the blood flow predictions in intracranial aneurysms
  146. Flow optimised design of a novel point-of-care diagnostic device for the detection of disease specific biomarkers
  147. Improved FPGA controlled artificial vascular system for plethysmographic measurements
  148. Minimally spaced electrode positions for multi-functional chest sensors: ECG and respiratory signal estimation
  149. Automated detection of alveolar arches for nasoalveolar molding in cleft lip and palate treatment
  150. Control scheme selection in human-machine- interfaces by analysis of activity signals
  151. Event-based sampling for reducing communication load in realtime human motion analysis by wireless inertial sensor networks
  152. Automatic pairing of inertial sensors to lower limb segments – a plug-and-play approach
  153. Contactless respiratory monitoring system for magnetic resonance imaging applications using a laser range sensor
  154. Interactive monitoring system for visual respiratory biofeedback
  155. Development of a low-cost senor based aid for visually impaired people
  156. Patient assistive system for the shoulder joint
  157. A passive beating heart setup for interventional cardiology training
Heruntergeladen am 24.4.2026 von https://www.degruyterbrill.com/document/doi/10.1515/cdbme-2016-0054/html?lang=de
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