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.
Referenze Bibliografiche
[1] P. S. ADDISON, Wavelet transforms and the ECG: a review, Physiol. Meas., 26 (2005), R155-R199.
[2] M. E. CAIN et al., Signal-Averaged Electrocardiography JACC 27 (1996), 238-249.
[3] C. ALBERT - C. YANG, SHU-SHYA HSEU, HUEY-WEN, YIEN, ARY L. GOLDBERGER, C. - K. PENG, Linguistic Analysis of the Human Heartbeat Using Frequency and Rank Order Statistics, Phys. Rev. Lett., 90 (2003).
[4]
R. BALOCCHI -
D. MENICUCCI -
L. LANDINI -
E. SANTARCANGELO -
L. SEBASTIANI -
A. GEMIGNANI -
B. GHELARDUCCI -
M. VARANINI,
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[6]
C. CAMMAROTA -
G. GUARINI -
M. AMBROSINI, ``
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]
C. CAMMAROTA -
E. ROGORA,
Testing indipendence in time series via universal distributions of permutations and words Int.
J. Bif Chaos,
15 (
2005), 1757-1765. |
fulltext (doi) |
MR 2154965 |
Zbl 1092.62580[8] C. CAMMAROTA - E. ROGORA, Independence and symbolic independence of nonstatio- nary heartbeat series during atrial fibrillation Physica A, 353 (2005), 323-335.
[10] F. CENSI et al., Recurrent patterns of atrial depolarization during atrial fibrillation assessed by recurrence plot quantification, Annals of Biomedical Engineering, 28 (2000), 61-70.
[11]
P. COLLI FRANZONE -
L. GUERRI -
M. PENNACCHIO,
Mathematical models and problems in electrocardiology,
Riv. Mat. Univ. Parma, (6)
2* (
1999) 123-142. |
MR 1752795 |
Zbl 0972.92018[12]
P. COLLI FRANZONE -
L. F. PAVARINO,
Parallel Solver for reaction-diffusion systems in Computational Electrocardiology Mathematical Models and Methods in Applied Sciences,
14 (
2004), 883-911. |
fulltext (doi) |
MR 2069498 |
Zbl 1068.92024[13]
M. COSTA -
A. L. GOLDBERGER -
C.-K. PENG,
Multiscale entropy analysis of biological signals.
Phys Rev E,
71 (
2005). |
fulltext (doi) |
MR 2139955[14]
D. DI BERNARDO -
M. G. SIGNORINI -
S. CERUTTI,
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]
F. DOMENICHINI -
G. PEDRIZZETTI -
B. BACCANI,
Three-dimensional filling flow into a model left ventricle;
J Fluid Mech 539 (
2005), 179-198. |
fulltext (doi) |
MR 2262047 |
Zbl 1075.76065[16] W. EINTHOVEN, Die galvanometrische Registrirung des menschlichen Elektrokardioramms, zugleich eine Beurtheilung der Anwendung des Capillar-Elektrometers in der Physiologie. Pfulgers Arch. Ges. Physiol. 99 (1903).
[18] G. GUARINI - G. FIORELLI - A. MALLIANI - F. VIOLI, M. VOLPE, Trattato Italiano di Medicina interna ``Teodori'', Soc. Ed. Universo, Roma (2001).
[19] Y. ISHIKAVA - F. MOCHIMARU, 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]
J. KEENER -
J. SNEYD,
Mathematical physiology Springer, New York (
1998). |
MR 1673204[21] A. MALLIANI, Principles of cardiovascular neural regulation in health and disease, Kluwer (2000).
[23] T. POGORELOV, File Mathematica disponibile all'indirizzo web http://library.wolfram.com/infocenter/MathSource/4476/
[24]
A. QUARTERONI,
Modeling the cardiovascular system - A Mathematical Adventure,
SIAM News,
34 (5), (
2001), Part I and
34 (6), (
2001), Part II. |
MR 1852197[25]
V. K. ROHATGI,
An introduction to Probability Theory and Mathematical Statistics,
Wiley, New York, (
1976). |
MR 407916 |
Zbl 0354.62001[26]
L. RUSSO,
La rivoluzione dimenticata Feltrinelli, Milano (
1996). |
MR 1629047[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] D. WALLER, A demonstration on man of electromotive changes accompanying the heart's beat. J Physiol 8 (1887), 229-234.
[31] W. WESSEL 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
Con il contributo del Ministero per i Beni e le Attività Culturali