Low Computational Cost for Sample Entropy

Sample Entropy is the most popular definition of entropy and is widely used as a measure of the regularity/complexity of a time series. On the other hand, it is a computationally expensive method which may require a large amount of time when used in long series or with a large number of signals. The computationally intensive part is the similarity check between points in m dimensional space. In this paper, we propose new algorithms or extend already proposed ones, aiming to compute Sample Entropy quickly. All algorithms return exactly the same value for Sample Entropy, and no approximation techniques are used. We compare and evaluate them using cardiac inter-beat (RR) time series. We investigate three algorithms. The first one is an extension of the kd-trees algorithm, customized for Sample Entropy. The second one is an extension of an algorithm initially proposed for Approximate Entropy, again customized for Sample Entropy, but also improved to present even faster results. The last one is a completely new algorithm, presenting the fastest execution times for specific values of m, r, time series length, and signal characteristics. These algorithms are compared with the straightforward implementation, directly resulting from the definition of Sample Entropy, in order to give a clear image of the speedups achieved. All algorithms assume the classical approach to the metric, in which the maximum norm is used. The key idea of the two last suggested algorithms is to avoid unnecessary comparisons by detecting them early. We use the term unnecessary to refer to those comparisons for which we know a priori that they will fail at the similarity check. The number of avoided comparisons is proved to be very large, resulting in an analogous large reduction of execution time, making them the fastest algorithms available today for the computation of Sample Entropy

A Super Fast Algorithm for Estimating Sample Entropy

: Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as − log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m + 1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N2) or O(N2− 1/m+1 ) computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and 1/ f noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy

Fuzzy and Sample Entropies as Predictors of Patient Survival Using Short Ventricular Fibrillation Recordings during out of Hospital Cardiac Arrest

[EN] Optimal defibrillation timing guided by ventricular fibrillation (VF) waveform analysis would contribute to improved survival of out-of-hospital cardiac arrest (OHCA) patients by minimizing myocardial damage caused by futile defibrillation shocks and minimizing interruptions to cardiopulmonary resuscitation. Recently, fuzzy entropy (FuzzyEn) tailored to jointly measure VF amplitude and regularity has been shown to be an efficient defibrillation success predictor. In this study, 734 shocks from 296 OHCA patients (50 survivors) were analyzed, and the embedding dimension (m) and matching tolerance (r) for FuzzyEn and sample entropy (SampEn) were adjusted to predict defibrillation success and patient survival. Entropies were significantly larger in successful shocks and in survivors, and when compared to the available methods, FuzzyEn presented the best prediction results, marginally outperforming SampEn. The sensitivity and specificity of FuzzyEn were 83.3% and 76.7% when predicting defibrillation success, and 83.7% and 73.5% for patient survival. Sensitivities and specificities were two points above those of the best available methods, and the prediction accuracy was kept even for VF intervals as short as 2s. These results suggest that FuzzyEn and SampEn may be promising tools for optimizing the defibrillation time and predicting patient survival in OHCA patients presenting VF.This work received financial support from Spanish Ministerio de Economia y Competitividad and jointly with the Fondo Europeo de Desarrollo Regional (FEDER), projects TEC2015-64678-R and DPI2017-83952-C3; from UPV/EHU through the grant PIF15/190 and through project GIU17/031; from the Basque Government through grant PRE-2016-1-0012; and from Junta de Comunidades de Castilla-La Mancha through SBPLY/17/180501/000411.Chicote, B.; Irusta, U.; Aramendi, E.; Alcaraz, R.; Rieta, JJ.; Isasi, I.; Alonso, D.... (2018). Fuzzy and Sample Entropies as Predictors of Patient Survival Using Short Ventricular Fibrillation Recordings during out of Hospital Cardiac Arrest. Entropy. 