Tutorials and ReviewsNo Access

NONLINEAR METHODS OF CARDIOVASCULAR PHYSICS AND THEIR CLINICAL APPLICABILITY

NIELS WESSEL

University of Potsdam, Department of Physics, Postfach 601553, 14415 Potsdam, Germany

Search for more papers by this author

HAGEN MALBERG

University of Karlsruhe, Institute for Applied Computer Science/Automation, Kaiserstr. 12, 76128 Karlsruhe, Germany

Search for more papers by this author

ROBERT BAUERNSCHMITT

German Heart Center Munich, Clinic for Cardiovascular Surgery, Lazarettstr. 36, 80636 Munich, Germany

Search for more papers by this author

and

JÜRGEN KURTHS

University of Potsdam, Department of Physics, Postfach 601553, 14415 Potsdam, Germany

Search for more papers by this author

https://doi.org/10.1142/S0218127407019093Cited by:78

Abstract

In this tutorial we present recently developed nonlinear methods of cardiovascular physics and show their potentials to clinically relevant problems in cardiology. The first part describes methods of cardiovascular physics, especially data analysis and modeling of noninvasively measured biosignals, with the aim to improve clinical diagnostics and to improve the understanding of cardiovascular regulation. Applications of nonlinear data analysis and modeling tools are various and outlined in the second part of this tutorial: monitoring-, diagnosis-, course and mortality prognoses as well as early detection of heart diseases. We show, that these data analyses and modeling methods lead to significant improvements in different medical fields.

Keywords:

