Characteristic and critical excitation length scales in 1-D and 2-D simulations of reentrant cardiac arrhythmias using simple two-variable models.
We discuss major characteristic lengths as the lumped parameters characterizing kinematics and dynamics of excitation waves in idealized one- and two-dimensional myocardium. First we consider the directional dependence of the length scale in the anisotropic bi- and monodomain myocardium. Next, we show that there is a well-defined smallness parameter that allows one to consider the monodomain equations as the first approximation to the bidomain theory. Then we use this approximation and turn our attention to the dynamics and to finding the major physiologic parameters governing such transient processes as the formation of a reentrant wave and its subsequent degradation into the malignant cardiac arrhythmia--ventricular fibrillation. It appears that in both the one- and two-dimensional cases the stability of a reentrant periodic process (representing a VT rhythm) is determined by the same two physiologic parameters: the wave width lambda, which is approximately the size of depolarized zone, and ratio of lambda to the critical length L(h)cr, which is defined as the wave width of an action potential propagating with the minimum possible speed. The parameter L(h)cr determines the length scale (size) of an ectopic region that may initiate a wave. It also determines the duration of the vulnerable window for initiating the unidirectional block as well as a minimum permissible length of the reentrant circuit. We also present some evidence that depending on the value of lambda the waveforms of the simulated ECGs for reentrant activity vary from monomorphic to polymorphic.
Chernyak
Y B
YB
Division of Health Sciences and Technology, Harvard University-Massachusetts Institute of Technology, Cambridge 02139, USA.
Starobin
J M
JM
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D016880:Anisotropy; D001145:Arrhythmias, Cardiac / Q000503:physiopathology*; D003198:Computer Simulation; D004562:Electrocardiography; D004566:Electrodes; D006321:Heart / Q000503:physiopathology*; D006801:Humans; D008962:Models, Theoretical; D013610:Tachycardia / Q000503:physiopathology