20(8):1-25. https://doi.org/10.3390/e20080591S125208Gräsner, J.-T., Lefering, R., Koster, R. W., Masterson, S., Böttiger, B. W., Herlitz, J., … Maurer, H. (2016). EuReCa ONE⿿27 Nations, ONE Europe, ONE Registry. Resuscitation, 105, 188-195. doi:10.1016/j.resuscitation.2016.06.004Benjamin, E. J., Virani, S. S., Callaway, C. W., Chamberlain, A. M., Chang, A. R., Cheng, S., … Deo, R. (2018). Heart Disease and Stroke Statistics—2018 Update: A Report From the American Heart Association. Circulation, 137(12). doi:10.1161/cir.0000000000000558Rubart, M. (2005). Mechanisms of sudden cardiac death. Journal of Clinical Investigation, 115(9), 2305-2315. doi:10.1172/jci26381Zoll, P. M. (1952). Resuscitation of the Heart in Ventricular Standstill by External Electric Stimulation. New England Journal of Medicine, 247(20), 768-771. doi:10.1056/nejm195211132472005Cobb, L. A. (1999). Influence of Cardiopulmonary Resuscitation Prior to Defibrillation in Patients With Out-of-Hospital Ventricular Fibrillation. JAMA, 281(13), 1182. doi:10.1001/jama.281.13.1182Wik, L., Hansen, T. B., Fylling, F., Steen, T., Vaagenes, P., Auestad, B. H., & Steen, P. A. (2003). Delaying Defibrillation to Give Basic Cardiopulmonary Resuscitation to Patients With Out-of-Hospital Ventricular Fibrillation. JAMA, 289(11), 1389. doi:10.1001/jama.289.11.1389Link, M. S., Atkins, D. L., Passman, R. S., Halperin, H. R., Samson, R. A., White, R. D., … Kerber, R. E. (2010). Part 6: Electrical Therapies: Automated External Defibrillators, Defibrillation, Cardioversion, and Pacing * 2010 American Heart Association Guidelines for Cardiopulmonary Resuscitation and Emergency Cardiovascular Care. Circulation, 122(18_suppl_3), S706-S719. doi:10.1161/circulationaha.110.970954Takata, T. S., Page, R. L., & Joglar, J. A. (2001). Automated External Defibrillators: Technical Considerations and Clinical Promise. Annals of Internal Medicine, 135(11), 990. doi:10.7326/0003-4819-135-11-200112040-00011Figuera, C., Irusta, U., Morgado, E., Aramendi, E., Ayala, U., Wik, L., … Alonso-Atienza, F. (2016). Machine Learning Techniques for the Detection of Shockable Rhythms in Automated External Defibrillators. PLOS ONE, 11(7), e0159654. doi:10.1371/journal.pone.0159654Telesz, B. J., Hess, E. P., Atkinson, E., & White, R. D. (2015). Recurrent ventricular fibrillation: Experience with first responders prior to advanced life support interventions. Resuscitation, 88, 138-142. doi:10.1016/j.resuscitation.2014.10.010Xie, J., Weil, M. H., Sun, S., Tang, W., Sato, Y., Jin, X., & Bisera, J. (1997). High-Energy Defibrillation Increases the Severity of Postresuscitation Myocardial Dysfunction. Circulation, 96(2), 683-688. doi:10.1161/01.cir.96.2.683Cheskes, S., Schmicker, R. H., Christenson, J., Salcido, D. D., Rea, T., Powell, J., … Morrison, L. (2011). Perishock Pause. Circulation, 124(1), 58-66. doi:10.1161/circulationaha.110.010736Reed, M. J., Clegg, G. R., & Robertson, C. E. (2003). Analysing the ventricular fibrillation waveform. Resuscitation, 57(1), 11-20. doi:10.1016/s0300-9572(02)00441-0Firoozabadi, R., Nakagawa, M., Helfenbein, E. D., & Babaeizadeh, S. (2013). Predicting defibrillation success in sudden cardiac arrest patients. Journal of Electrocardiology, 46(6), 473-479. doi:10.1016/j.jelectrocard.2013.06.007Ristagno, G., Li, Y., Fumagalli, F., Finzi, A., & Quan, W. (2013). Amplitude spectrum area to guide resuscitation—A retrospective analysis during out-of-hospital cardiopulmonary resuscitation in 609 patients