References

H. D. I. Abarbanel, R. Brown and M. B. Kennel, Int. J. Mod. Phys. B 5, 1347 (1991), DOI: 10.1142/S021797929100064X. Link, ISI, Google Scholar
S. Akselrodet al., Science 213, 220 (1981), DOI: 10.1126/science.6166045. Crossref, ISI, Google Scholar
C. Alberte and D. P. Zipes, J. Cardiov. Electrophysiol. 14, S87 (2003), DOI: 10.1046/j.1540-8167.14.s9.23.x. Crossref, Google Scholar
Y. Almoget al., Am. J. Physiol. Heart Circul. Physiol. 40, H396 (1996). Google Scholar
J. H. Argyris , G. Faust and M. Haase , An Exploration of Chaos ( North Holland , Amsterdam , 1994 ) . Google Scholar
A. Babloyantz and A. Destexhe, Biol. Cybern. 58, 203 (1988), DOI: 10.1007/BF00364139. Crossref, ISI, Google Scholar
P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987), DOI: 10.1103/PhysRevLett.59.381. Crossref, ISI, Google Scholar
H. V. Barron and M. D. Lesh, J. Am. Coll. Cardiol. 27, 1053 (1996), DOI: 10.1016/0735-1097(95)00615-X. Crossref, ISI, Google Scholar
P. Barthelet al., Circulation 108, 1221 (2003), DOI: 10.1161/01.CIR.0000088783.34082.89. Crossref, ISI, Google Scholar
G. Baselliet al., IEEE Trans. Biomed. Eng. 35, 1033 (1988), DOI: 10.1109/10.8688. Crossref, ISI, Google Scholar
R. Bauernschmittet al., Eur. J. Cardiothorac. Surg. 25, 320 (2004), DOI: 10.1016/j.ejcts.2003.12.019. Crossref, ISI, Google Scholar
R. Bauernschmittet al., Pace 30, 77 (2007). Crossref, Google Scholar
L. Bernardiet al., Arch. Ital. Biol. 143, 215 (2005). ISI, Google Scholar
G. G. Berntsonet al., Psychophysiology 27, 586 (1990), DOI: 10.1111/j.1469-8986.1990.tb01982.x. Crossref, ISI, Google Scholar
G. G. Berntsonet al., Psychophysiology 34, 623 (1997), DOI: 10.1111/j.1469-8986.1997.tb02140.x. Crossref, ISI, Google Scholar
M. Y. Bienet al., Intensive Care Med. 30, 241 (2004). Crossref, ISI, Google Scholar
J. T. Bigger Jr.et al., Circulation 85, 164 (1992). Crossref, ISI, Google Scholar
L. Breiman and J. Friedman, J. Am. Stat. Assoc. 80, 580 (1985), DOI: 10.2307/2288473. Crossref, ISI, Google Scholar
G. Breithardtet al., Eur. Heart J. 12, 473 (1991). Crossref, ISI, Google Scholar
M. Brennan, M. Palaniswami and P. Kamen, IEEE Trans. Biomed. Eng. 48, 1342 (2001), DOI: 10.1109/10.959330. Crossref, ISI, Google Scholar
J. D. Bristowet al., Circulation 39, 48 (1969). Crossref, ISI, Google Scholar
R. Brown, P. Bryant and H. D. I. Abarbanel, Phys. Rev. A 43, 2787 (1991), DOI: 10.1103/PhysRevA.43.2787. Crossref, ISI, Google Scholar
A. Busjahnet al., Am. J. Cardiol. 81, 755 (1998), DOI: 10.1016/S0002-9149(97)01019-9. Crossref, ISI, Google Scholar
H. Caoet al., Ann. Biomed. Eng. 32, 233 (2004), DOI: 10.1023/B:ABME.0000012743.81754.0b. Crossref, ISI, Google Scholar
R. Carvajalet al., Comput. Meth. Progr. Biomed. 78, 133 (2005), DOI: 10.1016/j.cmpb.2005.01.004. Crossref, ISI, Google Scholar
S. Ceruttiet al., Comput. Meth. Progr. Biomed. 51, 51 (1996), DOI: 10.1016/0169-2607(96)01762-2. Crossref, ISI, Google Scholar
R. Chen and R. Tsay, J. Am. Stat. Assoc. 88, 955 (1993), DOI: 10.2307/2290787. Crossref, ISI, Google Scholar
D. R. Chialvo, Nature 419, 263 (2002), DOI: 10.1038/419263a. Crossref, ISI, Google Scholar
I. M. Cohenet al., Eur. J. Clin. Pharmacol. 19, 25 (1981), DOI: 10.1007/BF00558378. Crossref, ISI, Google Scholar
