Abstract
Introduction
Although the autorhythmic cells in the heart beat at a wide range of frequencies (80–15 bpm) in culture, in the whole heart they beat at a common frequency set by the normal sinus rhythm. Two nonlinear oscillators operating at different frequencies can synchronize only under special conditions which are expected to be more stringent for a large network of oscillators with a range of intrinsic frequencies. In this paper we investigate this problem using simulations involving Noble cardiac cell model.
Methods and Materials
We conducted two sets of simulations. The first set involves cell-pair models of cardiac cells using the well-known Noble cell model, with and without neural feedback. The second set of experiments involves grid models of Noble cells with corner-to-corner variation of intrinsic frequencies.
External input, representing neural influence, is presented at varied locations and is adjusted to produce best synchronization.
Observations
Cardiac Cell pair without neural feedback: Lower resistance of coupling and lesser discrepancy in intrinsic frequencies improve synchronization.
Innervated Cell Pair
A pair of cells that otherwise do not synchronize are made to synchronize by appropriate neural feedback.
Grid of Cardiac Cells without neural feedback
Synchronization took longer with increasing frequency range and was never complete.
Innervated Grid of cardiac cells
Improved synchronization was achieved by neural feedback applied at specific locations in the grid. Input location and feedback gain are crucial for obtaining rapid synchronization.
Conclusion
Neural feedback seems to play a crucial role in forging the activities of cardiac oscillators to a unitary rhythm.
Similar content being viewed by others
References
Guyton AC and Hall JE. Textbook of Medical Physiology. Tenth Edition. WB Saunders Company, 2000
Strogatz SH. Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity), Addison Wesley, 1994.
Winslow RL, Kimball A, Varghese A and Noble D. “Simulating cardiac sinus and atrial network dynamics on the Connection Machine,” Physica D: Nonlinear Phenomena 1993; 64: 281–98.
Panfilov AV and Holden AV. Computational Biology of the Heart, John Wiley, 1997.
Davidenko JM, Kent P and Jalife J, “Spiral waves in normal isolated ventricular muscle,” Physica D, 1991, 49: 182–97.
Winfree AT. “Scroll-shaped waves of chemical activity in three-dimensions,” Science, 1973; 181: 937–39.
Noble D. “A Modification of the Hodgkin Huxley Equations Applicable to Purkinje Fiber Action and Pace-maker Potentials,” J. Physiol., 1962; 160: 317–52.
Gerstner W, Kistler W. Spiking neuron models: Single neurons, populations and plasticity, Cambridge University Press, 2002.
Armour JA. Cardiac neuronal hierarchy in health and disease. Am J Physiol Regul Integr Comp Physiol 2004; 287: R 262–71.
Wang XF and Chen, G. “Complex Networks: Small-World, Scale-Free and Beyond.” IEEE Circuits and Systems Magazine, pp. 6–20. First Quarter 2003.
Strogatz SH. “Exploring complex networks”. Nature, 2001, 410: Nature 2001: 410: 268–76.
Michaels DC, Matyas EP and Jalife J. “Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model,” Circulation Research, 1986; 58: 268–410.
Michaels DC, Matyas EP and Jalife J. “Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis,” Circulation Research, 1987; 61: 704–14.
Borne PVD, Montano N, Narkiewicz K, et al. Sympathetic rhythmicity in cardiac transplant recipients,” Circulation, 1999; 99: 1606–10.
Murphy DA, Thompson GW, Ardell JL. “The Heart Reinnervates After Transplantation,” Annals of Thoracic Surgery, 2000; 69: 1769–81.
Estorch M, Camprecios M, Flotats A, Mari C, et al. “Sympathetic reinnervation of cardiac allografts evaluated by 1231-MIBG imaging,” J Nucl Med, 1999; 40: 6: 911–16.
Pauza DH, Skripka V, Pauziene N. “Morphology of the Intrinsic Cardiac Nervous System in the Dog: A Whole-Mount Study Employing Histochemical Staining with Acetylcholinesterase,”. Cells. Tissues, Organs, 2002; 172: 4: 297–320.
Yuan BX, Ardell JL, Hopkins DA, Losier AM, Armour JA. “Gross and microscopic anatomy of the canine intrinsic cardiac nervous system,” Anat Rec., 1994; 239: 1: 75–87.
Levy MN & Vassalle M. Excitation and Neural Control of the Heart, American Physiological Society, 1982.
Kember GC, Fenton GA, Armour JA and Kalayaniwalla NA, “Competition model for aperiodic stochastic resonance in a Fitz-Hugh Nagumo model of cardiac sensory neurons,” physiol. Rev. 2001; 63: 1–6.
Armour JA “Cardiac neuronal hierarchy in health and disease”, Am J Physiol Regul Interg Comp Physiol 2004; 287: R262-R271.
Armour JA, and Ardell JL, eds. Neurocardiology, 1994. New York: Oxford University Press. Winslow RL, Cai D, and Lai YC. “Network models of the SA node.” Proc. IFAC Symposium on Modeling and Control in Biomedical Systems, 1994; 86–92.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krishnan, J., Chakravarthy, V.S., Radhakrishnan, S. et al. Neural influence is essential for synchronizing cardiac oscillators: A computational model. Indian J Thorac Cardiovasc Surg 21, 262–268 (2005). https://doi.org/10.1007/s12055-005-0003-9
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s12055-005-0003-9