with ventricular fibrillation cardiac arrest. Resuscitation, 84(12), 1697-1703. doi:10.1016/j.resuscitation.2013.08.017Callaway, C. W., & Menegazzi, J. J. (2005). Waveform analysis of ventricular fibrillation to predict defibrillation. Current Opinion in Critical Care, 11(3), 192-199. doi:10.1097/01.ccx.0000161725.71211.42He, M., Gong, Y., Li, Y., Mauri, T., Fumagalli, F., Bozzola, M., … Ristagno, G. (2015). Combining multiple ECG features does not improve prediction of defibrillation outcome compared to single features in a large population of out-of-hospital cardiac arrests. Critical Care, 19(1). doi:10.1186/s13054-015-1142-zBrown, C. G., & Dzwonczyk, R. (1996). Signal Analysis of the Human Electrocardiogram During Ventricular Fibrillation: Frequency and Amplitude Parameters as Predictors of Successful Countershock. Annals of Emergency Medicine, 27(2), 184-188. doi:10.1016/s0196-0644(96)70346-3Sherman, L. D., Callaway, C. W., & Menegazzi, J. J. (2000). Ventricular fibrillation exhibits dynamical properties and self-similarity. Resuscitation, 47(2), 163-173. doi:10.1016/s0300-9572(00)00229-xWEAVER, W. D. (1985). Amplitude of Ventricular Fibrillation Waveform and Outcome After Cardiac Arrest. Annals of Internal Medicine, 102(1), 53. doi:10.7326/0003-4819-102-1-53Jekova, I., Mougeolle, F., & Valance, A. (2004). Defibrillation shock success estimation by a set of six parameters derived from the electrocardiogram. Physiological Measurement, 25(5), 1179-1188. doi:10.1088/0967-3334/25/5/008Wu, X., Bisera, J., & Tang, W. (2013). Signal integral for optimizing the timing of defibrillation. Resuscitation, 84(12), 1704-1707. doi:10.1016/j.resuscitation.2013.08.005Hamprecht, F. A., Jost, D., Rüttimann, M., Calamai, F., & Kowalski, J. J. (2001). Preliminary results on the prediction of countershock success with fibrillation power. Resuscitation, 50(3), 297-299. doi:10.1016/s0300-9572(01)00360-4Neurauter, A., Eftestøl, T., Kramer-Johansen, J., Abella, B. S., Sunde, K., Wenzel, V., … Strohmenger, H.-U. (2007). Prediction of countershock success using single features from multiple ventricular fibrillation frequency bands and feature combinations using neural networks. Resuscitation, 73(2), 253-263. doi:10.1016/j.resuscitation.2006.10.002Ristagno, G., Mauri, T., Cesana, G., Li, Y., Finzi, A., Fumagalli, F., … Pesenti, A. (2015). Amplitude Spectrum Area to Guide Defibrillation. Circulation, 131(5), 478-487. doi:10.1161/circulationaha.114.010989Eftestøl, T., Sunde, K., Ole Aase, S., Husøy, J. H., & Steen, P. A. (2000). Predicting Outcome of Defibrillation by Spectral Characterization and Nonparametric Classification of Ventricular Fibrillation in Patients With Out-of-Hospital Cardiac Arrest. Circulation, 102(13), 1523-1529. doi:10.1161/01.cir.102.13.1523Povoas, H. P., & Bisera, J. (2000). Electrocardiographic waveform analysis for predicting the success of defibrillation. Critical Care Medicine, 28(Supplement), N210-N211. doi:10.1097/00003246-200011001-00010Podbregar, M., Kovačič, M., Podbregar-Marš, A., & Brezocnik, M. (2003). Predicting defibrillation success by ‘genetic’ programming in patients with out-of-hospital cardiac arrest. Resuscitation, 57(2), 153-159. doi:10.1016/s0300-9572(03)00030-3Callaway, C. W., Sherman, L. D., Mosesso, V. N., Dietrich, T. J., Holt, E., & Clarkson, M. C. (2001). Scaling Exponent Predicts Defibrillation Success for Out-of-Hospital Ventricular Fibrillation Cardiac Arrest. Circulation, 103(12), 1656-1661. doi:10.1161/01.cir.103.12.1656Sherman, L. D., Rea, T. D., Waters, J. D., Menegazzi, J. J., & Callaway, C. W. (2008). Logarithm of the absolute correlations of the ECG waveform estimates duration of ventricular fibrillation and predicts successful defibrillation. Resuscitation, 78(3), 346-354. doi:10.1016/j.resuscitation.2008.04.009Lin, L.-Y., Lo, M.-T., Ko, P. C.-I., Lin, C., Chiang, W.-C., Liu, Y.-B., … Ma, M. H.