M. Costa, A. L. Goldberger and C. K. Peng, Phys. Rev. Lett. 89, 068102 (2002), DOI: 10.1103/PhysRevLett.89.068102. Crossref, Google Scholar
M. Costa, A. L. Goldberger and C. K. Peng, Phys. Rev. E 71, 021906 (2005), DOI: 10.1103/PhysRevE.71.021906. Crossref, Google Scholar
R. J. J. Damiano, J. Card. Surg. 7, 36 (1992), DOI: 10.1111/j.1540-8191.1992.tb00774.x. Crossref, ISI, Google Scholar
M. Rienzoet al., Med. Biol. Eng. Comput. 23, 313 (1985). Google Scholar
W. L. Ditto and K. Showalter, Chaos 7, 509 (1998), DOI: 10.1063/1.166276. Crossref, ISI, Google Scholar
M. Ducheret al., Clin. Sci. (Lond) 88, 651 (1995). Crossref, ISI, Google Scholar
W. Ebelinget al., The Science of Disasters, eds. A. Bunde, J. Kropp and H. J. Schellnhuber (Springer, Berlin, 2002) pp. 2–25. Crossref, Google Scholar
D. L. Eckberg, M. Drabinsky and E. Braunwald, N. Engl. J. Med. 285, 877 (1971). Crossref, ISI, Google Scholar
J.-P. Eckmann, S. O. Kamphorst and D. Ruelle, Europhys. Lett. 4, 973 (1987), DOI: 10.1209/0295-5075/4/9/004. Crossref, Google Scholar
J. P. Eckmannet al., Phys. Rev. A 34, 4971 (1986), DOI: 10.1103/PhysRevA.34.4971. Crossref, ISI, Google Scholar
W. Einthoven, Herinneringsbundel, ed. P. S. Rosenstern (Eduard Ijdo, Leiden, The Netherlands, 1902) p. 101. Google Scholar
R. Engbertet al., Phys. Rev. E 56, 5823 (1997), DOI: 10.1103/PhysRevE.56.5823. Crossref, ISI, Google Scholar
R. Faberet al., J. Hum. Hypertens. 18, 707 (2004), DOI: 10.1038/sj.jhh.1001730. Crossref, ISI, Google Scholar
L. A. Fleisher, S. M. Pincus and S. H. Rosenbaum, Anesthesiology 78, 683 (1993). Crossref, ISI, Google Scholar
Chaos 5, 1 (1995), DOI: 10.1063/1.166069. Crossref, ISI, Google Scholar
Chaos 12, 732 (2002), DOI: 10.1063/1.1504061. Crossref, ISI, Google Scholar
J. B. Gao, Phys. Rev. Lett. 83, 3178 (1999), DOI: 10.1103/PhysRevLett.83.3178. Crossref, ISI, Google Scholar
J. B. Gao and H. Q. Cai, Phys. Lett. A 270, 7587 (2000). Google Scholar
A. Garfinkelet al., Science 257, 1230 (1992), DOI: 10.1126/science.1519060. Crossref, ISI, Google Scholar
H. Gebelein, Z. Angew. Math. Mech. 21, 364 (1941), DOI: 10.1002/zamm.19410210604. Crossref, Google Scholar
L. Glass and M. C. Mackey, From Clocks to Chaos (Princeton University Press, Princeton, 1988) p. 1241. Google Scholar
A. L. Goldbergeret al., Am. Heart J. 197, 612 (1984). ISI, Google Scholar
A. L. Goldbergeret al., Experientia 44, 983 (1988), DOI: 10.1007/BF01939894. Crossref, Google Scholar
A. L. Goldbergeret al., Circulation 101, E215 (2000). Google Scholar
P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983), DOI: 10.1103/PhysRevLett.50.346. Crossref, ISI, Google Scholar
R. A. Gray, A. M. Pertsov and J. Jalife, Nature 392, 75 (1998), DOI: 10.1038/32164. Crossref, ISI, Google Scholar
J. Haaksmaet al., Comput. Cardiol. 22, 197 (1995). Google Scholar
J. E. Hartikainenet al., J. Am. Coll. Cardiol. 28, 296 (1996). Crossref, ISI, Google Scholar
T. Hastie and R. Tibshirani , Generalized Additive Models ( Chapman and Hall , London, NY , 1990 ) . Google Scholar
H. Hering, Zschr. Exper. Path Therapie. 7, 363 (1909), DOI: 10.1007/BF02659994. Crossref, Google Scholar
H. O. Hirschfeld, Proc. Camb. Phil. Soc. 31, 520 (1935). Crossref, Google Scholar
