Secondary Logo

Journal Logo

Hilbert-Huang Transform Yields Improved Minute Volume Estimates from Respiratory Inductance Plethysmography During Transitions to Paradoxical Breathing

Mandel, Jeff E. MD, MS; Atkins, Joshua H. MD, PhD

doi: 10.1213/ANE.0000000000000969
Technology, Computing, and Simulation: Research Report

BACKGROUND: Anesthesia and sedation are associated with paradoxical breathing. Respiratory inductance plethysmography (RIP) permits measurement of respiratory motion in clinical settings not conducive to spirometry, but correlation of RIP volume changes and spirometer flow in the time domain is degraded by the development of paradoxical breathing. The Hilbert-Huang transform (HHT) is a nonlinear signal analysis method that permits the instantaneous magnitude and phase of nonstationary signals to be estimated in the frequency domain. We hypothesized that these frequency domain estimates would provide higher correlation between RIP and spirometer signals than time domain signals during the transition between normal and paradoxical breathing.

METHODS: From 51 patients undergoing sevoflurane anesthesia for minor procedures, a 5-minute epoch containing transitions between pressure support ventilation and spontaneous ventilation was selected for analysis. Pearson correlation for models based on HHT magnitude and phase was compared with models based on time domain signals. Bland-Altman analysis was performed to assess deviation from linearity in the models.

RESULTS: For the 51 patients analyzed, the modulation of tidal volume over the epoch ranged from 30% to 215% of epoch mean. The coefficient of determination for time domain analysis was 0.62 ± 0.2 compared with 0.93 ± 0.07 for the HHT model incorporating phase. This improvement of 0.31 (99% confidence interval, 0.24–0.37) was significant (P < 0.0001). No trend was observed in prediction residuals.

CONCLUSIONS: Under conditions of changing ventilation, HHT-derived magnitude and phase measures provide higher correlation with spirometry than those obtained with traditional time domain methods.

Published ahead of print September 22, 2015

From the Department of Anesthesiology & Critical Care, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania.

Accepted for publication July 6, 2015.

Published ahead of print September 22, 2015

Funding: Departmental.

The authors declare no conflicts of interest.

This report was previously presented, in part, at the 2014 American Society of Anesthesiologists.

LMA is a registered trade mark of The Laryngeal Mask Company Limited, an affiliate of Teleflex Incorporated.

Reprints will not be available from the authors.

Address correspondence to Jeff E. Mandel, MD, MS, Perelman School of Medicine, University of Pennsylvania, 7003 Dulles Bldg., 3400 Spruce St., Philadelphia, PA 19104. Address e-mail to

Anesthesia and sedation are associated with alterations in thoracoabdominal synchrony, referred to as “paradoxical breathing.” Many clinicians are familiar with the paradoxical breathing patterns seen under spontaneous ventilation (SV) during general anesthesia and appreciate that the minute volume is not as large as might be predicted from the observed external movement. The gold standard for measurement of minute volume is spirometry, but maintaining an occlusive seal for spirometry is not always practical, for example, during the period after extubation or during esophagogastroduodenoscopy. Respiratory inductance plethysmography (RIP) is a nonintrusive method for assessing ventilation, using elastic bands with coils encircling the chest and abdomen; the magnetic inductance of the coil is related to the cross-sectional area encircled. Given the assumption that the contribution of chest and abdominal movement to airflow remains constant over time, the minute volume can be estimated by linear regression. Unfortunately, this assumption may not be valid during anesthesia and sedation, because anesthetics, patient position changes, and ventilatory mode changes may alter the relative magnitude and phase of abdominal and chest motion.1–4

We have previously observed that, in patients breathing spontaneously under general anesthesia with sevoflurane, transitions between SV and pressure support ventilation (PSV) produced major changes in respiratory rate.5 An associated change in tidal volume was also seen; in some patients, this could transiently increase/decrease the tidal volume by 200%, with coincident changes in the relative magnitude of the chest and abdominal signals and their relative phases. These changes significantly lowered the accuracy of our predictions of minute volume from RIP signals using conventional time series methods. One of the goals in this study was to assess ventilation in the immediate postoperative period, leading us to examine whether better fidelity in estimation of minute volume from RIP was possible.