-M. (2010). Detrended fluctuation analysis predicts successful defibrillation for out-of-hospital ventricular fibrillation cardiac arrest. Resuscitation, 81(3), 297-301. doi:10.1016/j.resuscitation.2009.12.003Gong, Y., Lu, Y., Zhang, L., Zhang, H., & Li, Y. (2015). Predict Defibrillation Outcome Using Stepping Increment of Poincare Plot for Out-of-Hospital Ventricular Fibrillation Cardiac Arrest. BioMed Research International, 2015, 1-7. doi:10.1155/2015/493472Watson, J. N., Uchaipichat, N., Addison, P. S., Clegg, G. R., Robertson, C. E., Eftestol, T., & Steen, P. A. (2004). Improved prediction of defibrillation success for out-of-hospital VF cardiac arrest using wavelet transform methods. Resuscitation, 63(3), 269-275. doi:10.1016/j.resuscitation.2004.06.012Gundersen, K., Kvaløy, J. T., Kramer-Johansen, J., & Eftestøl, T. (2008). Identifying approaches to improve the accuracy of shock outcome prediction for out-of-hospital cardiac arrest. Resuscitation, 76(2), 279-284. doi:10.1016/j.resuscitation.2007.07.019Howe, A., Escalona, O. J., Di Maio, R., Massot, B., Cromie, N. A., Darragh, K. M., … McEneaney, D. J. (2014). A support vector machine for predicting defibrillation outcomes from waveform metrics. Resuscitation, 85(3), 343-349. doi:10.1016/j.resuscitation.2013.11.021Indik, J. H., Conover, Z., McGovern, M., Silver, A. E., Spaite, D. W., Bobrow, B. J., & Kern, K. B. (2014). Association of Amplitude Spectral Area of the Ventricular Fibrillation Waveform With Survival of Out-of-Hospital Ventricular Fibrillation Cardiac Arrest. Journal of the American College of Cardiology, 64(13), 1362-1369. doi:10.1016/j.jacc.2014.06.1196Coult, J., Sherman, L., Kwok, H., Blackwood, J., Kudenchuk, P. J., & Rea, T. D. (2016). Short ECG segments predict defibrillation outcome using quantitative waveform measures. Resuscitation, 109, 16-20. doi:10.1016/j.resuscitation.2016.09.020Endoh, H., Hida, S., Oohashi, S., Hayashi, Y., Kinoshita, H., & Honda, T. (2010). Prompt prediction of successful defibrillation from 1-s ventricular fibrillation waveform in patients with out-of-hospital sudden cardiac arrest. Journal of Anesthesia, 25(1), 34-41. doi:10.1007/s00540-010-1043-xChicote, B., Irusta, U., Alcaraz, R., Rieta, J., Aramendi, E., Isasi, I., … Ibarguren, K. (2016). Application of Entropy-Based Features to Predict Defibrillation Outcome in Cardiac Arrest. Entropy, 18(9), 313. doi:10.3390/e18090313Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), H2039-H2049. doi:10.1152/ajpheart.2000.278.6.h2039Weiting Chen, Zhizhong Wang, Hongbo Xie, & Wangxin Yu. (2007). Characterization of Surface EMG Signal Based on Fuzzy Entropy. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 15(2), 266-272. doi:10.1109/tnsre.2007.897025Xiao-Feng, L., & Yue, W. (2009). Fine-grained permutation entropy as a measure of natural complexity for time series. Chinese Physics B, 18(7), 2690-2695. doi:10.1088/1674-1056/18/7/011Fadlallah, B., Chen, B., Keil, A., & Príncipe, J. (2013). Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information. Physical Review E, 87(2). doi:10.1103/physreve.87.022911Eftestøl, T., Sunde, K., & Steen, P. A. (2002). Effects of Interrupting Precordial Compressions on the Calculated Probability of Defibrillation Success During Out-of-Hospital Cardiac Arrest. Circulation, 105(19), 2270-2273. doi:10.1161/01.cir.0000016362.42586.feEdelson, D. P., Abella, B. S., Kramer-Johansen, J., Wik, L., Myklebust, H., Barry, A. M., … Becker, L. B. (2006). Effects of compression depth and pre-shock pauses predict defibrillation failure during cardiac arrest. Resuscitation, 71(2), 137-145. doi:10.1016/j.resuscitation.2006.04.008Ibarguren, K., Unanue, J. M., Alonso, D., Vaqueriza, I., Irusta, U., Aramendi, E., & Chicote, B. (2015). Difference in survival from pre-hospital cardiac arrest between cities and villages in the Basque Autonomous Community. Resuscitation, 96, 114. doi:10.1016/j.resuscitation.2015.09.269Jacobs, I., Nadkarni, V., Bahr, J., Berg, R. A., Billi, J. E., Bossaert, L., … Zideman, D. (2004). Cardiac arrest and cardiopulmonary resuscitation outcome reports: update and simplification of the Utstein templates for resuscitation registries. Resuscitation, 63(3), 233-249. doi:10.1016/j.resuscitation.2004.09.008Rittenberger, J. C., Raina, K., Holm, M. B., Kim, Y. J., & Callaway, C. W. (2011). Association between Cerebral Performance Category, Modified Rankin Scale, and discharge disposition after cardiac arrest. Resuscitation, 82(8), 1036-1040. doi:10.1016/j.resuscitation.2011.03.034Marn-Pernat, A., Weil, M. H., Tang, W., Pernat, A., & Bisera, J. (2001). Optimizing timing of ventricular defibrillation. Critical Care Medicine, 29(12), 2360-2365. doi:10.1097/00003246-200112000-00019Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences, 88(6), 2297-2301. doi:10.1073/pnas.88.6.2297Chen, W., Zhuang, J., Yu, W., & Wang, Z. (2009). Measuring complexity using FuzzyEn, ApEn, and SampEn. Medical Engineering & Physics, 31(1), 61-68. doi:10.1016/j.medengphy.2008.04.005Alcaraz, R., Abásolo, D., Hornero, R., & Rieta, J. J. (2010). Optimal parameters study for sample entropy-based atrial fibrillation organization analysis. Computer Methods and Programs in Biomedicine, 99(1), 124-132. doi:10.1016/j.cmpb.2010.02.009Zou, K. H., O’Malley, A. J., & Mauri, L. (2007). Receiver-Operating Characteristic Analysis for Evaluating Diagnostic Tests and Predictive Models. Circulation, 115(5), 654-657. doi:10.1161/circulationaha.105.594929Perkins, N. J., & Schisterman, E. F. (2006). The Inconsistency of «Optimal» Cutpoints Obtained using Two Criteria based on the Receiver Operating Characteristic Curve. American Journal of Epidemiology, 163(7), 670-675. doi:10.1093/aje/kwj063Monsieurs, K. G., Nolan, J. P., Bossaert, L. L., Greif, R., Maconochie, I. K., Nikolaou, N. I., … Wyllie, J. (2015). European Resuscitation Council Guidelines for Resuscitation 2015. Resuscitation, 95, 1-80. doi:10.1016/j.resuscitation.2015.07.038Ruiz, J., Ayala, U., de Gauna, S. R., Irusta, U., González-Otero, D., Alonso, E., … Eftestøl, T. (2013). Feasibility of automated rhythm assessment in chest compression pauses during cardiopulmonary resuscitation. Resuscitation, 84(9), 1223-1228. doi:10.1016/j.resuscitation.2013.01.034Ayala, U., Irusta, U., Ruiz, J., Ruiz de Gauna, S., González-Otero, D., Alonso, E., … Eftestøl, T. (2015). Fully automatic rhythm analysis during chest compression pauses. Resuscitation, 89, 25-30. doi:10.1016/j.resuscitation.2014.11.022Singh, A., Saini, B. S., & Singh, D. (2015). An alternative approach to approximate entropy threshold value (r) selection: application to heart rate variability and systolic blood pressure variability under postural challenge. Medical & Biological Engineering & Computing, 54(5), 723-732. doi:10.1007/s11517-015-1362-zNeurauter, A., Eftestøl, T., Kramer-Johansen, J., Abella, B. S., Wenzel, V., Lindner, K. H., … Strohmenger, H.-U. (2008). Improving countershock success prediction during cardiopulmonary resuscitation using ventricular fibrillation features from higher ECG frequency bands. Resuscitation, 79(3), 453-459. doi:10.1016/j.resuscitation.2008.07.024Rosso, O. A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., & Başar, E. (2001). Wavelet entropy: a new tool for analysis of short duration brain electrical signals. Journal of Neuroscience Methods, 105(1), 65-75. doi:10.1016/s0165-0270(00)00356-3Weaver, B., & Wuensch, K. L. (2013). SPSS and SAS programs for comparing Pearson correlations and OLS regression coefficients. Behavior Research Methods, 45(3), 880-895. doi:10.3758/s13428-012-0289-7Sherman, L. D. (2006). The frequency ratio: An improved method to estimate ventricular fibrillation duration based on Fourier analysis of the waveform. Resuscitation, 69(3), 479-486. doi:10.1016/j.resuscitation.2005.09.024Weisfeldt, M. L., & Becker, L. B. (2002). Resuscitation After Cardiac Arrest. JAMA, 288(23), 3035. doi:10.1001/jama.288.23.3035Gazmuri, R. J., Berkowitz, M., & Cajigas, H. (1999). Myocardial effects of ventricular fibrillation in the isolated rat heart. Critical Care Medicine, 27(8), 