C. W. Hogue Jret al., Circulation 98, 429 (1998). Crossref, Google Scholar
K. K. Hoet al., Circulation 96, 842 (1997). Crossref, Google Scholar
H. V. Huikuriet al., Circulation 93, 1836 (1996). Crossref, ISI, Google Scholar
H. V. Huikuriet al., Circulation 100, 1416 (1999). Crossref, ISI, Google Scholar
P. C. Ivanovet al., Nature 399, 461 (1999), DOI: 10.1038/20924. Crossref, ISI, Google Scholar
P. C. Ivanovet al., Chaos 11, 641 (2001), DOI: 10.1063/1.1395631. Crossref, ISI, Google Scholar
M. Javorkaet al., Braz. J. Med. Biol. Res. 35, 991 (2002), DOI: 10.1590/S0100-879X2002000800018. Crossref, ISI, Google Scholar
H. Kantz and T. Schreiber , Nonlinear Time Series Analysis ( University Press , Cambridge , 1997 ) . Google Scholar
H. Kantz , J. Kurths and G. E. Mayer-Kress , Nonlinear Analysis of Physiological Data ( Springer , Berlin , 1998 ) . Crossref, Google Scholar
J. M. Karemaker and K. I. Lie, Eur. Heart J. 21, 435 (2000), DOI: 10.1053/euhj.1999.1969. Crossref, Google Scholar
J. H. Kimet al., Prog. Neuropsychopharmacol. Biol. Psychiatry 28, 371 (2004), DOI: 10.1016/j.pnpbp.2003.11.007. Crossref, ISI, Google Scholar
R. E. Kleigeret al., Am. J. Cardiol. 59, 256 (1987), DOI: 10.1016/0002-9149(87)90795-8. Crossref, ISI, Google Scholar
T. Klingenheben and S. H. Hohnloser, Ann. Noninvasive Electrocardiol. 8, 68 (2003), DOI: 10.1046/j.1542-474X.2003.08111.x. Crossref, ISI, Google Scholar
M. Kobayashi and T. Musha, IEEE Tran. Biomed. Eng. 29, 456 (1982). ISI, Google Scholar
M. Koebbe and G. Mayer-Kress, Nonlinear Modeling and Forecasting, eds. M. Casdagli and S. Eubank (Addison Wesley, Redwood City, 1992) pp. 361–378. Google Scholar
H. P. Koepchen, Verhandlungen der Deutschen Gesellschaft fuer Herzkreislaufforschung, ed. R. Thauer (Dr. Dietrich Steinkopf Verlag, Darmstadt, 1959) pp. 54–55. Google Scholar
K. Kopitzki, P. C. Warnke and J. Timmer, Phys. Rev. E 58, 4859 (1998), DOI: 10.1103/PhysRevE.58.4859. Crossref, ISI, Google Scholar
P. J. Kudenchuket al., J. Am. Coll. Cardiol. 32, 17 (1998), DOI: 10.1016/S0735-1097(98)00175-2. Crossref, ISI, Google Scholar
N. Kupperet al., Circulation 110, 2792 (2004), DOI: 10.1161/01.CIR.0000146334.96820.6E. Crossref, ISI, Google Scholar
J. Kurths and H. Herzel, Physica D 25, 165 (1987), DOI: 10.1016/0167-2789(87)90099-6. Crossref, ISI, Google Scholar
J. Kurthset al., Chaos 5, 88 (1995), DOI: 10.1063/1.166090. Crossref, ISI, Google Scholar
E. G. Lakatta and D. Levy, Circulation 107, 346 (2003), DOI: 10.1161/01.CIR.0000048893.62841.F7. Crossref, ISI, Google Scholar
M. T. La Rovere and P. J. Schwartz, Pacing Clin. Electrophysiol. 20, 2602 (1997), DOI: 10.1111/j.1540-8159.1997.tb06110.x. Crossref, ISI, Google Scholar
M. T. La Rovereet al., Lancet 351, 478 (1998), DOI: 10.1016/S0140-6736(97)11144-8. Crossref, ISI, Google Scholar
M. T. La Rovereet al., Circulation 103, 2072 (2001). Crossref, ISI, Google Scholar
M. T. La Rovereet al., Circulation 107, 565 (2003), DOI: 10.1161/01.CIR.0000047275.25795.17. Crossref, ISI, Google Scholar
M. S. Leeet al., Am. J. Chin. Med. 33, 579 (2005). Link, ISI, Google Scholar
R. Lehtinenet al., Am. J. Cardiol. 7, 1002 (1996). Google Scholar