Empirical mode decomposition (EMD) is a signal-processing method that decomposes signals into a series of modes that are locally symmetric about zero.6 The resulting intermediate mode functions (IMFs) are subjected to the Hilbert transform, which provides the instantaneous phase and magnitude of the IMF. The combination of EMD and the Hilbert transform is referred to as the “Hilbert-Huang Transform” (HHT). Although the HHT is distinct from the Fourier transform (which decomposes signals into a series of sine waves of constant frequency), both methods represent signals in the frequency domain. EMD will typically segregate most energy of the respiratory signal into a dominant IMF, permitting accurate tracking of respiratory rates, as we have previously described.5 We extended our work with the HHT to derive the instantaneous magnitude of the spirometer, chest, and abdomen, and the difference in phase between chest and abdomen. Our hypothesis was that during transitions between SV and PSV, correlations between RIP and spirometer would be higher when using these frequency domain signals than those obtained using time domain signals, allowing improved estimates of minute volume during these transitions with nonintrusive methods such as RIP.

Back to Top | Article Outline


With approval of the IRB of the Perelman School of Medicine, University of Pennsylvania, and written consent, 53 patients scheduled for elective urological surgical procedures were prospectively enrolled in this prospective observational study over the period November 16, 2011, to March 14, 2012, in the SurgiCentre of the Perelman Center for Advanced Medicine. In all patients, SV with sevoflurane via Laryngeal Mask Airway (LMA®) was the planned anesthetic. No muscle relaxants were used in any of the anesthetics. In all anesthetics, transitions between pressure support (8–10 cm H2O, 30 liters per minute flow without a backup rate) and SV modes using the Dräger Fabius (Dräger USA, Telford, PA) anesthesia machine were used to modulate ventilatory patterns. A Hans Rudolph 4700B pneumotachometer (Hans Rudolph, Inc., Shawnee, KS) was placed proximal to the heat and moisture exchange filter in the anesthesia circuit, and RIP bands (Ambulatory Monitoring Inc., Armonk, NY) were applied in accordance with the manufacturer’s instructions. Data were acquired by 12-bit A/D converter at 120 Hz using custom-built software developed in LabVIEW (National Instruments, Austin, TX). Data from 2 patients were excluded because of signal loss. The spirometer data (but not the RIP data) were used in our previous report.5

For each of the 51 patients, a contiguous 5-minute epoch of data was selected that contained at least 1 transition between pressure support and SV. In many cases, both transitions were present. During these transitions, there were considerable changes in the magnitude of spirometer signals, as well as changes in the relative magnitude of the chest and abdominal RIP signals, and the phase relationship between the chest and the abdominal signals. The epochs were selected to contain such changes. These 51 epochs were subjected to 2 analyses. The first used time domain signals. The original signal was filtered by 2 methods: an 8-tap finite impulse response filter, termed RAW, and EMD to remove the first 4 modes (composed of high-frequency noise), termed PREFILTER. Both signals were downsampled by a factor of 8. In the second analysis, the PREFILTER signals were decomposed by ensemble EMD using 900 realizations. Additive white noise was adjusted to reduce mode mixing.7 The resulting IMFs were transformed to instantaneous phase and magnitude using the HHT. Total magnitude was calculated as the sum of the magnitudes of all IMFs, and the dominant IMF was identified by determining which IMF was most correlated with total magnitude. The instantaneous magnitudes of the IMF signals are termed HHT spirometer, chest, and abdomen. The difference between instantaneous phase of the chest and abdomen IMFs is termed “HHT phase difference.”

We assumed that the RAW signals contained information that was not correlated with the respiratory process and that our analytical techniques would remove this. We also assumed that phase differences between the chest and the abdomen might alter the relationship between RIP and spirometry and that our techniques would incorporate this, leading to improvements in the coefficients of determination. To assess the impact of removing extraneous information and adding phase information, linear regression was performed using the following models:

  1. RAW Spirometer versus RAW Chest and RAW Abdomen
  2. RAW Spirometer versus RAW Chest
  3. RAW Spirometer versus RAW Abdomen
  4. PREFILTER Spirometer versus PREFILTER Chest and PREFILTER Abdomen
  5. HHT Spirometer versus HHT Chest
  6. HHT Spirometer versus HHT Abdomen
  7. HHT Spirometer versus HHT Chest and HHT Abdomen
  8. HHT Spirometer versus HHT Chest, HHT Abdomen, HHT Chest*Phase Difference, and HHT Abdomen*Phase Difference

For each patient, the Pearson coefficient of determination (r2) was determined using the fitlm routine of the Statistics Toolbox in MATLAB 2014a (The MathWorks, Natick, MA). Coefficients of determination for each of the models were fit to a β-distribution (a randomly distributed variable on the interval [0,1]), and means and SDs reported for the estimated probability density function.