1542-1550. doi:10.1097/00003246-199908000-00023JARDETZKY, O., GREENE, E. A., & LORBER, V. (1956). Oxygen Consumption of the Completely Isolated Dog Heart In Fibrillation. Circulation Research, 4(2), 144-147. doi:10.1161/01.res.4.2.144Hoogendijk, M. G., Schumacher, C. A., Belterman, C. N. W., Boukens, B. J., Berdowski, J., de Bakker, J. M. T., … Coronel, R. (2012). Ventricular fibrillation hampers the restoration of creatine-phosphate levels during simulated cardiopulmonary resuscitations. EP Europace, 14(10), 1518-1523. doi:10.1093/europace/eus078Neumar, R. W., Brown, C. G., Van Ligten, P., Hoekstra, J., Altschuld, R. A., & Baker, P. (1991). Estimation of myocardial ischemic injury during ventricular fibrillation with total circulatory arrest using high-energy phosphates and lactate as metabolic markers. Annals of Emergency Medicine, 20(3), 222-229. doi:10.1016/s0196-0644(05)80927-8Kern, K. B., Garewal, H. S., Sanders, A. B., Janas, W., Nelson, J., Sloan, D., … Ewy, G. A. (1990). Depletion of myocardial adenosine triphosphate during prolonged untreated ventricular fibrillation: effect on defibrillation success. Resuscitation, 20(3), 221-229. doi:10.1016/0300-9572(90)90005-yChoi, H. J., Nguyen, T., Park, K. S., Cha, K. C., Kim, H., Lee, K. H., & Hwang, S. O. (2013). Effect of cardiopulmonary resuscitation on restoration of myocardial ATP in prolonged ventricular fibrillation. Resuscitation, 84(1), 108-113. doi:10.1016/j.resuscitation.2012.06.006Salcido, D. D., Menegazzi, J. J., Suffoletto, B. P., Logue, E. S., & Sherman, L. D. (2009). Association of intramyocardial high energy phosphate concentrations with quantitative measures of the ventricular fibrillation electrocardiogram waveform. Resuscitation, 80(8), 946-950. doi:10.1016/j.resuscitation.2009.05.002Reynolds, J. C., Salcido, D. D., & Menegazzi, J. J. (2012). Correlation between coronary perfusion pressure and quantitative ECG waveform measures during resuscitation of prolonged ventricular fibrillation. Resuscitation, 83(12), 1497-1502. doi:10.1016/j.resuscitation.2012.04.013Didon, J.-P., Krasteva, V., Ménétré, S., Stoyanov, T., & Jekova, I. (2011). Shock advisory system with minimal delay triggering after end of chest compressions: Accuracy and gained hands-off time. Resuscitation, 82, S8-S15. doi:10.1016/s0300-9572(11)70145-9Ruiz de Gauna, S., Irusta, U., Ruiz, J., Ayala, U., Aramendi, E., & Eftestøl, T. (2014). Rhythm Analysis during Cardiopulmonary Resuscitation: Past, Present, and Future. BioMed Research International, 2014, 1-13. doi:10.1155/2014/386010Manis, G., Aktaruzzaman, M., & Sassi, R. (2018). Low Computational Cost for Sample Entropy. Entropy, 20(1), 61. doi:10.3390/e20010061Snyder, D., & Morgan, C. (2004). Wide variation in cardiopulmonary resuscitation interruption intervals among commercially available automated external defibrillators may affect survival despite high defibrillation efficacy. Critical Care Medicine, 32(Supplement), S421-S424. doi:10.1097/01.ccm.0000134265.35871.2bMenegazzi, J. J., Callaway, C. W., Sherman, L. D., Hostler, D. P., Wang, H. E., Fertig, K. C., & Logue, E. S. (2004). Ventricular Fibrillation Scaling Exponent Can Guide Timing of Defibrillation and Other Therapies. Circulation, 109(7), 926-931. doi:10.1161/01.cir.0000112606.41127.d2Lombardi, F. (2001). Sudden cardiac death: role of heart rate variability to identify patients at risk. Cardiovascular Research, 50(2), 210-217. doi:10.1016/s0008-6363(01)00221-8Moorman, J. R., Carlo, W. A., Kattwinkel, J., Schelonka, R. L., Porcelli, P. J., Navarrete, C. T., … Michael O’Shea, T. (2011). Mortality Reduction by Heart Rate Characteristic Monitoring in Very Low Birth Weight Neonates: A Randomized Trial. The Journal of Pediatrics, 159(6), 900-906.e1. doi:10.1016/j.jpeds.2011.06.044Sessa, F., Anna, V., Messina, G., Cibelli, G., Monda, V., Marsala, G., … Salerno, M. (2018). Heart rate variability as predictive factor for sudden cardiac death. Aging, 10(2), 166-1