T. Lewis, QJ. Med. 4, 141 (1910). Google Scholar
N. Lippman, K. M. Stein and B. B. Lerman, Am. J. Physiol. 267, H411 (1994). Google Scholar
Li, W. A bibliography on 1/f noise http://www.nslij-genetics.org/wli/1fnoise/ . Google Scholar
F. Lombardiet al., Cardiovas. Res. 32, 208 (1996), DOI: 10.1016/0008-6363(96)00116-2. Crossref, ISI, Google Scholar
F. Lombardiet al., Am. J. Cardiol. 77, 1283 (1996), DOI: 10.1016/S0002-9149(96)00193-2. Crossref, ISI, Google Scholar
E. N. Lorenz, Tellus 17, 321 (1965). Crossref, Google Scholar
C. Ludwig, Arch. Anat. Physiol. Leipzig 13, 242 (1847). Google Scholar
T. H. Makikallioet al., Am. J. Cardiol. 81, 27 (1998), DOI: 10.1016/S0002-9149(97)00799-6. Crossref, ISI, Google Scholar
T. H. Makikallioet al., Am. J. Cardiol. 87, 178 (2001), DOI: 10.1016/S0002-9149(00)01312-6. Crossref, ISI, Google Scholar
T. H. Makikallioet al., J. Am. Coll. Cardiol. 37, 1395 (2001), DOI: 10.1016/S0735-1097(01)01171-8. Crossref, ISI, Google Scholar
H. Malberget al., Z. Kardiol. 88, 331 (1999). Google Scholar
H. Malberget al., Clin. Sci. 102, 465 (2002), DOI: 10.1042/CS20010106. Crossref, ISI, Google Scholar
H. Malberget al., Z. Kardiol. 92, 547 (2003), DOI: 10.1007/s00392-003-0946-z. Crossref, Google Scholar
H. Malberget al., Indian Pacing Electrophysiol. J. 4, 162 (2004). Google Scholar
H. Malberg and N. Wessel, Somnologie 10, 33 (2006). Google Scholar
A. Mallianiet al., Circulation 84, 482 (1991). Crossref, ISI, Google Scholar
G. Manciaet al., J. Auton. Nerv. Syst. 11, 115 (1984), DOI: 10.1016/0165-1838(84)90070-5. Crossref, Google Scholar
G. Manciaet al., J. Cardiovasc. Pharmacol. 7, 152 (1985), DOI: 10.1097/00005344-198500073-00018. Crossref, ISI, Google Scholar
B. B. Mandelbrot , The Fractal Geometry of Nature ( W. H. Freeman , New York , 1983 ) . Crossref, Google Scholar
A. J. Man in't Veld et al. , Measurement of Heart Rate and Blood Pressure Variability in Man: Methods, Mechanisms and Clinical Applications of Continuous Finger Blood Pressure Measurement ( Van Zuiden Communications B.V. , 1995 ) . Google Scholar
Marwan, N. [1999] "Untersuchung der klimavariabilitt in nw argentinien mit hilfe der quantitativen analyse von recurrence plots," Masters Thesis, Dresden University of Technology . Google Scholar
N. Marwanet al., Phys. Rev. E 66, 026702 (2002), DOI: 10.1103/PhysRevE.66.026702. Crossref, Google Scholar
R. B. McCall and S. J. Humphrey, Am. J. Physiol. 244, R455 (1983). Google Scholar
U. Meyerfeldtet al., Int. J. Cardiol. 84, 141 (2002), DOI: 10.1016/S0167-5273(02)00139-0. Crossref, ISI, Google Scholar
H. A. T. Milhorn , The Application of Control Theory to Physiological Systems ( Saunders , Philadelphia London , 1966 ) . Google Scholar
A. Mortaraet al., Circulation 96, 3450 (1997). Crossref, Google Scholar
J. M. Nese, Physica D 35, 237 (1989), DOI: 10.1016/0167-2789(89)90105-X. Crossref, ISI, Google Scholar
G. Nolloet al., Am. J. Physiol. Heart Circ. Physiol. 288, H1777 (2005), DOI: 10.1152/ajpheart.00594.2004. Crossref, Google Scholar
G. Nolloet al., Am. J. Physiol. Heart. Circ. Physiol. 280, H1830 (2001). Crossref, Google Scholar
M. Osakaet al., Front Med. Biol. Eng. 5, 289 (1993). Google Scholar
V. I. Oseledec, Trans. Moscow Math. Soc. 19, 197 (1968). ISI, Google Scholar