The differences between coefficients of determination for model 1 (RAW) and models 4 to 8, as well as between model 2 and 5, and between model 3 and 6, were calculated for each of the 51 patients. These differences were assessed for normal distribution using the Lilliefors test. Means, Wald 99% confidence intervals, and P values for these comparisons are reported. Because of multiple observations, P < 0.007 was considered significant.

Bland-Altman analysis was performed to assess deviation from linearity in the models. After normalizing flow to the range of −1 to 1 (in the case of RAW) and magnitude to the range of 0 to 1 (in the case of HHT), fitted values were compared with actual values and the slope of error versus normalized value determined by linear regression.

Data sets were derived from previously collected data. All elements of the STROBE checklist (version 4) were addressed in that publication; power analysis for that study was performed for the primary end point of respiratory rate change.

Back to Top | Article Outline


In the 51 epochs analyzed, 47 transitions from PSV to SV and 34 transitions from SV to PSV were present. The modulation of tidal volume (ratio of range to mean) over these epochs varied from 30% to 215%, reflecting the considerable variability of patient response to the transitions between SV and PSV. The time course of alterations in tidal volume is depicted in Figure 1, which contains 3 transitions from SV to PSV and 2 transitions from PSV to SV over a 15-minute period. Greater detail is shown in Figure 2, which uses PREFILTER signals with DC offset removed and scaled to permit all 3 signals to have the same full swing amplitude to illustrate the relative magnitude and phase changes. At the start of the tracing, the patient is breathing with PSV. In the left inset, the chest (blue) and abdominal (green) RIP signals are of similar magnitude and phase and lag the spirometer signal (red) by approximately 90°, which is expected, as the spirometer signal is flow and the RIP signals are volume. At 40 seconds, pressure support is discontinued, and the tidal volume decreases considerably. In the right inset, the abdominal signal is of greater magnitude than the chest signal and lags the chest signal by approximately 90°, indicating the onset of paradoxical breathing. These features were associated with a coefficient of determination of 0.98 for HHT Chest + Abdomen + Phase in the entire 5-minute epoch for this patient.

Figure 1

Figure 1

Figure 2

Figure 2

Coefficients of determination obtained from the 8 models are listed in Table 1. When using RAW time domain signals, the correlation between RIP chest and abdominal signals and spirometer was 0.62 ± 0.20; for single band estimates using chest and abdomen, 0.27 ± 0.22 and 0.49 ± 0.20, respectively. Correlation between the HHT estimate of spirometer magnitude with the model including chest and abdomen magnitude and the phase difference between these signals rose to 0.93 ± 0.07.

Table 1

Table 1

Histograms of the differences in coefficients of determination derived from the various HHT models and the time domain models are depicted in Figure 3. For panels 1 and 5, the hypotheses that the samples were drawn from a normally distributed population were assessed by the Lilliefors test accepted with P < 0.01.

Figure 3

Figure 3

Comparisons between models are listed in Table 2. Differences between models based on both bands demonstrated improvements in correlation, ranging from 0.09 (0.04–0.13) for PREFILTER to 0.31 (0.24–0.37) for HHT Chest + Abdomen + Phase. In addition, the correlation of spirometer and a single band (chest or abdomen) performed by HHT was not significantly different from the RAW spirometer 2 bands; 0.05 (−0.05 to 0.15) and −0.03 (−0.13 to 0.07). Conversely, comparison of correlation using single band with HHT to single band with RAW demonstrated improvement; 0.44 (0.35–0.52) and 0.18 (0.08–0.29).

Table 2

Table 2

Figure 4

Figure 4

Bland-Altman analysis revealed no trend in prediction residuals over the range of flows (r2 << 0.01), indicating that the linear models adequately describe the data. Bland-Altman plots for RAW and HHT Chest + Abdomen + Phase are presented in Figure 4.

Back to Top | Article Outline


The principal result of this analysis is that during transitions between normal and paradoxical breathing the use of frequency domain signals derived with the HHT can track changes in minute volume with significantly higher fidelity than was achieved with time domain signals. The principal reason for this is that the distinguishing feature of paradoxical ventilation is the change in phase between chest and abdominal signals. HHT can quantify this phase shift so that it can be included in the regression, while this cannot be done in the time domain.