Single-lead electrocardiogram quality assessment in the context of paroxysmal atrial fibrillation through phase space plots

[EN] Current wearable electrocardiogram (ECG) recording systems have great potential to revolutionize early diagnosis of paroxysmal atrial fibrillation (AF). They are able to continuously acquire an ECG signal for long weeks and then increase the probability of detecting first brief, intermittent signs of the arrhythmia. However, the recorded signal is often broadly corrupted by noise and artifacts, and accurate assessment of its quality to avoid automated misdiagnosis and false alarms of AF is still an unsolved challenge. In this context, the present work is pioneer in exploring the usefulness of transforming the single-lead ECG signal into two common phase space (PS) representations, such as the Poincare plot and the first order difference graph, for evaluation of its quality. Several machine and deep learning models fed with features and images derived from these PS portraits reported a better performance than well-known previous methods, even when they were trained and validated on two separate databases. Indeed, in binary classification of high- and low-quality ECG excerpts, the generated PS-based algorithms reported a discriminant power greater than 85%, misclassifying less than 20% of high-quality AF episodes and non -normal rhythms as noisy excerpts. Moreover, because both PS reconstructions do not require any mathematical transformation, these algorithms also spent much less time in classifying each ECG excerpt in validation and testing stages than previous methods. As a consequence, ECG transformation to both PS portraits enables novel, simple, effective, and computational low-cost techniques, based both on machine and deep learning classifiers, for ECG quality assessment.This research has received financial support from Daiichi Sankyo SLU and from public grants PID2021-00X128525-IV0, PID2021-12380 4OB-I00, and TED2021-130935B-I00 of the Spanish Government 10.13039/501100011033 jointly with the European Regional Development Fund (EU) , SBPLY/21/180501/000186 from Junta de Comunidades de Castilla-La Mancha, Spain, and AICO/2021/286 from Generalitat Valenciana.Huerta, A.; Martínez-Rodrigo, A.; Bertomeu-González, V.; Ayo-Martin, O.; Rieta, JJ.; Alcaraz, R. (2024). Single-lead electrocardiogram quality assessment in the context of paroxysmal atrial fibrillation through phase space plots. Biomedical Signal Processing and Control. 91. https://doi.org/10.1016/j.bspc.2023.1059209

The structure of chaos: an empirical comparison of fractal physiology complexity indices using NeuroKit2

Complexity quantification, through entropy, information theory and fractal dimension indices, is gaining a renewed traction in psychophsyiology, as new measures with promising qualities emerge from the computational and mathematical advances. Unfortunately, few studies compare the relationship and objective performance of the plethora of existing metrics, in turn hindering reproducibility, replicability, consistency, and clarity in the field. Using the NeuroKit2 Python software, we computed a list of 112 (predominantly used) complexity indices on signals varying in their characteristics (noise, length and frequency spectrum). We then systematically compared the indices by their computational weight, their representativeness of a multidimensional space of latent dimensions, and empirical proximity with other indices. Based on these considerations, we propose that a selection of 12 indices, together representing 85.97% of the total variance of all indices, might offer a parsimonious and complimentary choice in regards to the quantification of the complexity of time series. Our selection includes CWPEn, Line Length (LL), BubbEn, MSWPEn, MFDFA (Max), Hjorth Complexity, SVDEn, MFDFA (Width), MFDFA (Mean), MFDFA (Peak), MFDFA (Fluctuation), AttEn. Elements of consideration for alternative subsets are discussed, and data, analysis scripts and code for the figures are open-source