Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases.

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue.

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup.

Small-conductance Ca-activated K channels promote J-wave syndrome and phase 2 reentry.

Background: Small-conductance Ca-activated potassium (SK) channels play complex roles in cardiac arrhythmogenesis. SK channels colocalize with L-type Ca channels, yet how this colocalization affects cardiac arrhythmogenesis is unknown.

Objective: The purpose of this study was to investigate the role of colocalization of SK channels with L-type Ca channels in promoting J-wave syndrome and ventricular arrhythmias.

Spatially Discordant Repolarization Alternans in the Absence of Conduction Velocity Restitution.

Spatially discordant alternans (SDA) of action potential duration (APD) has been widely observed in cardiac tissue and is linked to cardiac arrhythmogenesis. Theoretical studies have shown that conduction velocity restitution (CVR) is required for the formation of SDA. However, this theory is not completely supported by experiments, indicating that other mechanisms may exist.

Bifurcations Caused by Feedback between Voltage and Intracellular Ion Concentrations in Ventricular Myocytes.

We develop an iterated map model to describe the bifurcations and complex dynamics caused by the feedback between voltage and intracellular Ca^{2+} and Na^{+} concentrations in paced ventricular myocytes. Voltage and Ca^{2+} can form either a positive or a negative feedback loop, while voltage and Na^{+} form a negative feedback loop. Under certain diseased conditions, when the feedback between voltage and Ca^{2+} is positive, Hopf bifurcations occur, leading to periodic oscillatory behaviors.

Control of voltage-driven instabilities in cardiac myocytes with memory.

Sudden cardiac death is known to be associated with dynamical instabilities in the heart, and thus control of dynamical instabilities is considered a potential therapeutic strategy. Different control methods were developed previously, including time-delayed feedback pacing control and constant diastolic interval pacing control. Experimental, theoretical, and simulation studies have examined the efficacy of these control methods in stabilizing action potential dynamics.

Memory-induced nonlinear dynamics of excitation in cardiac diseases.

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation.

Memory-Induced Chaos in Cardiac Excitation.

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.

Quantitative modeling of chronic myeloid leukemia: insights from radiobiology.

Mathematical models of chronic myeloid leukemia (CML) cell population dynamics are being developed to improve CML understanding and treatment. We review such models in light of relevant findings from radiobiology, emphasizing 3 points. First, the CML models almost all assert that the latency time, from CML initiation to diagnosis, is at most ∼10 years.