Prediction of airflow from RIP signals was first demonstrated by Konno and Mead8 and has been used extensively in fields such as sleep medicine and pediatrics because of the ability to monitor patients without the intrusion imposed by an occlusive seal applied to the face. RIP has also been applied to the study of paradoxical breathing during halothane anesthesia.2 The changes in relative contribution of thoracic movement after spinal anesthesia and subsequent sedation further demonstrate the complex interaction of sensory feedback leading to paradoxical breathing.4 Although automated methods are able to track changes in tidal volume under stable ventilatory conditions, transitions into and out of paradoxical breathing pose significant obstacles for accurate estimation of tidal volume.9 Neural networks have been applied to generate nonlinear models relating RIP to spirometry under constant conditions that included examples of paradoxical breathing10 and have found improved accuracy compared with linear methods. None of these previous efforts has attempted to track ventilation during the transition between normal and paradoxical breathing. Although it is unlikely that all ventilatory depression seen during sedation or in the immediate postoperative period is coincident with transitions between normal and paradoxical breathing, any method that can accurately measure minute volume during these transitions should have high fidelity during periods of a stable respiratory pattern. This methodology may be useful in further characterizing anesthetic paradigms that place patients at risk for adverse respiratory events. Of particular interest is whether the phase difference between chest and abdominal motion (without calibration with spirometry) might be a useful monitor for these state changes.

This study has several limitations. First, we perturbed ventilation with only a single intervention-transition to and from PSV. We did not examine partial airway obstruction, opioids, or anesthetics other than sevoflurane. Second, the coefficients of determination assume access to spirometer data throughout the epoch, and a single calibration obtained during one set of conditions (e.g., before anesthetic induction) would be expected to have a lower correlation when conditions have changed. Third, we did not attempt to characterize the transitions between PSV and SV; we merely used them to assess the improvement in prediction of minute volume from RIP under changing conditions.

In summary, the HHT shows promise in improving our ability to assess changes in minute ventilation during transitions between normal and paradoxical breathing and in providing a means of quantifying paradoxical ventilation. The clinical significance of these findings will require further study.

Back to Top | Article Outline


Emil Pitkin, PhD, Statistics Department, Wharton School at the University of Pennsylvania assisted in the statistical analysis.

Back to Top | Article Outline


Name: Jeff E. Mandel, MD, MS.

Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.

Attestation: Jeff E. Mandel has seen the original study data, reviewed the analysis of the data, approved the final manuscript, and is the author responsible for archiving the study files.

Name: Joshua H. Atkins, MD, PhD.

Contribution: This author helped design the study, conduct the study, and write the manuscript.

Attestation: Joshua H. Atkins has seen the original study data, reviewed the analysis of the data, and approved the final manuscript.

This manuscript was handled by: Maxime Cannesson, MD, PhD.

Back to Top | Article Outline


1. Drummond GB, Dhonneur G, Kirov K, Duvaldestin P. Effects of an opioid on respiratory movements and expiratory activity in humans during isoflurane anaesthesia. Respir Physiol Neurobiol. 2013;185:425–34
2. Jones JG, Faithfull D, Jordan C, Minty B. Rib cage movement during halothane anaesthesia in man. Br J Anaesth. 1979;51:399–407
3. Lofaso F, d’Ortho MP, Fodil R, Delclaux C, Harf A, Lorino AM. Abdominal muscle activity in sleep apnea during continuous positive airway pressure titration. Chest. 2001;120:390–6
4. Yamakage M, Kamada Y, Toriyabe M, Honma Y, Namiki A. Changes in respiratory pattern and arterial blood gases during sedation with propofol or midazolam in spinal anesthesia. J Clin Anesth. 1999;11:375–9
5. Atkins JH, Mandel JE. Performance of Masimo rainbow acoustic monitoring for tracking changing respiratory rates under laryngeal mask airway general anesthesia for surgical procedures in the operating room: a prospective observational study. Anesth Analg. 2014;119:1307–14
6. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N-C, Tung CC, Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. R Soc Lond Ser A Math Phys Eng Sci. 1998;454:903–95
7. Torres ME, Colominas MA, Schlotthauer G, Flandrin P. A complete ensemble empirical mode decomposition with adaptive noise. In: IEEE International Conference on Acoustics, Speech and Signal Processing. 2011 Prague IEEE:4144–7
8. Konno K, Mead J. Measurement of the separate volume changes of rib cage and abdomen during breathing. J Appl Physiol. 1967;22:407–22
9. Brown KA, Platt R, Bates JH. Automated analysis of paradoxical ribcage motion during sleep in infants. Pediatr Pulmonol. 2002;33:38–46
© 2016 International Anesthesia Research Society