K. J. Osterzielet al., Br. Heart J. 73, 517 (1995), DOI: 10.1136/hrt.73.6.517. Crossref, Google Scholar
E. Ott , Chaos in Dynamical Systems ( University Press , Cambridge , 1993 ) . Google Scholar
M. Paganiet al., Hypertension 12, 600 (1988). Crossref, ISI, Google Scholar
G. Paratiet al., Hypertension 12, 214 (1988). Crossref, ISI, Google Scholar
D. J. Pattonet al., Am. J. Physiol. Heart Circ. Physiol. 270, H1240 (1996). Crossref, Google Scholar
J. Penaz , Photoelectric measurement of blood pressure volume and flow in the finger , Digest of the 10th Int. Conf. Medical and Biological Engineering, International Federation for Medical and Biological Engineering ( 1973 ) . Google Scholar
C. K. Penget al., Phys. Rev. E 49, 1685 (1994), DOI: 10.1103/PhysRevE.49.1685. Crossref, ISI, Google Scholar
C. K. Penget al., Chaos 5, 82 (1995), DOI: 10.1063/1.166141. Crossref, ISI, Google Scholar
J. S. Perkiomakiet al., Pacing Clin. Electrophysiol. 26, 1931 (2003), DOI: 10.1046/j.1460-9592.2003.00298.x. Crossref, ISI, Google Scholar
A. Pikovsky, M. Rosenblum and J. Kurths, Int. J. Bifurcation and Chaos 10, 2291 (2000). ISI, Google Scholar
B. Pilgram and D. T. Kaplan, Am. J. Physiol. 276, R1 (1999). Google Scholar
S. M. Pincus, Proc. Natl. Acad. Sci. USA 88, 2297 (1991), DOI: 10.1073/pnas.88.6.2297. Crossref, ISI, Google Scholar
S. M. Pincus, Novartis Found Symp. 227, 82 (2000), DOI: 10.1002/0470870796.ch6. Crossref, Google Scholar
C. S. Poon and C. K. Merrill, Nature 389, 492 (1997), DOI: 10.1038/39043. Crossref, ISI, Google Scholar
A. Portaet al., Am. J. Physiol. Heart Circ. Physiol. 279, H2558 (2000). Crossref, Google Scholar
C. Raab and J. Kurths, Phys. Rev. E 64, (2001), DOI: 10.1103/PhysRevE.64.016216. Google Scholar
C. Raabet al., Comput. Cardiol. 32, 985 (2005). Google Scholar
C. Raabet al., Phys. Rev. E 73, 041907 (2006), DOI: 10.1103/PhysRevE.73.041907. Crossref, Google Scholar
P. Ramanand, V. P. Nampoori and R. Sreenivasan, J. Integr. Neurosci. 3, 343 (2004), DOI: 10.1142/S0219635204000567. Link, Google Scholar
A. Renyi , Probability Theory ( Akadémiai Kiadó , Budapest , 1970 ) . Google Scholar
J. S. Richman and J. R. Moorman, Am. J. Physiol. Heart Circ. Physiol. 278, H2039 (2000). Crossref, Google Scholar
H. W. Robbeet al., Hypertension 10, 538 (1987). Crossref, ISI, Google Scholar
O. Rompelman and B. J. Ten Voorde , Measurement of Heart Rate and Blood Pressure Variability in Man: Methods, Mechanisms and Clinical Applications of Continuous Finger Blood Pressure Measurement , eds. A. J. Man in't Veld et al. ( Van Zuiden Communications B.V. , 1995 ) . Google Scholar
D. S. Rosenbaum, P. Albrecht and R. J. Cohen, J. Cardiovasc. Electrophysiol. 7, 1095 (1996), DOI: 10.1111/j.1540-8167.1996.tb00487.x. Crossref, ISI, Google Scholar
P. Saparinet al., Chaos Solit. Fract. 4, 1907 (1994), DOI: 10.1016/0960-0779(94)90006-X. Crossref, ISI, Google Scholar
C. Schaferet al., Nature 392, 239 (1998), DOI: 10.1038/32567. Crossref, ISI, Google Scholar
A. Schirdewanet al., J. Am. Coll. Cardiol. 43, 125A (2004), DOI: 10.1016/S0735-1097(04)90527-X. Crossref, Google Scholar
G. Schmidtet al., Lancet 353, 1390 (1999), DOI: 10.1016/S0140-6736(98)08428-1. Crossref, ISI, Google Scholar
