The Luo-Rudy I model, describing the electrophysiology of a ventricular cardiomyocyte, is associated with an 8-dimensional discontinuous dynamical system with logarithmic and exponential non-linearities depending on 15 parameters. The associated stationary problem was reduced to a nonlinear system in only two unknowns, the transmembrane potential V and the intracellular calcium concentration [Ca]( i ). By numerical approaches appropriate to bifurcation problems, sections in the static bifurcation diagram were determined. For a variable steady depolarizing or hyperpolarizing current (I (st)), the corresponding projection of the static bifurcation diagram in the (I (st), V) plane is complex, featuring three branches of stationary solutions joined by two limit points. On the upper branch oscillations can occur, being either damped at a stable focus or diverted to the lower branch of stable stationary solutions when reaching the unstable manifold of a homoclinic saddle, thus resulting in early after-depolarizations (EADs). The middle branch of solutions is a series of unstable saddle points, while the lower one a series of stable nodes. For variable slow inward and K(+) current maximal conductances (g (si) and g (K)), in a range between 0 and 4-fold normal values, the dynamics is even more complex, and in certain instances sustained oscillations tending to a limit cycle appear. All these types of behavior were correctly predicted by linear stability analysis and bifurcation theory methods, leading to identification of Hopf bifurcation points, limit points of cycles and period doubling bifurcations. In particular settings, e.g. one-fifth-of-normal g (si), EADs and sustained high amplitude oscillations due to an unstable resting state may occur simultaneously.
metabolic sink, but only when the sink exceeds a critical size (r>0.4cm). Phase singularity analysis indicates that the fibrillatory activity is initiated at sites close the border zone. The results emphasize the power of integrating cellular electrophysiological, Ca2þ handling, and metabolic subsystems into a multiscale model to simulate emergent macroscopic phenomena in the heart. Moreover, the results provide a proof-of-concept of the metabolic sink hypothesis and a new tool to study its role in arrhythmogenesis and sudden cardiac death.
in HEK293 cells showed that it does not generate any current (n=6). We utilized recently published computational models of the human atrial and ventricular action potential (Abraham et al., J Mol Cell Cardiol. 2010 and Grandi, et al. J Mol Cell Cardiol. 2010) to determine the effect that T322M has on cardiac Action Potential Duration (APD) stimulated at 1 Hz. A 100% reduction of I Ks resulted in a prolonged APD in the atrial simulation but not the ventricular simulation. We incorporated a beta-adrenergic stimulation component into the ventricular model and found that reducing I Ks by 100% in the modified simulation increased APD. We further modified the ventricular action potential simulation to compromise 'repolarization reserve' by reducing the rapidly-activating delayed-rectifier K þ current or I Kr component. This modification exacerbated that effect that 100% block of I Ks had on ventricular APD. Based on these results we conclude that T322M prolongs the atrial APD in the absence of betaadrenergic stimulation, and prolongs the ventricular APD in the presence of beta-adrenergic stimulation and a compromised repolarization reserve. 2362-Pos Board B348 A Mathematical Model Identifies Arrhythmia Susceptibility Factors inMice with Heart Failure Vladimir E. Bondarenko, Polina S. Petkova-Kirova, Barry London, Guy Salama, Randall L. Rasmusson. Tumor necrosis factor-a (TNF-a) is significantly elevated in the serum of patients with end-stage congestive heart failure and in the myocardium of patients with dilated cardiomyopathy and ischemic heart disease. This correlation suggests that the inflammatory cytokine TNF-a plays a significant role in promoting arrhythmias. To investigate the role of TNF-a, transgenic (TG) mice were generated with cardiac-specific overexpression of TNF-a which resulted in dilated cardiomyopathy, impaired Ca 2þ dynamics, and increased mortality. In this study, we modified our model of mouse ventricular myocytes to account for the experimentally observed electrical remodeling. The resulting model demonstrated potential arrhythmogenic changes due to changes in action potential (AP) properties and cellular coupling. The simulated differences in action potential shape and duration were predominantly due to changes in the rapidly-inactivating transient outward K þ current, I Kto,f , and an ultra-rapidly activating K þ current, I Kur . The model incorporated experimental measurements of differences in Ca 2þ handling in myocytes from wild type (WT) and TG mice: reduced [Ca 2þ ] i transients and slower Ca 2þ sequestration by the sarcoplasmic reticulum (SR) in TG mice. The model also predicted that Ca 2þ alternans developed at longer basic cycle lengths in TG compared to WT mice as observed experimentally. The greater susceptibility to Ca 2þ alternans was attributed to a slower Ca 2þ sequestration rate by the SR. Programmed stimulation with a premature impulse showed that longer S1-S2 intervals were effective at eliciting re-entry in TG vs. WT mice, suggesting a mechanism for the observed increase in...
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