Nonlinear Dynamics and Bifurcations in Cardiac Tissue

Cornell University, Ithaca NY

Investigators

Abstract

The heart utilizes electrical waves that normally spread in a coordinated manner to initiate a mechanical contraction, but in pathologic states, electrical wave propagation can be disrupted by pre-existing heterogeneous regions or by dynamic heterogeneities that develop as a consequence of rapid pacing and the nonlinear dynamics of the system. An important example of the latter that is often a precursor to life-threatening arrhythmias is electrical alternans, in which two successive paced beats elicit electrical responses (and thus mechanical responses) of different amplitudes and durations. Despite much attention, fundamental characteristics about alternans remain under-studied, and attempts to use electrical interventions to control alternans have not been successful on a global level. Our research aims to advance the understanding of cardiac alternans at the most basic level and to use this knowledge to implement improved schemes of electrical control using fundamental nonlinear dynamics principles. In particular, we will characterize the type of period-doubling bifurcation underlying electrical alternans, develop mathematical models to investigate the dynamical and biophysical mechanisms underlying alternans, and to implement and test novel control algorithms. Mathematical modeling and computer simulations in single-and multi-processor environments will be used in conjunction with experimental techniques, including microelectrodes, laser-scanning confocal microscopy, and optical mapping using fluorescence signals obtained with voltage-sensitive dyes in cardiac tissue. The proposed research will elucidate the nature of the period-doubling bifurcation to electrical alternans, quantify the roles of intracellular calcium dynamics and transmembrane voltage in the origin of alternans, and improve the understanding of global control algorithms in tissue. In the course of this project, graduate and undergraduate students will participate in this research and will benefit from an interdisciplinary environment. A key component of the project is to promote broad dissemination of information. The mathematical models and algorithms developed in this proposal will be made available free as stand alone codes and interactive Java applets via web sites. Results will be presented as well, with a special emphasis on interactive programs and animations for both scientists and the general public. Ultimately, this research may lead to improved treatments for life-threatening cardiac arrhythmias: by preventing alternans, the lethal cardiac arrhythmias that alternans can trigger also can be avoided. Furthermore, the improved understanding of electrical abnormalities and novel methods for controlling complex dynamics may translate to other related systems, including the brain and peripheral nervous system and other types of muscle.