Alcune applicazioni della Matematica all'analisi dell'elettrocardiogramma
Cammarota, Camillo ; Rogora, Enrico
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 537-561 / Harvested from Biblioteca Digitale Italiana di Matematica

Questo lavoro si propone di far conoscere due importanti applicazioni della Matematica all'analisi dell'elettrocardiogramma(ECG). La prima eè quella del riconoscimento delle principali caratteristiche dell'ECG e in particolare del picco R, che corrisponde alla sistole. Si considerano due metodi: i filtri lineari e l'analisi multiscala basata sulle wavelet. La seconda riguarda l'analisi della serie temporale degli intervalli che separano due picchi R consecutivi dell'ECG (sequenza RR), che descrive l'andamento nel tempo della frequenza cardiaca. Qui i metodi considerati sono quelli dell'analisi spettrale e dell'analisi simbolica. Di quest'ultima si illustra un'applicazione all'analisi di sequenze RR di fibrillazione atriale.

his paper describes two important applications of Mathematics to the analysis of electrocardiograms (ECG). The first consists of the recognition of the main features of ECG, in particular of the R peak corresponding to systole. We consider two methods: the linear filters and the wavelet analysis. The second consists of the analysis of the time series of intervals between two consecutive R peaks (RR series) which describes the heart rate evolution. Here we consider two methods: spectral analysis and symbolic analysis. We give an application of symbolic analysis to atrial fibrillation RR series.

Publié le : 2007-12-01
@article{BUMI_2007_8_10A_3_537_0,
     author = {Camillo Cammarota and Enrico Rogora},
     title = {Alcune applicazioni della Matematica all'analisi dell'elettrocardiogramma},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {537-561},
     mrnumber = {2394382},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10A_3_537_0}
}
Cammarota, Camillo; Rogora, Enrico. Alcune applicazioni della Matematica all'analisi dell'elettrocardiogramma. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 537-561. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10A_3_537_0/

[1] Addison, P. S., Wavelet transforms and the ECG: a review, Physiol. Meas., 26 (2005), R155-R199.

[2] Cain, M. E. et al., Signal-Averaged Electrocardiography JACC 27 (1996), 238-249.

[3] Yang, C. Albert - C., Hseu, Shu-Shya, Yien, Huey-Wen, Goldberger, Ary L., Peng, C. - K., Linguistic Analysis of the Human Heartbeat Using Frequency and Rank Order Statistics, Phys. Rev. Lett., 90 (2003).

[4] Balocchi, R. - Menicucci, D. - Landini, L. - Santarcangelo, E. - Sebastiani, L. - Gemignani, A. - Ghelarducci, B. - Varanini, M., Deriving the respiratory sinus arrhythmia from the heartbeat time series using empirical mode decomposition Chaos Solitons and Fractals 20 (2004), 171-177. | Zbl 1071.92014

[5] Bloomfield, P., Fourier analysis of time series. An introductionJohn Wiley and sons, New York, (2000) | MR 3410975 | Zbl 0994.62093

[6] Cammarota, C. - Guarini, G. - Ambrosini, M., ``Analysis of stationary periods of heart rate via symbolic dynamics'', Medical Data Analysis, Lecture Notes in Computer Science vol. 2526, Colosimo, Giuliani and Sirabella eds. Springer 2002, 13-19. | Zbl 1024.68656

[7] Cammarota, C. - Rogora, E., Testing indipendence in time series via universal distributions of permutations and words Int. J. Bif Chaos, 15 (2005), 1757-1765. | MR 2154965 | Zbl 1092.62580

[8] Cammarota, C. - Rogora, E., Independence and symbolic independence of nonstatio- nary heartbeat series during atrial fibrillation Physica A, 353 (2005), 323-335.

[9] Cammarota, C. - Rogora, E., Time reversal, symbolic series and irreversibility To be published on Chaos, Solitons and Fractals. | MR 2299060 | Zbl 1195.92014

[10] Censi, F. et al., Recurrent patterns of atrial depolarization during atrial fibrillation assessed by recurrence plot quantification, Annals of Biomedical Engineering, 28 (2000), 61-70.

