Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and

Department of Physics, Lancaster University, Lancaster, United Kingdom

Signals derived from the human cardiovascular system are well known to exhibit highly complex, nearly periodic, oscillatory behaviour whose nature is something of an enigma and still the subject of vigorous debate. The variation of cardiac frequency with time, known as heart rate variability (HRV), has been intensively investigated using both deterministic and stochastic methods. It has, for example, been variously described as chaotic, fractal, stochastic, and subject to 1/f fluctuations and it was proposed that the state of the system can be classified by the slope of its power spectrum on a log-log plot.

We illustrate some problems in characterising slow modes in real measurements and show that oscillatory dynamics under the influence of strong noise, coupled with a limited time of observation, can lead to a -like behaviour. We review and describe some recent experiments that illuminate the problem and discuss a combination of almost periodic and stochastic frequency modulation as a signature of the system dynamics.

**References**

Akselrod S, Gordon D, Ubel F A, Shannon D C, Barger A C and Cohen
R J, *Science* **213** 220

Babloyantz A and Destexhe A 1988 *Biol. Cybern.* **58** 203

Bracic M, McClintock P V E and Stefanovska A 2000 in *Stochastic and Chaotic Dynamics in the Lakes* eds. D S Broomhead,
E A Luchinskaya, P V E McClintock, and T Mullin (AIP, Melville,
New York) pp146-153

Bracic Lotric M, Stefanovska A, Štajer D and
Urbancic Rovan V 2000 *Physiol. Meas.* **21** 441

Di Renzo M, Parati G, Pedotti A, and Zanchetti A eds 1997 *Frontiers of Blood Pressure and Heart Rate Analysis* (Amsterdam,
IOS Press)

Hyndman B W, Kitney R I and Sayers B Mc A 1971 Nature **233**
339

Ivanov P C, Amaral L A N, Goldberger A L, Havlin S,
Rosenblum M G, Struzik Z R and Stanley H E 1999 *Nature* **399** 461

Kvernmo H D, Stefanovska A, Kirkebøen K A and Kvernebo K 1999
*Microvasc. Res.* **57** 298

Penáz J 1978, *Automedica ***2** 135

Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E and
Goldberger A R 1993 *Phys. Rev. Lett.* **70** 1343

Poon C S and Merrill C K 1997 *Nature* **389** 492

Söderström T, Stefanovska A, Veber M and Svenson H 2002
*Am. J. Physiol.*

Stanley H E, Goldberger A L, Havlin S, Ivanov P C, Peng C K 1999
*Physica D* **270** 309

Stefanovska A and Bracic M 1999 *Contemporary Phys.*
**40** 31

Stefanovska A, Bracic M and Kvernmo H D 1999 *IEEE
Trans. Biomed. Eng.* **46** 1230

Stefanovska A, Bracic Lotric M, Strle S and Haken H
2001 *Physiol. Meas.* **22** 535

Stefanovska A, Luchinsky D G and McClintock P V E 2001 *Physiol. Meas.* **22** 551

Faculty of Electrical Engineering, University of Ljubljana, Slovenia, and

Department of Physics, Lancaster University, Lancaster, United Kingdom

In a healthy subject in repose a volume of blood equivalent to the total amount in the body returns to the heart every minute. Several oscillatory processes characterise cardiovascular dynamics within this circulation time. Cardiac and respiratory activities act on higher frequency scales, with characteristic frequencies of 1 Hz and 0.2 Hz, respectively. The lowest frequency component, at around 0.01 Hz, has been associated with the activity of the layer of endothelial cells forming the inner surfaces of all blood vessels.

The characteristic frequencies of all the cardiovascular oscillations are found to vary in time, apparently because the oscillatory processes mutually interact. Hales and Ludwig independently described the modulation of cardiac frequency by respiration, in 1773 and 1847 respectively, a process that today is known as respiratory sinus arrhythmia. The occurrence of episodes of synchronization between the cardiac and respiratory rhythms has also been demonstrated.

Recent developments of methods based on dynamical and information theory are facilitating studies of synchronization and of the directionality of couplings between the cardiovascular oscillations. We review and discuss their characteristics in health and disease. The characteristics of the cardiac and respiratory interaction during paced respiration are used to illustrate the role of directionality of coupling in the interplay between synchronization and modulation.

**References**

Bracic Lotric M and Stefanovska A, *Physica A*
**283** 451

Hales S 1773 *Statistical Essays II, Haemastatisticks*
(Innings Manby, London)

Hildebrandt G 1987 in *Temporal
Disorder in Human Oscillatory System* eds L Rensing, U an der
Heiden and M C Mackey, (Springer, Berlin) pp160-174

Janson N B, Balanov A G, Anishchenko V S and McClintock P V E
2001 *Phys. Rev. Lett.* **86** 1749

Kenner T and Passenhofer H 1975 *Pflgers
Archiv.* **355** 77

Ludwig C 1847 *Arch. Anat. Phys.* **13** 242

Mrowka R, Patzak A and Rosenblum M 2000 *Int. J. Bif. Chaos*
**10** 2479

Palus M, Komarek V, Hrncir Z and Sterbova K 2001
*Phys. Rev. E* **63** 046211

Passenhofer H and Kenner T 1975 *Pflgers
Archiv.* **355** 77

Raschke F 1987 in *Temporal Disorder in Human Oscillatory
System* eds L Rensing, U an der Heiden and M C Mackey, (Springer,
Berlin) pp152-158

Raschke F 1991 in *Rhythms in Physiological Systems* eds H
Haken and H P Koepchen (Springer, Berlin) pp155-164

Rosenblum M G, Cimponeriu L, Bezerianos A, Patzak A and Mrowka R
2002 *Phys. Rev. E* **65** 041909

Schäfer C Rosenblum M G, Kurths J and Abel H H 1998 *Nature* **293** 239

Schäfer C Rosenblum M G, Abel H H and Kurths J 1999 *Phys.
Rev. E* **60** 857

Stefanovska A and Hozic M 2000 *Prog. Theor. Phys.
Suppl.* **No139** 270.

Stefanovska A *et al* 2000 *Phys. Rev. Lett.* **85** 4831