We propose a new algorithm for real-time estimation of instantaneous heart rate (HR) from noise-laden electrocardiogram (ECG) waveforms typical of unstructured, ambulatory field environments. The estimation of HR from ECG waveforms is an indirect measurement problem that requires differencing, which invariably amplifies high-frequency noise. We circumvented noise amplification by considering the estimation of HR as the solution of a weighted regularized least squares problem, which, in addition, directly provided analytically based confidence intervals (CIs) for the estimated HRs. To evaluate the performance of the proposed algorithm, we applied it to simulated data and to noise-laden ECG records that were collected during helicopter transport of trauma-injured patients to a trauma center. We compared the proposed algorithm with HR estimates produced by a widely used vital-sign travel monitor and a standard HR estimation technique, followed by postprocessing with Kalman filtering or spline smoothing. The simulation results indicated that our algorithm consistently produced more accurate HR estimates, with estimation errors as much as 67% smaller than those attained by the postprocessing methods, while the results with the field-collected data showed that the proposed algorithm produced much smoother and reliable HR estimates than those obtained by the vital-sign monitor. Moreover, the obtained CIs reflected the amount of noise in the ECG recording and could be used to statistically quantify uncertainties in the HR estimates. We conclude that the proposed method is robust to different types of noise and is particularly suitable for use in ambulatory environments where data quality is notoriously poor.
This is a preview of subscription content, log in via an institution to check access.
Access this article Subscribe and saveSpringer+ Basic
€34.99 /Month
Price includes VAT (Germany)
Instant access to the full article PDF.
Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. ReferencesANSI/AAMIEC57. Testing and Reporting Performance Results of Cardiac Rhythm and ST Segment Measurement Algorithms. American National Standards Institute, 1998.
Arzeno, N. M., Z. D. Deng, and C. S. Poon. Analysis of first-derivative based QRS detection algorithms. IEEE Trans. Biomed. Eng. 55(2):478–484, 2008.
Bassil, H. E., J. H. Dripps, and P. M. Grant. Detection and correction of outliers in foetal heart rate time series. Electron. Lett. 28(4):382–383, 1992.
Berntson, G. G., T. J. Bigger, D. L. Eckberg, P. Grossman, P. G. Kaufmann, M. Malik, H. N. Nagaraja, S. W. Porges, J. P. Saul, P. H. Stone, et al. Heart rate variability: origins, methods, and interpretive caveats. Psychophysiology 34(6):623–648, 1997.
Berntson, G. G., and J. R. Stowell. ECG artifacts and heart period variability: don’t miss a beat! Psychophysiology 35(1):127–132, 1998.
Björck, A. Numerical Methods for Least Squares Problems. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1996.
Chen, L., T. McKenna, A. T. Reisner, and J. Reifman. Algorithms to qualify respiratory data collected during the transport of trauma patients. Physiol. Meas. 27(9):797–816, 2006.
Chen, L., T. M. McKenna, A. T. Reisner, A. Gribok, and J. Reifman. Decision tool for the early diagnosis of trauma patient hypovolemia. J. Biomed. Inform. 41(3):469–478, 2008.
Chen, L., A. T. Reisner, A. Gribok, T. M. McKenna, and J. Reifman. Can we improve the clinical utility of respiratory rate as a monitored vital sign? Shock 31(6):574–580, 2009.
Draper, N. R., and H. Smith. Applied Regression Analysis. New York, NY: Wiley, 1966.
Ebrahim, M. H., J. M. Feldman, and I. Bar-Kana. A robust sensor fusion method for heart rate estimation. J. Clin. Monit. 13(6):385–393, 1997.
Engl, H. W., M. Hanke, and A. Neubauer. Regularization of Inverse Problems. New York, NY: Springer, 2000.
Friesen, G. M., T. C. Jannett, M. A. Jadallah, S. L. Yate, S. R. Quint, and H. T. Nagle. A comparison of the noise sensitivity of nine QRS detection algorithms. IEEE Trans. Biomed. Eng. 37(1):85–98, 1990.
Golub, G. H., M. Heath, and G. Wahba. Generalized cross validation as a method for choosing a good ridge parameter. Technometrics 21(2):215–223, 1979.
Hamilton, P. S., and W. J. Tompkins. Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database. IEEE Trans. Biomed. Eng. 33(12):1157–1165, 1986.
Hoerl, A. E., and R. W. Kennard. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67, 1970.
Li, Q., R. G. Mark, and G. D. Clifford. Robust heart rate estimation from multiple asynchronous noisy sources using signal quality indices and a Kalman filter. Physiol. Meas. 29:15–32, 2008.
Liu, J., T. M. McKenna, A. Gribok, B. A. Beidleman, W. J. Tharion, and J. Reifman. A fuzzy logic algorithm to assign confidence levels to heart and respiratory rate time series. Physiol. Meas. 29(1):81–94, 2008.