G. Schmidtet al., Lancet 353, 1390 (1999), DOI: 10.1016/S0140-6736(98)08428-1. Crossref, ISI, Google Scholar
U. Schwarzet al., Astron. Astrophys. 277, 215 (1993). ISI, Google Scholar
L. A. Smith, Phil. Trans. R. Soc. Lond. A 348, 371 (1994), DOI: 10.1098/rsta.1994.0097. Crossref, ISI, Google Scholar
Int. J. Bifurcation and Chaos 13, 3531 (2003), DOI: 10.1142/S0218127403008752. Link, ISI, Google Scholar
H. E. Stanleyet al., Physica A 270, 309 (1999), DOI: 10.1016/S0378-4371(99)00230-7. Crossref, ISI, Google Scholar
P. Steinbigler, R. Haberl and G. Jilge, Eur. Heart J. 19, 435 (1998), DOI: 10.1053/euhj.1997.0768. Crossref, ISI, Google Scholar
T. Sugiuraet al., J. Med. Eng. Technol. 15, 107 (1991), DOI: 10.3109/03091909109016207. Crossref, ISI, Google Scholar
M. Suurkulaet al., Clin. Physiol. 21, 541 (2001), DOI: 10.1046/j.1365-2281.2001.00367.x. Crossref, Google Scholar
B. M. Szaboet al., Am. J. Cardiol. 79, 978 (1997), DOI: 10.1016/S0002-9149(97)00026-X. Crossref, ISI, Google Scholar
N. Takahashiet al., J. Am. Coll. Cardiol. 34, 211 (1999), DOI: 10.1016/S0735-1097(99)00158-8. Crossref, ISI, Google Scholar
F. Takens , Dynamical Systems and Turbulence, Warwick (1980) , Lecture Notes in Mathematics 898 , eds. E. Rand and L. S. Young ( Springer Verlag , Berlin , 1981 ) . Google Scholar
Circulation 93, 1043 (1996). Crossref, ISI, Google Scholar
K. Tateno and L. Glass, Med. Biol. Eng. Comput. 39, 664 (2001), DOI: 10.1007/BF02345439. Crossref, ISI, Google Scholar
L. L. Trullaet al., Phys. Lett. A 223, 255 (1996), DOI: 10.1016/S0375-9601(96)00741-4. Crossref, ISI, Google Scholar
H. Tsujiet al., Circulation 94, 2850 (1996). Crossref, Google Scholar
E. Vanoli and P. B. Adamson, Pacing Clin. Electrophysiol. 17, 434 (1994), DOI: 10.1111/j.1540-8159.1994.tb01410.x. Crossref, ISI, Google Scholar
P. Verdecchiaet al., Blood Press Monit. 4, 303 (1999). Crossref, Google Scholar
S. Vikmanet al., Circulation 100, 2079 (1999). Crossref, ISI, Google Scholar
S. Vikmanet al., J. Am. Coll. Cardiol. 45, 278 (2005), DOI: 10.1016/j.jacc.2004.10.033. Crossref, ISI, Google Scholar
A. Vosset al., J. Electrocardiol. 29, 154 (1996), DOI: 10.1016/S0022-0736(96)80045-8. Crossref, ISI, Google Scholar
A. Vosset al., Cardiovasc. Res. 31, 419 (1996). Crossref, ISI, Google Scholar
A. Vosset al., Clin. Sci. (Colch) 91, 120 (1996). Crossref, Google Scholar
H. Voss and J. Kurths, Phys. Lett. A 234, 336 (1997), DOI: 10.1016/S0375-9601(97)00598-7. Crossref, ISI, Google Scholar
A. Vosset al., Pacing Clin. Electrophysiol. 21, 186 (1998), DOI: 10.1111/j.1540-8159.1998.tb01086.x. Crossref, ISI, Google Scholar
H. U. Vosset al., Phys. Rev. Lett. 83, 3422 (1999), DOI: 10.1103/PhysRevLett.83.3422. Crossref, ISI, Google Scholar
A. Vosset al., Am. J. Hypertens. 13, 1218 (2000), DOI: 10.1016/S0895-7061(00)01199-7. Crossref, ISI, Google Scholar
H. Voss, J. Timmer and J. Kurths, Int. J. Bifurcation and Chaos 14, 1905 (2004). Link, ISI, Google Scholar
R. Wackerbaueret al., Chaos Solit. Fract. 4, 133 (1994), DOI: 10.1016/0960-0779(94)90023-X. Crossref, ISI, Google Scholar
T. Waltheret al., Hypertens. Res. 28, 113 (2005), DOI: 10.1291/hypres.28.113. Crossref, ISI, Google Scholar
