Dynamics of the Heart Muscle

Sudden cardiac death is the leading cause of death in the industrialized world with the majority of such tragedies due to ventricular fibrillation (VF). VF is a frenzied and irregular heart rhythm disturbance that quickly renders the heart incapable of pumping blood and hence sustaining life. Instead of contracting regularly and uniformly, the ventricles writhe and fibrillate at a frequency some ten times faster than the normal heart rate. The presently existing defibrillation techniques are based on either applying electrical stimuli or using antiarrhythmic drugs; both approaches have significant drawbacks. Electrical stimuli, which use strong discharges to attempt "resetting" the heart have large failure rates. Antiarrhythmic drugs have proved even less effective, mostly because fibrillatory dynamics are not understood well enough to properly assess pharmacological dependencies. Despite many failures, this is a very active and exciting subject with great scientific potential and even greater practical significance.

Our research uses the tools and techniques of dynamical systems and pattern formation to study the self-sustaining fibrillatory dynamics and the mechanisms responsible for their initiation and maintenance, with the ultimate goal of developing effective and reliable defibrillation methods. Numerical simulations and experimental studies have identified fibrillation with the breakup of spiral waves of excitation in the heart tissue. However, neither approach has produced a clear picture of what the mechanism of spiral breakup is. Furthermore, it is well known that both the normal beating and fibrillation are natural behaviors even in healthy hearts. Fibrillation can be provoked and stopped by an external perturbation. However the threshold for fibrillatory dynamics is much lower in desease-ridden hearts. The transition mechanism therefore is not related to the classical linear instabilities typical of pattern-forming systems but rather of a finite-amplitude bypass scenario somewhat akin to the onset of turbulence in shear flows in fluid dynamics.

Spiral breakup in the Fitz-Hugh Nagumo model of the heart tissue:

  
 
Traveling spiral wave (normal beating) 		    
Spiral wave breakup (fibrillation)

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