Morozov, V. A. Regularization Methods for Ill-Posed Problems. Florida: CRC Press, 1993.
Pan, J., and W. J. Tompkins. A real-time QRS detection algorithm. IEEE Trans. Biomed. Eng. 32(3):230–236, 1985.
Pu, Y., and R. P. Patterson. Comparison of R-wave detection errors of four wireless heart rate belts in the presence of noise. Physiol. Meas. 24:913–924, 2003.
Ramsay, J. O., and B. W. Silverman. Functional Data Analysis. New York, NY: Springer, 2005.
Reisner, A. T., L. Chen, T. M. McKenna, and J. Reifman. Automatically-computed prehospital severity scores are equivalent to scores based on medic documentation. J. Trauma 65(4):915–923, 2008.
Tarantola, A. Inverse Problem Theory. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2005.
Task Force of the European Society of Cardiology; North American Society of Pacing Electrophysiology. Heart rate variability: standards of measurement, physiological interpretation, and clinical use. Circulation 93:1043–1065, 1996.
Thuraisingham, R. A. Preprocessing RR interval time series for heart rate variability analysis and estimates of standard deviation of RR intervals. Comput. Methods Programs Biomed. 83(1):78–82, 2006.
Tikhonov, A. N., and V. Y. Arsenin. Solution of Ill-Posed Problems. Washington: Winston & Sons, 1977.
Wahba, G. Spline Models for Observational Data. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1990.
White, H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817–838, 1980.
Wilcoxon, F. Individual comparisons by ranking methods. Biometrics Bull. 1(6):80–83, 1945.
Yu, C., Z. Liu, T. McKenna, A. T. Reisner, and J. Reifman. A method for automatic identification of reliable heart rates calculated from ECG and PPG waveforms. J. Am. Med. Inform. Assoc. 13(3):309–320, 2006.
We thank Y. Lu, S. Rajaraman, and C. Meng for providing stimulating feedback. This study was supported by a War Supplemental competitive grant managed by the Combat Casualty Care Directorate of the U.S. Army Medical Research and Materiel Command, Fort Detrick, MD.
DisclaimerThe opinions and assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the U.S. Army or of the U.S. Department of Defense. This paper has been approved for public release with unlimited distribution.
Author information Authors and AffiliationsBioinformatics Cell, Telemedicine and Advanced Technology Research Center, U.S. Army Medical Research and Materiel Command, ATTN: MCMR-TT, 504 Scott Street, Fort Detrick, MD, 21702, USA
Andrei V. Gribok, Xiaoxiao Chen & Jaques Reifman
Nuclear Engineering Department of the University of Tennessee, Knoxville, TN, 37996, USA
Andrei V. Gribok
Correspondence to Jaques Reifman.
Additional informationAssociate Editor Berj L. Bardakjian oversaw the review of this article.
Appendix AppendixBecause HRWRLS is reciprocal to RRIWRLS, we approximated Var(HRWRLS) using the mean and variance of RRIWRLS through a Taylor expansion, i.e.,
$$ {\text{Var}}({\text{HR}}_{\text{WRLS}} ) \approx \left( {{\frac{60}{{[{\text{mean}}({\text{RRI}}_{\text{WRLS}} )]^{2} }}}} \right)^{2} \cdot {\text{Var}}({\text{RRI}}_{\text{WRLS}} ), $$
(A1)
where Var(RRIWRLS) was estimated as the diagonal of the covariance of RRIWRLS, Cov(RRIWRLS), which was calculated from Eqs. (2), (3), and (5) as
$$ {\text{Cov}}\left( {{\text{RRI}}_{\text{WRLS}} } \right) = C \cdot B \cdot {\text{Cov}}\left( \varepsilon \right) \cdot B^{\text{T}} \cdot C^{\text{T}} , $$
(A2)
where \( B = \left( {A^{\text{T}} \cdot A} \right)^{ - 1} \cdot A^{\text{T}} ,\;C = \left( {W^{\text{T}} \cdot A^{\text{T}} \cdot A \cdot W + \lambda^{2} \cdot L^{\text{T}} \cdot L} \right)^{ - 1} \cdot W^{\text{T}} \cdot A^{\text{T}} \cdot A \cdot W, \) and Cov(ε) denotes the covariance of the measurement noise, which was estimated as a diagonal matrix with elements equal to half of the square of the residual between RRIOLS and RRIWRLS.29
About this article Cite this articleGribok, A.V., Chen, X. & Reifman, J. A Robust Method to Estimate Instantaneous Heart Rate from Noisy Electrocardiogram Waveforms. Ann Biomed Eng 39, 824–834 (2011). https://doi.org/10.1007/s10439-010-0204-2
Received: 06 July 2010
Accepted: 08 November 2010
Published: 20 November 2010
Issue Date: February 2011
DOI: https://doi.org/10.1007/s10439-010-0204-2
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4