Arnold tongues in human cardiorespiratory systems.

Arnold tongues are phase-locking regions in parameter space, originally studied in circle-map models of cardiac arrhythmias. They show where a periodic system responds by synchronizing to an external stimulus. Clinical studies of resting or anesthetized patients exhibit synchronization between heart-beats and respiration. Here we show that these results are successfully modeled by a circle-map, neatly combining the phenomena of respiratory sinus arrhythmia (RSA, where inspiration modulates heart-rate) and cardioventilatory coupling (CVC, where the heart is a pacemaker for respiration). Examination of the Arnold tongues reveals that while RSA can cause synchronization, the strongest mechanism for synchronization is CVC, so that the heart is acting as a pacemaker for respiration.

[1]  Tracy Allen,et al.  On the arithmetic of phase locking: Coupled neurons as a lattice on R2 , 1983 .

[2]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[3]  P. Larsen,et al.  Cardioventilatory coupling during anaesthesia. , 1997, British journal of anaesthesia.

[4]  P. Larsen,et al.  Cardioventilatory coupling: effects of IPPV. , 1999, British journal of anaesthesia.

[5]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[6]  A. J. Bart,et al.  Mathematical analysis and digital simulation of the respiratory control system. , 1967, Journal of applied physiology.

[7]  H H Abel,et al.  Synchronization in the human cardiorespiratory system. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  D. Galletly,et al.  Inspiratory timing during anaesthesia: a model of cardioventilatory coupling. , 2001, British journal of anaesthesia.

[9]  P. Larsen,et al.  Cardioventilatory coupling in atrial fibrillation. , 1999, British journal of anaesthesia.

[10]  P. Larsen,et al.  Coupling of spontaneous ventilation to heart beat during benzodiazepine sedation. , 1997, British journal of anaesthesia.

[11]  C. T. Genís.  Entrainment in pacemakers characterized by a V-shaped PRC. , 1986 .

[12]  G Kember,et al.  A mathematical analysis of the Grodins model of respiratory control. , 1993, IMA journal of mathematics applied in medicine and biology.

[13]  Solvable models for the quasi-periodic transition to chaos , 1992 .

[14]  P. Larsen,et al.  Cardioventilatory coupling in heart rate variability: methods for qualitative and quantitative determination. , 2001, British journal of anaesthesia.

[15]  Leon Glass,et al.  Cardiac arrhythmias and circle maps-A classical problem. , 1991, Chaos.

[16]  V. I. Arnold.  Cardiac arrhythmias and circle mappingsa) , 1991 .

[17]  J Bélair,et al.  Periodic pulsatile stimulation of a nonlinear oscillator , 1986, Journal of mathematical biology.

[18]  Leon Glass,et al.  BIFURCATIONS IN A DISCONTINUOUS CIRCLE MAP: A THEORY FOR A CHAOTIC CARDIAC ARRHYTHMIA , 1995 .