Origin of arrhythmias in a heart model

✍ Scribed by Hiba Sheheitli; Richard Rand

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 631 KB
• Volume: 14
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2009.03.016

✦ Synopsis

An investigation of the nonlinear dynamics of a heart model is presented. The model compartmentalizes the heart into one part that beats autonomously (the x oscillator), representing the pacemaker or SA node, and a second part that beats only if excited by a signal originating outside itself (the y oscillator), representing typical cardiac tissue. Both oscillators are modeled by piecewise linear differential equations representing relaxation oscillators in which the fast time portion of the cycle is modeled by a jump. The model assumes that the x oscillator drives the y oscillator with coupling constant a. As a decreases, the regular behavior of y oscillator deteriorates, and is found to go through a series of bifurcations. The irregular behavior is characterized as involving a large amplitude cycle followed by a number n of small amplitude cycles. We compute critical bifurcation values of the coupling constant, a n , using both numerical methods as well as perturbations.