T. Waltheret al., J. Hypertens. 24, 747 (2006), DOI: 10.1097/01.hjh.0000217858.27864.50. Crossref, ISI, Google Scholar
C. L. Webber and J. P. Zbilut, J. Appl. Physiol. 76, 965 (1994). Crossref, ISI, Google Scholar
M. L. Weisfeldt, G. L. Edward and G. Gerstenblith, Heart Disease: A Textbook of Cardiovascular Medicine, ed. E. Braunwald (WB Saunders, Philadelphia, 1992) pp. 1656–1669. Google Scholar
D. Wernickeet al., Biomed. Tech. (Berl) 52, 50 (2007). Crossref, ISI, Google Scholar
N. Wesselet al., Comput. Cardiol. 21, 137 (1994). Google Scholar
N. Wesselet al., Med. Biol. Eng. Comput. 38, 680 (2000), DOI: 10.1007/BF02344875. Crossref, ISI, Google Scholar
N. Wesselet al., Herzschr. Elektrophys. 11, 159 (2000), DOI: 10.1007/s003990070035. Crossref, Google Scholar
N. Wesselet al., Phys. Rev. E 61, 733 (2000), DOI: 10.1103/PhysRevE.61.733. Crossref, ISI, Google Scholar
N. Wessel, A. Schirdewan and J. Kurths, Phys. Rev. Lett. 91, 119801 (2003), DOI: 10.1103/PhysRevLett.91.119801. Crossref, Google Scholar
N. Wesselet al., Int. J. Bifurcation and Chaos 14, 2125 (2004). Link, ISI, Google Scholar
N. Wesselet al., Chaos 14, 23 (2004), DOI: 10.1063/1.1622351. Crossref, ISI, Google Scholar
N. Wessel, H. Malberg and T. Walther, Circulation 109, e150 (2004), DOI: 10.1161/01.CIR.0000118175.80885.28. Google Scholar
N. Wesselet al., Med. Biol. Eng. Comput. 44, 321 (2006), DOI: 10.1007/s11517-006-0038-0. Crossref, ISI, Google Scholar
B. E. Westerhofet al., J. Hypertens. 22, 1371 (2004), DOI: 10.1097/01.hjh.0000125439.28861.ed. Crossref, ISI, Google Scholar
J. P. J. Wikswo, S. F. Lin and R. A. Abbasm, Biophys. J. 69, 2195 (1995). Crossref, ISI, Google Scholar
F. X. Witkowskiet al., Nature 392, 78 (1998), DOI: 10.1038/32170. Crossref, ISI, Google Scholar
A. Wolfet al., Physica D 16, 285 (1985), DOI: 10.1016/0167-2789(85)90011-9. Crossref, ISI, Google Scholar
M. W. Wolfet al., Med. J. Austral. 2, 52 (1978). Google Scholar
M. A. Wooet al., J. Am. Coll. Cardiol. 23, 56 (1994). ISI, Google Scholar
Y. Yamamoto and R. L. Hughson, Am. J. Physiol. 266, R40 (1994). Google Scholar
Y. Yamamoto and R. L. Hughson, Am. J. Physiol. 266, R40 (1994). Google Scholar
A. C. Yanget al., Phys. Rev. Lett. 90, 108103 (2003), DOI: 10.1103/PhysRevLett.90.108103. Crossref, ISI, Google Scholar
S. Yoden and M. Nomura, J. Atmosph. Sci. 50, 1531 (1993). Crossref, ISI, Google Scholar
W. Zareba , P. Maison-Blanche and E. H. Locati , Noninvasive Electrocardiology in Clinical Practice ( Futura Publishing Co , NY , 2001 ) . Google Scholar
J. P. Zbilut and C. L. Webber Jr., Phys. Lett. A 171, 199 (1992), DOI: 10.1016/0375-9601(92)90426-M. Crossref, ISI, Google Scholar
J. J. Zebrowskiet al., Comput. Cardiol. 22, 377 (1995). Google Scholar
C. Ziehmann, L. A. Smith and J. Kurths, Physica D 126, 49 (1999), DOI: 10.1016/S0167-2789(98)00256-5. Crossref, Google Scholar
D. P. Zipes and H. J. Wellens, Circulation 98, 2334 (1998). Crossref, ISI, Google Scholar

Vol. 17, No. 10

Metrics

Downloaded 104 times

History

Received 18 August 2006

Keywords

PDF download

System Upgrade on Mon, Jun 21st, 2021 at 1am (EDT)

NONLINEAR METHODS OF CARDIOVASCULAR PHYSICS AND THEIR CLINICAL APPLICABILITY

Abstract

References

Recommended