[11] Colli Franzone, P. - Guerri, L. - Pennacchio, M., Mathematical models and problems in electrocardiology, Riv. Mat. Univ. Parma, (6) 2* (1999) 123-142. | MR 1752795 | Zbl 0972.92018

[12] Colli Franzone, P. - Pavarino, L. F., Parallel Solver for reaction-diffusion systems in Computational Electrocardiology Mathematical Models and Methods in Applied Sciences, 14 (2004), 883-911. | MR 2069498 | Zbl 1068.92024

[13] Costa, M. - Goldberger, A. L. - Peng, C.-K., Multiscale entropy analysis of biological signals. Phys Rev E, 71 (2005). | MR 2139955

[14] Di Bernardo, D. - Signorini, M. G. - Cerutti, S., A model of two non linear coupled oscillators for the study of heart beat dynamics Int. J. Bif Chaos, 8 (1998), 1975- 1985. | Zbl 0936.92016

[15] Domenichini, F. - Pedrizzetti, G. - Baccani, B., Three-dimensional filling flow into a model left ventricle; J Fluid Mech 539 (2005), 179-198. | MR 2262047 | Zbl 1075.76065

[16] Einthoven, W., Die galvanometrische Registrirung des menschlichen Elektrokardioramms, zugleich eine Beurtheilung der Anwendung des Capillar-Elektrometers in der Physiologie. Pfulgers Arch. Ges. Physiol.99 (1903).

[17] Glass, L. - Mackey, M. C., From clocks to chaos P.U.P., Princeton (1988). | MR 952149 | Zbl 0705.92004

[18] Guarini, G. - Fiorelli, G. - Malliani, A. - Violi, F., Volpe, M., Trattato Italiano di Medicina interna ``Teodori'', Soc. Ed. Universo, Roma (2001).

[19] Ishikava, Y. - Mochimaru, F., Wavelet Theory-Based Analysis of High-Frequency, High-Resolution Electrocardiograms: A New Concept for Clinical Uses Progress in biomedical research 7 (2002), 179-184.

[20] Keener, J. - Sneyd, J., Mathematical physiology Springer, New York (1998). | MR 1673204

[21] Malliani, A., Principles of cardiovascular neural regulation in health and disease, Kluwer (2000).

[22] Percival, D. B. - Walden, A. T., Wavelet Methods for Time Series Analysis, Cambridge University Press (2000). | MR 1770693 | Zbl 0963.62079

[23] Pogorelov, T., File Mathematica disponibile all'indirizzo web http://library.wolfram.com/infocenter/MathSource/4476/

[24] Quarteroni, A., Modeling the cardiovascular system - A Mathematical Adventure, SIAM News, 34 (5), (2001), Part I and 34 (6), (2001), Part II. | MR 1852197

[25] Rohatgi, V. K., An introduction to Probability Theory and Mathematical Statistics, Wiley, New York, (1976). | MR 407916 | Zbl 0354.62001

[26] Russo, L., La rivoluzione dimenticataFeltrinelli, Milano (1996). | MR 1629047

[27] Shiryayev, A. N., Probability, Springer-Verlag, New York (1984). | MR 737192

[28] Task force of the european society of chardiology and the north american society of pacing and electrophysiology. Heart rate variability. Standards of measuremant, physiological interpretation and clinical use. Circulation, 93 (1996), 1043-1065.

[29] W. J. Tompkins ed., Biomedical Digital Signal Processing. Prentice Hall, Englewood Cliffs, N. J. (1993).

[30] Waller, D., A demonstration on man of electromotive changes accompanying the heart's beat. J Physiol8 (1887), 229-234.

[31] Wessel, W. et al. Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates, Physical Review E, 61 (2000), 733-739.

[32] http://www.physionet.org

[33] http://www.R-project.org